!!!Overview

They say that you cannot compare apples to oranges. In the investment world, there are thousands of potential and conflicting investment candidates with different combinations of risk and return characteristics. Such being the case, you cannot compare two different investment opportunities directly (apples and oranges) with different risk profiles without doing something to standardize either risk or return.

In this context, the Sharpe Ratio is the most popular tool to measure the risk-adjusted performance of portfolio or mutual fund managers among other available measuring formulas.

!!!Definition of the Sharpe Ratio

As a measure for calculating risk-adjusted return, the __Sharpe Ratio__ is named after William F. Sharpe of the Stanford University. The way adopted by the Sharpe Ratio to compare apples to oranges in the investment world is to subtract return in excess of the risk-free rate per unit of volatility since volatility is a proxy for the risk in investment world when we assume that average investors are risk averse. Now we can compare apples to oranges with this ratio; the higher the ratio, the better investment opportunity.

[{Image src=’sharpe-ratio.png’ alt=’Sharpe ratio’}]

Here, S stands for Sharpe Ratio. The numerator in the parenthesis is the excess return of a portfolio; that is, R(p) is portfolio return and R(f) risk-free rate. The denominator in the parenthesis is the standard deviation (a proxy unit of risk) of the same portfolio. Standard deviation is the extent of volatility for the portfolio.

!!!Examples of the __Sharpe Ratio__

!!Example 1

A financial asset has an expected return of 8% with the risk-free rate of 2%. When the standard deviation of the asset’s excess return is 10%, the Sharpe Ratio will be:

(0.08 – 0.02)/0.1 = 0.6

!!Example 2

You have a portfolio of investments with an expected return of 15% and a volatility of 10%. The risk-free rate is 2%. The Sharpe Ratio will be:

(0.15 – 0.02)/0.1 = 1.3

You should note, however, that the ex-post Sharpe Ratio uses ”realized” returns while the ex-ante Sharpe Ratio uses ”expected” returns.

!! Applications in Finance

The Sharpe Ratio tells us how well the portfolio’s return compensates for the risk taken. It is also often used to compare the change in a portfolio’s overall risk-return characteristics when a new asset is added to it. The modern ‘Portfolio Theory’ argues that a well-diversified portfolio can decrease portfolio risk without corresponding lower return. In this context, if the addition of a new financial asset increases the __Sharpe Ratio__, it should be added to the portfolio.

On the other hand, even if a portfolio of financial assets can produce higher returns, it is only a good investment if its higher return does not come with an additional risk. In other words, the higher return should be the result of astute investment management, not a consequence of excessive risk-taking.

!!!Lesson Summary

Developed by Nobel Laureate Dr. William F. Sharpe, the Sharpe Ratio quantifies a portfolio’s return in excess of a risk-free investment relative to its risk measure (standard deviation in most cases), since different portfolios have different risk-return profiles. The __Sharpe Ratio__ usually uses the standard deviation as its proxy for the volatility to measure a portfolio’s risk-adjusted returns. In conclusion, the higher a portfolio’s Sharpe Ratio is, the better the relative performance of the portfolio has been in terms of risk.