The Sharpe Ratio: A measure of investment performance

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Sharpe Ratio measures the risk adjusted return of a portfolio. The ratio quantifies the excess return per unit of the risk (Standard Deviation of the returns of a portfolio) in comparison to the returns on risk free investment.

In simple terms, Sharpe ratio helps investor to ascertain the incremental return of a risky portfolio over and above the risk free asset like government bond or fixed deposits.

Formula for Sharpe Ratio: Below is the formula for calculating the Sharpe ratio:

{R (p) – R (f)} /StdDev(p)

Where

R (p): Portfolio return

R (f): Risk free rate of return (Generally on government bond or fixed deposits)

StdDev(p): Standard deviation of the portfolio

The numerator in the above formula i.e. R (p) – R (f) computes the excess return of the portfolio which is further divided by standard deviation of the returns of portfolio.  Generally, the risk inherent in an investment is determined using standard deviation of the returns of a portfolio. So, Sharpe ratio gives us excess return per unit of risk taken by the investor.

Thus, a higher Sharpe ratio indicates better return yielding capacity of a fund for every additional unit of risk taken by it.

Significance of Sharpe Ratio: Sharpe ratio indicates the investor’s willingness to earn higher return than the lower returns provided by risk free assets.

Sharpe Ratio- A measure of fund comparison: Sharpe ratio can be used to compare funds falling into same categories; like comparing returns on large-cap equity funds. By looking at the Sharpe ratio we can assess the return per unit of risk taken and decide upon the preferred fund investment.

As higher Sharpe ratio indicates the better return capabilities of funds.

Optimum Risk-Return Tradeoff

Ideally, you might consider a fund desirable which has a higher Sharpe Ratio. However, this kind of perception may not always be fruitful if the fund took a lot of additional volatility. It means that a fund that achieves 7% returns with moderate volatility will always be better than a fund which gives 8% returns with a lot of ups and downs. A higher Sharpe ratio, thus, means that the relationship between fund’s risk and return is ideal.

Shortcomings of Sharpe Ratio:

  1. Investment return should be normally/ symmetrically distributed: The Standard deviation which is used as a measure of risk is appropriate to use only if returns are normally distributed. E.G. certain investment strategies like options have asymmetric distribution; several options strategies have large probability of small gains coupled with small probability of large losses. Such investment strategies could underestimate the risk or standards deviation in the denominator and could reflect higher Sharpe ratio.
  2. Portfolio with negative Sharpe Ratios: While comparing two portfolios with negative Sharpe ratio; an investor should be very careful. For negative Sharpe ratio, if we simply increase the risk associated with investment it would push Sharpe ratio closer to zero (As we increase the denominator; the absolute value of the Sharpe ratio would decrease but when we take negative sign into consideration it would actually move ratio closer to zero and overall impact would be higher Sharpe ratio).

Conclusion: If two funds offer similar returns, the one with higher standard deviation will have a lower Sharpe ratio. In order to compensate for the higher standard deviation, the fund needs to generate a higher return to maintain a higher Sharpe ratio. In simple terms, it shows how much additional return an investor earns by taking additional risk. Intuitively, it can be inferred that the Sharpe ratio of a risk-free asset is zero.

In the next article we would calculate Sharpe Ratio for a fund using Python.

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