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Sharpe & Sortino Ratios

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Sharpe Ratio expresses the relationship between performance of a scheme and its volatility. A higher ratio signifies a relatively less risky scheme.

Sharpe Ratio expresses the relationship between performance of a scheme and its volatility. A higher ratio signifies a relatively less risky scheme.

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• 1. How do you select funds? The most simple approach would be peformance i.e. returns, right?! But is it sufficient to track only returns?
• 2. There is something more… The reliability of the scheme too is a critical aspect. Reliability is nothing but volatility. A scheme giving good returns but is extremely volatile or unreliable may not find favor with a larger number of investors. This calls for a measure of performance which takes into account both returns as well as volatility / reliability.
• 3. Understanding Sharpe & Sortino Ratios Sharpe Ratio expresses the relationship between performance of a scheme and its volatility. A higher ratio signifies a relatively less risky scheme. Mathematically is can be expressed as: Sharpe ratio = Average returns / Volatility (Std. Deviation)
• 4. What does it mean? Thus if the performance is average while the volatility is very low, the ratio becomes large. If one were to look at cricket for an example, a player like Rahul Dravid will have a decent average (let’s say 40) and a low volatility (lets say 0.5). Hence his Sharpe Ratio would be 40/0.5 =80.
• 5. On the other hand… Virendra Sehwag could have a slightly higher average than Dravid (let’s say 45) but his volatility, as we all know, is quite high. Either he makes big hundreds or gets out for a very low score. Let’s presume his volatility is 0.75. His Sharpe ratio will then be 45/.75 = 60 (which is lower than the Sharpe Ratio of Dravid).
• 6. So what does this suggest? Despite a higher average, Sehwag’s Sharpe ratio is lower than that of Dravid. This indicates that simply looking at performance from the average point of view is not enough to judge a player. One needs to take a look at different dimensions as well.
• 7. Hence… It may be wiser to pick up Dravid for the longer version of the game, say Test Matches and Sehwag might be a better pick for the shortest version of the game, say T-20. Also, the ratio will become large if either the numerator increases or the denominator decreases.
• 8. The Sharpe Ratio of TataInfrastructure Fund is 0.0899 forthe period of three years from1st June, ’06 to 31st May, ’09,wherein Risk Free Rate isassumed at 6%.
• 9. So what is the Sortino Ratio? The Sortino ratio is similar to the Sharpe ratio, except while Sharpe ratio uses Standard Deviation in the denominator, Sortino ratio uses downside deviation. It is important to note that while standard deviation does not discriminate between upward and downward volatility, downward deviation does so.
• 10. Thus… Standard deviation can be high in the case of excessive upward movement of price and it may result into a lower Sharpe Ratio. Sharpe ratio will be low because the high standard deviation is the denominator. Now we may believe that the scheme is unsuitable and therefore misrepresent the real picture (since upward movement is desirable from an investor’s perspective!).
• 11.  Hence it was necessary to find another ratio which differentiates harmful volatility from volatility in general by replacing standard deviation with downside deviation in the denominator. Thus, the Sortino Ratio was calculated by subtracting the risk free rate from the return of the portfolio and then dividing it by the downside deviation.
• 12. Conceptually speaking… Sortino Ratio = Performance/ Downside deviation. The Sortino ratio measures the return to ‘bad’ volatility. This ratio allows investors to assess risk in a better manner than simply looking at excess returns to total volatility. A large Sortino Ratio indicates a low risk of large losses occurring.
• 13.  To give an example, assume investment A has a return of +10% in year one and -10% in year two. Investment B has a 0% return in year one and a 20% return in year two. The total variance in these investments is the same, i.e. 20%. However, investment B is obviously more favorable. Why?? As the Sharpe ratio measures risk using standard deviation only, it does not differentiate between positive and negative volatility.
• 14. The Sortino ratio, on the other hand,measures performance against thedownward deviation… so it is able to spotthe negative volatility associated withinvestment A immediately and help usclassify investment B as a more favorableinvestment!
• 15. The Sortino Ratio of Tata InfrastructureFund is 12.796 for the period of threeyears from 1st June, ’06 to 31st May, ’09,wherein Risk Free Rate is assumed at 6%.
• 16. To Sum Up Sharpe Ratio: Sharpe Ratio expresses the relationship between performance of a scheme and its volatility. A higher ratio signifies a relatively less risky scheme. Sortino Ratio: The Sortino Ratio is calculated by subtracting the risk free rate from the return of the portfolio and then dividing it by the downside deviation.