5. (13 marks) You have information on several possible investments as laid out i

Question

5. (13 marks) You have information on several possible investments as laid out in the table below. A, B, and C are individual risky securities. For now, assume these are the only these 3 risky investments that comprise the market. F is the risk-free asset. M is the market portfolio. All returns are annual returns. Correlation Matrix Investment E(ri 19.20% 36% 1.0000 0.7000 0.6000 0.0000 0.5 21.90% 35% 12.00% 25% 3.00% 0% 12.00% 10% 1.0000 0.5000 0.0000 0.6 1.0000 0.00000.4 1.0000 0.0 1.0 Answer the following questions with respect to this investment information: Using the correlation matrix, compute the covariance of asset A with the market. (1 mark) a. b. Using the correlation matrix, compute the beta of asset C. (1 mark) c. What is the expected excess return of B according to the Capital Asset Pricing Model (CAPM)? Is security B priced correctly, undervalued or overvalued? (2mark) d. Suppose the risk free rate is 5%, how much of security F is included in the market portfolio M? Briefly explain. (1 mark) Suppose the market capitalization of asset B is $10M and the total market capitalization if $1,000M. If you invest $1M in the market portfolio, how many dollars are you investing in asset B? (1 mark) f. You have $100,000 to invest You would like use a combination of M and F to obtain a standard deviation of 4% on your overall portfolio. How much (in dollars) do you invest in F if you choose the most efficient portfolio possible? (1 mark)

Explanation / Answer

5 A :- to calculate Covariance of asset security A with market

Covariancexy = correlation xy * standard deviation X * standard deviation Y

= 0.5 * .36 * .1 = .018 or 1.8%

B:- To calculate Beta of asset C

Beta = Covariance xm / Variance m

Where m refers to market

also while substituting covariance with formula

Covariancexy = correlation xy * standard deviation X * standard deviation Y

we are left with

Beta =( Correlation xm * Standard Deviation X )/ standard deviation M

= (0.4 *0.25 )/ 0.1 = 1

C :-As per Capital Asset Pricing Model

E(R) = Rf + Beta ( Rm - Rf)

First we need to calculate Beta for security B

Beta =(Correlation BM* standard deviation b)/ Standard Deviation m

=(0.6 *0.35 )/ 0.1

2.1

therefore as per CAPM

E(R) = 3% + 2.1( 21.9 -12 )

= 23.79 %

Therefore expected excess return as per CAPM is = 23.79 -21.9 %

=1.89%

since CAPM is greater than Expected Return therefore the security is overvalued

Explanation

Individual cash flows are DISCOUNTED at the rate of return to arrive at the Value of the company.

If RETURN increases - you would have a lower value.

So if Expected Return < CAPM Return -> based on the Expected Return you would have a higher value for a series of Cash flows. This would mean that you would end up with a higher valuation (OVERVALUED) when compared to the CAPM return.

[Very similar in concept to Higher Interest rate - lower value of BOND].

F :- We have 100000($) to invest

and desired risk (S.D.) of portfolio is 4 % therefore since we have 2 securities to invest in i.e. security M and F

S.D. of portfolio = weight of RF *S.D. of RF + Weight of risky asset * S.D. OF M

Since S.D. of risk free asset is zero

4% = weight of M * 10%

Weight of M = 40%

weight of risk free asset = 100% - 40%

= 60 %

Hence amount to be invested in Risk free asset is 60000 ($)

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