Welcome back. In this lecture we discuss about r square r square is a very important metric. However, r square is not a measure of performance of a mutual fund, we will see what exactly r square is and what it interprets to R squared is a statistical measure, it is also known as coefficient of determination. r square is the measurement of the correlation between the investments performance and the performance of the benchmark index. That means that r square basically tells us how closely the investment performance mimics the performance of the benchmark index. If the R squared is very high, that that means to say that the performance of the index can interpret the performance of the portfolio of the investment.
That is as the index moves the investment also will move in the same direction. If the correlation is weak That means to say we cannot the index performance does not tell anything about the performance of the investment. This is a reason, investors use our square measurement to compare the portfolio's performance with the performance of the broader market and predict the trends of the portfolio's performance as they may occur in the future. r squared can take a value between zero percent and 100%. As you'd have guessed by now, index funds have r squared very close to hundred percent. We will see how to calculate r square using Excel It is rather easy.
The formulation of r square is a little complicated. So we will use Excel which gives an easy method of determining r squared. You're familiar with this worksheet by now. So we have the month on the first column. We have the Sensex on the second column and we have the nav index of our mutual fund in the third column. We've already calculated the returns from the index as The mutual fund.
Earlier we select this data, then we select a line graph. So there we have the line graph. Now we want the line graph between the index performance and the mutual fund performance. So we make some modification, we put the index performance or index returns on the x axis, and we put the mutual funds performance on the y axis. So now that is done, so we get the graph. They show the relationship between the index and the mutual fund, we add a trendline to this.
After adding trendline, we use linear regression. And then you see this option for calculating r squared. So, we select that option and it gives the value of r squared. I'll just expand this graph a little bit so that you can see it more clearly. So there you have the value of r squared. So point three basically means it's about 30% relationship between the index Under mutual fund, so this is not a very strong correlation.
Now that we have figured out how to calculate r squared, let's see how to use r squared. Now first of all r squared and beta are closely related concepts. Now, a high R squared value indicates that the data figure what we get for a mutual fund is a useful figure for making interpretations. If r squared is low, then the beta is not very relevant for determining the performance of the fund. One thumb rule for investors is that when the R squared is high for a particular mutual fund, and also the beta for the mutual fund is high, then that particular mutual fund is likely to produce very high returns as compared to that of the index. That is that mutual fund is likely to beat the market.
Thank you for listening. See you in the next lecture.