00:01
Hello students, we are given a question here.
00:02
A portfolio is composed of two stocks, stock a and stock b.
00:06
Stock a has a standard deviation of return of 18 percentage, while stock p has a standard deviation of return of 24 percentage.
00:15
Students, further what we are given? stock a comprises 60 % of the portfolio, while stock p comprises 40 % of the portfolio.
00:26
Now we are asked that if the variance of the return on the portfolio is given as 0 .003, then the correlation coefficient between the returns on a and b is.
00:36
Okay.
00:36
So first of all, we are supposed to know that here for portfolio, we can write here for a portfolio variance, portfolio variance, what we can state? it should be like a sigma p square, sigma p square is equal to wa square times sigma a square okay students plus w b square times sigma b square plus two times w a times w a times r b okay students now here what we are given see we need to ultimately we are given here sigma p is given as here as we can see zero point 033 okay so we can even mention below because it is the variance of return on the portfolio so basically sigma b square it means 0 point sorry it can be written as equals to 0 .0 3 3 and its whole square okay students which is equal to as we are supposed to know that here sorry variance is all about the sigma square so basically this term will be already sigma b square equivalent to the sigma p square which is 0 .033 is equal to w a square so what we are supposed to know that here w a is nothing but the compromiseation offer here we are given that as stock a comprises 60 percentage of the portfolio it means it will be equal to obviously 0 .60 and its whole square sigma a square as we are supposed to know that here sigma a okay students so here we can just say that the for a portfolio is composed of two stocks stock a has a standard deviation of return of 18 percentage so standard deviation is nothing but the under root of variance okay so basically we can just say that it should be like 0 .18 whole square so sigma a square can be written as equals to 0 .18 whole square plus for wb what we are given here stock p comprises 40 percentage of the portfolio so it should be like a 0 .40 whole square.
03:07
Okay students times for sigma b what we are given here that the while stop b has a standard deviation of return of 24 percentage.
03:18
Okay students so it should be like a 0 .24 whole square we can write here 0 .24 whole square plus two times of w a is nothing but equal to 0 .60 times times.
03:32
Wb is given as here .40 times sigma and sigma b so sigma is nothing but equal to point of 1 8 and times sigma b which is nothing but equal to point of 24 and times row a b okay students now 0 .033 is equal to see here we are supposed to know that what we can state see we need to make a little bit calculation like point 0 .0 3 3 is equal to see here we are supposed to know that the what we can state see we need to make a little bit calculation like 0 .6 whole square is 0 .6 times 0 .18 times 0 .18.
04:09
So what we will get, it will be called to obviously 0 .0116 .4 plus 0 .4 times 0 .4 times 0 .24.
04:20
So it should be equal to 0 .009216.
04:20
Okay, students plus 2 times 0 .4 times of 0 .4 times of 4...