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miƩrcoles, 10 de mayo de 2017

What is the Sharpe ratio?

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The Sharpe Ratio was developed by Nobel Prize William Sharpe of Stanford University. It measure numerically the historical Profitability/Volatility (standard deviation) ratio of an Investment Fund. It is calculated by dividing the yield of a fund minus the risk-free interest rate between the volatility or standard deviation of that return over the same period.

Sharpe Ratio = Fund performance - Risk-free interest rate (3-month bills)/Standard deviation of fund performance (historical volatility)

The higher the Sharpe Ratio, the better the fund's return relative to the amount of risk that has been taken on the investment. The higher the volatility, the greater the risk, since the probability that the fund has negative returns is greater the greater the volatility of its yields. Likewise, the greater the volatility, the greater the likelihood of high positive returns. Therefore, when the volatility of the fund is large, the greater the denominator of the equation and the smaller the Sharpe Ratio.
A fund whose net asset value has fluctuated for a year between 80 and 120 has greater historical volatility than one that has fluctuated between 95 and 105.

Many investors not only seek funds that historically have reported higher returns, but also seek funds that have evolved consistently over time, without major ups and downs.

Imagine two Equity investment funds investing in the same market, and we measure their Sharpe Ratio over a period of 1 year:

Investment fund AInvestment fund B
1 year profitability 18 % 1 year profitability 25 %
1 year volatility 15 % 1 year volatility 24 %
3-month bills 5 % 3-month bills 5 %
Sharpe Ratio (18-5)/15 = 0.86 Sharpe Ratio (25-5)/24 = 0.83
Annual minimum -5 % Annual minimum -15 %
Annual maximum + 22 % Annual maximum + 32 %

As we can see, fund A, although it has a lower return than fund B, has a higher Sharpe Ratio since its volatility has been lower, ie has oscillated less, has had fewer ups and downs. Although the final profitability has been lower, we can see that while in the worst moment Fund B lost 15%, Fund A only did 5%. 

The Sharpe ratio is used to compare two funds or a group of funds. Knowing that a fund has a Sharpe Ratio of 0.83 has little utility if we do not compare this number at the same time with another fund. 

Unlike other indicators that measure a fund relative to its deviation from its benchmark, the Sharpe Raio is a good method to measure the standard deviation of the profitability of any fund individually and compare it with others.

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