Question

1. Chloe plans to invest some of her savings into two blue-chip stocks, namely Stock A and Stock B. Suppose that the mean and standard deviation of the annual return of Stock A are 5% and 5%, respectively, and the mean and standard deviation for the annual return of Stock B are 10% and 10%, respectively. In this investment portfolio, Chloe will put 50% of her money into Stock A and 50% of her money into Stock B.

   1. (i) [3 marks] If the correlation coefficient of the two stock returns is -0.2, do you think that this investment portfolio can achieve diversification? (for this one, i think corr is the indicator of diversification, in this question, Corr=-0.2<0, which means achieve diversification. But the answer gives: "V[R]=26.25, cannot achieve portfolio diversification". please help, thx!

   2. (ii) [1 bonus mark] In order to achieve portfolio diversification, what advice will you give Chloe?

Answer 1

	Stock A	Stock B
X	0.5	0.5
mean	5%	10%
SD	5%	10%
Corr(A,B)	-0.2

(i) [3 marks] If the correlation coefficient of the two stock returns is -0.2, do you think that this investment portfolio can achieve diversification? (for this one, i think corr is the indicator of diversification, in this question, Corr=-0.2<0, which means achieve diversification. But the answer gives: "V[R]=26.25, cannot achieve portfolio diversification". please help, thx!

Var of portfolio = V (XA +XB)

=

=

Where X represents the proportion and Corr (a,b)=

Therefore

V(portfolio) = 28.75%%

SD(portfolio) = 5.36%

If we see this the individual vairance of Stock A is smaller than overall portfolio variance. A good portfolio should have a vairance lower than its individual stocks. Also the correlation is very poorly negative so the relationship between the stocks is negatively weak. Therefore even with negative correlation, the portfolio isn't well diversified.

(ii) [1 bonus mark] In order to achieve portfolio diversification, what advice will you give Chloe?

To get a less riskier portfolio, Chloe should invest more in the less riskier stock A and decrease the investment in Stock B. The return will be not reduced by a lot but the variance will be reduced lower than both the Stocks.

	Stock A	Stock B
X	0.7	0.3
mean	5%	10%
SD	5%	10%
Corr(A,B)	-0.2

Var (portfolio) = 19.15

SD (portfolio) = 4.37%

Exp return = 0.065 = 6.5%

If the portfolio isn't changed then the exp return was 0.075 = 7.5%.

So we can see by increasing investment in less risky gives a good low variance portfolio with a return close to the old one.