Adding a Real Asset Sleeve: Does the Sharpe Ratio Survive the Assumptions?

Current portfolio (70/30)

• Return: 0.70 × 7.25 + 0.30 × 2.90 = 5.075 + 0.870 = 5.95%
• Variance: (0.70² × 15²) + (0.30² × 5²) + (2 × 0.70 × 0.30 × 15 × 5 × −0.10) = 110.25 + 2.25 − 3.15 = 109.35 → σ = 10.46%
• Sharpe: (5.95 − 2.50) / 10.46 = 0.33

Proposed portfolio (59.5% equity / 25.5% bonds / 15% real assets)

• Return: (0.595 × 7.25) + (0.255 × 2.90) + (0.15 × 5.50) = 4.314 + 0.740 + 0.825 = 5.88%
• Variance:
  • Equity: 0.595² × 225 = 79.66
  • Bonds: 0.255² × 25 = 1.63
  • Real assets: 0.15² × 81 = 1.82
  • Equity–bond: 2 × 0.595 × 0.255 × 15 × 5 × (−0.10) = −2.28
  • Equity–real: 2 × 0.595 × 0.15 × 15 × 9 × 0.25 = +6.02
  • Bond–real: 2 × 0.255 × 0.15 × 5 × 9 × 0.25 = +0.86
  • Total = 87.71 → σ = 9.37%
• Sharpe: (5.88 − 2.50) / 9.37 = 0.36

Answer to the client's objection: expected return falls by 7bp, but volatility falls by 109bp, so risk-adjusted return improves. The real asset earns its place through diversification (correlation 0.25, not 1.0), not through its own return.

Return sensitivity: hold volatility and correlations fixed and solve for the return at which the new portfolio's Sharpe equals the current 0.33.

• Required Sharpe: (R − 2.50) / 9.37 = 0.33 → R = 2.50 + 3.09 = 5.59%
• Current proposed return is 5.88%, so the portfolio can absorb a 29bp shortfall: the real asset's own return can fall from 5.50% to 5.50 − (0.29/0.15) ≈ 3.57% before the Sharpe advantage disappears.
• In other words, the real asset adds risk-adjusted value at any return above roughly 3.6% - well below its 5.50% assumption, and only ~1.1% above the risk-free rate.

The assumption doing the work: volatility reduction. Almost all of the improvement comes from σ falling 10.46% → 9.37%. That in turn is driven by the 0.25 correlations. If the true correlation with equities is 0.60 (which is what many listed infrastructure vehicles delivered in 2022's rate shock, when everything fell together), the equity–real cross term becomes 2 × 0.595 × 0.15 × 15 × 9 × 0.60 = +14.45 instead of +6.02, lifting variance to 96.14 and σ to 9.81%.

• New Sharpe: (5.88 − 2.50) / 9.81 = 0.34 - a marginal improvement, essentially inside the estimation error.

Judgement: the case for the sleeve is real but fragile to the correlation assumption, and correlations rise in stress precisely when the diversification is needed. Size it at 15% and re-underwrite the correlation, not the return.

No - not on a probabilistic basis, and the IPS wording needs to be challenged.

Working from annual σ of 9.37% and expected return 5.88%:

• A 95% one-year outcome (1.645σ below the mean) = 5.88 − (1.645 × 9.37) = −9.5%
• A 12% loss sits at (12 + 5.88) / 9.37 = 1.91σ below the mean → roughly a 2.8% annual probability if returns were normal.

That looks compliant. It is not, for three reasons:

1. Returns are fat-tailed. Normality understates the frequency of 3σ-plus events; the 2.8% figure is a floor, not an estimate.
2. Drawdown ≠ annual return. A 12% drawdown means peak-to-trough, which for an 8-year hold is a path statistic, not a single-year statistic. A portfolio with 9.4% annual volatility will almost certainly experience a 12% peak-to-trough decline at some point over eight years.
3. The 2008 and 2022 evidence: a 60/40-style portfolio lost 20–30% peak-to-trough in 2008 and roughly 16% in 2022. The IPS figure is not achievable with 60% equity.

What to do:

• Go back to the client and re-specify the tolerance as a drawdown and a duration - e.g. "−12% measured on a rolling 12-month basis" or "−20% peak-to-trough, provided the plan is not abandoned".
• If 12% peak-to-trough is genuinely non-negotiable, the equity weight has to come down to roughly 40–45% and the expected return falls accordingly - which breaks the retirement funding arithmetic.
• Never leave the IPS with a number that the recommended portfolio will breach; the breach is what makes clients sell at the bottom.