MTUM: 60-day history, VaR(99%)=-0.0383, max drawdown threshold=10%.

Question:
Asset: MTUM
Daily returns (past 60 days): mean=-0.0010, std=0.0180, worst_day=-0.0383
Maximum acceptable portfolio drawdown: 10%
Market regime: sideways
Recent filing/news:
[Kaggle 2025-05-06] ["ADP Announces Pricing of its Senior Notes Due 2032 ROSELAND, N.J., May 6, 2025 /PRNewswire/ -- ADP (Nasdaq: ADP), a leading global technology company providing comprehensive cloud-based human capital management (HCM) solutions, yesterday announced the pricing of a public offering of $1.0 billion aggregate principal amount of its 4.750% senior notes due 2032. ADP expects to receive the net offering proceeds upon closing on or about May 8, 2025. The intended use of proceeds from the offering is to refinance existing debt, and any remainder for general corporate purposes. ADP has filed a registration statement (including a prospectus and preliminary prospectus supplement) with the Securities and Exchange Commission (\"SEC\") for the offering to which this communication relates. Before you invest, you should read the base prospectus in that registration statement, the applicable preliminary prospectus supplement and the other documents ADP has filed with the SEC for more complete information about ADP and this offering. You may get these documents for free by visiting EDGAR on the SEC website at www.sec.gov. Alternatively, ADP, any underwriter or any dealer participating in the offering will arrange to send investors the prospectus and preliminary prospectus supplement upon request by contacting BofA Securities, Inc. by telephone at 1-800-294-1322 or by email at dg.prospectus_requests@bofa.com, J.P. Morgan Securities LLC by telephone (collect) at (212) 834-4533 or Morgan Stanley & Co. LLC by telephone at (866) 718-1649. This press release does not constitute an offer to sell or a solicitation of an offer to buy the debt securities or any other securities, nor shall there be any sale of these securities in any jurisdiction in which such an offer, solicitation or sale would be unlawful prior to registration or qualification under the securities laws of any such jurisdiction. The offering of these securities may be made only by means of the prospectus supplement and the accompanying prospectus. This press release also does not constitute an offer to purchase, a solicitation of an offer to sell, or notice of redemption with respect to any securities of ADP. About ADP (NASDAQ \u2013 ADP)Designing better ways to work through cutting-edge products, premium services and exceptional experiences that enable people to reach their full potential. HR, Talent, Time Management, Benefits and Payroll. Informed by data and designed for people. Forward-Looking Statements This document and other written or oral statements made from time to time by ADP may contain \"forward-looking statements\" within the meaning of the Private Securities Litigation Reform Act of 1995. Statements that are not historical in nature and which may be identified by the use of words like \"outlook,\" \"expects,\" \"assumes,\" \"projects,\" \"anticipates,\" \"estimates,\" \"we believe,\" \"could,\" \"is designed to\" and other words of similar meaning, are forward-looking statements. These st

Determine the maximum fraction of total portfolio capital that should be allocated to MTUM, given the drawdown constraint. Report as a decimal between 0.00 and 1.00 (e.g., 0.25 = 25%; maximum is 1.00 = 100% of portfolio).

Answer: 1.0000

Explanation:
Step 1: Compute |VaR(99%)| from historical returns = 0.0383 (i.e., a 3.83% loss in the worst 1% of days).
Step 2: Fixed-fractional formula: f* = 10% / 0.0383 = 2.6134, capped at 1.0.
Maximum position size = 1.0000 (100.0% of portfolio).


BNB-USD: 60-day history, VaR(99%)=-0.0733, max drawdown threshold=10%.

Question:
Asset: BNB-USD
Daily returns (past 60 days): mean=-0.0008, std=0.0320, worst_day=-0.0767
Maximum acceptable portfolio drawdown: 10%
Market regime: sideways
Recent filing/news:
[Kaggle 2023-12-19]

Determine the maximum fraction of total portfolio capital that should be allocated to BNB-USD, given the drawdown constraint. Report as a decimal between 0.00 and 1.00 (e.g., 0.25 = 25%; maximum is 1.00 = 100% of portfolio).

Answer: 1.0000

Explanation:
Step 1: Compute |VaR(99%)| from historical returns = 0.0733 (i.e., a 7.33% loss in the worst 1% of days).
Step 2: Fixed-fractional formula: f* = 10% / 0.0733 = 1.3641, capped at 1.0.
Maximum position size = 1.0000 (100.0% of portfolio).


PALL: 60-day history, VaR(99%)=-0.0567, max drawdown threshold=10%.

Question:
Asset: PALL
Daily returns (past 60 days): mean=0.0040, std=0.0240, worst_day=-0.0619
Maximum acceptable portfolio drawdown: 10%
Market regime: bull

Determine the maximum fraction of total portfolio capital that should be allocated to PALL, given the drawdown constraint. Report as a decimal between 0.00 and 1.00 (e.g., 0.25 = 25%; maximum is 1.00 = 100% of portfolio).

Answer: 1.0000

Explanation:
Step 1: Compute |VaR(99%)| from historical returns = 0.0567 (i.e., a 5.67% loss in the worst 1% of days).
Step 2: Fixed-fractional formula: f* = 10% / 0.0567 = 1.7622, capped at 1.0.
Maximum position size = 1.0000 (100.0% of portfolio).


Question:
Assets: DOT-USD, HAUZ
DOT-USD: annualized_mean_return=-0.1260, daily_std=0.0410
HAUZ: annualized_mean_return=0.2772, daily_std=0.0068
Minimum required portfolio return (annualized): 0.0660
Market regime: bull

Compute portfolio weights (w_DOT-USD, w_HAUZ) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_DOT-USD=X.XXXX, w_HAUZ=X.XXXX

Answer: w_DOT-USD=0.0329, w_HAUZ=0.9671

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000047 - -0.000011) / (0.001685 + 0.000047 - -0.000022)
  Unconstrained: w_DOT-USD=0.0331
  After long-only clamp: w_DOT-USD=0.0331, w_HAUZ=0.9669.


Question:
Assets: EEM, BTC-USD
EEM: annualized_mean_return=0.2016, daily_std=0.0094
BTC-USD: annualized_mean_return=-1.1592, daily_std=0.0241
Minimum required portfolio return (annualized): 0.0916
Market regime: sideways

Compute portfolio weights (w_EEM, w_BTC-USD) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_EEM=X.XXXX, w_BTC-USD=X.XXXX

Answer: w_EEM=0.9192, w_BTC-USD=0.0808

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000579 - -0.000030) / (0.000088 + 0.000579 - -0.000060)
  Unconstrained: w_EEM=0.8381
  After long-only clamp: w_EEM=0.8381, w_BTC-USD=0.1619.


LINK-USD σ=0.0359, SGOV σ=0.0001, ρ=-0.120. Min-variance weights: LINK-USD=0.001, SGOV=1.000.

Question:
Assets: LINK-USD, SGOV
LINK-USD: annualized_mean_return=0.2520, daily_std=0.0359
SGOV: annualized_mean_return=0.0504, daily_std=0.0001
Minimum required portfolio return (annualized): 0.0969
Market regime: bull

Compute portfolio weights (w_LINK-USD, w_SGOV) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_LINK-USD=X.XXXX, w_SGOV=X.XXXX

Answer: w_LINK-USD=0.2307, w_SGOV=0.7693

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - -0.000001) / (0.001291 + 0.000000 - -0.000001)
  Unconstrained: w_LINK-USD=0.0005
  After long-only clamp: w_LINK-USD=0.0005, w_SGOV=0.9995.


Question:
Assets: AVAX-USD, IYR
AVAX-USD: annualized_mean_return=-0.1512, daily_std=0.0603
IYR: annualized_mean_return=-0.2016, daily_std=0.0134
Minimum required portfolio return (annualized): -0.1997
Market regime: bear

Compute portfolio weights (w_AVAX-USD, w_IYR) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_AVAX-USD=X.XXXX, w_IYR=X.XXXX

Answer: w_AVAX-USD=0.0509, w_IYR=0.9491

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000181 - -0.000015) / (0.003640 + 0.000181 - -0.000029)
  Unconstrained: w_AVAX-USD=0.0508
  After long-only clamp: w_AVAX-USD=0.0508, w_IYR=0.9492.


Question:
Assets: XLRE, STIP
XLRE: annualized_mean_return=0.3276, daily_std=0.0092
STIP: annualized_mean_return=0.0504, daily_std=0.0012
Minimum required portfolio return (annualized): 0.2285
Market regime: sideways

Compute portfolio weights (w_XLRE, w_STIP) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_XLRE=X.XXXX, w_STIP=X.XXXX

Answer: w_XLRE=0.6425, w_STIP=0.3575

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000001 - -0.000001) / (0.000085 + 0.000001 - -0.000001)
  Unconstrained: w_XLRE=0.0245
  After long-only clamp: w_XLRE=0.0245, w_STIP=0.9755.


Question:
Assets: VTI, SOYB
VTI: annualized_mean_return=-0.6804, daily_std=0.0130
SOYB: annualized_mean_return=-0.1008, daily_std=0.0097
Minimum required portfolio return (annualized): -0.4758
Market regime: bear

Compute portfolio weights (w_VTI, w_SOYB) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_VTI=X.XXXX, w_SOYB=X.XXXX

Answer: w_VTI=0.2909, w_SOYB=0.7091

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000095 - 0.000043) / (0.000169 + 0.000095 - 0.000085)
  Unconstrained: w_VTI=0.2915
  After long-only clamp: w_VTI=0.2915, w_SOYB=0.7085.


Question:
Assets: ADA-USD, XLY
ADA-USD: annualized_mean_return=-0.8568, daily_std=0.0611
XLY: annualized_mean_return=-0.9072, daily_std=0.0179
Minimum required portfolio return (annualized): -0.8888
Market regime: bear

Compute portfolio weights (w_ADA-USD, w_XLY) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_ADA-USD=X.XXXX, w_XLY=X.XXXX

Answer: w_ADA-USD=0.3651, w_XLY=0.6349

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000322 - 0.000199) / (0.003727 + 0.000322 - 0.000398)
  Unconstrained: w_ADA-USD=0.0335
  After long-only clamp: w_ADA-USD=0.0335, w_XLY=0.9665.


Question:
Assets: VLUE, CSHI
VLUE: annualized_mean_return=-0.0756, daily_std=0.0138
CSHI: annualized_mean_return=-0.0252, daily_std=0.0032
Minimum required portfolio return (annualized): -0.0267
Market regime: sideways

Compute portfolio weights (w_VLUE, w_CSHI) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_VLUE=X.XXXX, w_CSHI=X.XXXX

Answer: w_VLUE=0.0298, w_CSHI=0.9702

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000010 - -0.000009) / (0.000191 + 0.000010 - -0.000017)
  Unconstrained: w_VLUE=0.0867
  After long-only clamp: w_VLUE=0.0867, w_CSHI=0.9133.


BNB-USD σ=0.0297, CSHI σ=0.0004, ρ=0.012. Min-variance weights: BNB-USD=0.000, CSHI=1.000.

Question:
Assets: BNB-USD, CSHI
BNB-USD: annualized_mean_return=0.2520, daily_std=0.0297
CSHI: annualized_mean_return=0.0756, daily_std=0.0004
Minimum required portfolio return (annualized): 0.0756
Market regime: sideways

Compute portfolio weights (w_BNB-USD, w_CSHI) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_BNB-USD=X.XXXX, w_CSHI=X.XXXX

Answer: w_BNB-USD=0.0002, w_CSHI=0.9998

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - 0.000000) / (0.000884 + 0.000000 - 0.000000)
  Unconstrained: w_BNB-USD=0.0000
  After long-only clamp: w_BNB-USD=0.0000, w_CSHI=1.0000.


Question:
Assets: XLI, SHV
XLI: annualized_mean_return=-0.2520, daily_std=0.0084
SHV: annualized_mean_return=0.0504, daily_std=0.0001
Minimum required portfolio return (annualized): 0.0162
Market regime: sideways

Compute portfolio weights (w_XLI, w_SHV) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_XLI=X.XXXX, w_SHV=X.XXXX

Answer: w_XLI=0.0002, w_SHV=0.9998

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - 0.000000) / (0.000071 + 0.000000 - 0.000000)
  Unconstrained: w_XLI=-0.0003
  After long-only clamp: w_XLI=0.0000, w_SHV=1.0000.


Question:
Assets: XRP-USD, SHV
XRP-USD: annualized_mean_return=-0.7308, daily_std=0.0648
SHV: annualized_mean_return=0.0504, daily_std=0.0001
Minimum required portfolio return (annualized): 0.0504
Market regime: sideways

Compute portfolio weights (w_XRP-USD, w_SHV) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_XRP-USD=X.XXXX, w_SHV=X.XXXX

Answer: w_XRP-USD=-0.0000, w_SHV=1.0000

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - -0.000001) / (0.004196 + 0.000000 - -0.000003)
  Unconstrained: w_XRP-USD=0.0003
  After long-only clamp: w_XRP-USD=0.0003, w_SHV=0.9997.


Question:
Assets: QQQ, IYR
QQQ: annualized_mean_return=0.1260, daily_std=0.0116
IYR: annualized_mean_return=-0.1512, daily_std=0.0104
Minimum required portfolio return (annualized): 0.0900
Market regime: sideways

Compute portfolio weights (w_QQQ, w_IYR) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_QQQ=X.XXXX, w_IYR=X.XXXX

Answer: w_QQQ=0.8701, w_IYR=0.1299

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000108 - 0.000030) / (0.000135 + 0.000108 - 0.000060)
  Unconstrained: w_QQQ=0.4267
  After long-only clamp: w_QQQ=0.4267, w_IYR=0.5733.


LINK-USD σ=0.0462, ICSH σ=0.0003, ρ=0.040. Min-variance weights: LINK-USD=0.000, ICSH=1.000.

Question:
Assets: LINK-USD, ICSH
LINK-USD: annualized_mean_return=0.7056, daily_std=0.0462
ICSH: annualized_mean_return=0.0756, daily_std=0.0003
Minimum required portfolio return (annualized): 0.0756
Market regime: sideways

Compute portfolio weights (w_LINK-USD, w_ICSH) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_LINK-USD=X.XXXX, w_ICSH=X.XXXX

Answer: w_LINK-USD=0.0000, w_ICSH=1.0000

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - 0.000001) / (0.002132 + 0.000000 - 0.000001)
  Unconstrained: w_LINK-USD=-0.0002
  After long-only clamp: w_LINK-USD=0.0000, w_ICSH=1.0000.


BTC-USD σ=0.0154, ICSH σ=0.0002, ρ=0.257. Min-variance weights: BTC-USD=0.000, ICSH=1.000.

Question:
Assets: BTC-USD, ICSH
BTC-USD: annualized_mean_return=0.3780, daily_std=0.0154
ICSH: annualized_mean_return=0.0504, daily_std=0.0002
Minimum required portfolio return (annualized): 0.0504
Market regime: bull

Compute portfolio weights (w_BTC-USD, w_ICSH) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_BTC-USD=X.XXXX, w_ICSH=X.XXXX

Answer: w_BTC-USD=0.0000, w_ICSH=1.0000

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - 0.000001) / (0.000236 + 0.000000 - 0.000001)
  Unconstrained: w_BTC-USD=-0.0028
  After long-only clamp: w_BTC-USD=0.0000, w_ICSH=1.0000.


ADA-USD σ=0.0378, CSHI σ=0.0005, ρ=0.138. Min-variance weights: ADA-USD=0.000, CSHI=1.000.

Question:
Assets: ADA-USD, CSHI
ADA-USD: annualized_mean_return=0.5040, daily_std=0.0378
CSHI: annualized_mean_return=0.0504, daily_std=0.0005
Minimum required portfolio return (annualized): 0.0504
Market regime: bull

Compute portfolio weights (w_ADA-USD, w_CSHI) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_ADA-USD=X.XXXX, w_CSHI=X.XXXX

Answer: w_ADA-USD=0.0000, w_CSHI=1.0000

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - 0.000003) / (0.001432 + 0.000000 - 0.000005)
  Unconstrained: w_ADA-USD=-0.0017
  After long-only clamp: w_ADA-USD=0.0000, w_CSHI=1.0000.


AVAX-USD σ=0.0460, CPER σ=0.0130, ρ=0.112. Min-variance weights: AVAX-USD=0.047, CPER=0.953.

Question:
Assets: AVAX-USD, CPER
AVAX-USD: annualized_mean_return=-1.2852, daily_std=0.0460
CPER: annualized_mean_return=0.2772, daily_std=0.0130
Minimum required portfolio return (annualized): 0.2623
Market regime: sideways

Compute portfolio weights (w_AVAX-USD, w_CPER) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_AVAX-USD=X.XXXX, w_CPER=X.XXXX

Answer: w_AVAX-USD=0.0095, w_CPER=0.9905

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000168 - 0.000067) / (0.002114 + 0.000168 - 0.000134)
  Unconstrained: w_AVAX-USD=0.0470
  After long-only clamp: w_AVAX-USD=0.0470, w_CPER=0.9530.


Question:
Assets: XLI, DBC
XLI: annualized_mean_return=-0.1764, daily_std=0.0100
DBC: annualized_mean_return=0.1764, daily_std=0.0074
Minimum required portfolio return (annualized): -0.0775
Market regime: bear

Compute portfolio weights (w_XLI, w_DBC) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_XLI=X.XXXX, w_DBC=X.XXXX

Answer: w_XLI=0.3251, w_DBC=0.6749

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000055 - 0.000013) / (0.000100 + 0.000055 - 0.000025)
  Unconstrained: w_XLI=0.3260
  After long-only clamp: w_XLI=0.3260, w_DBC=0.6740.


Question:
Assets: SOL-USD, BNO
SOL-USD: annualized_mean_return=-2.3184, daily_std=0.0596
BNO: annualized_mean_return=-0.1008, daily_std=0.0139
Minimum required portfolio return (annualized): -0.1974
Market regime: sideways

Compute portfolio weights (w_SOL-USD, w_BNO) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_SOL-USD=X.XXXX, w_BNO=X.XXXX

Answer: w_SOL-USD=0.0436, w_BNO=0.9564

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000192 - -0.000136) / (0.003551 + 0.000192 - -0.000273)
  Unconstrained: w_SOL-USD=0.0818
  After long-only clamp: w_SOL-USD=0.0818, w_BNO=0.9182.


Question:
Assets: IWM, MORT
IWM: annualized_mean_return=-0.1008, daily_std=0.0109
MORT: annualized_mean_return=0.2016, daily_std=0.0107
Minimum required portfolio return (annualized): -0.0297
Market regime: sideways

Compute portfolio weights (w_IWM, w_MORT) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_IWM=X.XXXX, w_MORT=X.XXXX

Answer: w_IWM=0.4707, w_MORT=0.5293

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000115 - 0.000081) / (0.000119 + 0.000115 - 0.000163)
  Unconstrained: w_IWM=0.4705
  After long-only clamp: w_IWM=0.4705, w_MORT=0.5295.


Question:
Assets: EFA, SHY
EFA: annualized_mean_return=0.1512, daily_std=0.0064
SHY: annualized_mean_return=0.0504, daily_std=0.0007
Minimum required portfolio return (annualized): 0.0774
Market regime: bull

Compute portfolio weights (w_EFA, w_SHY) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_EFA=X.XXXX, w_SHY=X.XXXX

Answer: w_EFA=0.2679, w_SHY=0.7321

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000001 - 0.000000) / (0.000042 + 0.000001 - 0.000001)
  Unconstrained: w_EFA=0.0011
  After long-only clamp: w_EFA=0.0011, w_SHY=0.9989.


Question:
Assets: EWJ, DBB
EWJ: annualized_mean_return=0.0756, daily_std=0.0098
DBB: annualized_mean_return=-0.1512, daily_std=0.0073
Minimum required portfolio return (annualized): -0.1122
Market regime: sideways

Compute portfolio weights (w_EWJ, w_DBB) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_EWJ=X.XXXX, w_DBB=X.XXXX

Answer: w_EWJ=0.3637, w_DBB=0.6363

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000053 - -0.000004) / (0.000096 + 0.000053 - -0.000009)
  Unconstrained: w_EWJ=0.3645
  After long-only clamp: w_EWJ=0.3645, w_DBB=0.6355.


Question:
Assets: BTC-USD, XLY
BTC-USD: annualized_mean_return=0.2016, daily_std=0.0168
XLY: annualized_mean_return=0.2520, daily_std=0.0099
Minimum required portfolio return (annualized): 0.2450
Market regime: bull

Compute portfolio weights (w_BTC-USD, w_XLY) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_BTC-USD=X.XXXX, w_XLY=X.XXXX

Answer: w_BTC-USD=0.1389, w_XLY=0.8611

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000097 - -0.000041) / (0.000282 + 0.000097 - -0.000082)
  Unconstrained: w_BTC-USD=0.2991
  After long-only clamp: w_BTC-USD=0.2991, w_XLY=0.7009.


Question:
Assets: XLRE, BIL
XLRE: annualized_mean_return=-0.2520, daily_std=0.0110
BIL: annualized_mean_return=0.0504, daily_std=0.0001
Minimum required portfolio return (annualized): -0.1266
Market regime: sideways

Compute portfolio weights (w_XLRE, w_BIL) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_XLRE=X.XXXX, w_BIL=X.XXXX

Answer: w_XLRE=0.0002, w_BIL=0.9998

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - -0.000000) / (0.000122 + 0.000000 - -0.000001)
  Unconstrained: w_XLRE=0.0024
  After long-only clamp: w_XLRE=0.0024, w_BIL=0.9976.


Question:
Assets: BNB-USD, PDBC
BNB-USD: annualized_mean_return=-0.4284, daily_std=0.0247
PDBC: annualized_mean_return=0.2268, daily_std=0.0072
Minimum required portfolio return (annualized): 0.2097
Market regime: sideways

Compute portfolio weights (w_BNB-USD, w_PDBC) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_BNB-USD=X.XXXX, w_PDBC=X.XXXX

Answer: w_BNB-USD=0.0261, w_PDBC=0.9739

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000052 - -0.000001) / (0.000610 + 0.000052 - -0.000001)
  Unconstrained: w_BNB-USD=0.0789
  After long-only clamp: w_BNB-USD=0.0789, w_PDBC=0.9211.


Question:
Assets: XLB, GLD
XLB: annualized_mean_return=-0.1512, daily_std=0.0091
GLD: annualized_mean_return=0.8568, daily_std=0.0113
Minimum required portfolio return (annualized): 0.4682
Market regime: sideways

Compute portfolio weights (w_XLB, w_GLD) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_XLB=X.XXXX, w_GLD=X.XXXX

Answer: w_XLB=0.3855, w_GLD=0.6145

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000127 - -0.000009) / (0.000084 + 0.000127 - -0.000018)
  Unconstrained: w_XLB=0.5945
  After long-only clamp: w_XLB=0.5945, w_GLD=0.4055.


Question:
Assets: SPY, BIL
SPY: annualized_mean_return=0.2268, daily_std=0.0066
BIL: annualized_mean_return=0.0504, daily_std=0.0001
Minimum required portfolio return (annualized): 0.1455
Market regime: sideways

Compute portfolio weights (w_SPY, w_BIL) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_SPY=X.XXXX, w_BIL=X.XXXX

Answer: w_SPY=0.5391, w_BIL=0.4609

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - 0.000000) / (0.000044 + 0.000000 - 0.000000)
  Unconstrained: w_SPY=0.0003
  After long-only clamp: w_SPY=0.0003, w_BIL=0.9997.


Question:
Assets: BNB-USD, SGOV
BNB-USD: annualized_mean_return=-0.3528, daily_std=0.0320
SGOV: annualized_mean_return=0.0504, daily_std=0.0001
Minimum required portfolio return (annualized): -0.1275
Market regime: sideways

Compute portfolio weights (w_BNB-USD, w_SGOV) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_BNB-USD=X.XXXX, w_SGOV=X.XXXX

Answer: w_BNB-USD=0.0010, w_SGOV=0.9990

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - -0.000001) / (0.001026 + 0.000000 - -0.000001)
  Unconstrained: w_BNB-USD=0.0006
  After long-only clamp: w_BNB-USD=0.0006, w_SGOV=0.9994.


Question:
Assets: EFA, SGOV
EFA: annualized_mean_return=-0.0252, daily_std=0.0068
SGOV: annualized_mean_return=0.0504, daily_std=0.0001
Minimum required portfolio return (annualized): 0.0504
Market regime: sideways

Compute portfolio weights (w_EFA, w_SGOV) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_EFA=X.XXXX, w_SGOV=X.XXXX

Answer: w_EFA=-0.0000, w_SGOV=1.0000

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - 0.000000) / (0.000047 + 0.000000 - 0.000000)
  Unconstrained: w_EFA=-0.0012
  After long-only clamp: w_EFA=0.0000, w_SGOV=1.0000.


ETH-USD σ=0.0428, SGOV σ=0.0001, ρ=0.076. Min-variance weights: ETH-USD=0.000, SGOV=1.000.

Question:
Assets: ETH-USD, SGOV
ETH-USD: annualized_mean_return=-1.7388, daily_std=0.0428
SGOV: annualized_mean_return=0.0504, daily_std=0.0001
Minimum required portfolio return (annualized): 0.0504
Market regime: sideways

Compute portfolio weights (w_ETH-USD, w_SGOV) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_ETH-USD=X.XXXX, w_SGOV=X.XXXX

Answer: w_ETH-USD=-0.0000, w_SGOV=1.0000

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - 0.000000) / (0.001832 + 0.000000 - 0.000001)
  Unconstrained: w_ETH-USD=-0.0002
  After long-only clamp: w_ETH-USD=0.0000, w_SGOV=1.0000.


Question:
Assets: XLP, ICSH
XLP: annualized_mean_return=-0.0504, daily_std=0.0104
ICSH: annualized_mean_return=0.0504, daily_std=0.0003
Minimum required portfolio return (annualized): 0.0415
Market regime: sideways

Compute portfolio weights (w_XLP, w_ICSH) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_XLP=X.XXXX, w_ICSH=X.XXXX

Answer: w_XLP=0.0010, w_ICSH=0.9990

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - -0.000000) / (0.000108 + 0.000000 - -0.000001)
  Unconstrained: w_XLP=0.0056
  After long-only clamp: w_XLP=0.0056, w_ICSH=0.9944.


Question:
Assets: ADA-USD, SHV
ADA-USD: annualized_mean_return=-2.1672, daily_std=0.0475
SHV: annualized_mean_return=0.0504, daily_std=0.0001
Minimum required portfolio return (annualized): 0.0496
Market regime: sideways

Compute portfolio weights (w_ADA-USD, w_SHV) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_ADA-USD=X.XXXX, w_SHV=X.XXXX

Answer: w_ADA-USD=0.0004, w_SHV=0.9996

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - -0.000001) / (0.002257 + 0.000000 - -0.000002)
  Unconstrained: w_ADA-USD=0.0005
  After long-only clamp: w_ADA-USD=0.0005, w_SHV=0.9995.


LINK-USD σ=0.0465, IGOV σ=0.0051, ρ=-0.111. Min-variance weights: LINK-USD=0.023, IGOV=0.977.

Question:
Assets: LINK-USD, IGOV
LINK-USD: annualized_mean_return=-1.3860, daily_std=0.0465
IGOV: annualized_mean_return=0.0504, daily_std=0.0051
Minimum required portfolio return (annualized): 0.0423
Market regime: bull

Compute portfolio weights (w_LINK-USD, w_IGOV) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_LINK-USD=X.XXXX, w_IGOV=X.XXXX

Answer: w_LINK-USD=0.0056, w_IGOV=0.9944

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000026 - -0.000026) / (0.002158 + 0.000026 - -0.000053)
  Unconstrained: w_LINK-USD=0.0234
  After long-only clamp: w_LINK-USD=0.0234, w_IGOV=0.9766.


Question:
Assets: XRP-USD, SHY
XRP-USD: annualized_mean_return=-0.4032, daily_std=0.0330
SHY: annualized_mean_return=0.0504, daily_std=0.0008
Minimum required portfolio return (annualized): 0.0502
Market regime: bull

Compute portfolio weights (w_XRP-USD, w_SHY) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_XRP-USD=X.XXXX, w_SHY=X.XXXX

Answer: w_XRP-USD=0.0004, w_SHY=0.9996

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000001 - 0.000000) / (0.001090 + 0.000001 - 0.000000)
  Unconstrained: w_XRP-USD=0.0005
  After long-only clamp: w_XRP-USD=0.0005, w_SHY=0.9995.


Question:
Assets: USMV, SGOV
USMV: annualized_mean_return=-0.0756, daily_std=0.0089
SGOV: annualized_mean_return=0.0504, daily_std=0.0001
Minimum required portfolio return (annualized): 0.0504
Market regime: bear

Compute portfolio weights (w_USMV, w_SGOV) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_USMV=X.XXXX, w_SGOV=X.XXXX

Answer: w_USMV=-0.0000, w_SGOV=1.0000

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - -0.000000) / (0.000079 + 0.000000 - -0.000000)
  Unconstrained: w_USMV=0.0021
  After long-only clamp: w_USMV=0.0021, w_SGOV=0.9979.


Question:
Assets: VLUE, ICSH
VLUE: annualized_mean_return=-0.0000, daily_std=0.0137
ICSH: annualized_mean_return=0.0504, daily_std=0.0003
Minimum required portfolio return (annualized): 0.0228
Market regime: sideways

Compute portfolio weights (w_VLUE, w_ICSH) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_VLUE=X.XXXX, w_ICSH=X.XXXX

Answer: w_VLUE=0.0058, w_ICSH=0.9942

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - -0.000001) / (0.000188 + 0.000000 - -0.000002)
  Unconstrained: w_VLUE=0.0064
  After long-only clamp: w_VLUE=0.0064, w_ICSH=0.9936.


Question:
Assets: EWJ, PPLT
EWJ: annualized_mean_return=0.1764, daily_std=0.0132
PPLT: annualized_mean_return=-0.0504, daily_std=0.0114
Minimum required portfolio return (annualized): 0.0675
Market regime: bear

Compute portfolio weights (w_EWJ, w_PPLT) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_EWJ=X.XXXX, w_PPLT=X.XXXX

Answer: w_EWJ=0.5198, w_PPLT=0.4802

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000129 - 0.000049) / (0.000173 + 0.000129 - 0.000098)
  Unconstrained: w_EWJ=0.3920
  After long-only clamp: w_EWJ=0.3920, w_PPLT=0.6080.


Question:
Assets: XLF, WEAT
XLF: annualized_mean_return=0.0756, daily_std=0.0088
WEAT: annualized_mean_return=-0.2016, daily_std=0.0105
Minimum required portfolio return (annualized): -0.1251
Market regime: sideways

Compute portfolio weights (w_XLF, w_WEAT) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_XLF=X.XXXX, w_WEAT=X.XXXX

Answer: w_XLF=0.5866, w_WEAT=0.4134

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000110 - -0.000002) / (0.000077 + 0.000110 - -0.000004)
  Unconstrained: w_XLF=0.5868
  After long-only clamp: w_XLF=0.5868, w_WEAT=0.4132.


AVAX-USD σ=0.0494, IWM σ=0.0106, ρ=0.098. Min-variance weights: AVAX-USD=0.025, IWM=0.975.

Question:
Assets: AVAX-USD, IWM
AVAX-USD: annualized_mean_return=-1.4112, daily_std=0.0494
IWM: annualized_mean_return=-0.4536, daily_std=0.0106
Minimum required portfolio return (annualized): -0.4665
Market regime: sideways

Compute portfolio weights (w_AVAX-USD, w_IWM) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_AVAX-USD=X.XXXX, w_IWM=X.XXXX

Answer: w_AVAX-USD=0.0135, w_IWM=0.9865

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000112 - 0.000051) / (0.002436 + 0.000112 - 0.000102)
  Unconstrained: w_AVAX-USD=0.0249
  After long-only clamp: w_AVAX-USD=0.0249, w_IWM=0.9751.


Question:
Assets: XRP-USD, TLT
XRP-USD: annualized_mean_return=-1.0080, daily_std=0.0355
TLT: annualized_mean_return=0.2268, daily_std=0.0066
Minimum required portfolio return (annualized): -0.2822
Market regime: bull

Compute portfolio weights (w_XRP-USD, w_TLT) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_XRP-USD=X.XXXX, w_TLT=X.XXXX

Answer: w_XRP-USD=0.0163, w_TLT=0.9837

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000044 - 0.000023) / (0.001261 + 0.000044 - 0.000046)
  Unconstrained: w_XRP-USD=0.0165
  After long-only clamp: w_XRP-USD=0.0165, w_TLT=0.9835.


Question:
Assets: SPY, ADA-USD
SPY: annualized_mean_return=0.3528, daily_std=0.0054
ADA-USD: annualized_mean_return=0.3528, daily_std=0.0372
Minimum required portfolio return (annualized): 0.3528
Market regime: bull

Compute portfolio weights (w_SPY, w_ADA-USD) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_SPY=X.XXXX, w_ADA-USD=X.XXXX

Answer: w_SPY=0.9506, w_ADA-USD=0.0494

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.001383 - -0.000045) / (0.000029 + 0.001383 - -0.000090)
  Unconstrained: w_SPY=0.9507
  After long-only clamp: w_SPY=0.9507, w_ADA-USD=0.0493.


Question:
Assets: XLI, BIL
XLI: annualized_mean_return=0.2016, daily_std=0.0141
BIL: annualized_mean_return=0.0504, daily_std=0.0002
Minimum required portfolio return (annualized): 0.1256
Market regime: sideways

Compute portfolio weights (w_XLI, w_BIL) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_XLI=X.XXXX, w_BIL=X.XXXX

Answer: w_XLI=0.4974, w_BIL=0.5026

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - -0.000000) / (0.000200 + 0.000000 - -0.000001)
  Unconstrained: w_XLI=0.0017
  After long-only clamp: w_XLI=0.0017, w_BIL=0.9983.


DOT-USD σ=0.0491, MORT σ=0.0090, ρ=0.287. Min-variance weights: DOT-USD=0.000, MORT=1.000.

Question:
Assets: DOT-USD, MORT
DOT-USD: annualized_mean_return=-1.6380, daily_std=0.0491
MORT: annualized_mean_return=0.1008, daily_std=0.0090
Minimum required portfolio return (annualized): -0.3696
Market regime: sideways

Compute portfolio weights (w_DOT-USD, w_MORT) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_DOT-USD=X.XXXX, w_MORT=X.XXXX

Answer: w_DOT-USD=0.0000, w_MORT=1.0000

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000082 - 0.000127) / (0.002414 + 0.000082 - 0.000255)
  Unconstrained: w_DOT-USD=-0.0204
  After long-only clamp: w_DOT-USD=0.0000, w_MORT=1.0000.


Question:
Assets: DOT-USD, STIP
DOT-USD: annualized_mean_return=2.1924, daily_std=0.0697
STIP: annualized_mean_return=0.0252, daily_std=0.0009
Minimum required portfolio return (annualized): 0.5628
Market regime: sideways

Compute portfolio weights (w_DOT-USD, w_STIP) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_DOT-USD=X.XXXX, w_STIP=X.XXXX

Answer: w_DOT-USD=0.2481, w_STIP=0.7519

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000001 - -0.000004) / (0.004862 + 0.000001 - -0.000009)
  Unconstrained: w_DOT-USD=0.0011
  After long-only clamp: w_DOT-USD=0.0011, w_STIP=0.9989.


Question:
Assets: SPY, WEAT
SPY: annualized_mean_return=0.1512, daily_std=0.0081
WEAT: annualized_mean_return=-0.0000, daily_std=0.0103
Minimum required portfolio return (annualized): 0.0456
Market regime: sideways

Compute portfolio weights (w_SPY, w_WEAT) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_SPY=X.XXXX, w_WEAT=X.XXXX

Answer: w_SPY=0.6411, w_WEAT=0.3589

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000106 - 0.000013) / (0.000065 + 0.000106 - 0.000026)
  Unconstrained: w_SPY=0.6407
  After long-only clamp: w_SPY=0.6407, w_WEAT=0.3593.


Question:
Assets: AVAX-USD, XLK
AVAX-USD: annualized_mean_return=1.6632, daily_std=0.0445
XLK: annualized_mean_return=0.4788, daily_std=0.0088
Minimum required portfolio return (annualized): 0.5358
Market regime: bull

Compute portfolio weights (w_AVAX-USD, w_XLK) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_AVAX-USD=X.XXXX, w_XLK=X.XXXX

Answer: w_AVAX-USD=0.0584, w_XLK=0.9416

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000077 - -0.000049) / (0.001981 + 0.000077 - -0.000098)
  Unconstrained: w_AVAX-USD=0.0585
  After long-only clamp: w_AVAX-USD=0.0585, w_XLK=0.9415.


AVAX-USD σ=0.0400, CPER σ=0.0159, ρ=0.077. Min-variance weights: AVAX-USD=0.116, CPER=0.884.

Question:
Assets: AVAX-USD, CPER
AVAX-USD: annualized_mean_return=0.5292, daily_std=0.0400
CPER: annualized_mean_return=0.6300, daily_std=0.0159
Minimum required portfolio return (annualized): 0.6265
Market regime: bull

Compute portfolio weights (w_AVAX-USD, w_CPER) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_AVAX-USD=X.XXXX, w_CPER=X.XXXX

Answer: w_AVAX-USD=0.0347, w_CPER=0.9653

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000252 - 0.000049) / (0.001599 + 0.000252 - 0.000098)
  Unconstrained: w_AVAX-USD=0.1157
  After long-only clamp: w_AVAX-USD=0.1157, w_CPER=0.8843.


Question:
Assets: XLF, LQD
XLF: annualized_mean_return=0.0000, daily_std=0.0113
LQD: annualized_mean_return=0.1260, daily_std=0.0038
Minimum required portfolio return (annualized): 0.1205
Market regime: bear

Compute portfolio weights (w_XLF, w_LQD) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_XLF=X.XXXX, w_LQD=X.XXXX

Answer: w_XLF=0.0437, w_LQD=0.9563

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000014 - 0.000005) / (0.000129 + 0.000014 - 0.000010)
  Unconstrained: w_XLF=0.0710
  After long-only clamp: w_XLF=0.0710, w_LQD=0.9290.


Question:
Assets: EWJ, BNDX
EWJ: annualized_mean_return=0.4536, daily_std=0.0113
BNDX: annualized_mean_return=0.0756, daily_std=0.0022
Minimum required portfolio return (annualized): 0.3171
Market regime: sideways

Compute portfolio weights (w_EWJ, w_BNDX) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_EWJ=X.XXXX, w_BNDX=X.XXXX

Answer: w_EWJ=0.6389, w_BNDX=0.3611

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000005 - -0.000001) / (0.000128 + 0.000005 - -0.000001)
  Unconstrained: w_EWJ=0.0399
  After long-only clamp: w_EWJ=0.0399, w_BNDX=0.9601.


Question:
Assets: SOL-USD, IYR
SOL-USD: annualized_mean_return=0.5292, daily_std=0.0471
IYR: annualized_mean_return=-0.1764, daily_std=0.0110
Minimum required portfolio return (annualized): -0.1764
Market regime: sideways

Compute portfolio weights (w_SOL-USD, w_IYR) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_SOL-USD=X.XXXX, w_IYR=X.XXXX

Answer: w_SOL-USD=0.0000, w_IYR=1.0000

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000121 - 0.000174) / (0.002218 + 0.000121 - 0.000348)
  Unconstrained: w_SOL-USD=-0.0266
  After long-only clamp: w_SOL-USD=0.0000, w_IYR=1.0000.


Question:
Assets: ^VIX, SOYB
^VIX: annualized_mean_return=-0.8064, daily_std=0.0804
SOYB: annualized_mean_return=0.1764, daily_std=0.0079
Minimum required portfolio return (annualized): 0.1694
Market regime: sideways

Compute portfolio weights (w_^VIX, w_SOYB) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_^VIX=X.XXXX, w_SOYB=X.XXXX

Answer: w_^VIX=0.0071, w_SOYB=0.9929

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000062 - -0.000023) / (0.006462 + 0.000062 - -0.000046)
  Unconstrained: w_^VIX=0.0129
  After long-only clamp: w_^VIX=0.0129, w_SOYB=0.9871.


Question:
Assets: XLF, TLH
XLF: annualized_mean_return=0.0756, daily_std=0.0084
TLH: annualized_mean_return=0.1764, daily_std=0.0061
Minimum required portfolio return (annualized): 0.1398
Market regime: bull

Compute portfolio weights (w_XLF, w_TLH) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_XLF=X.XXXX, w_TLH=X.XXXX

Answer: w_XLF=0.3619, w_TLH=0.6381

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000037 - -0.000007) / (0.000070 + 0.000037 - -0.000014)
  Unconstrained: w_XLF=0.3617
  After long-only clamp: w_XLF=0.3617, w_TLH=0.6383.


Question:
Assets: XLB, VNQ
XLB: annualized_mean_return=0.2268, daily_std=0.0100
VNQ: annualized_mean_return=0.2016, daily_std=0.0090
Minimum required portfolio return (annualized): 0.2140
Market regime: bull

Compute portfolio weights (w_XLB, w_VNQ) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_XLB=X.XXXX, w_VNQ=X.XXXX

Answer: w_XLB=0.4921, w_VNQ=0.5079

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000081 - 0.000064) / (0.000100 + 0.000081 - 0.000128)
  Unconstrained: w_XLB=0.3190
  After long-only clamp: w_XLB=0.3190, w_VNQ=0.6810.


Question:
Assets: SPY, PPLT
SPY: annualized_mean_return=0.4284, daily_std=0.0063
PPLT: annualized_mean_return=0.9828, daily_std=0.0235
Minimum required portfolio return (annualized): 0.4561
Market regime: bull

Compute portfolio weights (w_SPY, w_PPLT) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_SPY=X.XXXX, w_PPLT=X.XXXX

Answer: w_SPY=0.9232, w_PPLT=0.0768

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000554 - -0.000007) / (0.000040 + 0.000554 - -0.000015)
  Unconstrained: w_SPY=0.9229
  After long-only clamp: w_SPY=0.9229, w_PPLT=0.0771.


Question:
Assets: BNB-USD, ACWI
BNB-USD: annualized_mean_return=0.2016, daily_std=0.0297
ACWI: annualized_mean_return=0.1260, daily_std=0.0077
Minimum required portfolio return (annualized): 0.1493
Market regime: sideways

Compute portfolio weights (w_BNB-USD, w_ACWI) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_BNB-USD=X.XXXX, w_ACWI=X.XXXX

Answer: w_BNB-USD=0.3082, w_ACWI=0.6918

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000059 - -0.000040) / (0.000881 + 0.000059 - -0.000079)
  Unconstrained: w_BNB-USD=0.0973
  After long-only clamp: w_BNB-USD=0.0973, w_ACWI=0.9027.


ETH-USD σ=0.0378, BNDX σ=0.0023, ρ=0.120. Min-variance weights: ETH-USD=0.000, BNDX=1.000.

Question:
Assets: ETH-USD, BNDX
ETH-USD: annualized_mean_return=1.3608, daily_std=0.0378
BNDX: annualized_mean_return=0.0756, daily_std=0.0023
Minimum required portfolio return (annualized): 1.0887
Market regime: sideways

Compute portfolio weights (w_ETH-USD, w_BNDX) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_ETH-USD=X.XXXX, w_BNDX=X.XXXX

Answer: w_ETH-USD=0.7883, w_BNDX=0.2117

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000005 - 0.000010) / (0.001426 + 0.000005 - 0.000021)
  Unconstrained: w_ETH-USD=-0.0036
  After long-only clamp: w_ETH-USD=0.0000, w_BNDX=1.0000.


MATIC-USD σ=0.0460, STIP σ=0.0011, ρ=0.050. Min-variance weights: MATIC-USD=0.000, STIP=1.000.

Question:
Assets: MATIC-USD, STIP
MATIC-USD: annualized_mean_return=-2.7468, daily_std=0.0460
STIP: annualized_mean_return=0.0756, daily_std=0.0011
Minimum required portfolio return (annualized): -0.6490
Market regime: sideways

Compute portfolio weights (w_MATIC-USD, w_STIP) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_MATIC-USD=X.XXXX, w_STIP=X.XXXX

Answer: w_MATIC-USD=0.0000, w_STIP=1.0000

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000001 - 0.000002) / (0.002118 + 0.000001 - 0.000005)
  Unconstrained: w_MATIC-USD=-0.0006
  After long-only clamp: w_MATIC-USD=0.0000, w_STIP=1.0000.


Question:
Assets: ADA-USD, IAU
ADA-USD: annualized_mean_return=0.6048, daily_std=0.0431
IAU: annualized_mean_return=0.3528, daily_std=0.0128
Minimum required portfolio return (annualized): 0.3582
Market regime: sideways

Compute portfolio weights (w_ADA-USD, w_IAU) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_ADA-USD=X.XXXX, w_IAU=X.XXXX

Answer: w_ADA-USD=0.0448, w_IAU=0.9552

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000164 - 0.000081) / (0.001860 + 0.000164 - 0.000162)
  Unconstrained: w_ADA-USD=0.0447
  After long-only clamp: w_ADA-USD=0.0447, w_IAU=0.9553.


Question:
Assets: BNB-USD, TLT
BNB-USD: annualized_mean_return=0.5292, daily_std=0.0201
TLT: annualized_mean_return=-0.1260, daily_std=0.0089
Minimum required portfolio return (annualized): 0.1558
Market regime: sideways

Compute portfolio weights (w_BNB-USD, w_TLT) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_BNB-USD=X.XXXX, w_TLT=X.XXXX

Answer: w_BNB-USD=0.4301, w_TLT=0.5699

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000078 - 0.000004) / (0.000405 + 0.000078 - 0.000007)
  Unconstrained: w_BNB-USD=0.1569
  After long-only clamp: w_BNB-USD=0.1569, w_TLT=0.8431.


Question:
Assets: VEA, SGOV
VEA: annualized_mean_return=-0.0000, daily_std=0.0076
SGOV: annualized_mean_return=0.0756, daily_std=0.0002
Minimum required portfolio return (annualized): 0.0536
Market regime: sideways

Compute portfolio weights (w_VEA, w_SGOV) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_VEA=X.XXXX, w_SGOV=X.XXXX

Answer: w_VEA=0.0004, w_SGOV=0.9996

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - -0.000000) / (0.000057 + 0.000000 - -0.000000)
  Unconstrained: w_VEA=0.0019
  After long-only clamp: w_VEA=0.0019, w_SGOV=0.9981.


Question:
Assets: EEM, ICSH
EEM: annualized_mean_return=0.2016, daily_std=0.0104
ICSH: annualized_mean_return=0.0756, daily_std=0.0003
Minimum required portfolio return (annualized): 0.1108
Market regime: bear

Compute portfolio weights (w_EEM, w_ICSH) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_EEM=X.XXXX, w_ICSH=X.XXXX

Answer: w_EEM=0.2794, w_ICSH=0.7206

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - 0.000000) / (0.000109 + 0.000000 - 0.000000)
  Unconstrained: w_EEM=-0.0002
  After long-only clamp: w_EEM=0.0000, w_ICSH=1.0000.


Question:
Assets: BNB-USD, XHB
BNB-USD: annualized_mean_return=-0.1008, daily_std=0.0423
XHB: annualized_mean_return=-0.6048, daily_std=0.0134
Minimum required portfolio return (annualized): -0.5674
Market regime: sideways

Compute portfolio weights (w_BNB-USD, w_XHB) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_BNB-USD=X.XXXX, w_XHB=X.XXXX

Answer: w_BNB-USD=0.0946, w_XHB=0.9054

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000179 - -0.000009) / (0.001791 + 0.000179 - -0.000018)
  Unconstrained: w_BNB-USD=0.0946
  After long-only clamp: w_BNB-USD=0.0946, w_XHB=0.9054.


Question:
Assets: EWJ, BIL
EWJ: annualized_mean_return=0.2268, daily_std=0.0127
BIL: annualized_mean_return=0.0504, daily_std=0.0002
Minimum required portfolio return (annualized): 0.0885
Market regime: sideways

Compute portfolio weights (w_EWJ, w_BIL) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_EWJ=X.XXXX, w_BIL=X.XXXX

Answer: w_EWJ=0.2160, w_BIL=0.7840

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - -0.000000) / (0.000162 + 0.000000 - -0.000001)
  Unconstrained: w_EWJ=0.0020
  After long-only clamp: w_EWJ=0.0020, w_BIL=0.9980.


Question:
Assets: XRP-USD, TIP
XRP-USD: annualized_mean_return=0.8568, daily_std=0.0415
TIP: annualized_mean_return=0.1008, daily_std=0.0010
Minimum required portfolio return (annualized): 0.4889
Market regime: bull

Compute portfolio weights (w_XRP-USD, w_TIP) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_XRP-USD=X.XXXX, w_TIP=X.XXXX

Answer: w_XRP-USD=0.5134, w_TIP=0.4866

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000001 - 0.000009) / (0.001720 + 0.000001 - 0.000017)
  Unconstrained: w_XRP-USD=-0.0044
  After long-only clamp: w_XRP-USD=0.0000, w_TIP=1.0000.


Question:
Assets: LINK-USD, FXI
LINK-USD: annualized_mean_return=-1.1844, daily_std=0.0393
FXI: annualized_mean_return=-0.2016, daily_std=0.0114
Minimum required portfolio return (annualized): -0.5706
Market regime: sideways

Compute portfolio weights (w_LINK-USD, w_FXI) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_LINK-USD=X.XXXX, w_FXI=X.XXXX

Answer: w_LINK-USD=0.1017, w_FXI=0.8983

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000131 - -0.000050) / (0.001548 + 0.000131 - -0.000100)
  Unconstrained: w_LINK-USD=0.1017
  After long-only clamp: w_LINK-USD=0.1017, w_FXI=0.8983.


Question:
Assets: VLUE, BIL
VLUE: annualized_mean_return=0.5040, daily_std=0.0087
BIL: annualized_mean_return=0.0504, daily_std=0.0001
Minimum required portfolio return (annualized): 0.1694
Market regime: bull

Compute portfolio weights (w_VLUE, w_BIL) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_VLUE=X.XXXX, w_BIL=X.XXXX

Answer: w_VLUE=0.2623, w_BIL=0.7377

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - 0.000000) / (0.000075 + 0.000000 - 0.000000)
  Unconstrained: w_VLUE=-0.0000
  After long-only clamp: w_VLUE=0.0000, w_BIL=1.0000.


Question:
Assets: VLUE, HAUZ
VLUE: annualized_mean_return=0.5292, daily_std=0.0087
HAUZ: annualized_mean_return=0.0252, daily_std=0.0069
Minimum required portfolio return (annualized): 0.1537
Market regime: sideways

Compute portfolio weights (w_VLUE, w_HAUZ) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_VLUE=X.XXXX, w_HAUZ=X.XXXX

Answer: w_VLUE=0.3010, w_HAUZ=0.6990

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000048 - 0.000027) / (0.000075 + 0.000048 - 0.000055)
  Unconstrained: w_VLUE=0.2993
  After long-only clamp: w_VLUE=0.2993, w_HAUZ=0.7007.


Question:
Assets: EFA, VCIT
EFA: annualized_mean_return=0.3528, daily_std=0.0115
VCIT: annualized_mean_return=0.0252, daily_std=0.0040
Minimum required portfolio return (annualized): 0.1998
Market regime: sideways

Compute portfolio weights (w_EFA, w_VCIT) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_EFA=X.XXXX, w_VCIT=X.XXXX

Answer: w_EFA=0.5330, w_VCIT=0.4670

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000016 - 0.000014) / (0.000133 + 0.000016 - 0.000028)
  Unconstrained: w_EFA=0.0172
  After long-only clamp: w_EFA=0.0172, w_VCIT=0.9828.


Question:
Assets: VLUE, BIL
VLUE: annualized_mean_return=-0.1008, daily_std=0.0085
BIL: annualized_mean_return=0.0504, daily_std=0.0002
Minimum required portfolio return (annualized): 0.0396
Market regime: sideways

Compute portfolio weights (w_VLUE, w_BIL) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_VLUE=X.XXXX, w_BIL=X.XXXX

Answer: w_VLUE=0.0003, w_BIL=0.9997

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - 0.000000) / (0.000073 + 0.000000 - 0.000001)
  Unconstrained: w_VLUE=-0.0036
  After long-only clamp: w_VLUE=0.0000, w_BIL=1.0000.


Question:
Assets: ETH-USD, IEF
ETH-USD: annualized_mean_return=-1.4616, daily_std=0.0384
IEF: annualized_mean_return=0.0756, daily_std=0.0026
Minimum required portfolio return (annualized): 0.0704
Market regime: sideways

Compute portfolio weights (w_ETH-USD, w_IEF) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_ETH-USD=X.XXXX, w_IEF=X.XXXX

Answer: w_ETH-USD=0.0011, w_IEF=0.9989

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000007 - 0.000005) / (0.001472 + 0.000007 - 0.000009)
  Unconstrained: w_ETH-USD=0.0015
  After long-only clamp: w_ETH-USD=0.0015, w_IEF=0.9985.


Question:
Assets: VEA, ICSH
VEA: annualized_mean_return=0.2268, daily_std=0.0074
ICSH: annualized_mean_return=0.0756, daily_std=0.0003
Minimum required portfolio return (annualized): 0.1540
Market regime: bull

Compute portfolio weights (w_VEA, w_ICSH) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_VEA=X.XXXX, w_ICSH=X.XXXX

Answer: w_VEA=0.5185, w_ICSH=0.4815

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - -0.000000) / (0.000055 + 0.000000 - -0.000000)
  Unconstrained: w_VEA=0.0020
  After long-only clamp: w_VEA=0.0020, w_ICSH=0.9980.


Question:
Assets: FXI, HAUZ
FXI: annualized_mean_return=0.0756, daily_std=0.0171
HAUZ: annualized_mean_return=0.4284, daily_std=0.0097
Minimum required portfolio return (annualized): 0.2485
Market regime: sideways

Compute portfolio weights (w_FXI, w_HAUZ) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_FXI=X.XXXX, w_HAUZ=X.XXXX

Answer: w_FXI=0.0000, w_HAUZ=1.0000

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000094 - 0.000102) / (0.000293 + 0.000094 - 0.000203)
  Unconstrained: w_FXI=-0.0402
  After long-only clamp: w_FXI=0.0000, w_HAUZ=1.0000.


BTC-USD σ=0.0237, PALL σ=0.0185, ρ=0.222. Min-variance weights: BTC-USD=0.344, PALL=0.656.

Question:
Assets: BTC-USD, PALL
BTC-USD: annualized_mean_return=0.2268, daily_std=0.0237
PALL: annualized_mean_return=-0.8820, daily_std=0.0185
Minimum required portfolio return (annualized): -0.5833
Market regime: sideways

Compute portfolio weights (w_BTC-USD, w_PALL) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_BTC-USD=X.XXXX, w_PALL=X.XXXX

Answer: w_BTC-USD=0.3436, w_PALL=0.6564

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000341 - 0.000097) / (0.000562 + 0.000341 - 0.000194)
  Unconstrained: w_BTC-USD=0.3435
  After long-only clamp: w_BTC-USD=0.3435, w_PALL=0.6565.


Question:
Assets: LINK-USD, QQQ
LINK-USD: annualized_mean_return=0.5040, daily_std=0.0515
QQQ: annualized_mean_return=0.3528, daily_std=0.0069
Minimum required portfolio return (annualized): 0.4662
Market regime: bull

Compute portfolio weights (w_LINK-USD, w_QQQ) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_LINK-USD=X.XXXX, w_QQQ=X.XXXX

Answer: w_LINK-USD=0.7500, w_QQQ=0.2500

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000048 - -0.000073) / (0.002652 + 0.000048 - -0.000147)
  Unconstrained: w_LINK-USD=0.0425
  After long-only clamp: w_LINK-USD=0.0425, w_QQQ=0.9575.


Question:
Assets: FXI, ETH-USD
FXI: annualized_mean_return=-0.0252, daily_std=0.0120
ETH-USD: annualized_mean_return=-1.2348, daily_std=0.0396
Minimum required portfolio return (annualized): -0.0955
Market regime: sideways

Compute portfolio weights (w_FXI, w_ETH-USD) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_FXI=X.XXXX, w_ETH-USD=X.XXXX

Answer: w_FXI=0.9419, w_ETH-USD=0.0581

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.001570 - 0.000009) / (0.000144 + 0.001570 - 0.000017)
  Unconstrained: w_FXI=0.9201
  After long-only clamp: w_FXI=0.9201, w_ETH-USD=0.0799.


Question:
Assets: VTI, ETH-USD
VTI: annualized_mean_return=-0.6804, daily_std=0.0130
ETH-USD: annualized_mean_return=-1.9152, daily_std=0.0494
Minimum required portfolio return (annualized): -0.6978
Market regime: bear

Compute portfolio weights (w_VTI, w_ETH-USD) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_VTI=X.XXXX, w_ETH-USD=X.XXXX

Answer: w_VTI=0.9859, w_ETH-USD=0.0141

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.002438 - 0.000094) / (0.000170 + 0.002438 - 0.000189)
  Unconstrained: w_VTI=0.9688
  After long-only clamp: w_VTI=0.9688, w_ETH-USD=0.0312.


Question:
Assets: ADA-USD, SHV
ADA-USD: annualized_mean_return=-1.1340, daily_std=0.0413
SHV: annualized_mean_return=0.0504, daily_std=0.0002
Minimum required portfolio return (annualized): -0.2178
Market regime: bull

Compute portfolio weights (w_ADA-USD, w_SHV) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_ADA-USD=X.XXXX, w_SHV=X.XXXX

Answer: w_ADA-USD=0.0000, w_SHV=1.0000

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - 0.000001) / (0.001710 + 0.000000 - 0.000002)
  Unconstrained: w_ADA-USD=-0.0005
  After long-only clamp: w_ADA-USD=0.0000, w_SHV=1.0000.


Question:
Assets: SOL-USD, JNK
SOL-USD: annualized_mean_return=0.5292, daily_std=0.0344
JNK: annualized_mean_return=0.1512, daily_std=0.0025
Minimum required portfolio return (annualized): 0.4380
Market regime: bull

Compute portfolio weights (w_SOL-USD, w_JNK) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_SOL-USD=X.XXXX, w_JNK=X.XXXX

Answer: w_SOL-USD=0.7587, w_JNK=0.2413

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000006 - -0.000004) / (0.001180 + 0.000006 - -0.000008)
  Unconstrained: w_SOL-USD=0.0084
  After long-only clamp: w_SOL-USD=0.0084, w_JNK=0.9916.


Question:
Assets: BNB-USD, REZ
BNB-USD: annualized_mean_return=1.9908, daily_std=0.0388
REZ: annualized_mean_return=-0.0252, daily_std=0.0090
Minimum required portfolio return (annualized): 1.3294
Market regime: bull

Compute portfolio weights (w_BNB-USD, w_REZ) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_BNB-USD=X.XXXX, w_REZ=X.XXXX

Answer: w_BNB-USD=0.6719, w_REZ=0.3281

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000081 - -0.000006) / (0.001503 + 0.000081 - -0.000011)
  Unconstrained: w_BNB-USD=0.0541
  After long-only clamp: w_BNB-USD=0.0541, w_REZ=0.9459.


Question:
Assets: ETH-USD, ITB
ETH-USD: annualized_mean_return=1.9404, daily_std=0.0376
ITB: annualized_mean_return=-0.2016, daily_std=0.0198
Minimum required portfolio return (annualized): 1.2267
Market regime: sideways

Compute portfolio weights (w_ETH-USD, w_ITB) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_ETH-USD=X.XXXX, w_ITB=X.XXXX

Answer: w_ETH-USD=0.6668, w_ITB=0.3332

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000393 - -0.000025) / (0.001410 + 0.000393 - -0.000049)
  Unconstrained: w_ETH-USD=0.2254
  After long-only clamp: w_ETH-USD=0.2254, w_ITB=0.7746.


Question:
Assets: XLB, CSHI
XLB: annualized_mean_return=-0.1512, daily_std=0.0147
CSHI: annualized_mean_return=-0.0504, daily_std=0.0032
Minimum required portfolio return (annualized): -0.0542
Market regime: sideways

Compute portfolio weights (w_XLB, w_CSHI) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_XLB=X.XXXX, w_CSHI=X.XXXX

Answer: w_XLB=0.0377, w_CSHI=0.9623

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000010 - -0.000007) / (0.000216 + 0.000010 - -0.000014)
  Unconstrained: w_XLB=0.0725
  After long-only clamp: w_XLB=0.0725, w_CSHI=0.9275.


Question:
Assets: EFA, AVAX-USD
EFA: annualized_mean_return=0.2268, daily_std=0.0089
AVAX-USD: annualized_mean_return=-2.4192, daily_std=0.0569
Minimum required portfolio return (annualized): 0.1938
Market regime: bear

Compute portfolio weights (w_EFA, w_AVAX-USD) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_EFA=X.XXXX, w_AVAX-USD=X.XXXX

Answer: w_EFA=0.9875, w_AVAX-USD=0.0125

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.003235 - -0.000016) / (0.000079 + 0.003235 - -0.000031)
  Unconstrained: w_EFA=0.9717
  After long-only clamp: w_EFA=0.9717, w_AVAX-USD=0.0283.


BNB-USD σ=0.0271, IGOV σ=0.0057, ρ=0.184. Min-variance weights: BNB-USD=0.006, IGOV=0.994.

Question:
Assets: BNB-USD, IGOV
BNB-USD: annualized_mean_return=0.1008, daily_std=0.0271
IGOV: annualized_mean_return=0.0756, daily_std=0.0057
Minimum required portfolio return (annualized): 0.0947
Market regime: sideways

Compute portfolio weights (w_BNB-USD, w_IGOV) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_BNB-USD=X.XXXX, w_IGOV=X.XXXX

Answer: w_BNB-USD=0.7579, w_IGOV=0.2421

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000033 - 0.000029) / (0.000732 + 0.000033 - 0.000057)
  Unconstrained: w_BNB-USD=0.0061
  After long-only clamp: w_BNB-USD=0.0061, w_IGOV=0.9939.


AVAX-USD σ=0.0496, INDS σ=0.0148, ρ=-0.188. Min-variance weights: AVAX-USD=0.121, INDS=0.879.

Question:
Assets: AVAX-USD, INDS
AVAX-USD: annualized_mean_return=1.3356, daily_std=0.0496
INDS: annualized_mean_return=-0.0756, daily_std=0.0148
Minimum required portfolio return (annualized): 0.0030
Market regime: sideways

Compute portfolio weights (w_AVAX-USD, w_INDS) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_AVAX-USD=X.XXXX, w_INDS=X.XXXX

Answer: w_AVAX-USD=0.1212, w_INDS=0.8788

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000220 - -0.000138) / (0.002456 + 0.000220 - -0.000277)
  Unconstrained: w_AVAX-USD=0.1214
  After long-only clamp: w_AVAX-USD=0.1214, w_INDS=0.8786.


Question:
Assets: USMV, VNQI
USMV: annualized_mean_return=0.1008, daily_std=0.0055
VNQI: annualized_mean_return=0.3780, daily_std=0.0063
Minimum required portfolio return (annualized): 0.2452
Market regime: bull

Compute portfolio weights (w_USMV, w_VNQI) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_USMV=X.XXXX, w_VNQI=X.XXXX

Answer: w_USMV=0.4791, w_VNQI=0.5209

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000039 - 0.000023) / (0.000031 + 0.000039 - 0.000045)
  Unconstrained: w_USMV=0.6723
  After long-only clamp: w_USMV=0.6723, w_VNQI=0.3277.


XRP-USD σ=0.0647, CSHI σ=0.0006, ρ=0.136. Min-variance weights: XRP-USD=0.000, CSHI=1.000.

Question:
Assets: XRP-USD, CSHI
XRP-USD: annualized_mean_return=-0.6300, daily_std=0.0647
CSHI: annualized_mean_return=0.0504, daily_std=0.0006
Minimum required portfolio return (annualized): -0.1559
Market regime: sideways

Compute portfolio weights (w_XRP-USD, w_CSHI) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_XRP-USD=X.XXXX, w_CSHI=X.XXXX

Answer: w_XRP-USD=0.0000, w_CSHI=1.0000

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - 0.000005) / (0.004187 + 0.000000 - 0.000011)
  Unconstrained: w_XRP-USD=-0.0012
  After long-only clamp: w_XRP-USD=0.0000, w_CSHI=1.0000.


Question:
Assets: IVV, UNG
IVV: annualized_mean_return=0.7056, daily_std=0.0095
UNG: annualized_mean_return=-0.5796, daily_std=0.0337
Minimum required portfolio return (annualized): 0.2181
Market regime: sideways

Compute portfolio weights (w_IVV, w_UNG) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_IVV=X.XXXX, w_UNG=X.XXXX

Answer: w_IVV=0.9160, w_UNG=0.0840

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.001139 - -0.000015) / (0.000091 + 0.001139 - -0.000029)
  Unconstrained: w_IVV=0.9162
  After long-only clamp: w_IVV=0.9162, w_UNG=0.0838.


Question:
Assets: VEA, HAUZ
VEA: annualized_mean_return=0.2016, daily_std=0.0073
HAUZ: annualized_mean_return=0.0504, daily_std=0.0068
Minimum required portfolio return (annualized): 0.0840
Market regime: sideways

Compute portfolio weights (w_VEA, w_HAUZ) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_VEA=X.XXXX, w_HAUZ=X.XXXX

Answer: w_VEA=0.3117, w_HAUZ=0.6883

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000046 - 0.000039) / (0.000054 + 0.000046 - 0.000078)
  Unconstrained: w_VEA=0.3105
  After long-only clamp: w_VEA=0.3105, w_HAUZ=0.6895.


SOL-USD σ=0.0454, VCIT σ=0.0039, ρ=0.033. Min-variance weights: SOL-USD=0.005, VCIT=0.995.

Question:
Assets: SOL-USD, VCIT
SOL-USD: annualized_mean_return=0.3528, daily_std=0.0454
VCIT: annualized_mean_return=0.1008, daily_std=0.0039
Minimum required portfolio return (annualized): 0.2351
Market regime: sideways

Compute portfolio weights (w_SOL-USD, w_VCIT) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_SOL-USD=X.XXXX, w_VCIT=X.XXXX

Answer: w_SOL-USD=0.5329, w_VCIT=0.4671

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000016 - 0.000006) / (0.002060 + 0.000016 - 0.000012)
  Unconstrained: w_SOL-USD=0.0046
  After long-only clamp: w_SOL-USD=0.0046, w_VCIT=0.9954.


Question:
Assets: FXI, XHB
FXI: annualized_mean_return=-0.3528, daily_std=0.0191
XHB: annualized_mean_return=-0.6048, daily_std=0.0140
Minimum required portfolio return (annualized): -0.5691
Market regime: sideways

Compute portfolio weights (w_FXI, w_XHB) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_FXI=X.XXXX, w_XHB=X.XXXX

Answer: w_FXI=0.2852, w_XHB=0.7148

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000197 - 0.000085) / (0.000365 + 0.000197 - 0.000169)
  Unconstrained: w_FXI=0.2857
  After long-only clamp: w_FXI=0.2857, w_XHB=0.7143.


Question:
Assets: XLK, ICSH
XLK: annualized_mean_return=0.4788, daily_std=0.0085
ICSH: annualized_mean_return=0.0756, daily_std=0.0004
Minimum required portfolio return (annualized): 0.3519
Market regime: bull

Compute portfolio weights (w_XLK, w_ICSH) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_XLK=X.XXXX, w_ICSH=X.XXXX

Answer: w_XLK=0.6853, w_ICSH=0.3147

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - 0.000000) / (0.000073 + 0.000000 - 0.000000)
  Unconstrained: w_XLK=0.0015
  After long-only clamp: w_XLK=0.0015, w_ICSH=0.9985.


Question:
Assets: XRP-USD, XHB
XRP-USD: annualized_mean_return=0.6300, daily_std=0.0675
XHB: annualized_mean_return=-0.7056, daily_std=0.0148
Minimum required portfolio return (annualized): -0.6536
Market regime: sideways

Compute portfolio weights (w_XRP-USD, w_XHB) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_XRP-USD=X.XXXX, w_XHB=X.XXXX

Answer: w_XRP-USD=0.0548, w_XHB=0.9452

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000218 - -0.000049) / (0.004554 + 0.000218 - -0.000099)
  Unconstrained: w_XRP-USD=0.0549
  After long-only clamp: w_XRP-USD=0.0549, w_XHB=0.9451.


Question:
Assets: VEA, DBC
VEA: annualized_mean_return=0.2772, daily_std=0.0089
DBC: annualized_mean_return=0.1260, daily_std=0.0074
Minimum required portfolio return (annualized): 0.2587
Market regime: bear

Compute portfolio weights (w_VEA, w_DBC) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_VEA=X.XXXX, w_DBC=X.XXXX

Answer: w_VEA=0.8776, w_DBC=0.1224

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000055 - 0.000013) / (0.000078 + 0.000055 - 0.000025)
  Unconstrained: w_VEA=0.3934
  After long-only clamp: w_VEA=0.3934, w_DBC=0.6066.


Question:
Assets: ADA-USD, SGOV
ADA-USD: annualized_mean_return=-1.6632, daily_std=0.0593
SGOV: annualized_mean_return=0.0504, daily_std=0.0001
Minimum required portfolio return (annualized): -0.1647
Market regime: bear

Compute portfolio weights (w_ADA-USD, w_SGOV) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_ADA-USD=X.XXXX, w_SGOV=X.XXXX

Answer: w_ADA-USD=0.0003, w_SGOV=0.9997

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - -0.000001) / (0.003515 + 0.000000 - -0.000002)
  Unconstrained: w_ADA-USD=0.0003
  After long-only clamp: w_ADA-USD=0.0003, w_SGOV=0.9997.


BNB-USD σ=0.0220, IGOV σ=0.0066, ρ=0.094. Min-variance weights: BNB-USD=0.060, IGOV=0.940.

Question:
Assets: BNB-USD, IGOV
BNB-USD: annualized_mean_return=0.5796, daily_std=0.0220
IGOV: annualized_mean_return=0.1512, daily_std=0.0066
Minimum required portfolio return (annualized): 0.3405
Market regime: sideways

Compute portfolio weights (w_BNB-USD, w_IGOV) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_BNB-USD=X.XXXX, w_IGOV=X.XXXX

Answer: w_BNB-USD=0.4419, w_IGOV=0.5581

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000044 - 0.000014) / (0.000484 + 0.000044 - 0.000027)
  Unconstrained: w_BNB-USD=0.0602
  After long-only clamp: w_BNB-USD=0.0602, w_IGOV=0.9398.


Question:
Assets: BNB-USD, PALL
BNB-USD: annualized_mean_return=0.3024, daily_std=0.0205
PALL: annualized_mean_return=0.3024, daily_std=0.0150
Minimum required portfolio return (annualized): 0.3024
Market regime: sideways

Compute portfolio weights (w_BNB-USD, w_PALL) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_BNB-USD=X.XXXX, w_PALL=X.XXXX

Answer: w_BNB-USD=0.3563, w_PALL=0.6437

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000224 - -0.000021) / (0.000421 + 0.000224 - -0.000042)
  Unconstrained: w_BNB-USD=0.3564
  After long-only clamp: w_BNB-USD=0.3564, w_PALL=0.6436.


Question:
Assets: DOT-USD, IGOV
DOT-USD: annualized_mean_return=-0.3780, daily_std=0.0408
IGOV: annualized_mean_return=0.0504, daily_std=0.0046
Minimum required portfolio return (annualized): 0.0472
Market regime: bull

Compute portfolio weights (w_DOT-USD, w_IGOV) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_DOT-USD=X.XXXX, w_IGOV=X.XXXX

Answer: w_DOT-USD=0.0075, w_IGOV=0.9925

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000021 - -0.000013) / (0.001664 + 0.000021 - -0.000026)
  Unconstrained: w_DOT-USD=0.0201
  After long-only clamp: w_DOT-USD=0.0201, w_IGOV=0.9799.


Question:
Assets: EFA, IGOV
EFA: annualized_mean_return=0.1260, daily_std=0.0115
IGOV: annualized_mean_return=0.3024, daily_std=0.0058
Minimum required portfolio return (annualized): 0.2676
Market regime: bear

Compute portfolio weights (w_EFA, w_IGOV) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_EFA=X.XXXX, w_IGOV=X.XXXX

Answer: w_EFA=0.1321, w_IGOV=0.8679

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000034 - 0.000016) / (0.000133 + 0.000034 - 0.000031)
  Unconstrained: w_EFA=0.1340
  After long-only clamp: w_EFA=0.1340, w_IGOV=0.8660.


Question:
Assets: XLI, WEAT
XLI: annualized_mean_return=-0.1512, daily_std=0.0090
WEAT: annualized_mean_return=-0.3780, daily_std=0.0106
Minimum required portfolio return (annualized): -0.2116
Market regime: sideways

Compute portfolio weights (w_XLI, w_WEAT) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_XLI=X.XXXX, w_WEAT=X.XXXX

Answer: w_XLI=0.7337, w_WEAT=0.2663

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000113 - -0.000012) / (0.000080 + 0.000113 - -0.000025)
  Unconstrained: w_XLI=0.5744
  After long-only clamp: w_XLI=0.5744, w_WEAT=0.4256.


Question:
Assets: BTC-USD, USO
BTC-USD: annualized_mean_return=0.2016, daily_std=0.0159
USO: annualized_mean_return=0.2772, daily_std=0.0202
Minimum required portfolio return (annualized): 0.2199
Market regime: bull

Compute portfolio weights (w_BTC-USD, w_USO) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_BTC-USD=X.XXXX, w_USO=X.XXXX

Answer: w_BTC-USD=0.6099, w_USO=0.3901

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000408 - -0.000019) / (0.000254 + 0.000408 - -0.000037)
  Unconstrained: w_BTC-USD=0.6100
  After long-only clamp: w_BTC-USD=0.6100, w_USO=0.3900.


Question:
Assets: XLV, XHB
XLV: annualized_mean_return=0.0756, daily_std=0.0081
XHB: annualized_mean_return=-0.8568, daily_std=0.0144
Minimum required portfolio return (annualized): -0.4223
Market regime: sideways

Compute portfolio weights (w_XLV, w_XHB) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_XLV=X.XXXX, w_XHB=X.XXXX

Answer: w_XLV=0.9246, w_XHB=0.0754

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000207 - 0.000053) / (0.000066 + 0.000207 - 0.000105)
  Unconstrained: w_XLV=0.9223
  After long-only clamp: w_XLV=0.9223, w_XHB=0.0777.


Question:
Assets: XLV, SLV
XLV: annualized_mean_return=0.6048, daily_std=0.0087
SLV: annualized_mean_return=1.1340, daily_std=0.0194
Minimum required portfolio return (annualized): 0.6874
Market regime: sideways

Compute portfolio weights (w_XLV, w_SLV) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_XLV=X.XXXX, w_SLV=X.XXXX

Answer: w_XLV=0.8325, w_SLV=0.1675

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000376 - -0.000000) / (0.000076 + 0.000376 - -0.000001)
  Unconstrained: w_XLV=0.8318
  After long-only clamp: w_XLV=0.8318, w_SLV=0.1682.


Question:
Assets: SOL-USD, TIP
SOL-USD: annualized_mean_return=1.2852, daily_std=0.0367
TIP: annualized_mean_return=0.0756, daily_std=0.0010
Minimum required portfolio return (annualized): 0.9255
Market regime: bull

Compute portfolio weights (w_SOL-USD, w_TIP) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_SOL-USD=X.XXXX, w_TIP=X.XXXX

Answer: w_SOL-USD=0.7026, w_TIP=0.2974

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000001 - 0.000004) / (0.001346 + 0.000001 - 0.000008)
  Unconstrained: w_SOL-USD=-0.0021
  After long-only clamp: w_SOL-USD=0.0000, w_TIP=1.0000.


Question:
Assets: SOL-USD, SHY
SOL-USD: annualized_mean_return=-2.2932, daily_std=0.0596
SHY: annualized_mean_return=0.0756, daily_std=0.0008
Minimum required portfolio return (annualized): -1.0965
Market regime: sideways

Compute portfolio weights (w_SOL-USD, w_SHY) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_SOL-USD=X.XXXX, w_SHY=X.XXXX

Answer: w_SOL-USD=0.0010, w_SHY=0.9990

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000001 - -0.000003) / (0.003556 + 0.000001 - -0.000006)
  Unconstrained: w_SOL-USD=0.0011
  After long-only clamp: w_SOL-USD=0.0011, w_SHY=0.9989.


Question:
Assets: XRP-USD, USMV
XRP-USD: annualized_mean_return=0.2772, daily_std=0.0285
USMV: annualized_mean_return=0.0252, daily_std=0.0091
Minimum required portfolio return (annualized): 0.0423
Market regime: sideways

Compute portfolio weights (w_XRP-USD, w_USMV) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_XRP-USD=X.XXXX, w_USMV=X.XXXX

Answer: w_XRP-USD=0.1433, w_USMV=0.8567

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000082 - -0.000064) / (0.000811 + 0.000082 - -0.000128)
  Unconstrained: w_XRP-USD=0.1434
  After long-only clamp: w_XRP-USD=0.1434, w_USMV=0.8566.


Question:
Assets: VEA, BIL
VEA: annualized_mean_return=0.3780, daily_std=0.0104
BIL: annualized_mean_return=0.0504, daily_std=0.0002
Minimum required portfolio return (annualized): 0.0504
Market regime: sideways

Compute portfolio weights (w_VEA, w_BIL) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_VEA=X.XXXX, w_BIL=X.XXXX

Answer: w_VEA=0.0002, w_BIL=0.9998

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - -0.000000) / (0.000109 + 0.000000 - -0.000000)
  Unconstrained: w_VEA=0.0024
  After long-only clamp: w_VEA=0.0024, w_BIL=0.9976.


Question:
Assets: VTI, PDBC
VTI: annualized_mean_return=0.6552, daily_std=0.0113
PDBC: annualized_mean_return=0.3024, daily_std=0.0104
Minimum required portfolio return (annualized): 0.4255
Market regime: sideways

Compute portfolio weights (w_VTI, w_PDBC) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_VTI=X.XXXX, w_PDBC=X.XXXX

Answer: w_VTI=0.4665, w_PDBC=0.5335

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000108 - -0.000024) / (0.000127 + 0.000108 - -0.000048)
  Unconstrained: w_VTI=0.4665
  After long-only clamp: w_VTI=0.4665, w_PDBC=0.5335.


Question:
Assets: XLE, TLH
XLE: annualized_mean_return=0.0000, daily_std=0.0112
TLH: annualized_mean_return=-0.0000, daily_std=0.0042
Minimum required portfolio return (annualized): -0.0000
Market regime: sideways

Compute portfolio weights (w_XLE, w_TLH) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_XLE=X.XXXX, w_TLH=X.XXXX

Answer: w_XLE=0.1505, w_TLH=0.8495

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000017 - -0.000006) / (0.000125 + 0.000017 - -0.000012)
  Unconstrained: w_XLE=0.1500
  After long-only clamp: w_XLE=0.1500, w_TLH=0.8500.


AVAX-USD σ=0.0442, ICSH σ=0.0002, ρ=-0.001. Min-variance weights: AVAX-USD=0.000, ICSH=1.000.

Question:
Assets: AVAX-USD, ICSH
AVAX-USD: annualized_mean_return=-0.5292, daily_std=0.0442
ICSH: annualized_mean_return=0.0504, daily_std=0.0002
Minimum required portfolio return (annualized): -0.2270
Market regime: sideways

Compute portfolio weights (w_AVAX-USD, w_ICSH) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_AVAX-USD=X.XXXX, w_ICSH=X.XXXX

Answer: w_AVAX-USD=0.0000, w_ICSH=1.0000

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - -0.000000) / (0.001955 + 0.000000 - -0.000000)
  Unconstrained: w_AVAX-USD=0.0000
  After long-only clamp: w_AVAX-USD=0.0000, w_ICSH=1.0000.


Question:
Assets: ADA-USD, VNQ
ADA-USD: annualized_mean_return=-0.9828, daily_std=0.0484
VNQ: annualized_mean_return=0.0000, daily_std=0.0104
Minimum required portfolio return (annualized): -0.3057
Market regime: sideways

Compute portfolio weights (w_ADA-USD, w_VNQ) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_ADA-USD=X.XXXX, w_VNQ=X.XXXX

Answer: w_ADA-USD=0.0000, w_VNQ=1.0000

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000109 - 0.000129) / (0.002340 + 0.000109 - 0.000259)
  Unconstrained: w_ADA-USD=-0.0093
  After long-only clamp: w_ADA-USD=0.0000, w_VNQ=1.0000.


AVAX-USD σ=0.0405, CSHI σ=0.0005, ρ=0.237. Min-variance weights: AVAX-USD=0.000, CSHI=1.000.

Question:
Assets: AVAX-USD, CSHI
AVAX-USD: annualized_mean_return=1.1592, daily_std=0.0405
CSHI: annualized_mean_return=0.0504, daily_std=0.0005
Minimum required portfolio return (annualized): 0.0504
Market regime: bull

Compute portfolio weights (w_AVAX-USD, w_CSHI) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_AVAX-USD=X.XXXX, w_CSHI=X.XXXX

Answer: w_AVAX-USD=0.0000, w_CSHI=1.0000

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - 0.000005) / (0.001637 + 0.000000 - 0.000010)
  Unconstrained: w_AVAX-USD=-0.0030
  After long-only clamp: w_AVAX-USD=0.0000, w_CSHI=1.0000.


Question:
Assets: XLK, CSHI
XLK: annualized_mean_return=0.4536, daily_std=0.0085
CSHI: annualized_mean_return=0.0504, daily_std=0.0004
Minimum required portfolio return (annualized): 0.2889
Market regime: bull

Compute portfolio weights (w_XLK, w_CSHI) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_XLK=X.XXXX, w_CSHI=X.XXXX

Answer: w_XLK=0.5915, w_CSHI=0.4085

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - -0.000000) / (0.000072 + 0.000000 - -0.000001)
  Unconstrained: w_XLK=0.0071
  After long-only clamp: w_XLK=0.0071, w_CSHI=0.9929.


LINK-USD σ=0.0475, DBB σ=0.0086, ρ=0.197. Min-variance weights: LINK-USD=0.000, DBB=1.000.

Question:
Assets: LINK-USD, DBB
LINK-USD: annualized_mean_return=-1.9152, daily_std=0.0475
DBB: annualized_mean_return=0.5292, daily_std=0.0086
Minimum required portfolio return (annualized): -0.2277
Market regime: sideways

Compute portfolio weights (w_LINK-USD, w_DBB) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_LINK-USD=X.XXXX, w_DBB=X.XXXX

Answer: w_LINK-USD=0.0000, w_DBB=1.0000

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000075 - 0.000081) / (0.002255 + 0.000075 - 0.000161)
  Unconstrained: w_LINK-USD=-0.0028
  After long-only clamp: w_LINK-USD=0.0000, w_DBB=1.0000.


Question:
Assets: DOT-USD, SHY
DOT-USD: annualized_mean_return=0.3780, daily_std=0.0401
SHY: annualized_mean_return=0.0504, daily_std=0.0011
Minimum required portfolio return (annualized): 0.2343
Market regime: sideways

Compute portfolio weights (w_DOT-USD, w_SHY) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_DOT-USD=X.XXXX, w_SHY=X.XXXX

Answer: w_DOT-USD=0.5614, w_SHY=0.4386

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000001 - 0.000005) / (0.001607 + 0.000001 - 0.000010)
  Unconstrained: w_DOT-USD=-0.0025
  After long-only clamp: w_DOT-USD=0.0000, w_SHY=1.0000.


Question:
Assets: FXI, HAUZ
FXI: annualized_mean_return=0.6804, daily_std=0.0125
HAUZ: annualized_mean_return=0.3528, daily_std=0.0070
Minimum required portfolio return (annualized): 0.6069
Market regime: bull

Compute portfolio weights (w_FXI, w_HAUZ) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_FXI=X.XXXX, w_HAUZ=X.XXXX

Answer: w_FXI=0.7756, w_HAUZ=0.2244

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000048 - 0.000015) / (0.000156 + 0.000048 - 0.000030)
  Unconstrained: w_FXI=0.1920
  After long-only clamp: w_FXI=0.1920, w_HAUZ=0.8080.


Question:
Assets: ETH-USD, SCHH
ETH-USD: annualized_mean_return=1.1592, daily_std=0.0378
SCHH: annualized_mean_return=-0.0756, daily_std=0.0130
Minimum required portfolio return (annualized): 0.0003
Market regime: sideways

Compute portfolio weights (w_ETH-USD, w_SCHH) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_ETH-USD=X.XXXX, w_SCHH=X.XXXX

Answer: w_ETH-USD=0.1166, w_SCHH=0.8834

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000169 - -0.000022) / (0.001427 + 0.000169 - -0.000045)
  Unconstrained: w_ETH-USD=0.1168
  After long-only clamp: w_ETH-USD=0.1168, w_SCHH=0.8832.


Question:
Assets: ACWI, TLH
ACWI: annualized_mean_return=0.3276, daily_std=0.0116
TLH: annualized_mean_return=-0.0252, daily_std=0.0074
Minimum required portfolio return (annualized): 0.1830
Market regime: sideways

Compute portfolio weights (w_ACWI, w_TLH) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_ACWI=X.XXXX, w_TLH=X.XXXX

Answer: w_ACWI=0.5901, w_TLH=0.4099

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000055 - 0.000023) / (0.000135 + 0.000055 - 0.000047)
  Unconstrained: w_ACWI=0.2227
  After long-only clamp: w_ACWI=0.2227, w_TLH=0.7773.


Question:
Assets: XLK, PPLT
XLK: annualized_mean_return=-0.4788, daily_std=0.0161
PPLT: annualized_mean_return=0.3276, daily_std=0.0107
Minimum required portfolio return (annualized): 0.2379
Market regime: bear

Compute portfolio weights (w_XLK, w_PPLT) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_XLK=X.XXXX, w_PPLT=X.XXXX

Answer: w_XLK=0.1112, w_PPLT=0.8888

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000114 - 0.000001) / (0.000258 + 0.000114 - 0.000002)
  Unconstrained: w_XLK=0.3056
  After long-only clamp: w_XLK=0.3056, w_PPLT=0.6944.


Question:
Assets: SOL-USD, CPER
SOL-USD: annualized_mean_return=1.4112, daily_std=0.0408
CPER: annualized_mean_return=0.3276, daily_std=0.0129
Minimum required portfolio return (annualized): 0.3861
Market regime: bull

Compute portfolio weights (w_SOL-USD, w_CPER) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_SOL-USD=X.XXXX, w_CPER=X.XXXX

Answer: w_SOL-USD=0.0959, w_CPER=0.9041

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000168 - -0.000010) / (0.001666 + 0.000168 - -0.000019)
  Unconstrained: w_SOL-USD=0.0957
  After long-only clamp: w_SOL-USD=0.0957, w_CPER=0.9043.


Question:
Assets: DOT-USD, IAU
DOT-USD: annualized_mean_return=-0.7056, daily_std=0.0391
IAU: annualized_mean_return=0.1764, daily_std=0.0145
Minimum required portfolio return (annualized): 0.1185
Market regime: sideways

Compute portfolio weights (w_DOT-USD, w_IAU) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_DOT-USD=X.XXXX, w_IAU=X.XXXX

Answer: w_DOT-USD=0.0656, w_IAU=0.9344

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000210 - 0.000019) / (0.001527 + 0.000210 - 0.000038)
  Unconstrained: w_DOT-USD=0.1125
  After long-only clamp: w_DOT-USD=0.1125, w_IAU=0.8875.


Question:
Assets: BTC-USD, HYG
BTC-USD: annualized_mean_return=0.5040, daily_std=0.0153
HYG: annualized_mean_return=0.1260, daily_std=0.0017
Minimum required portfolio return (annualized): 0.1269
Market regime: bull

Compute portfolio weights (w_BTC-USD, w_HYG) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_BTC-USD=X.XXXX, w_HYG=X.XXXX

Answer: w_BTC-USD=0.0032, w_HYG=0.9968

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000003 - 0.000002) / (0.000235 + 0.000003 - 0.000004)
  Unconstrained: w_BTC-USD=0.0027
  After long-only clamp: w_BTC-USD=0.0027, w_HYG=0.9973.


Question:
Assets: QUAL, LQD
QUAL: annualized_mean_return=0.5040, daily_std=0.0111
LQD: annualized_mean_return=0.2016, daily_std=0.0042
Minimum required portfolio return (annualized): 0.2415
Market regime: sideways

Compute portfolio weights (w_QUAL, w_LQD) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_QUAL=X.XXXX, w_LQD=X.XXXX

Answer: w_QUAL=0.1860, w_LQD=0.8140

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000018 - -0.000013) / (0.000122 + 0.000018 - -0.000026)
  Unconstrained: w_QUAL=0.1851
  After long-only clamp: w_QUAL=0.1851, w_LQD=0.8149.


LINK-USD σ=0.0407, CSHI σ=0.0008, ρ=0.141. Min-variance weights: LINK-USD=0.000, CSHI=1.000.

Question:
Assets: LINK-USD, CSHI
LINK-USD: annualized_mean_return=-0.4536, daily_std=0.0407
CSHI: annualized_mean_return=0.0504, daily_std=0.0008
Minimum required portfolio return (annualized): -0.1309
Market regime: sideways

Compute portfolio weights (w_LINK-USD, w_CSHI) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_LINK-USD=X.XXXX, w_CSHI=X.XXXX

Answer: w_LINK-USD=0.0000, w_CSHI=1.0000

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000001 - 0.000004) / (0.001654 + 0.000001 - 0.000009)
  Unconstrained: w_LINK-USD=-0.0023
  After long-only clamp: w_LINK-USD=0.0000, w_CSHI=1.0000.


Question:
Assets: VTI, MORT
VTI: annualized_mean_return=0.2520, daily_std=0.0070
MORT: annualized_mean_return=0.1008, daily_std=0.0099
Minimum required portfolio return (annualized): 0.2386
Market regime: bull

Compute portfolio weights (w_VTI, w_MORT) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_VTI=X.XXXX, w_MORT=X.XXXX

Answer: w_VTI=0.9114, w_MORT=0.0886

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000099 - 0.000029) / (0.000049 + 0.000099 - 0.000058)
  Unconstrained: w_VTI=0.7802
  After long-only clamp: w_VTI=0.7802, w_MORT=0.2198.


SOL-USD σ=0.0413, CSHI σ=0.0007, ρ=0.072. Min-variance weights: SOL-USD=0.000, CSHI=1.000.

Question:
Assets: SOL-USD, CSHI
SOL-USD: annualized_mean_return=-0.9072, daily_std=0.0413
CSHI: annualized_mean_return=0.0504, daily_std=0.0007
Minimum required portfolio return (annualized): 0.0403
Market regime: sideways

Compute portfolio weights (w_SOL-USD, w_CSHI) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_SOL-USD=X.XXXX, w_CSHI=X.XXXX

Answer: w_SOL-USD=0.0000, w_CSHI=1.0000

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - 0.000002) / (0.001704 + 0.000000 - 0.000004)
  Unconstrained: w_SOL-USD=-0.0009
  After long-only clamp: w_SOL-USD=0.0000, w_CSHI=1.0000.


Question:
Assets: VLUE, PPLT
VLUE: annualized_mean_return=0.6048, daily_std=0.0085
PPLT: annualized_mean_return=1.6128, daily_std=0.0235
Minimum required portfolio return (annualized): 0.9338
Market regime: bull

Compute portfolio weights (w_VLUE, w_PPLT) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_VLUE=X.XXXX, w_PPLT=X.XXXX

Answer: w_VLUE=0.6736, w_PPLT=0.3264

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000552 - 0.000001) / (0.000073 + 0.000552 - 0.000001)
  Unconstrained: w_VLUE=0.8843
  After long-only clamp: w_VLUE=0.8843, w_PPLT=0.1157.


Question:
Assets: VLUE, VNQ
VLUE: annualized_mean_return=-0.1260, daily_std=0.0101
VNQ: annualized_mean_return=0.0504, daily_std=0.0114
Minimum required portfolio return (annualized): -0.0955
Market regime: bear

Compute portfolio weights (w_VLUE, w_VNQ) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_VLUE=X.XXXX, w_VNQ=X.XXXX

Answer: w_VLUE=0.7143, w_VNQ=0.2857

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000129 - 0.000083) / (0.000101 + 0.000129 - 0.000166)
  Unconstrained: w_VLUE=0.7149
  After long-only clamp: w_VLUE=0.7149, w_VNQ=0.2851.


Question:
Assets: USMV, BIL
USMV: annualized_mean_return=0.0756, daily_std=0.0051
BIL: annualized_mean_return=0.0504, daily_std=0.0001
Minimum required portfolio return (annualized): 0.0666
Market regime: bull

Compute portfolio weights (w_USMV, w_BIL) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_USMV=X.XXXX, w_BIL=X.XXXX

Answer: w_USMV=0.6429, w_BIL=0.3571

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - -0.000000) / (0.000026 + 0.000000 - -0.000000)
  Unconstrained: w_USMV=0.0014
  After long-only clamp: w_USMV=0.0014, w_BIL=0.9986.


Question:
Assets: EFA, VCIT
EFA: annualized_mean_return=0.1764, daily_std=0.0072
VCIT: annualized_mean_return=0.1008, daily_std=0.0020
Minimum required portfolio return (annualized): 0.1212
Market regime: sideways

Compute portfolio weights (w_EFA, w_VCIT) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_EFA=X.XXXX, w_VCIT=X.XXXX

Answer: w_EFA=0.2698, w_VCIT=0.7302

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000004 - 0.000002) / (0.000052 + 0.000004 - 0.000004)
  Unconstrained: w_EFA=0.0349
  After long-only clamp: w_EFA=0.0349, w_VCIT=0.9651.


Question:
Assets: XLU, SCHH
XLU: annualized_mean_return=0.3024, daily_std=0.0089
SCHH: annualized_mean_return=-0.0000, daily_std=0.0091
Minimum required portfolio return (annualized): 0.0745
Market regime: bull

Compute portfolio weights (w_XLU, w_SCHH) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_XLU=X.XXXX, w_SCHH=X.XXXX

Answer: w_XLU=0.5299, w_SCHH=0.4701

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000083 - 0.000048) / (0.000079 + 0.000083 - 0.000097)
  Unconstrained: w_XLU=0.5303
  After long-only clamp: w_XLU=0.5303, w_SCHH=0.4697.


Question:
Assets: ADA-USD, CORN
ADA-USD: annualized_mean_return=-1.8396, daily_std=0.0603
CORN: annualized_mean_return=0.2016, daily_std=0.0116
Minimum required portfolio return (annualized): 0.1152
Market regime: sideways

Compute portfolio weights (w_ADA-USD, w_CORN) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_ADA-USD=X.XXXX, w_CORN=X.XXXX

Answer: w_ADA-USD=0.0423, w_CORN=0.9577

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000135 - -0.000159) / (0.003641 + 0.000135 - -0.000318)
  Unconstrained: w_ADA-USD=0.0719
  After long-only clamp: w_ADA-USD=0.0719, w_CORN=0.9281.