Assignment 3 FIN 310 Prof. Hanh Le Due: Friday April 8 Read the following instructions carefully.

Assignment 3
FIN 310
Prof. Hanh Le
Due: Friday April 8
Read the following instructions carefully. Failure to follow these instructions
will result in points being subtracted from your grade:
(i) Write your answers in a separate clean sheet. Do not write on this document.
(ii) If you work in a group, hand in only one submission (not separate submissions as we
have done so far).
(iii) Write the names of all group members on your submission.
(iv) Staple all answer sheets together.
ASSIGNMENT STARTS HERE. ANSWER THE THREE QUESTIONS
BELOW
1. Here are some characteristics of two securities:
2
Security 1 E(R1 ) = .10 σ1 = .0025
2
Security 2 E(R2 ) = .16 σ2 = .0064
Answer the following questions:
(a) Suppose the investor can only hold a single stock.
(i) Which security should she choose if she wants to maximize expected returns
only?
(ii) Which security should she choose if she wants to minimize risk only?
(b) Suppose the correlation of returns is -1.0, what fraction of the investor’s net
worth should be held in security 1 and in security 2 in order to produce a zero
risk portfolio?
(c) What is the expected return on the portfolio in (c)? How does this compare
with the riskless return on Treasury Bills of 10%? Would an investor who is risk
averse and likes high expected return want to invest in Treasury Bills?
2. Given the following information, Rf = .06, E(RM ) = .12, σM = .15,where E(RM ) is
expected market return and σM is volatility of market return, answer the following
questions.
(a) What is the equilibrium expected return on a risky asset with a β of 1.2? With
a β of .6?
(b) What is the β of a security with an equilibrium expected return of .03?
(c) Is it possible in equilibrium for the expected return on a risky security to be less
than the risk-free rate? Explain. (Hint: look at part (b))

3. Consider the following two equations:
E(Ri ) = Rf + (E(RM ) − Rf )βi
E(RM ) − Rf
σp
E(Rp ) = Rf +
σM

(1)
(2)

You also have the following information: the expected return on the market
E(RM ) = .15, the risk free rate Rf = .06, and the standard deviation of the market
σM = .15. Answer the following questions, assuming that the capital asset pricing
model is correct:
(a) Which equation would you use to determine the expected return on an
individual security with a standard deviation equal to σ = .5 and a β = 2?
Given the parameters above, what is the expected return on that security?
(b) Which equation would you use to determine the expected return on an efficient
portfolio with a standard deviation equal to σM ? What is the expected return
on this portfolio? What is the β of this portfolio?
(c) What is the expected return on an efficient portfolio with a standard deviation
equal to twice the standard deviation of the market? What is the β of this
portfolio?
(d) Given your answers above, describe what type of risky assets equation (1) can
be used for. What kind of risky assets can equation (2) be used for?