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Concept# Sharpe ratio

Summary

In finance, the Sharpe ratio (also known as the Sharpe index, the Sharpe measure, and the reward-to-variability ratio) measures the performance of an investment such as a security or portfolio compared to a risk-free asset, after adjusting for its risk. It is defined as the difference between the returns of the investment and the risk-free return, divided by the standard deviation of the investment returns. It represents the additional amount of return that an investor receives per unit of increase in risk.
It was named after William F. Sharpe, who developed it in 1966.
Definition
Since its revision by the original author, William Sharpe, in 1994, the ex-ante Sharpe ratio is defined as:
: S_a = \frac{E[R_a-R_b]}{\sigma_a} = \frac{E[R_a-R_b]}{\sqrt{\mathrm{var}[R_a-R_b]}},
where R_a is the asset return, R_b is the risk-free return (such as a U.S. Treasury security). E[R_a-R_b] is the expected val

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This paper investigates variance risk premia in energy commodities, particularly crude oil and natural gas, using a robust model-independent approach. Over a period of 11 years, we find that the average variance risk premia are significantly negative for both energy commodities. However, it is difficult to explain the level and variation in energy variance risk premia with systematic or commodity specific factors. The return profile of a natural gas variance swap resembles that of a call option, while the return profile of a crude oil variance swap, if anything, resembles the return profile of a put option. The annualized Sharpe ratios from shorting energy variance are sizable; although not nearly as high as the annualized Sharpe ratio of shorting S&P 500 index variance, they are comparable to those of shorting interest rate volatility or variance on individual stocks.

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