Corporate Finance
MGRS 365 – Exam IV
Ali Nejadmalayeri
November 5, 2002
NAME:
ID: R 0 0 0 __ __ __ __ __ __ __ __ __
Each question has 12½ points. Please answer all questions and show your work. Good Luck.
Use the following to answer questions 1 – 3:
Over the 1926–1998 period, the major assets perform as following:
Asset
Large-company stocks
Small-company stocks
Long-term government bonds
US Treasury bills
Average Return
13.2%
17.4%
5.7%
3.8%
Standard Deviation
20.3%
33.8%
9.2%
3.2%
1. Assume that the dividend yield for a prototypical small-stock company is 1.4%, and the stock is selling for
$100. After one year, what will be the value of a portfolio consisting of 1000 shares of such a company?
Total Return = Capital Gain (Loss) + Dividend Yield
Capital Gain Small Stocks = 17.4% – 1.4% = 16% = Price End / Price Beg. – 1
Price End = 1.16  100 = 116  Value End = Price End  #Shares = $116,000
2. If all assets’ returns are normally distributed, what range of returns can you NOT state, with 99%
confidence, that next year's large-company stocks return might be equal to?
With 99% change outcomes fall in the range of [avg. – 3  std. , avg. + 3  std.]
So outside this is the range that ( , avg. – 3  std.] AND [avg. + 3  std., + ) or in this case
( , 13.2% – 60.9%] AND [13.2% + 60.9%, + )
= ( , 47.7%] AND [74.1%, + )
3. Assume the small stock returns are normally distributed. With 95% confidence, what is the highest return
you would expect to earn on small stocks?
With 95% change outcomes fall in the range of [avg. – 2  std. , avg. + 2  std.]
So the largest outcome is avg. + 2  std. = 7.4% + 67.6% = 85%
Use the following to answer questions 4 – 5:
State
Boom
Bust
4.
Probability
0.60
0.40
Return on A
25%
–15%
Return on B
15%
5%
What is the expected return on a portfolio with weights of 75% in asset A and 25% in asset B?
State
Boom
Bust
Probability
0.60
0.40
Return on Portfolio
¾  25% + ¼  15% = 22.5%
¾  –15% + ¼  5% = –10%
Expected return = 0.60  22.5% + 0.40  –10% = 9.5%
Corporate Finance
MGRS 365 – Exam IV
Ali Nejadmalayeri
November 5, 2002
NAME:
ID: R 0 0 0 __ __ __ __ __ __ __ __ __
5. What is the standard deviation of returns on a portfolio with weights of 75% in asset A and 25% in asset B?
State
Boom
Bust
Probability
0.60
0.40
( Expected Return on Portfolio – Return on Portfolio)2
( 22.5% – 9.5% ) 2 = 132 = 169
(–10% – 9.5% ) 2 = –19.52 = 380.25
Var. of return = 0.60  169 + 0.40  380.25 = 253.5
Std. Dev. of return = 15.92%
Use the following to answer questions 6 – 8:
Security
A
B
Risk-free asset
Standard Deviation
8%
14%
???
Beta
1.2
?
???
An equally weighted portfolio of stocks A and B has a beta of 1.10. What’s the stock B’s beta?
6.

Return
15%
12%
3%

 portfolio = wA  A + wB  B = ½ 1.2 + ½  B = 1.1
B = 1
7. Assume that stock A is justly-priced. Is stock B also justly-priced? or, under-priced? or, over-priced?
Prove your answer.
Since A is justly priced then: rm – rf = 15% – 3% / 1.2 = 10%
However the reward to risk ratio of B is 12% – 3% / 1 = 9% which is less than 10%, so B is
overpriced, i.e., it does not generate high enough return.
8. What’s the risk-free asset’s beta? What’s the risk-free asset’s standard deviation? Which of A and B has the
least total risk? Which of A and B has the least systematic risk? Justify your answer.

 
f = 0; f = 0; no systematic or idiosyncratic risk!
B >A  B has more total risk, note total risk is measured by variance
B < A  A has more systematic risk, note total risk is measured by beta
For idiosyncratic risk we need to know market total risk,
then the idiosyncratic risk = [2 –   2M] ½