Question

A portfolio consists of two stocks:

 

Stock                 Expected Return            Standard Deviation             Weight

 

Stock 1                          10%                                     15%                            0.30

Stock 2                          13%                                     20%                            ???

 

The correlation between the two stocks’ return is 0.50

 

1. Calculate the expected return and standard deviation of the portfolio.

Expected Return:

Standard Deviation:

2. (i) Briefly explain, in general, when there would be “benefits of diversification” (for any       portfolio of two securities).

 

 

 

 

      (ii) Describe whether the above portfolio would exhibit “benefits of diversification” (and why).       [No calculations are required.]

 

 

 

 

3. Show your calculations re: whether the above portfolio exhibits “benefits of diversification” and indicate whether it does/doesn’t (and why).

Answer 1

Ans a) Expected return of portfolio = weight of stock 1 * expected return of stock 1 + weight of stock 2 * expected return of stock 2

weigh of stock 2 = 100% - weight of stock 1

= 100% - 30%

= 70%

= .3 * 10% + .7 * 13%

= 3% + 9.1%

= 12.1%

Standard deviation of portfolio = ((weight of stock 1 ^2 * standard deviation of stock 1^2) + (weight of stock 2^2 * standard deviation of stock 2^2)* (2*correlation between stock 1 and 2 * weigh of stock 1 * weight of stock 2 * standard deviation of stock 1 * standard deviation of stock 2)^(1/2)

=( (.3^2 * .15^2 )+ (.7^2 * .2^2) + (2 * .5 * .3*.7*.15*.2))^(1/2)

= ( .002025 +.0196 + .0063)^(1/2)

= 16.71%

Ans b) When the correlation between two stock is less than one than one can be benefit by the diversification. Yes above portfolio exhibits the advantage of the diversification because the standard deviation decreases for the portfolio with significant increase in the portfolio return.

Ans c) if we see the per unit return to risk ratio then with the diversification it increases.

Stock 1 = 10/15 = .667

Stock 2 = 13/20 = .65

For portfolio = 12.1/16.71 = .724

so we can see that return to risk ratio is highest for the portfolio and we can conclude that portfolio has diversification benefits.