Sharpe attribution calculator
Computes how adding a candidate asset to an existing portfolio changes the portfolio Sharpe ratio. Inputs: existing portfolio return and volatility, candidate asset return / volatility / correlation to existing, and the candidate's proposed allocation weight. Output: portfolio Sharpe before and after, the delta, and the analytical optimal weight for maximum Sharpe. Designed for AU-resident investors evaluating diversification candidates (a new asset class, alt-coin, prop firm allocation, etc) against an existing portfolio.
Calculator
Enter your existing portfolio's annualised return and volatility, plus the candidate asset's return, vol, correlation, and proposed allocation weight. The optimal-weight output is the analytical Sharpe-maximising allocation.
Existing portfolio
Candidate asset
Reference
Default 4.2% = current AU 10-year government bond yield reference. Adjust if you prefer a different benchmark.
What this calculator shows
Three outputs help the decision:
- Combined Sharpe at proposed weight. The Sharpe ratio of the combined portfolio at the weight you proposed. Compare against existing Sharpe to see the contribution.
- Sharpe delta. Positive = the candidate improves portfolio Sharpe at this weight. Negative = degrades. Magnitude tells you how meaningful the change is.
- Optimal weight. The analytical solution for the weight that maximises combined Sharpe. If the optimal weight is far from your proposed weight, you may be over- or under-allocating.
Key insight: correlation matters most
Portfolio volatility shrinks via diversification when assets are imperfectly correlated. The formula:
σ_portfolio = sqrt(w1²σ1² + w2²σ2² + 2 × w1 × w2 × σ1 × σ2 × ρ)
The cross-term scales with correlation. Two scenarios with identical returns and volatilities but different correlations produce wildly different portfolio Sharpe:
- ρ = +0.9. Cross-term is large and positive; portfolio vol is close to the weighted average of the two component vols. Minimal diversification benefit.
- ρ = +0.3. Cross-term is moderate; portfolio vol is meaningfully less than the weighted average. Standard diversification benefit.
- ρ = -0.3. Cross-term is negative; portfolio vol is significantly less than the weighted average. Strong diversification benefit.
- ρ = -0.9. Cross-term substantially reduces portfolio vol. Excellent diversification (rare in practice; gold during equity drawdowns sometimes shows this).
This is why a high-Sharpe candidate with high correlation often doesn't improve combined Sharpe, and a moderate-Sharpe candidate with low correlation often does.
Methodology
- Combined portfolio return. Weighted average: w1 × r1 + w2 × r2.
- Combined portfolio vol. sqrt(w1²σ1² + w2²σ2² + 2 × w1 × w2 × σ1 × σ2 × ρ).
- Combined Sharpe. (Combined return - risk-free rate) / combined vol.
- Optimal weight. Analytical solution from setting d(Sharpe)/dw = 0. Bounded to [0, 1] for practical purposes (no short-selling).
- Standalone Sharpe per asset. (Asset return - risk-free rate) / asset vol. Surfaced as reference.
Limitations
- Estimation error. Mean-variance optimisation is notoriously sensitive to input estimation errors. The optimal-weight output should be treated as a directional reference, not a precise target.
- Two-asset model. Real portfolios have more than two components. For multi-asset Sharpe analysis, use the calculator iteratively (existing portfolio = previous combined; new candidate = each asset added in turn).
- Stationary distributions assumed. Real returns, vols, and correlations are non-stationary. Correlation regimes shift, especially during crisis events (correlations often jump to +1 during equity crashes, exactly when diversification benefit was supposed to materialise).
- Pre-tax economic model. No tax drag. After-tax Sharpe can differ meaningfully for income-heavy assets in personal-tax structures.
- Risk-free rate is a moving target. AU 10y bond yield shifts daily. The calculator uses a single reference rate; results scale with the rf input.
Related tools
- Sharpe / Sortino / Calmar Calculator - compute risk-adjusted ratios for a single strategy's track record.
- Risk of Ruin Calculator - survival probability at a given edge and risk-per-trade.
- Kelly Criterion Position Sizer - optimal bet size for log-equity growth.
- Tax Bracket Optimisation Calculator - after-tax structure planning for AU-resident investors.
- Crypto Portfolio Rebalancing Calculator - target allocation tool for multi-asset crypto portfolios.
Frequently asked questions
Sharpe attribution measures how much of a portfolio's risk-adjusted return comes from each asset, and what would happen to portfolio Sharpe if you added (or removed) a specific asset. The mechanic: portfolio Sharpe depends on the weighted return MINUS risk-free rate divided by portfolio volatility, where volatility incorporates the correlation between assets. A high-Sharpe candidate with low correlation to the existing portfolio improves combined Sharpe meaningfully; a high-Sharpe candidate with near-1 correlation provides little incremental benefit.
Portfolio volatility shrinks via diversification when assets are imperfectly correlated. The portfolio vol formula: sqrt(w1²σ1² + w2²σ2² + 2w1w2σ1σ2ρ). With ρ = 0, the cross term vanishes and portfolio vol is less than the weighted vol average. With ρ = -1 (perfect negative correlation), portfolio vol can theoretically reach zero. With ρ = +1, portfolio vol equals the weighted average and you've just averaged two assets without diversification gain. This is why low-correlation candidates (commodities vs equities, market-neutral hedge funds, certain crypto strategies) can improve portfolio Sharpe even with modest standalone Sharpe.
Three methods. (1) Historical: compute 30 to 60-month rolling correlation between the candidate asset's monthly returns and your portfolio's monthly returns. Most data providers (Bloomberg, FactSet, Yahoo Finance free tier) expose this. (2) Conceptual: if the candidate is in a different asset class with a different fundamental driver (e.g., gold vs equities, BTC vs ASX 200), expect lower correlation. (3) Reference values: equities-equities typically ρ = 0.5-0.85; equities-bonds ρ = -0.3 to +0.3; equities-gold ρ = -0.1 to +0.3; equities-BTC ρ = 0.2 to 0.6 (post-2020 institutional adoption pushed it up). For the AU-resident investor evaluating a non-AU asset, also factor in AUD/USD correlation impact.
The analytical solution for the two-asset weight that MAXIMISES Sharpe ratio. Derived from setting the derivative of portfolio Sharpe with respect to weight to zero. For a candidate with standalone Sharpe above the existing portfolio's, the optimal weight is positive; for a candidate below, the optimal weight is zero (allocate nothing). With correlation in the mix, the optimal weight can be non-trivial - a candidate with lower standalone Sharpe can still earn an optimal allocation if its correlation is low enough that the diversification benefit outweighs the standalone disadvantage.
Not necessarily. Three caveats. (1) Estimation error: the inputs (return, vol, correlation) are noisy estimates of unknown true values. Mean-variance optimisation is famously sensitive to small input errors and can produce extreme weights from small input changes. (2) Constraints: you may have practical constraints (max position size, liquidity, tax implications) not captured in the math. (3) Risk tolerance: the optimal-Sharpe portfolio may have a higher absolute volatility than you're comfortable with. The optimal weight is a reference point, not a target.
Sharpe attribution applies to any portfolio decision: adding a forex strategy to a stock portfolio, adding crypto to a balanced portfolio, adding an alternative income stream. The tool happens to live in the forex section because it's most often used by traders evaluating whether a new strategy adds to or detracts from their existing trading book. It applies equally well to crypto, equity, or multi-asset evaluation.
No. The Sharpe ratio is a pre-tax economic metric. For AU-resident investors, tax-effective vehicles (super, family trust, holding-company structures) produce different after-tax Sharpe than the raw pre-tax calculation. For income-heavy assets in personal accounts, the tax drag can be material. Use this tool for the strategic decision; use the Tax Bracket Optimisation Calculator separately for after-tax structure planning.
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