Welcome back. The second metrics that we will calculate for our mutual fund portfolio is the standard deviation of the mutual fund portfolio. We know that the standard deviation of the mutual fund portfolio will give us how risky our mutual fund portfolio is. So, let us see how to calculate the standard deviation of a mutual fund portfolio. The formula for calculating standard deviation of a mutual fund portfolio is given here here sigma p is the standard deviation of the mutual fund portfolio. sigma i is the standard deviation is if mutual fund in the mutual fund portfolio, why is the weight of the mutual fund in the mutual fund portfolio and rho ij is the correlation between the if and the Jade mutual fund in the portfolio.

Now, the formula is sigma p squared is equal to W one squared into sigma one squared plus w two squared and two sigma two squared all the way up to w n squared into sigma n squared plus Two times w one, sigma one into w two sigma two into row one, two. Now, we have to combine all this w one w i's and W J's to get the terms, ending with two w n minus one into sigma n minus one into w n into sigma n into row n minus one and now, we find that we are getting the value of sigma p squared, so, we get the value of sigma p by doing a square root of this number. You'd have noticed that the formula is rather lengthy and there are a lot of terms. In fact, when you have a number of mutual funds in a portfolio, you would have n squared minus n number of terms.

So, when you have 10 for mutual funds in the portfolio, you will have 10 squared minus 10 which is equal to 90 number of terms in the portfolio in the formula. So, we will not calculate this because it will take a lot of time instead, I will show you the snapshots of the calculation in the x So, we have all the different mutual funds that we had included in the portfolio. For each of the mutual funds, I have taken out the standard deviation of the mutual fund from the Economic Times website. So, these are given here, then, we had made our initial allocation based on the calculation for maximizing the expected returns. So, we will use that allocation for the time being also, previously we had calculate the correlation between each of the mutual funds in the portfolio. So, all these figures that are available to us right now, to be able to calculate the value of sigma p squared, we will divide the terms into two types in one type, we will have w I's squared into sigma squared calculated.

So, this is shown here. Then in the second set, we will have two w i into sigma phi into w i plus one into sigma i plus one into rho i plus one. So, we'll calculate all of these terms then add up all of these terms to find the value of sigma p squared. So, we find that the standard deviation of the mutual fund portfolio that we have form is 10.44%. So, we have seen how we can calculate standard deviation for a mutual fund portfolio. As we had discussed during the calculation of expected returns for the mutual fund portfolio, you can optimize the portfolio so that you can minimize the standard deviation for the mutual fund portfolio.

I leave it to you to try this on your own. Thank you for listening. See you in the next lecture.