Econ 134A summer 2010, Midterm2A
Dandan Zhu
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This quiz consists of 11 questions and has a total of 6 pages, including the
cover page. Please show your work clearly. You have 80 minutes. Good
Luck!
1
Econ 134A summer 2010, Midterm2A
Dandan Zhu
1. Which of the following statements are correct concerning the variance of the annual
returns on an investment?
I. The larger the variance, the more the actual returns tend to differ from the average
return.
II. The larger the variance, the larger the standard deviation.
III. The larger the variance, the greater the risk of the investment.
IV. The larger the variance, the higher the expected return.
A. I and III only
B. II, III, and IV only
C. I, III, and IV only
D. I, II, and III only
E. I, II, III, and IV
2. One year ago, you purchased a stock at a price of $32 a share. Today, you sold the stock
and realized a total return of 25%. Your capital gain was $6 a share. What was your
dividend yield on this stock?
A. 1.25%
B. 3.75%
C. 6.25%
D. 18.75%
E. 21.25%
3. A stock had returns of 8%, -2%, 4%, and 16% over the past four years. What is the
standard deviation of this stock for the past four years?
A. 6.3%
B. 6.6%
C. 7.1%
D. 7.5%
E. 7.9%
4. What are the arithmetic and geometric average returns for a stock with annual returns of
21%, 8%, -32%, 41%, and 5%?
A. 5.6%; 8.6%
B. 5.6%; 6.3%
C. 8.6%; 5.6%
D. 8.6%; 8.6%
E. 8.6%; 6.3%
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Econ 134A summer 2010, Midterm2A
Dandan Zhu
5. You would like to combine a risky stock with a beta of 1.5 with U.S. Treasury bills in
such a way that the risk level of the portfolio is equivalent to the risk level of the overall
market. What percentage of the portfolio should be invested in Treasury bills?
A. 25%
B. 33%
C. 50%
D. 67%
E. 75%
6. The market has an expected rate of return of 9.8%. The long-term government bond is
expected to yield 4.5% and the U.S. Treasury bill is expected to yield 3.4%. The inflation
rate is 3.1%. What is the market risk premium?
A. 2.2%
B. 3.3%
C. 5.3%
D. 6.4%
E. 6.7%
7. What is the portfolio variance if 30% is invested in stock S and 70% is invested in stock
T?
A. .002220
B. .004056
C. .006224
D. .008080
E. .098000
8.
The beta of a security provides an:
A. estimate of the market risk premium.
B. estimate of the slope of the Capital Market Line.
C. estimate of the slope of the Security Market Line.
D. estimate of the systematic risk of the security.
E. None of the above.
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Econ 134A summer 2010, Midterm2A
Dandan Zhu
9. You have $1 million currently invested entirely in mutual fund A. You are considering
switching into a combination of T-bills and mutual fund B for the next year. Mutual fund
B is invested 50% in stock 1 and 50% in stock 2. A one year T-bill (zero coupon) with
face value $10,000 is currently selling for $9523. You have come up with the following
assessments of the return to mutual fund A along with the returns to stock 1 and 2 for the
next year.
E=
( RA ) 0.1,
=
σ A 0.2;
E=
( R1 ) 0.1,
=
σ 1 0.2;
=
E ( R2 ) 0.18,
=
σ 2 0.3;
Using just the T-bill and mutual fund B show how you
ρ1,2 = 0.5
can construct an investment of your $1 million such that the portfolio is better than your
current investment in mutual fund A. You must show clearly why the new portfolio is
better and indicate the dollar investment in T-bills and mutual fund B. (6 points)
Mutual fund B,
E ( RB ) =
0.5(0.1) + (0.5)(0.18) =
0.14
Var ( RB ) = (0.5) 2 (0.2) 2 + (0.5) 2 (0.3) 2 + 2(0.5)(0.5)(0.5)(0.2)(0.3) = 0.0475
=
σ ( RB )
=
0.0475 0.22
(2 points)
9523
=
From T-bill, we can find risk-free rate,
10, 000
, rf 0.05 (1point), if we can
=
1 + rf
construct a portfolio of T-bills and mutual fund B, that has same expected return as
mutual fund A, but smaller standard deviation, then the portfolio is better investment than
mutual fund A.
Set E ( R
=
wB (0.14) + (1 − wB )(0.05)
= 0.1,=
wB 0.56
p)
Thus σ ( R
=
wB=
σ B (0.56)(0.22)
= 0.12 < σ A
p)
4
(2 points)
(1 point)
Econ 134A summer 2010, Midterm2A
Dandan Zhu
10. You are analyzing two stocks, let’s call them “Stock A” and “Stock B”. Based on current
dividend yields and expected growth rates, the stocks are currently providing a return of
11% and 14% respectively. Also, the standard deviation on the returns of the two stocks
is 10% and 11%.
Your statistical analysis of both stocks revealed the betas to be 0.8 and 1.5 respectively.
In addition to this information, you know that the return on the T-bill is currently 6% and
the expected return of the S&P 500 Index is 12%
(a) What’s your advice on stock A and B, to buy or to sell, why? (3 points)
(b) Stock A is currently selling at $75 and stock B is selling at $60. Given that, at the
current price, the dividend yield for both stocks is 5%, what would you expect the
price of these stocks to be, one year from now, if the expected growth rate of
dividends does not change?(4 points) (part b is a challenging question)
(a) By CAPM, (1 point)
E ( RA ) =R f + β A ( Rm − R f ) =6% + 0.8(12% − 6%) =10.8% < 11%
E ( RB ) =R f + β B ( Rm − R f ) =6% + 1.5(12% − 6%) =15% > 14%
Buy A, sell B. (2 points)
(b) The formula you use to calculate price is p1 =
Div2
, because you are asked the
r−g
expected price of stock, you should use expected rate of return as your discount rate,
which comes from part (a).
Next, you need to find the growth rate of dividends (assuming it doesn’t change). The
total return on stock has two parts, current yield plus capital gain, and capital gain
rate is equal to growth rate of dividends.
Div
Div1
r = 1 + g, g =
r−
p0
p0

current yield
g A = 11% − 5% = 6%
g B = 14% − 5% = 9%
, notice we are using the realized return here. (1 point)
=
Div1 A $75(5%)
= 3.75
=
Div1B $60(5%)
= 3
=
p1 A
, (1 point)
Div1 A (1 + g A ) 3.75(1 + 0.06)
= = $82.81
0.108 − 0.06
E ( RA ) − g A
Div2 A (1 + g B ) 3(1 + 0.09)
=
= = $54.5
p2 A
0.15 − 0.09
E ( RB ) − g B
5
(2 points)
Econ 134A summer 2010, Midterm2A
Dandan Zhu
11. Jack's Construction Co. has 80,000 bonds outstanding that are selling at par value. Bonds
with similar characteristics are yielding 8.5%. The company also has 4 million shares of
common stock outstanding. The stock has a beta of 1.1 and sells for $40 a share. The U.S.
Treasury bill is yielding 4% and the market risk premium is 8%. Jack's tax rate is 35%.
What is Jack's weighted average cost of capital? (5 points)
Re = .04 + (1.1 × .08) = .128 (1 point)
Debt: 80,000 × $1,000 = $80m (1 point)
Common: 4m × $40 = $160m (1 point)
Total = $80m + $160m = $240m
(2 points)
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Econ 134A summer 2010, Midterm2A
7
Dandan Zhu