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Unformatted text preview: 7M 3% ACTSC 372 — Corporate Finance 2
Assignment #2 — Solutions Question 1: (a) What would be the variance of the returns on the asset X assuming the correlation
between the returns on the factors is zero? Solution: Var(RX) = 1.52Var(F1) + 0.52Var(Fz) = 0.025 (b) If the correlation between the factors is greater than 0, would the asset be more or less
risky than you found in (a)? Explain. Solution:
Since we have
Var(RX) = 1.52Var(F1) + 0.52Var(F2) — 2(0.5)(1.5)po(F1)o(F2) It follows that risk is a decreasing function of correlation. Thus if correlation is greater than 0,
risk is reduced. (0) What correlation between the factors would minimize the risk of the asset? Find the
standard deviation of returns in this case. Solution: By (b), risk is minimized when correlation is maximized, i.e. at 1. Thus the minimum risk is
Var(RX) = 1.52Var(F1) + 0.52Var(F2) — 2(0.5)(1.5)o(F1)o(F2) = 0.01 Thus 0(RX) = 10%. Question 2: Assume the market model is valid. That is, assume the returns on a given security are given by _ _”_
RX = RX + 3X(RM — RM) + EX Assume the nonmarket risks of all securities are all independent of each other and the market
risk. Assume further that 0(RM) = 0(EX) = 20% t for all securities X. (a) What is the standard deviation of the returns on a portfolio 100% weighted in one
security X , as a function of ﬁx? Solution: We have, Var(RX) = ,BZVar(RM) + Var(eX) = (20%)2(ﬁ2 + 1). (Since all the other terms are constants). Thus
(7(RX) = 20%432 + 1. (b) Now assume that the beta for all securities in the market is equal to 1. Consider a portfolio consisting of N equally weighted assets of type X. How big does N have to be in
order that the portfolio has only 75% of the risk that of the portfolio consisting of 100% weighting in a single asset? Solution: Since the betas of all the securities is 1, and since the beta of the portfolio is the weighted
average of the betas of the assets, it follows that the beta of the portfolio is 1. Thus we have _ __ 1
RP=RP+(RM—RM)+N(61+"+6N)
Since all the risks are independent, we have
1 2 1
Var(Rp) = Var(RM) + N—Z(Var(el)+ ..+Var(eN)) = (20%) (1 + N) Thus 0(Rp) = 20%Jﬁ + 1 / N ). Now from (a) the risk on a portfolio of one security is given by
.O'(RX) = 20%x/2. So, the portfolio has 75% of the risk when [(1 + 5 = 75%x/2 Thus N = 8. Question 3: ABC Inc is deciding on the size of the bonus it should give its CEO. Assume the
following data is available. The beta of ABC is 1.1 The market risk premium is 7% and the risk free rate is 4%
ABC debt has a YTM of 5% and a debttoequity ratio of 2
ABC made EBIT of $125 million ABC has 10 million shares outstanding trading at $50 per share.
Corporate taxes are 25%. Calculate the EVA. Does the CEO deserve a bonus? Solution: Note that r5 = 4% + 1.1 (7%) = 11.7%. Thus
1 2 1 2
Twacc = g7} +§rD(1 _ T) = §117% + §5%(1 — 25%) = 6.4%
Thus EVA = EBIT(1 — T) — rwaCCAssets = $125(1 — 25%) — 6.4%($1.5 billion) = —2.25 m Thus the CEO does not deserve a bonus. Question 4: Deﬁne each of the following trading strategies (if you have never heard of them, try
Google). Suppose these strategies generate abnormal returns. Which form(s) (if any) of the
EMH does each strategy violate? (a) momentum investing.
Solution:
Momentum investing (also called herd investing) is essentially following the crowd. It consists
of buying stocks that are moving up and selling stocks that are moving down. If this works, then it violates weak form of the EMH. (b) value investing
Solution: Value investing consists of buying “undervalued” stocks, usually measured by low market to
book value ratios or other such measures. If this works, it violates semi—strong EMH. (c) insider trading.
Insider trading consists of using private information to trade in securities before the information
is released to the public. If this works, it would violate strong form EMH. ...
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 Winter '09
 MARYHARDY

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