University of Southern California
Marshall School of Business
FBE 441: Investments - Fall 2002
Professor Joe Chen
Homework Assignment #1
Note: This homework assignment is due on Thursday, September 12th at the beginning
of class. Late submissions will not be accepted.
1. Suppose that the initial margin requirement for margin purchases is 60%. We buy on
margin 500 shares of a stock XYZ at $30 (we use full margin). The maintenance
margin is 40%. At what stock price will we get a margin call?
2. You cannot borrow a stock at the time it goes IPO since the lenders haven’t received
the stock, yet. Therefore, bearish investors would not be able to sell the stock short.
What does that imply for the price of an IPO – more likely to be overvalued or
undervalued? Why?
3. Consider the following situation in which you have 3 scenarios and 2 securities.
R1
R2
R3
a)
b)
c)
d)
Scenario 1
Prob = 35%
15%
9%
12%
Scenario 2
Prob = 45%
3%
12%
8%
Scenario 3
Prob = 20%
1%
14%
10%
Determine E[R1], E[R2] and E[R3].
Determine s1, s2 and s3.
Calculate r12, r13 and r23.
Let p be a portfolio with weights w1p=.2, w2p=.4 and w3p=.4, and let q be a
portfolio with weights w1p=.5, w2p=.3 and w3p=.2. Determine E[Rp], E[Rq], sp, sq
and rpq.
4. Stock A’s expected return and standard deviation are E[RA] = 8% and sA= 15%,
while stock B’s expected return and standard deviation are E[RB] = 12% and sB=
21%.
a) Determine the expected return and standard deviation of the return on a portfolio
with weights wA=.35 and wB=.65 for the following alternative values of
correlation between A and B: rAB=0.6 and rAB= -0.4.
b) Assume now that rAB=-1.0 and find the portfolio p of stocks A and B that has no
risk (i.e. such that sp=0). Can you do the same when rAB=1.0? If not, why? If
so, find that portfolio.
c) Finally, assume that rAB=0. Find the standard deviations of portfolios with the
following expected returns: 8%, 9%, 10%, 11%, 12%, 13%, 14% and 15%. Plot
the expected return—standard deviation pairs on a graph (with the standard
deviations on the horizontal axis, and the expected returns on the vertical axis).
5. Consider three stocks, A, B and C. Suppose that both rAB=0 and rBC=0. Does that
imply rAC=0? Show that it is, or find a counter-example.
6. Excel Exercises on BKM pg 90-91. Goto the textbook’s website located under
http://www.mhhe.bkm, and download their spreadsheet to do Exercise A. Long
Margins, and answer question 1 through 6. (You don’t need to do Exercise B.)