In this lecture, we discuss a very important metric that is known as the Sharpe ratio. Sharpe ratio is named after the founder of this ratio that is William Sharpe, he formulated this particular metrics in 1966. Later it was modified in 1994. We will discuss the more formulation as for the modified version in 1994 Sharpe ratio is also known as revert to variability ratio. This is because it's a it's a ratio between the reward and the variability. The reward we can understand as the returns that we get from a mutual fund and variability we can understand as the standard deviation of the mutual fund.
We know that returns is nothing but the performance of the investment and standard deviation is nothing but a measure of the risk. So, Sharpe ratio is essentially a way to examine the performance of an investment by adjusting for its risk. So Sharpe ratio measures the excess return or the risk premium per unit of deviation in the investment asset. In layman's term, when we are using a common benchmark, then the asset with the higher Sharpe ratio provides more returns for the same amount of risk. So, in general, when we are comparing mutual funds the mutual fund with the higher Sharpe ratio can be considered to be most likely to provide a higher return. So, as we have discussed So, far, Sharpe ratio is nothing but the ratio between the mean of excess returns against the benchmark index and the standard deviation of excess returns against a benchmark index.
We will see how to calculate Sharpe ratio and then it should become more clear. Now, by now this Excel should be familiar with you we have the dates, we have the recording of the Sensex and we have the recording of a particular mutual fund and IVs. Now, we have we will add an extra column here for calculating the excess return, we had calculated the returns from the index and also we had calculated the returns from the mutual fund. So, we will now calculate the excess returns for the mutual fund as compared to the index. Okay, so we have the column ready right now. The excess return is nothing but the difference between the return of the mutual fund and the return of the index.
So, we calculated that now we copy this across the entire date range that we have gotten So, we have got the values of the excess return. Now, we first need to compute the mean of the excess return. Now, you can see that the excess return is against the benchmark index. So, this is as for the definition, so, we will find the mean then we will find the standard deviation This is the requirement for calculating the Sharpe ratio standard deviation we denote by as d. So, mean is nothing but an average of all these returns. So, we got that now the standard deviation we can find by using the function St. Deb Okay, we got the standard deviation. Now we can find the Sharpe ratio as the ratio between the mean and the standard deviation Okay, so, we got the Sharpe ratio Sharpe ratio can be both positive and negative.
Now that we have seen how to calculate Sharpe ratio, let us see the strengths and the weaknesses of Sharpe ratio. Now, biggest 10th of Sharpe ratio is that it observes both the systematic and unsystematic risks. So, we know that the systematic risks are which are the ones which are prevalent in the market and then cannot be diversified, non systematic risk are specific to a company or industry and they can be diversified. Now, Sharpe ratio takes into consideration both the systematic and unsystematic risks. Another big advantage of Sharpe ratio is that it is directly computable for from any series of returns. Now, I have demonstrated the same to you I have taken the returns from a website for a defined period of time and for based on the returns or from the observed values, we have computed the Sharpe ratio.
One weakness of Sharpe ratio is that it relies on the notion that risk equals volatility and volatility is bad. How are we we know that when we take more amount of risk, the chances of getting higher returns is also higher. So, those arrays can result in a loss, but the chances that we may get a higher return is only possible when we take more amount of risk. So, this is a very big criticism of Sharpe ratio. Thank you for listening. See you in the next lecture.