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 5 months ago

Consider two stocks with returns RA and RB with the following properties. RA takes values -10...

Consider two stocks with returns RA and RB with the following properties. RA takes values -10 and +20 with probabilities 1/2. RB takes value -20 with probability 1/3 and +50 with probability 2/3. Corr(RA,RB) = r (some number between -1 and 1). Answer the following questions (a) Express Cov(RA,RB) as a function of r (b) Calculate the expected return of a portfolio that contains share α of stock A and share 1−α of stock B. Your answer should be a...

Consider 3 stocks: A with E(RA)= 15% and SD(RA)=20%, B with E(RB) =14% and SD(RB)=24% and...

Consider 3 stocks: A with E(RA)= 15% and SD(RA)=20%, B with E(RB) =14% and SD(RB)=24% and C with E(RC)=18% and SD(RC)=30%. The risk free rate RF= 6%, 1. which stock would you combine with the risk free to form a portfolio? 2. write the equation of Capital market line 3. If you consider that your target risk is 15%, what would be the composition of your final portfolio?

Consider a portfolio with three assets E[rA]=10% E[rB]=12% E[rC]=8%; σA2 =0.008 σB2 =0.010 σC2 =0.005; ρA,B...

Consider a portfolio with three assets E[rA]=10% E[rB]=12% E[rC]=8%; σA2 =0.008 σB2 =0.010 σC2 =0.005; ρA,B =0.2 ρB,C = 0.0 ρA,C = −0.2 a) Consider the portfolio weights xA = 0.3 and xB = 0.3. Calculate the portfolio weight xC , the expected portfolio return, and the variance of the portfolio returns. b) Consider the portfolio weights xA = 0.3. Calculate the expected portfolio return as a function of xB c) Consider the portfolio weights xA = 0.3. Calculate the...

2. Two stocks A and B have expected returns, and a variance-covariance matrix of returns given...

2. Two stocks A and B have expected returns, and a variance-covariance matrix of returns given in Table 1. Table 1 Stock A Stock B E(R) 0.14 0.08 Variance-covariance matrix: Stock A Stock B Stock A 0.04 0.012 Stock B 0.012 0.0225 a) What is the correlation coefficient between the returns on stock A and stock B? b) What is the expected return and standard deviation of portfolio S which is invested 80% in stock A and 20% in stock...

The market and stock A have the following probability distributions: Probability Rm Ra .3...

The market and stock A have the following probability distributions: Probability Rm Ra .3 15% 20% .4 9% 5% .3 18% 12% Q1. Calculate the expected rates of return for the market and stock A. Q2. Calculate the standard deviation for the market and stock A. Q3. Calculate the coefficient of variation for the market and stock a.

Stock A Stock B Mean 8.22% 9.14% Variance 2.26% 11.64% Standard Deviation 15.03% 34.12% Cov(rA,rB) 1.34%...

Stock A Stock B Mean 8.22% 9.14% Variance 2.26% 11.64% Standard Deviation 15.03% 34.12% Cov(rA,rB) 1.34% Use the statistics from the above table to calculate portfolio returns, portfolio variance, and portfolio standard deviation for each investment allocation from Cell A9 to A19 Percentage in Stock A Portfolio Return Portfolio Variance Portfolio Standard Deviation 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

Consider two well-diversified portfolios, A and C, rf = 4%, E(rA) = 10%, E(rC) = 6%,...

Consider two well-diversified portfolios, A and C, rf = 4%, E(rA) = 10%, E(rC) = 6%, bA = 1, bC = ½ If the maximum amount you can borrow is $1,000,000, what is your arbitrage strategy and profit? A. Long 1 A , short 0.5 C , short 0.5 rf, profit=$5,000 B. Long 1C , short 0.5 A, short 0.5 rf, profit=$5,000 C. Long 0.5 C, Long 0.5 rf, short 1 A, profit=$10,000 D. Long 0.5...

q1) Write all the steps used in finding the variance-covariance matrix directly from returns. Which steps...

q1) Write all the steps used in finding the variance-covariance matrix directly from returns. Which steps can be skipped in Excel? Write the steps in plain English q2) What are the diagonal entries of a variance-covariance matrix? If you have two assets with correlation of 0.65 and variances of 0.03 and 0.04, what would be the entries in the variance-covariance matrix (write in terms of (1,1), (1,2), (2,1), (2,2) where the first value refers to row number and the second...

1.) Two securities have the following characteristics: E(Ra)= 0.06 0.04 E(Rb)= 0.08 0.10 A) Fill in...

1.) Two securities have the following characteristics: E(Ra)= 0.06 0.04 E(Rb)= 0.08 0.10 A) Fill in the missing cells in the table. For each of two correlation cases, corr. = -1 and corr. = 0, calculate the attainable portfolios' mean and standard deviation from combining the two assets together using weights in increments of 25% from 1 to 0. Also, calculate the minimum risk portfolio's weights, mean and standard deviation for each correlation case. Assume that the risk free rate...

Answer questions 10-14 following this information. Mean -variance investor risk aversion (RA) level is 2. The...

Answer questions 10-14 following this information. Mean -variance investor risk aversion (RA) level is 2. The expected return and standard deviation of three assets classes are as bellow, Assets Class Expected Return Standard deviation of return A 10% 25% B 8% 15% C 6% 12% risk- free rate of return is 3% and the short fall level is 5% select the investors. (12) Risk adjusted rate of return (Expected utility) is, A. 7.98%, 5.97% and 9.94% B. 5.97%, 9.94% and...

Question