Sharpe Ratio: Definition, Meaning, Formula, How To Use It

Last Updated: 13 Jun 2024

If you have invested in mutual funds, you have surely heard of Sharpe and Treynor ratios. In fact, if you open the fund factsheet of any equity mutual fund, you will find the Sharpe ratio disclosed of the fund under the fund analytics section. Some funds even disclose the Treynor ratio for the particular equity fund. What exactly are these Sharpe Ratios and Treynor ratios and how can investors interpret them?

Are sharpe and treynor like a narmal returns ratio?

Both the Sharpe and Treynor ratio are measures of risk-adjusted returns. What does that means? Let us understand. Say Fund X gives 14% returns and Fund Y gives 16% returns and both are diversified equity funds. Which is better? Your obvious answer would be that Fund Y is better because it is giving 2% higher returns.

Now let us add one more detail. The risk of Fund X as measured by standard deviation is 17% and the risk of Fund Y as measured by standard deviation is 42%. Now which would you select. Clearly, Fund Y appears to be generating higher returns by taking on substantially higher risk. You don’t want that because in bad times this could backfire.

That is where Sharpe and Treynor ratio come in handy. They calculate risk adjusted returns instead of just returns. In other words, Sharpe and Treynor measure the return of a fund per unit of risk. It gives a much better view of whether the fund is earning returns by taking on higher risk or not.

Can you explain what exactly is the sharpe ratio?

The typical metrics for measuring the performance of a mutual fund is whether the fund has outperformed the benchmark index or not. So if Nifty has earned 16% returns last year and your diversified equity fund has earned 18% last year then your fund has outperformed the index by 200 basis points. This is simple and elegant and so easy to­ understand.

The problem arises, as we saw earlier, if your fund manager has earned 2% additional return by taking on twice as much as risk as the Nifty. In such cases, risk-adjusted returns is a better metrics. Once such approach to calculating the risk adjusted returns is the highly popular Sharpe Ratio. Here is how the Sharpe formula looks like.

Sharpe Ratio = {(Return on the Fund – Risk-Free returns) / Standard deviation of fund returns}

The return of the fund is the return that your fund manager generates in absolute terms. Here, risk-free return is what you would have earned without any risk as in case of a bank FD or a 10-year government bond. That is the base minimum you do expect. Standard deviation measures the risk through volatility. More volatile the returns of the fund, higher the standard deviation. Sharpe measures excess returns per unit of total risk.

But, Then how is the treynor ratio different from sharpe?

In Sharpe and Treynor ratio, the numerator is the same. However, it is the denominator that changes. While Sharpe uses standard deviation as the denominator, Treynor uses the Beta as the denominator. Therefore, while Sharpe measures excess returns per unit of total risk, the Treynor ratio measures excess returns per unit of systematic risk. This systematic risk is the risk that cannot be diversified away by the fund manager.

To understand Treynor, we need to understand Beta better. Beta, as we know, is a measure of systematic risk of the portfolio and calculates to what extent the stock or the portfolio correlates with the index. Typically, a portfolio with a Beta > 1 is considered to be an aggressive portfolio whereas a portfolio with a Beta < 1 is considered defensive portfolio. The market index (Nifty or Sensex as the case may be) will have a Beta of 1. Here is how Treynor ratio is calculated in practice.

Treynor Ratio = {(Return on the Fund – Risk-Free returns) / Beta of the fund }

Having understood Sharpe and Treynor ratios, here is why they are important. Let us look at a more practical perspective.

How are sharpe and treynor ratios useful to an investor in practice?

Both Sharpe and Treynor measure excess return per unit of risk. Let us understand with a live illustration how return per unit of risk can give you better insights.

Fund Alpha	Details	Fund Kappa	Details
1-Year returns	21%	1-Year Returns	18%
Risk Free Rate	9%	Risk Free Rate	9%
Beta of the Fund	1.8	Beta of the Fund	1.1

In the above example, both Fund Alpha and Fund Kappa are diversified equity funds as per the classification of SEBI. So they are surely comparable. Now, if we were to compare Fund Alpha and Fund Kappa purely on the basis of their returns then there is no rocket science in figuring out that Fund Alpha has done a lot better than Fund Kappa; nearly 3% better.

But that is misleading. Fund Alpha has earned 21% in the last one year whereas Fund Kappa has earned 18% in the last one year. But let us not miss the point here. What this return number misses out is the risk that the fund manager has taken. Let us now use the Treynor Ratio in this case to fine tune our calculation.

Treynor Ratio of Fund A = (21%-9%) / 1.8 = 12% / 1.8 = 6.67

Treynor Ratio of Fund B – (18% – 9% / 1.1 = 9% / 1.1 = 8.18

When Treynor ratio or return per unit of systematic risk is calculated it is evident that the manager of Fund B has actually done better. Fund Alpha has certainly earned higher return but that has come at the cost of much higher risk. That is what Treynor helps you to pinpoint. In the case of Sharpe, you would have used standard deviation instead of Beta; that is the only difference. Both are solid measures of returns per unit of risk.

When to use sharpe and when to use the treynor ratio?

That is the million dollar question. Let us highlight some key points to understand the application of Sharpe and Treynor in specific circumstances.

• Just to recap, Sharpe and Treynor measure returns per unit of risk. However, Sharpe uses standard deviation as the denominator while Treynor uses Beta as denominator.
• It is already well known that while standard deviation measures the total risk of the portfolio, Beta measures systematic risk that cannot be diversified by fund manager.
• In any business there are unsystematic risks demand, supply, price, competition etc. There are also systematic risks like inflation, interest rates, government policy etc
• Sharpe is a good measure of risk adjusted returns where the portfolio is not properly diversified, which is often the case, which is why Sharpe is more popular.
• Treynor is a better measure where the portfolios are well diversified. However, there is too much reliance on Nifty being a perfect index and that is the flaw in Treynor.
• Typically, fund managers are supposed to eliminate unsystematic risk in the portfolio by diversifying, so they should only be rewarded for systematic risk.
• However, while Treynor is theoretically a better measures, from a practical standpoint, it is Sharpe that gives a more unbiased view of risk

Finally, it must be remembered that most portfolios disclose Sharpe as there is less of index bias in them. Also, in case of mid-caps and small-caps, the index itself is not representative due to these stocks being heterogeneous. That surely makes a more pragmatic case for the Sharpe ratio.