One of the very important matrices is Mita. And we discuss it in this lecture beta is relevant for any stock market trading, we will look at it from the perspective of mutual funds. Now, the concept of beta comes from capital asset pricing model cap m, we will very briefly look at what is cap m studying cap m by itself will require that entire course, beta is the sensitivity of the expected excess asset returns to the expected excess market returns. Now, asset return here means the returns from the mutual fund and the market returns means what the what we can expect to get from the market. Beta is a measure of volatility or systematic risk of an individual stock in comparison to the unsystematic risk of the entire market. Like we have studied in the previous section.

Systematic risk is something which cannot be done away with they are always existing to the market and these cannot be taken away through waste. Like diversification etc. So, this is systematic risk is always available in the market, I always prevalent rather in the market and nothing can be done about it it has to be lived with. So, beta measures the volatility, how much of systematic this there is in the market for individuals mutual fund in comparison to the unsystematic risk of the entire market. As you would have understood by now, since beta is a measure of volatility, beta is essentially a meta measure of risk. So, beta measures how risky a particular mutual fund is, in comparison to other mutual funds.

In layman's term we can understand that if beta is high, then the mutual fund is more risky and if beta is low then the mutual fund is less risky. Beta is interpreted as follows. If beta is equal to one, then the mutual fund is as risky as the current market situation is. If beta is greater than one then the main One is more risky as compared to the market. If the mutual fund is more risky as compared to the market, which means that we should expect more returns from the mutual fund as compared to what is the returns we can expect from the market. Similarly, if beta is less than one, then the mutual fund is supposed to be less risky as compared to that of the market.

So, a beta is less than one we should expect less returns from the mutual fund as compared to the returns we would expect to get from the market. Now, beta can be less than zero also, a beta is less than zero, it means the mutual fund returns will move in the opposite direction to that of the market. Now, let's look at the formula for calculating beta. We will study two formulae with five which you can calculate beta. First let's look at the formula that is stated here. So beta is equal to covariance between the returns of the mutual fund and the returns of the market divided by the variance of the returns of the market.

There is take a mutual fund arbitrarily and see how to calculate the beta for that particular mutual fund. So, we required two values, one is returned from the mutual fund and returned from the market. Now, in the lecture on mean we have seen how to calculate the return from the mutual fund, we will use the same strategy. Now, to get the values of the nav for the mutual fund I will explore one site there are many sites where this is available, but I will show you from one side how this information can be gathered for gathering the historical data regarding Sensex we will use the website www BSE india.com. Now, we opened this site, this site we can see there is something called indices. So, we will click on that look at the site address properly.

Okay. We click on indices here We select the historical prices. So it asked me which index Isaac BSE Sensex I want monthly data from January 2016 and click Submit. So all the data is presented here from January 2016 on a monthly basis This data can be downloaded also cybil download this data and utilize it next to gather the data for nav of a mutual fund. This we can get from a website called www dot m fi india.com. So, we open this website.

Here you can see the website. Now first we select the fund house so this is access mutual funds. Then we specify the fund name. So we are trying to select access long term Equity Plan. The equity fund Growth Plan. Now, this is a little more tedious because I have to give three months intervals because it announced of axiom 90 days of NAB.

So, I will give every three months interval from 2016 onwards to gather all the nav for this particular fund. So, let us see I provide a three months interval. So, there I get the nav for this particular mutual fund. Now, I have taken all this data and put it in a excel sheet. So, here you can see the different months. Now, here is the Sensex data Here is the nav data for that particular mutual fund.

We will freeze this pane so that the screen doesn't move around. So, we have done that. Now, we will consider that we purchase hundred units on the first of January 2016. So hundred units. So for let's first calculate the time intervals, like we have seen in the discussion on mean we need the time intervals for calculating the returns. So, we calculate the number of time intervals in terms of number of years.

So, I will copy this down so, now the time is intervals haven't calculated. Next is calculate the purchase price, in case we buy 100 units of the same sex, so we know that the purchase has to be negative value because it's an outflow of money. So we will subtract by zero. Okay, now let's calculate the value as on the different months. So this is simple just multiply the hundred quantity by the value of the Sensex and then I will copy this across for all the other months. So there we have the value from first year AnneMarie to first of Jan, first January 16 to first January 19.

Now I will just copy this in the next column. So, this gives the purchase value for the mutual fund. So, once we have this we can calculate the CAGR, that is the returns on the different months. So, we will use the same formula for same function called rate will give the time interval. The installments of zero the present value is the purchase price and the future value is the value as on that particular month. So, we will copy this down we'll do the same thing for the mutual fund also Okay, so now we have the returns from the Sensex as well as we have the returns from the mutual fund.

Next thing we have to do is find the covariance between these two returns. So, for covariance we use the function covariance in Excel and this function requires two areas to be provided the first area we provide is a Sensex returns the second array we provide the returns from the mutual fund. So, we have got a covariance Now, next we find the variance of the market returns that is the returns of the Sensex So, we find the variance using the word function okay now, we have got the covariance of the covariance as well as we have got the variance now, we calculate beta as covariance divided by the variance of the market. So, there we get the beta. Now, we see another way of calculating beta, this time we will utilize capital asset pricing model. Now, capital asset pricing model is a theoretical model, it has not been proved but however it is very widely used, and it is by far the most popular pricing model.

It's a pricing model which is used to determine the appropriate rate of return of an asset to make decisions regarding whether the asset needs to be added to the portfolio or not. The formula for capm is as shown here. Ra is equal to RF plus beta into RM minus RF Here are is the return on the asset. So, how much return we can extract from the asset. Now, to determine that RF is the risk free rate, risk free rate is normally taken as the rate at which we are assured to get a return in every country normally the returns from a government bonds are considered to be risk free. So, we normally take the rate of return of a government bond to be the risk free rate RM like EFC just some time back is a rate of return from the market that we can expect.

So, when we have the value of rate of return from the market RM, we can assume a risk free rate based on the situation in the country RF and we have the rate of return on the asset. Then, we can calculate beta by D arranging this formula as RM minus RF divided by RM minus RF jealous calculate beta according to this formula. So, we will return to our Excel now we use the same Excel that we used for calculating beta earlier, first thing is we will consider a risk free rate to be 4% in the Indian Indian context 4% is a fair idea or regarding the risk free rate that is prevalent in the country. Now, we know we just discussed that the formula for our cap M is our A is equal to RF plus beta into RM minus RF. So, from this formula we can get that beta is equal to ra minus RF divided by RM minus RF.

So, first let us determine RM RM is nothing but the average of all the returns that we have computed for the Sensex. For the same time period we consider ra which is the average of all the returns that we have got from the mutual fund. So now we have got rm rf and RA, let's calculate beta using the formula that we have just discussed divided by RM minus Ra. So, we see that the beta is fairly close to the beta we had earlier calculated. So we have seen two ways how we can calculate beta. Now, beta is based on historical values of returns.

That's why it is very good for predicting short term risks in a mutual fund. However, it is not very useful for predicting at all Long term, what would be the mutual funds price be? With that we come to the end of the discussion on beta. Thank you for listening. See you in the next lecture.