# Two-strategy portfolio Sharpe calculator

What Sharpe ratio do two uncorrelated strategies give when combined at equal weights?

With excess returns of 8 and 6 percent and volatilities of 10 and 12 percent, equal weights give a 7 percent return and a volatility of sqrt(0.25 x 100 + 0.25 x 144) = 7.81 percent, so the Sharpe ratio is 0.896.

The identity uses point estimates; correlations often rise in stress, and costs, leverage and estimation error are left out.

Combine two expected returns and volatilities at a declared weight and correlation. Inspect covariance at a selected weight and shared return horizon.

## Covariance of the mixture

Returns, volatility and correlation refer to the same horizon, currency and excess-return convention. The weights sum to one and remain constant within that horizon.

```
mu = w muA + (1−w) muB; sigma² = w² sigmaA² + (1−w)² sigmaB² + 2w(1−w) rho sigmaA sigmaB; SR = mu/sigma
```

Lower correlation can reduce portfolio variance without lowering the weighted expected return. The result is an arithmetic portfolio identity rather than evidence of future diversification.

## When correlation moves

The result uses point estimates. Correlation often changes during stress, and rebalancing, leverage, cost and estimation error are excluded. A zero portfolio variance with a nonzero mean has no finite Sharpe ratio.

## Equal-weight audit

With returns of 8% and 6%, volatilities of 10% and 12%, zero correlation and equal weights, expected excess return is 7%, volatility is 7.81025% and Sharpe is 0.89626.

The same two strategies can yield different portfolio risk while their weighted expected return stays fixed. Correlation enters the covariance term. At a weight of zero the answer reduces to strategy B, and at a weight of one it reduces to strategy A; these two boundary cases are useful checks on any implementation. This calculator takes both means as excess returns, so any common financing benchmark has already been removed. If the input means are raw total returns instead, subtract the matching financing benchmark return before entering them. Matching frequencies matters as much as matching currency: combining an annual mean with monthly volatility creates a meaningless ratio. The covariance formula is a single-period identity for stable weights. Rebalancing costs and correlations during market stress require separate inputs. Inspect the answer again at correlation one when testing the value of diversification.

## Markowitz and portfolio selection

Markowitz, H. (1952), Portfolio Selection, Journal of Finance 7(1), 77–91. The two-asset covariance identity is a direct special case of mean-variance portfolio theory. [Original or institutional source](https://doi.org/10.2307/2975974).

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```
<iframe id="stochastly-twosharpe" src="https://stochastly.com/embed/two-strategy-portfolio-sharpe-calculator" title="Two-strategy portfolio Sharpe calculator by Stochastly" width="100%" height="700" style="border:0;max-width:720px" loading="lazy" sandbox="allow-scripts allow-same-origin allow-popups allow-popups-to-escape-sandbox" allow="clipboard-write"></iframe>
<p style="font-size:13px"><a href="https://stochastly.com/tools/two-strategy-portfolio-sharpe-calculator">Two-strategy portfolio Sharpe calculator</a> by Stochastly</p>
<script>
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var f = document.getElementById("stochastly-twosharpe");
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if (!(d.height >= 200 && d.height <= 4000)) return;
f.style.height = Math.ceil(d.height) + "px";
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```

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```
Stochastly (2026). Two-strategy portfolio Sharpe calculator [web calculator]. https://stochastly.com/tools/two-strategy-portfolio-sharpe-calculator
```

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The method behind the two-strategy portfolio Sharpe calculator comes from the paper below: cite that paper for the method, and the reference above for the two-strategy portfolio Sharpe calculator itself.

Markowitz, H. (1952). Portfolio Selection. Journal of Finance 7(1), 77-91.

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