Question

Consider the following:

You have Stock A and Stock B

Expected Return of A is  25%

Expected Return of B is 35%

Standard Deviation (volatility) of A is 17%

Standard Deviation (volatility) of B is 28%

a) Calculate the expected return and standard deviation of your portfolio if you invest $4,000 in A and $6,000 in B. The correlation between A and B is 0.40.

b) Do you derive any diversification benefits by investing in both A and B? Why or why not? Explain concisely.

c) Are there circumstances, if any, under which you are not likely to obtain any diversification benefits? Explain concisely.

d) Suppose you borrow $2,000 from your bank at a risk-free rate of 6% and invest this amount (of $2,000) along with your $10,000 in Stock B only. Calculate the expected return and the standard deviation of this portfolio.

Show all your work and thorough explanations where necessary.

Answer 1

	Stock A	Stock B
Expected return	25%	35%
Standard deviation()	17%	28%

a.

Amount invested in Stcok A = $4000

Amount invested in Stcok B = $6000

Weight of Stock A (WA)= $4000/$10000 = 0.4

Weight of Stock B (WB)= $6000/$10000 = 0.6

The correlation between A and B = (rAB) =0.40

Expected return on the portfolio =

=> Expected return on portfolio = (25%*0.4) + (35%*0.6) = 31%

Standard deviation of portfolio =

=> Standard deviation of portfolio = = 20.49%

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b.

	Invest only in Stock A	Invest only in Stock B	Invest both in stock A & B
Expected return	25%	35%	31%
Standard deviation()	17%	28%	20.49%
Coefficient of variation(CV) =Standard deviation/Expected vreturn	=17/25 =0.68	=28/35 =0.80	=20.49/31 =0.66

by investing both in stock A & B or by diversification the CV is less. Means lesser risk associated with the return.

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c.

-If the assets are highly or positively correlated or if the Correlation is more , then there will be no diversification benefit bacause the risk or standard deviation will be more in the case of positively or highly correlated assets.

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d.

	Amount invested	Weight	Expected return	Standard deviation
Risk Free(A)	-2000	=-2000/10000 =-0.2	6%	0%
Stock B (B)	12000	1.2	35%	28%
Total	10000	1.00

Expected return on the portfolio =

=> Expected return = (6%*-0.2) + (35%*1.2) = -1.2% + 42% = 40.8%

Standard deviation of portfolio =

As standard deviation of risk free asset is 0% hence

Henec now the SD of the portfolio =

=> Standard deviation = = 28% *1.2 = 33.6%

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