Welcome back. So far we have discussed the Sharpe ratio and the treynor ratio. Now let's discuss another ratio which is the sortino ratio sortino ratio measures the risk adjusted return of an investment like a mutual fund. What is risk adjusted return will become clear shortly, when we do the calculation for the sortino ratio sortino ratio is a modification of the Sharpe ratio. So, it is also a revert to variability ratio. while calculating Sharpe ratio, you'd have noticed that we took the average of all the returns that we had recorded.
So, Sharpe ratio penalizes all the returns both the upside returns and the downside returns the returns which are positive and negative. This is a major difference with the sortino ratio sortino ratio only penalizes the returns which are below user specified target. This will become more clear when we do the calculation for sortino ratio. The investor would like to keep the deferred returns and only avoid the downward returns. So sortino ratio is used to store the portfolio's risk adjusted returns relative to an investment target using the downside risk sortino ratio is expressed in terms of a percentage. So, it can be used for ranking the investments like we can rank the mutual funds based on the sortino ratio.
The formula for sortino ratio is sortino ratio is equal to return from the asset minus target returns divided by the downside risk. Now, we will see how this is calculated and from that all of these terms should be very clear. You must be aware of what is returned from the asset. This is the basically the mean or the CAGR of average returns from the CAGR at Target return is what we set as a user what is the target return that we are expecting and downside this we will see through the example. Now we return to our Excel, you're familiar with it. We have the dates, we have Sensex and have the nav for the mutual fund.
Now, we have calculated the returns of the mutual fund. Now, what we will have to first do is set a minimum target what we would like to achieve as a return. So, we will set this target arbitrarily to 10% right now, so, the return target return what we have said is 10% Next we need to calculate what is the excess return on top of the target that we get. So, we subtract the target return from the return which we are actually getting over the period of time. So, now I copy this Okay. So now we have got the excess return above the target that we are trying to capture now In sortino ratio, we always consider the downward risk.
So, we will eliminate the upward risks. So, we can say that the excess returns that forgetting if it is less than zero then only consider the excess return. Otherwise do not consider it otherwise marketers 03 enter the formula and there it is calculated. Next, we calculate the average return of the asset. This is nothing but average of all the excess returns that we have got. So, we get the average of the excess returns.
Now we calculate the downside risk formula for downside risk is we do the sum squared of all the downside excess returns. Some Sq of all the downside it says returns divided by the number of excess returns that we have considered. And we have to find the square root of this. So we find the square root of this raise it to the power of 0.5. So now we have the excess return average or excess return and the downside risk, we can calculate short sortino ratio By dividing the average excess return by the downside risk. So there you have the sortino ratio.
In layman's term, higher the sortino ratio, more returns you can expect from a particular feature fund. Thank you for listening. See you in the next lecture.