Question

EXTRA RISK PROBLEMS Stock A Stock B Expected Return 10% 16% Standard Deviation Correlation coefficient with the Market Correlation coefficient with Stock B Risk free rate 25% Expected return on the Market 12% Standard deviation of the Market 18 1. What is the expected return on a portfolio comprised of $6000 of Stock A and $4000 of Stock B? 2. What is the Standard deviation of this portfolio? 3. Does it make sense to combine these two in this way? Pease explain why. 4. What is the coefficient of variation for Stock A? What is the coefficient of variation for Stock B?

Answer 1

Note: As per answering guidelines, only the first four sub-parts have been answered

Solution- 1

Calculation of expected return of portfolio with $6,000 of Stock A and $4,000 of stock B which makes total portfolio value equal to $10,000.

Expected return of portfolio= [Expected return Stock A *(6000/10000) + Expected return Stock B *(4000/10000)]

Expected return of portfolio= [10%*(6/10) + 16%*(4/10)] = 6% + 6.4% = 12.4%

Solution- 2

Weight of Stock A in portfolio= (6,000/10,000)= 0.6

Weight of Stock B in portfolio= (4,000/10,000)= 0.4

Standard deviation of Stock A [SD(A)]= 6% or 0.06

Standard deviation of Stock B [SD(B)]= 12% or 0.12

Correlation coefficient = -0.4

The standard deviation (SD) of a two asset portfolio (P) is calculated as follows:

SD(P)= {SD(A)² 0.6² + SD(B)² 0.4² + 2*SD(A)*0.6*SD(B)*0.4*(-0.4)}^(1/2)

SD(P)= {0.06² 0.6² + 0.12² 0.4² + 2*0.06*0.6*0.12*0.4*(-0.4)}^(1/2)

SD(P)= {0.06² 0.6² + 0.12² 0.4² + 2*0.06*0.6*0.12*0.4*(-0.4)}^(1/2)

SD(P)= {0.001296+0.002304-0.00138}^(1/2)

SD(P)= (0.0022176)^(1/2)

Standard deviation (portfolio)= 4.71%

Solution- 3

Weighted average of standard deviation of stocks A & B= SD(A)*(6/10) + SD(B)*(4/10)= 6%*0.6+12%*(4/10)= 8.4%

The two stocks have negative coefficient of correlation of -0.4. This means that their combined risk (4.71% as calculated above) is lower than the weighted average of their standard deviations (8.4% calculated above) which means that they hedge each other's risk to an extent. Let's calculate the coefficient of variations for stock A, stock B and the portfolio to find their respective risk-reward scenarios:

Coefficient of variation= Standard deviation / Expected return of an investment

Coefficient of variation (Stock A)= SD(A)/ Expected return= 6%/10%= 0.6

Coefficient of variation (Stock B)= SD(B)/ Expected return= 12%/16%= 0.75

Coefficient of variation (Portfolio)= SD(P)/ Expected return of portfolio= 4.71%/12.4%= 0.38

The above shows that the coefficient of variation of portfolio is lower than that of stock A and stock B which means that it has least volatility per unit of expected return and that the portfolio offers better risk reward trade-off as compared to stock A and stock B. Hence, these stocks should be combined together.

Solution- 4

Coefficient of variation= Standard deviation / Expected return of an investment

Coefficient of variation (Stock A)= SD(A)/ Expected return= 6%/10%= 0.6

Coefficient of variation (Stock B)= SD(B)/ Expected return= 12%/16%= 0.75