The first metric that we discuss is the expected return for the mutual fund portfolio. Now expected return for the mutual fund portfolio should give us how much return we can expect from the portfolio of the mutual funds that we have created. The formula for calculating expected returns of a mutual fund portfolio is to find the weighted sum of all the individual expected returns of the mutual funds in the mutual fund portfolio. We will use the following notation and expressing our formula for the expected return of a mutual fund portfolio. Now, er is the expected return of the mutual fund portfolio that we want to determine e ri is the expected return of the higher mutual fund in the mutual fund portfolio. And why is the weight of the higher mutual fund in the mutual fund portfolio.

So, we can write the formula as your is equal to summation over i is equal to one to n Off Wi Fi into E R is in a simpler form, we can write the formula as E r is equal to W one into er one plus w two into er two plus w three into year three, so on and so on up to WN into er n. Now, we will use Excel to calculate the expected returns of a mutual fund portfolio. In Excel we can simply use the function sum product. Now, let us see how we can find the expected return of a mutual fund portfolio using Excel. Now in this Excel, I have planted the different mutual funds which we have included in our portfolio. So you can see the different mutual funds are in the portfolio. Now for each of the mutual funds I have recorded the expected returns, which we have determined from the Economic Times website.

Now we give a location to each of the virtual funds. Let's say we start with a location Getting equal amount of funds to each of the mutual funds. So, we give 10% to each of the mutual funds. So, we are giving 10% to each of the mutual funds. So, this means that we have allocated hundred percent of the money in the 10 mutual funds. Now, let us calculate the expected returns, expected returns like we said can be calculated using the function sum product.

So, we say sum product. Now, we need to give the expected returns as the first parameter and the weights as a second parameter. So, the expected returns now we convert this into a percentage the expected return works out to be 12.4 Zero. Now, let us try to optimize our portfolio. So we go to solver, which is under data. Now, we set the objective function as we want to maximize the expected returns.

So, we select the cell which contains the expected returns and we say maximize, we say that all the values should be non negative. And the values which you want to change are the weights of the different mutual funds, we add the constraints that each weight should be greater than or equal to 5%. And each weight should be less than or equal to 25%. So we do this exercise we take the first weight, make it greater than or equal to the minimum allocation of 5%. So we add all the weights in the constraints with this particular constraint, that is the weight should be greater than 5% So we have to do this process for all the 10 weights. Now we check for that we have added all the weights or not, with this particular constraint that they should be greater than or equal to 5%.

We notice that we have taken from Sensi three from sale row row number three to row number 12. And we have added. Now let's add the constraint that all the weight should be less than or equal to 25%. So, now we have added all the constraints that are assessed have a final check, and we should have two constraints for each of the allocation cells. Once we have done that, select the simplex method now what exactly simplex method, you need to study operation research. Now, after you selected the method didn't say solve, when it says solve, it solves the linear programming problem and gives the solution that we should have under these allocation waters calculated We will get an expected return of 14.38% which is the maximum we can expect.

So, we have seen how to calculate the expected returns for a mutual fund portfolio and also we have seen how to optimize the portfolio so that we get the maximum expected returns. Thank you for listening. See you in the next lecture.