Question

You are hired to make investment decisions for a large pension fund. You meet with representatives from the company to figure out what kind of choices to make. To get things started you try to figure out their risk preferences. You discuss the concept of risk and return with them to figure out what their level of risk aversion is. You ask them if they would rather invest in the portfolio that offers an expected rate of return of 10% and a standard deviation of 15% or in the short term money market which offers a risk-free 5% rate of return. They say that they prefer the risky portfolio.

STEP BY STEP SHOW:

A) What is the maximum level of risk aversion for which the risky portfolio is still preferred to the risk-free investment? What can you now say about the company’s employee’s risk preferences? Hint: the easiest way to think about this is to find the level of risk aversion A for which an investor is indifferent between two investments

Now, you ask them: if a risky portfolio had an 18% standard deviation, at what rate of return would they prefer it to a risk-free investment that offers 5%? They say the expected return would need to be at least 10%. They say that at that rate they would be exactly indifferent between the two investments

B) What can you determine about their risk preferences? You decide to invest in the risky portfolio because your analysis suggests that the expected return is equal to 11%. Now news comes to the market that makes you revise your estimate of the portfolio’s standard deviation to 2-%.

You can not reach the representative by phone

C) Should you change the pension fund investments to a risk-free investment which still offers 5%?

Answer #1

A pension fund manager is considering three mutual funds. The
first is a stock fund, the second is a long-term government and
corporate bond fund, and the third is a T-bill money market fund
that yields a sure rate of 5.5%. The probability distributions of
the risky funds are:
Expected Return
Standard Deviation
Stock fund (S)
15
%
32
%
Bond fund (B)
9
%
23
%
The correlation between the fund
returns is 0.15.
a.
What...

A pension fund manager is considering three mutual funds. The
first is a stock fund, the second is a long term government and
corporate bond fund, and the third is a T-Bill money market fund
that yields a sure rate of 4.8%. The probability distributions of
the risky funds are:
expected return standard deviation
Stock Fund ( S )---------18%-------------38%
Bond Fund ( B )----------9----------------32
the correlation between the fund returns is .13
Standard deviation of optimal risky portfolio is 30.92%....

A pension fund manager is considering three mutual funds. The
first is a stock fund, the second is a long-term government and
corporate bond fund, and the third is a T-bill money market fund
that yields a sure rate of 5.5%. The probability distributions of
the risky funds are:
Expected Return
Standard Deviation
Stock fund (S)
15%
32%
Bond fund (B)
9
23
The correlation between the fund returns is 0.15.
What is the Sharpe ratio for the minimum variance...

You estimate that a passive portfolio, for example, one invested
in a risky portfolio that mimics the S&P 500 stock index,
offers an expected rate of return of 13% with a standard deviation
of 24%. You manage an active portfolio with expected return 18% and
standard deviation 29%. The risk-free rate is 5%. Your client's
degree of risk aversion is A = 2.5.
a. If he chose to invest in the passive portfolio,
what proportion, y, would he select? (Do...

A pension fund manager is considering three mutual funds. The
first is a stock fund, the second is a long-term government and
corporate bond fund, and the third is a T-bill money market fund
that yields a sure rate of 5.5%. The probability distributions of
the risky funds are:
Expected Return
Standard Deviation
Stock fund (S)
15 %
32%
Bond fund (B)
9 %
23%
The correlation between the fund returns is 0.15.
1. What would be the investment proportions...

A pension fund manager is considering three mutual funds. The
first is a stock fund, the second is a long-term government and
corporate bond fund, and the third is a T-bill money market fund
that yields a rate of 8%. The probability distribution of the risky
funds is as follows:
Expected Return
Standard Deviation
Stock fund (S)
18
%
35
%
Bond fund (B)
15
20
The correlation between the fund returns is 0.12.
What are the investment proportions in...

You manage a risky mutual fund with expected rate of return of
18% and standard deviation of 28%. The T-bill rate is 8%.
Your client chooses to invest 70% of a portfolio in your fund
and 30% in a T-bill. What is the expected value and standard
deviation of the rate of return on his portfolio?
Suppose that your risky mutual fund includes the following
investments in the given proportions. What are the investment
proportions of your client’s overall portfolio,...

A pension fund manager is considering 3 mutual funds. The 1st is
a stock fund, the 2nd is a long-term government and corporate bond
fund, and the 3rd is a T-bill money market fund that yields a rate
of 8%. The probability distribution of the risky funds is as
follows:
Expected Return
Standard Deviation
Stock Fund (S)
18%
35%
Bond Fund (B)
15
20
The correlation between the fund returns is 0.12.
What are the investment proportions in the minimum-variance...

Suppose you manage a risky fund (call it P) with an expected
return of 18% and a standard deviation of 25%. The risky fund is
comprised of three stocks in the following investment proportions:
A = 20%; B = 30%; C = 50%. The risk-free rate is 2%.
Given the data above, the equation of the CAL is E(rC) = rF + σC
(E(rP) - rF/σP) = E(rC) = 2 + σC ((18-2)/25) = E(rC) = 2 +
.64σC
A...

A pension fund manager is considering three mutual
funds. The first is a stock fund, the second is a long-term
government and corporate bond fund, and the third is a T-bill money
market fund that yields a rate of 8%. The probability distribution
of the risky funds is as follows:
FUND
EXPECTED
RETURN
STANDARD DEVIATION
Stock
(S)
20%
30%
Bond
(B)
12%
15%
NOTE: The correlation between the fund returns is
.10.
What are the investment proportions in the minimum-variance...

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