An investor is considering a portfolio consisting of investment in three securit

Question

An investor is considering a portfolio consisting of investment in three securities 1, 2, and 3.
The means and standard deviations of expected returns for the three individual securities
are:
Security Expected Return Std. Dev.
1 2.0% 2.5%
2 4.0% 6.0%
3 3.0% 4.0%
Table 4: Mean and Standard Deviation of Returns
The investor is only interested in portfolios that are long the three securities (no short selling).
He asks you as his investment advisor to construct a portfolio of the three securities that
has the highest expected return possible but with a standard deviation of return of no more
than 4.2%. You run a standard portfolio optimization model and determine that the highest
return portfolio with a standard deviation of no more than 4.2% has an expected return of
3.6%. After considering your recommendation, he tells you that he is very risk averse and
would be willing to accept a return of 2.0% for a portfolio with a standard deviation of 1.8%
or less.
The plot in Figure 1 shows the expected return plotted against the standard deviation for
five points described below:

Point Description
A Portfolio consisting entirely of security 1
B Portfolio consisting entirely of security 2
C Portfolio consisting entirely of security 3
D Portfolio with maximum return given a standard deviation of 4.2% or less.
E Investor’s desired risk/return point
Table 5: Portfolio Descriptions

Please answer the following questions about these points. Answer each question either T
(True), F (False) or CT (Cannot Tell given the information given).
a) Point A is on the efficient frontier (T/F/CT)
b) Point B is on the efficient frontier (T/F/CT)
c) Point D is on the efficient frontier (T/F/CT)
d) Point E is achievable; that is, there is some portfolio consisting only of the three securities
with the same mean and standard deviation of return (T/F/CT)

Explanation / Answer

Definition of efficient frontier: The efficient frontier is the set of optimal portfolios that offers the highest expected return for a defined level of risk or the lowest risk for a given level of expected return

a) Point A is on the efficient frontier

Ans - True, offers highest return for lowest risk

b) Point B is on the efficient frontier

Ans – False, does not offer highest return for given level of risk

c) Point D is on the efficient frontier

Ans – True, offers highest return for a given level of risk

d) Point E is achievable; that is, there is some portfolio consisting only of the three securities
with the same mean and standard deviation of return

Ans – False, Point E is not achievable, since lowest risk is 2%

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