Portfolio construction

The Sharpe ratio: return per unit of risk

The most used yardstick for comparing portfolios: how much return above cash each unit of volatility earned.

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ایده به زبان ساده

A portfolio that made 12% with wild swings is not obviously better than one that made 8% calmly. The Sharpe ratio puts them on one scale: excess return divided by volatility. With leverage you can scale any portfolio up or down, but you cannot change its Sharpe ratio, so it measures the quality of the mix, not its size.

روش محاسبه

Take the annual expected (or realised) return, subtract the risk-free rate (cash; 0% by default in the optimiser, change it under Settings), divide by the annual volatility.

Sharpe = (μₚ − r_f) ÷ σₚ
Sortino (a cousin) = (μₚ − r_f) ÷ downside deviation

نحوه استفاده

Sort a study's results table by Sharpe to see which mix paid best for its risk.
Compare the in-sample Sharpe with the OOS (out-of-sample) Sharpe next to it: a model whose Sharpe collapses out of sample was fitting noise.
Set the risk-free rate to today's cash rate if you want the ratio to reflect what cash would have paid.

نتیجه‌گیری

Below 0.3: little reward for the risk. 0.5–1: decent for a diversified portfolio. Above 1.5 over years: rare; check for mistakes or a lucky period.
Two portfolios with the same Sharpe differ only in how much leverage you would use to reach the same risk.

مثال

Running example (used in every portfolio guide): US500, GER40, gold (XAUUSD) and EURUSD, two years of daily data. Expected returns 8%, 7%, 7% and 1% a year; volatilities 18%, 20%, 15% and 7%. US500 and GER40 move together (correlation about 0.7); gold hardly moves with the indices (about 0.04). Equal weights: 5.75% return ÷ 10.5% volatility = Sharpe 0.55. The Maximum Sharpe model finds about 40% US500, 5% GER40 and 55% gold: 7.4% ÷ 11.7% = 0.63. Minimum variance is calmer (6.8% volatility) but earns only 1.9%: Sharpe 0.28.

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مراقب این‌ها باشید

It treats upside and downside swings alike, and it assumes returns are roughly bell-shaped; option-like strategies can show a great Sharpe until the day they blow up.
Measured over a short period it is very noisy: a year of data gives a standard error of about 1.

کمی تاریخچه

William F. Sharpe introduced the "reward-to-variability ratio" in 1966 ("Mutual Fund Performance", Journal of Business). He shared the 1990 Nobel prize with Markowitz and Merton Miller.

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