# Sharpe Ratio

Sharpe ratio measures the excess return earned by an investment portfolio per unit of risk. It is calculated by dividing excess return (which equals portfolio return minus risk free rate) by standard deviation of the investment returns.

Investment management requires a trade-off between return and risk. Investments that generate higher return typically have higher risk. Comparing return earned by a high growth technology company with return earned on a mature utility company is meaningless because both companies have differing risk levels. Sharpe ratio standardizes investment returns so that they are compared across investment portfolios, companies, investment classes, industries, etc.

## Formula

 Sharpe Ratio = Investment Return – Risk Free Rate Standard Deviation

Investment return is the actual realized return or expected return on an investment or portfolio over a period.

Risk free rate is the rate earned on risk-free assets. Yield on government treasury bills is normally used a proxy for risk-free rate.

Standard deviation is a statistic which measures the total risk of an investment portfolio.

## Analysis

Risk free investments such a Treasury bills have zero Sharpe ratio because its investment return equals risk free rate and the standard deviation of its returns is zero.

Investors target a return which is in line with their risk tolerance. However, since they are risk averse, they are willing to take on more risk only if there is excess return. Sharpe ratio measures just that i.e. the amount of excess return per unit of risk.

Higher Sharpe ratio is better.

Even though Sharpe ratio is useful, some of its assumptions are problematic. First, it uses standard deviation which is a measure of total risk of a portfolio or investment. Since unsystematic risk can be diversified, beta coefficient, which is a measure of the systematic risk is a better indicator of risk in the context of a diversified portfolio. Second, it assumes that investment returns are normally distributed, which is not the case for many investment classes such as derivatives, etc. Treynor’s ratio, which is a variant of the Sharpe’s ratio, attempts to address the first weakness by using beta coefficient in the denominator instead of standard deviation. Sortino’s ratio attempts to address the second weakness.

## Example

Alphamania is an asset management company which has only two funds: Alpha Driller (AD), an oil and gas focused fund, and Alphologics (AL), a technology focused fund.

For the year ended 31 June 2017, Alpha Driller earned annual return of 6.49% and Alphologics earned 10.86%.

Secure Pensions, Inc. (SP) has placed 5% of their total assets equally in both the funds. Considering the annual returns, SP’s trustee suggested that the whole 5% assets should be placed in Alphologics.

Let’s see if the suggestion carries any merit. On the face of it, a decision based only on the realized or expected return is a poor decision because it ignores the associated risks. Investment decisions should be made by considering both the risk tolerance and return per unit of risk.

Here is the monthly returns for both the funds from July 2016 to June 2017:

Alpha DrillerAlphalogics
0.20%2.00%
0.50%1.00%
-0.30%3.00%
0.60%-8.00%
1.00%1.00%
2.00%2.50%
0.25%0.50%
0.10%3.00%
-0.20%5.00%
-0.30%-3.00%
0.00%2.00%
2.50%2.00%

Let’s assume risk free rate for the period is 1.5%.

Using MS Excel STDEV function, we find out that Alpha Driller and Alphologics have standard deviation of 0.90% and 3.39% respectively.

 Sharpe Ratio of Alpha Driller = 6.49% - 1.5% = 5.54 0.90%
 Sharpe Ratio of Alphologics = 10.86% - 1.5% = 2.76 3.39%

This shows that even though Alphologics earned way higher return than Alpha Driller it has higher risk. In fact, when we compare the return per unit of risk Alpha Driller is a much better fund.

Written by Obaidullah Jan, ACA, CFAhire me at