Consider the following variance-covariance matrix rm rA rB rC rD rM 0.41 rA 0.43 0.65 rB...

Consider the following variance-covariance matrix

	rm	rA	rB	rC	rD
rM	0.41
rA	0.43	0.65
rB	0.49	0.39	0.84
rC	0.30	0.13	0.30	0.58
rD	0.50	0.43	0.61	0.34	1.48

Average return

	rM	rA	rB	rC	rD	R
average return	0.0585	0.1122	0.0314	0.0525	-0.0563	0.03

a. if you would like to create a risky protfolio X of two stocks - stock A and stock C, how would you allocate your investments? identify the minimum variance portfolio consisting of stocks A and C

b. what is the risk(standard deviation) and return(mean) of your minimum variance portfolio consisting of stock A & C in part (a)? Compute the Sharpe ratio of your minimum variance portfolio.

c. if your complete portfolio Z consists of risky portfolio X and risk-free assets(t-bill) with capital allocation of 20% on T-bills and remaining on risky assets, what is the return and standard deviation of your complete portfolio Z. Compare your answers with answer in part (b)

d. Estimate the systematic risk(beta) of each stock(stock A, B,C and D) required rate of return for each stock.

e. Identify each stock whether it is overpriced or underpriced or correctly priced

f. If you have a risky portfolio Y which consists of all four stocks with eq. what is your portfolio beta. What is the required rate of return on you as postulated by SML.

Expert Solution

Answer to 1st 4 parts

Answer a	Minimum Variance Portfolio X of A & C

	Proportion for Portfolio X			Variance as per chart above
	wA	46%		vA	0.65		Note: Proportions are solved for using Excel - Solver feature under Data Tool
	wC	54%		vC	0.58
		1		Covar(A,C)	0.13

Answer b	Variance of portfolio X		wA^2vA+wC^2vC+2wAwC*CoVar(A,C)=				37.12%
	Return of Portfolio X		wArA+wBrC		8.02%
	S.D of portfolio X = Square Root of Variance					60.93%

Answer c	Portfolio Y
	wX	80%		vX	37.12%		rX	8.02%
	wRf	20%		vRf	0%		rRf	3%


	Variance of Portfolio Y =			wX^2*vX	23.76%	Given Risk Free asset has no variance
	S.D of Portfolio Y = Sqrt (Var Y)=				48.74%
	Return of Portfolio Y=		wXrX + wRfrRf		7.02%


Answer d	Beta for Asset A
	From CAPM Formula
	i.e. Expected Return For A = Risk Free Rate + Asset A's Beta * Market Risk Premium
	rA = R + Beta(A)*(rM - R)
	Beta = (rA-R)/(rM-R)

		r	R	rM-R	Beta
	A	11.220%	3.00%	2.850%	2.88
	B	3.140%	3.00%	2.850%	0.05
	C	5.250%	3.00%	2.850%	0.79
	D	-5.630%	3.00%	2.850%	(3.03)

jeff jeffy answered 1 year ago

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