A portfolio is composed of two stocks. Given the following...

A portfolio is composed of two stocks. Given the following parameters associated with the returns of the two stocks: Stock 1 2 Proportion of portfolio 0.30 0.70 Mean 0.12 0.25 Standard Deviation 0.02 0.15 a. Determine the mean and standard deviation of the return on the portfolio when the coefficient of correlation is equal to 0.5; 0.25; and 0. b. Describe what happens to the expected value and standard deviation of the portfolio returns when the coefficient of correlation decreases.

Transcript

00:01 Hi everyone, welcome to the question.

00:02 So in this question, they have given us a tabber column of portion of portfolio and stock one, stock two, mean, and they have given us standard deviations of both the stock one and stock two.

00:13 Now we have to determine the mean and standard deviation of the return on the portfolio and the coefficient of correlation is equal to 0 .5, 0 .25 and 0.

00:25 First best, let's find mean.

00:29 Mean of the return on the portfolio is mean is equal to 0 .12 multiplied 0 .30 plus we are multiplying this mean value with our proportion here.

01:01 Okay so 0 .1 2 multiplied by 0 .30 0 .25 multiplied by 0 .70.

01:09 So plus 0 .25 multiplied by 0 .70 so when you multiply you get 0 .036 plus 0 .175 which is equal to 0 .211.

01:30 So this is the mean.

01:32 Now let's calculate the standard deviation.

01:36 So first when correlation is equal to 0 .5.

01:44 So standard deviation.

01:44 So first, when correlation is equal to 0 .5.

01:52 Is standard deviation is square root of 0 .30 the whole square multiplied by 0 .02 the whole square so 0 .30 is the proportion of the first top 0 .02 is the standard deviation of the first top plus 0 .70 the whole square multiplied by 0 .15 the whole square.

02:25 So 0 .05 the whole square.

02:25 So 0 .70 is proportion of the second stop, 15 is the standard deviation of the second stock, multiplied by 2.

02:35 So 2 is the number of stocks are 2, multiplied by, again, 0 .30, proportion of the first store, multiplied by 70, proportion of the second stock, multiplied by 0 .02, standard deviation of first store, 0 .15, standard deviation of second store, multiplied by the correlation, 0 .5 so that is equal to square root of 0 .09 multiplied by 0 .004 plus 0 .49 0 .49 multiplied by 0 .0 .25 multiplied by 0 .0063.

03:18 Square root that is equal to 225 multiplied by 0 .000000663.

03:27 Square root that is equal to square root of 0 .0036 plus 0 .0066945.

03:43 So that is equal to 0 .0 .0 .00263.

03:50 So this is the standard deviation for correlation 0 .5.

03:54 Now we are going to find the correlation for 0 .25.

03:59 So when correlation is equal to 0 .25, so standard deviation is equal to 0 .25.

04:21 That's square root of same thing, 0 .30 whole square.

04:27 We're just going to represent 0 .15.

04:33 For that, we're going to represent 0 .15.

04:36 That's all...

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