Question

a. If Mary invests half her money in each of the two common​stocks, what is the​ portfolio's expected rate of return and standard deviation in portfolio​ return?

b. Answer part a where the correlation between the two common stock investments is equal to zero.

c. Answer part a where the correlation between the two common stock investments is equal to plus+1.

d. Answer part a where the correlation between the two common stock investments is equal to minus−1.

e. Using your responses to questions along dash—d​, describe the relationship between the correlation and the risk and return of the portfolio.

(Computing the standard deviation for a portfolio of two risky investments) Mary Guilott recently graduated from Nichols State University and is anxious to begin investing her meager savings as a way of applying what she has learned in business school. Specifically, she is evaluating an investment in a portfolio comprised of two firms' common stock. She has collected the following information about the common stock of Firm A and Firm B: . a. If Mary invests half her money in each of the two common stocks, what is the portfolio's expected rate of return and standard deviation in portfolio return? b. Answer part a where the correlation between the two common stock investments is equal to zero. c. Answer part a where the correlation between the two common stock investments is equal to +1. d. Answer part a where the correlation between the two common stock investments is equal to - 1. e. Using your responses to questions a—d, describe the relationship between the correlation and the risk and return of the portfolio. a. If Mary decides to invest 50% of her money in Firm A's common stock and 50% in Firm B's common stock and the correlation between the two stocks is 0.50, then the expected rate of return in the portfolio is %. A Data Table - X Expected Return 0.15 0.18 0.50 Standard Deviation 0.18 0.25 Firm A's common stock Firm B's common stock Correlation coefficient Enter your answer in the answer box and the

Answer 1

a]	Expected return = 0.15*50%+0.18*50% =	16.50%
	Standard deviation of the portfolio:
	=[w1^2*sd1^2+w2^2*sd2^2+2*w1*w2*sd1*sd2*Cor-r1,r2]^0.5
	where
	w1, w2 are weights of the two securities & sd1, sd2 their
	standard deviation.
	Substituting values, the standard deviation
	of the portfolio is:
	= (0.50^2*18^2+0.50^2*25^2+2*0.5*0.5*18*25*0.5)^0.5 =	18.70%
b]	= (0.50^2*18^2+0.50^2*25^2+2*0.5*0.5*18*25*0)^0.5 =	15.40%
c]	= (0.50^2*18^2+0.50^2*25^2+2*0.5*0.5*18*25*1)^0.5 =	21.50%
d]	= (0.50^2*18^2+0.50^2*25^2+2*0.5*0.5*18*25*-1)^0.5 =	3.50%
e]	When two assets are combined the standard deviation [risk] of the portfolio
	depends on the correlation coefficient between the two assets.
	Thus, it is the cor coeff that determines whether there would be any
	reduction in risk due to diversification.
	When the cor coeff is 1, there is no reduction in risk as the SD of the portfolio
	is the weighted average of the SD of the individual assets.
	When the cor coeff is -1, there is maximum reduction in risk as the SD of the portfolio
	becomes 3.50%
	When the cor coeff is 0 or 0.5, there is reduction in SD of the portfolio.
	Hence, it can be said that maximum reduction in portfolio SD [benefit of diversification]
	occurs when the corr coeff is -1 and as it moves towards +1, the SD of the portfolio
	increases and reaches a maximum when cor coeff is +1.
	To conclude diversification will be effective only if the cor coeff is less than 1 and
	the reduction in risk increases as the cc moves towards -1.