Unformatted text preview: Part 3 Risk 12.9 Assume that the following market model adequately describes the return—generating behaviour of risky assets:
Riv : 0‘: + BiRMI + 8a ‘ Here: R), = The return for the 1th asset at time t. RM, = The return on a portfolio containing
R M, and 8;, are statistically independent.
positions) is allowed in the market. You all risky assets in some proportion at Short selling (i.e., negative
information: Asset et is 0.0121 and there are no transaction costs. '.
deviation of returns for each asset. L of return of three portfolios containing The variance of the mark
(1. Calculate the standard [0. Calculate the variance asset types A, B, or C, respectively.
c. Assume the risk—free rate is 3.3 percent and the expected return on the market is ‘
t) I 10.6 percent. Which asset will not be held by rational investors. d. What equilibrium state wi rtunities exist? ll emerge such that no arbitrage oppo
12.10. Assume that the returns of individual securities are generated by the following two '
factor model: an inﬁnite number‘m' Rn = E(Rir) + BUF11+ Bi’lFZy Here:
urity i at time t. RE, is the return for sec
ith zero expectatio F 1, and F 2, are market factors w n and zero covariance. ities. and the capital . '
action costs and short In addition, assume that there is a capital market for four secur
four securities follow for these four assets is perfect in the sense that there are no trans
ted. The characteristics of the (i.e.. negative positions) are permit
32 HR) Security Bl l.0 1.5 20% 0.5 2.0 20
1.0 0.5 10
l. .5 0.75 10 1 2
3
4 securities 1 and 2, with a return :21}. y way. (Hint: Such a portfolio wfj
ted return and B2 coefﬁcient for this portfolio. b. Following the procedure in (a), construct a portfolio containing securities 3 an
a return that does not depend on the market factor F .. Compute the expected an; and B2 coefficient for this portfolio.
equal to 5 percent, 131 = 0, and B; = 0 c. There is a riskfree asset with expected return
h detail that an investor could imple Describe a possible arbitrage opportunity in suc
d. What effect would the existence of these kinds of arbitrage opportunities have on capital markets for these securities in the short and long run? Graph your analysr
I hing (long or short) a. Construct a portfolio contai
ctor, F U, in an does not depend on the market fa
have [51 = 0.) Compute the expec ...
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 Winter '09
 MARYHARDY

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