Hello, welcome back. In the last lecture, we saw how we can find information regarding mutual funds. Among the information that we studied, we saw that there are some matrices, which we need to to very carefully study with when dealing with mutual funds. In this lecture series, we start by exploring each of the matrices individually, we start our discussion with a matrix called mean. Now, mean is actually in terms of mutual funds, it is the average returns that we get over a period of time. Now, here the period of time is very important.

However, before we get on to discussing what exactly is average returns or what exactly is mean, let us understand what is the return to understand what is returns suppose the following an investor purchases 500 units of mutual fund and one at the rate of rupees 20 per unit on first of January 2017. Please note all of these 500 units produced 20 per unit are first of January 2017, then the investor sold these 500 units in mutual fund and one at rupees 26 per unit on first of January 2019. So, under this circumstance, what is the returns that the investor got, we can do this calculation using a paper and a pencil or a calculator however, we will use Excel as other times the problem may not be always so, simple. So, we will see that technique how to do such things in Excel to understand returns there is calculate the returns.

Now, the problem that we have stated is planted here. So, this is the first column is the date of transaction. So, on first January we have purchased 500 units at a nav of 20 rupees per unit and on first of January 2019 we have sold 500 units or nav of 226 rupees. So, the value of the purchase on first of January 2017 was rupees 10,000. Now, however, this is a purchase So, the money has flown out. So, we need to consider this as a negative figure.

So, we will consider this to be a negative figure, so we'll be surprised by zero. So, on first of January, we have spent 10,000 rupees on first of January 2019 we have sold it, so, we have earned money. So, this can be calculated by multiplying nav with the number of units. So, we get the value of 13,000 rupees. So, the net income what we have had or the interest what we have received is the value of the sale minus the value of the purchase. So, since the value of the purchase is a negative figure we will add the two values to get the total amount that we have earned from this particular mutual fund.

Now, the time elapsed, is the date of sale minus the date of purchase. So, that is reasonable have supplied the date of sale from the date of purchase to get the time elapsed. However, this is the number of days elapsed, but we want to calculate the figure of number of years lab because we are considering annual interest. So, we will divide this figure by 365 to get the number of years elapsed. So, this will be divided by 365 we get two years have elapsed. So, this is time in years Okay.

Now, let's compute the simple interest. First, we the simple interest rate computing just for the sake of illustration, actually, when we are considering the returns from a mutual fund, we do not consider the simple interest. We as we have already studied in the previous section, we consider the CAGR which is the compounded annual rate of growth growth rate. So, for simple interest you know the formula is interest is equal to principal into rate into time From this formula we get that rate is equal to interest divided by principal into time. So now let's put this formula for rate and compute the value. So, here we get, the interest we earned was 3000 rupees divided by the principal the principal is a negative, so we will convert it into positive.

So, that is zero minus 10,000 into the time that is two years. So, according to simple interest we have earned the interest of 15% on this particular mutual fund. However, we are interested in the CAGR that is a compounded annual growth rate. let us calculate this value next. To compute CAGR, we can use the excel formula rate. So, in rate, the first parameter is number of periods passed that is we have got the time two years have passed.

The second parameter is the number of installments, we have not received any installment, so, it is zero. Now, the present value when we invested was 10,000 and the future value what we got was 13,000. So, he put these are the next two parameters. Now, let's compute when we compute we see that the CAGR is 14.02%. So, we computed that in this particular transaction, the returns was 14.02%. Now, when we are computing returns, we will not always sell on that particular day we will assume that if we sold on that particular day, what would With the returns, then based on what is a computation of returns we get we may decide whether we would like to go ahead to the sale or not.

Another important aspect to note is that in our computation, we have not considered exit load taxes etc. Now that we have understood what is returned, let us proceed to understand what is average return. Now, let us understand mean or average annual rate of return through this illustration. Now, this Excel I have planted the different dates first January 16, first July 16, etc. Now, on these dates, we have recorded the nav of a particular mutual fund. Now, supposing we have purchased 500 units of the mutual fund on first January 16, then the value of this mutual fund on first century 16 was 10,000 rupees.

However, like we know this is a purchase So, this has to be a negative figure. So, we subtract this vice zero. So, we have made outflow of 10,000 rupees on first January 16 Now, on first July 16 the value of this fund is equal to nav into quantity that is C three into B three. This as we have seen here, we can copy this formula down and we get the nav on the we get the value on the different dates that we have planted on this Excel. Now we compute the time elapsed time elapsed is first July 16 minus four January 16. Now, like we saw before, this gives the number of days so we will convert it into number of years by dividing by 365.

OK, now we get the number of years. Now, we want to I will anchor this a to sell because we want the number of years elapsed since the date of purchase. So, I anchor the A to sell and copy this formula across, down the div all the other rows of this particular x So, now we have got the different time elapsed. So now based on this figure we can calculate the CAGR using the rate formula. So, we say rate, the number of periods is the time elapsed, comma there is no installment. So, zero comma the present value, the present value is in D two that is a purchase value, and then the future value is in the, against the different dates.

Now, we will anchor D two because we would always compute the result will always compute the purchase price as the present value. So, now we can copy this formula down to the other rows also. So, now we have got the different returns for the different dates. So, this is a three year period returns every six months. Now, we can compute the average return by simply doing average of these returns and we get the mean value Now important thing to notice that the mean value is always computed based on a particular period of time. So, we have seen how the average annual rate of return or the value of mean is computed.

Now, when you browse different websites for a particular mutual fund, you will find that the value of mean is different on different websites. It is not because the values are calculated wrongly or the values are misleading it simply because you must see what is the concentration what is the time duration for which the values have been computed and what is the intervals at which the enemies have been considered. With this we come to the conclusion of our discussion on Main. I hope you have enjoyed it. Thank you for watching see in the next lecture.