Question #1:
You work as an analyst for your firm. You are assigned the stock 3M Co. (MMM) to analyze. You have estimated the following probabilities of next year's state of the economy. You have also estimated the price and dividend per share for the stock given the future potential state (see table). The current price is $167.41.
|
State of Economy
|
Probability of State
|
Stock Price
|
Dividend
|
|
Boom
|
0.07
|
$ 208.94
|
$ 2.45
|
|
Good
|
0.22
|
$ 196.51
|
$ 1.90
|
|
Normal
|
0.40
|
$ 184.16
|
$ 1.35
|
|
Recession
|
0.18
|
$ 148.84
|
$ 0.80
|
|
Credit Crisis
|
0.13
|
$ 118.83
|
$ 0.25
|
Given this information, what is the expected holding-period return of MMM?
What is the standard deviation of the expected return forMMM?
If the expected return of the risk-free asset is 1.75%, what is the expected return and standard deviation of a portfolio comprised 80% invested in 3M and 20% in the risk-free asset.
Construct a 95% Confidence Interval for 3M.
Question #2:
Consider the last ten years annual returns for MUC fund., in the table.
|
MUC
|
Year
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
|
10
|
|
Return
|
|
11.123%
|
38.492%
|
19.134%
|
12.663%
|
16.721%
|
-7.437%
|
-18.380%
|
7.245%
|
-28.860%
|
21.184%
|
Given this information, what is the geometric average return for the last ten years?
What is the 5% VaR for this fund?
If the ten year treasury over the same period returned 3%, what is the revealed preference for you the investor and are you risk seeking, risk adverse, or approximately risk neutral?
Question #3:
Consider the last ten years annual returns for SOF fund., in the table.
|
SOF
|
Year
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
|
10
|
|
Return
|
|
26.40%
|
5.21%
|
43.73%
|
14.47%
|
11.40%
|
17.71%
|
6.68%
|
-5.03%
|
-0.07%
|
-2.69%
|
The return for the ten-year treasury over the same time was 3.15%. Average annual inflation over the period was 1.85%.
Given this information what was SOF fund's Sharpe Ratio?
What was the annual average real return of the fund?
If the market had an average return of 10.25% and a standard deviation of 11%, did this fund perform better or worse than the market over the period considered on average?
Question#4
You are a professional money manager for the State of Wisconsin. Suppose you note that the average return of the Wilshire 5000 (a very broad stock index) over the past ten years is 10.7%. For the same period, the annual standard deviation of returns was 22.13%. Given this information, what was the market price of risk (average investor risk aversion)?
For the upcoming year, either you can invest in a passive market index (the market) or one of two actively managed funds, CONV and CRCR. The current one-year T-bill rate is .47%. Your expected return for the market is 9.85% the standard deviation of the market is 22.13%. Your expected return for CONV is 7.31% and its σ is 16.44%. Your expected return for CRCR is 21.92% with a σ of 48.87%. Of these three risky assets, which should you choose and why?
For the upcoming year you are bearish, your personal risk aversion (A) is three. Given this fact, should be your allocation to the risky asset you just selected? What is the expected return of this new portfolio composed of the one-year T-bill and risky asset?
Question #5
According to your professor, how many assets at minimum should you hold before the benefits of diversification begin to diminish significantly?
Consider the following:
|
State of Economy
|
Probability of State
|
Asset G
|
Asset D
|
Asset E
|
|
Boom
|
0.19
|
32.379
|
31.905
|
28.521
|
|
Good
|
0.22
|
20.921
|
-6.919
|
17.824
|
|
Normal
|
0.31
|
2.153
|
-8.840
|
4.360
|
|
Recession
|
0.24
|
-11.719
|
-11.552
|
-11.014
|
|
Credit Crisis
|
0.04
|
-30.153
|
-17.023
|
-29.560
|
With this information, calculate the standard deviation of each of the assets as well as the portfolio. Is what you observe between the standard deviation of returns for the asset and the whole portfolio what you would expect?
Question #6
Consider the following information regarding two assets.
|
Asset L
|
Asset Q
|
|
Expected return
|
7.51%
|
21.89%
|
|
Initial Weight
|
60.00%
|
40.00%
|
|
σ
|
15.79%
|
38.61%
|
|
ρ
|
0.28
|
|
Given the initial weighting what is the expected return from this portfolio?
Given this initial weighting what is the standard deviation of the portfolio?
What would be the weights of the minimum variance portfolio?
What is the expected return of the minimum variance portfolio?