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Portfolio & Asset Pricingintermediate

Multi-Asset Allocation

Asset allocation spreads capital across broad classes such as equities, bonds, gold, and commodities, and increasingly a small cryptocurrency sleeve. The case for each addition rests on its expected return and, just as importantly, its correlation with the rest of the portfolio. Gold and commodities have historically diversified equity risk, while bonds provide ballast. Bitcoin offers a high expected return but with extreme volatility, a low and time-varying correlation to stocks, and real questions of investability, which together argue for only a small portfolio weight sized by its risk contribution rather than its allure.

Why it matters

The biggest decision an investor makes is not which stock to pick but how to divide money across asset classes, because that split drives most of the long-run risk and return. Each class earns its place by what it adds to the whole, and a volatile asset can still help if it moves out of step with everything else. That is the honest case for a sliver of crypto. Its correlation with equities is low on average, so a small weight can improve diversification, but its volatility is several times that of stocks and its correlation jumps in crises, so it must be sized small and judged by its contribution to portfolio risk, not by headline returns. The discipline is the same one that built the efficient frontier, now applied across whole asset classes.

Formulas

Portfolio return across asset classes
E(Rp)=∑k=1Kwk E(Rk),∑k=1Kwk=1E(R_p) = \sum_{k=1}^{K} w_k\,E(R_k), \qquad \sum_{k=1}^{K} w_k = 1
Weighted average of asset-class expected returns, with class weights wkw_k summing to one. Risk still follows the variance-covariance form across classes.
Risk contribution of an asset class
RCk=wk ∂σp∂wk=wk (Σw)kσp\mathrm{RC}_k = w_k\,\dfrac{\partial \sigma_p}{\partial w_k} = w_k\,\dfrac{(\boldsymbol{\Sigma}\mathbf{w})_k}{\sigma_p}
How much class kk adds to total portfolio risk. A high-volatility sleeve like crypto can dominate risk even at a small weight, which is why sizing is set by RCk\mathrm{RC}_k.

Worked examples

Scenario

A portfolio holds 60% equities at 8% expected return, 35% bonds at 3%, and 5% bitcoin at 20%. Find the expected portfolio return.

Solution

Take the weighted average. The total is E(Rp)=0.6(8%)+0.35(3%)+0.05(20%)=4.8%+1.05%+1.0%=6.85%E(R_p)=0.6(8\%)+0.35(3\%)+0.05(20\%)=4.8\%+1.05\%+1.0\%=6.85\%. The small crypto sleeve adds a full percentage point of expected return, but its risk contribution would be checked separately because its volatility dwarfs the other classes.

Scenario

Why might a 5% bitcoin weight contribute far more than 5% of total portfolio risk?

Solution

Risk contribution depends on weight times volatility and correlation, not weight alone. If bitcoin volatility is roughly five times that of equities, even a 5% weight can supply a disproportionate share of portfolio standard deviation. That is why crypto is sized by its risk contribution and capped small, especially since its correlation rises precisely in market stress.

Common mistakes

  • ✗Asset allocation is less important than picking individual securities. The allocation across classes drives most of the variation in a portfolio’s long-run return over time, typically outweighing security selection.
  • ✗A higher expected return justifies a large crypto weight. Position size should follow the risk contribution, and crypto’s extreme volatility means even a small weight can dominate portfolio risk.
  • ✗Bitcoin is always uncorrelated with stocks, so it is a reliable hedge. Its correlation is low on average but time-varying and tends to spike during crises, exactly when a hedge is needed most.
  • ✗Adding more asset classes always improves diversification. A new class helps only if it brings a sufficiently low correlation and is genuinely investable at scale, otherwise it adds cost and risk without benefit.

Revision bullets

  • •Asset allocation divides capital across equities, bonds, gold, commodities, and crypto
  • •Each class earns inclusion by its return and its correlation with the rest
  • •Allocation drives most long-run portfolio risk and return
  • •Bitcoin has high volatility and low but time-varying correlation to stocks
  • •Size a crypto sleeve by its risk contribution and keep the weight small

Quick check

What is the main reason a small bitcoin allocation can still improve a diversified portfolio?

Why is a crypto position sized by its risk contribution rather than its weight alone?

Connected topics

Active vs PassiveReturn & RiskDiversificationMean-VarianceEfficient Frontier

Sources

  1. Brailsford, Heaney & Bilson (2015), Ch. 11
    Brailsford, T., Heaney, R., & Bilson, C. Investments: Concepts and Applications. 5th ed. Cengage Learning Australia, 2015.
    Covers strategic asset allocation across classes and the role of correlation in class selection.
  2. Bodie, Kane & Marcus (2021), Ch. 5-6
    Bodie, Z., Kane, A., & Marcus, A. J. Investments. 12th ed. McGraw-Hill Education, 2021.
    Reference treatment of asset allocation, the capital allocation decision, and alternative assets.
How to cite this page
Dr. Phil's Quant Lab. (2026). Multi-Asset Allocation. Derivatives Atlas. https://phucnguyenvan.com/concept/im-asset-allocation
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