Final Exam
Fall 2011
Econ 180-367
Closed Book.
Formula Sheet Provided. Calculators OK.
Time Allowed: 3 hours
1. The price of a stock today is $50. The risk-free interest rate is zero. There are four possible
scenarios
a. The stock price rises to $52 in six months and to $55 in one year
b. The stock price rises to $52 in six months and falls back to $50 in one year
c. The stock price falls to $48 in six months and rises back to $50 in one year
d. The stock price falls to $48 in six months and to $46 in one year
If these are the four possible scenarios, what is the price of a European call option to buy one share for
$52 in one year’s time?
2. Suppose that a stock price is $100. The risk-free interest rate is 0 percent. The volatility
(standard deviation) of the stock is 20 percent. The stock pays no dividend. Consider a European
put option with a strike price of $100 and a maturity of one year. According to the Black Scholes
formula, what is the price of this option?
3. Please rank the following four bonds in order of descending duration:
Bond
Coupon (%)
Years to Maturity
A
15
20
B
0
25
C
0
20
D
8
20
Yield (%)
10
8
10
10
4. The market price of a security is $40. The stock is expected to pay a constant dividend forever.
Its expected rate of return is 13%. The risk- free rate is 7%. What will be the market price of the
security if the CAPM holds and the beta of the stock doubles (while all other variables remain
unchanged)?
5. Toyota stock has the following probability distribution of prices one year from now:
Price
Probability
$50
25%
$60
40%
$70
35%
Toyota will pay a dividend of $4 for sure. Toyota shares are worth $55 each today.
a.
What is the expected return on holding Toyota stock?
b.
What is the standard deviation of the return on Toyota stock?
6. a.
What is the difference between covered interest parity and uncovered interest parity?
b.
If the euro-dollar exchange rate is 1 euro = 1.31 dollars today, the one-year risk-free
interest rate is 0.25 percent in the US and 1.25 percent in Europe, what must the one-year forward
euro-dollar exchange rate be, under covered interest parity?
1 7. You purchased an annual interest coupon bond one year ago with 6 years remaining to maturity at
the time of purchase. The coupon interest rate is 10% and par value is $1,000. At the time you
purchased the bond, the yield to maturity was 8%. If you sold the bond after receiving the first
interest payment and the bond's yield to maturity had changed to 7%, what would your holding
period return on the bond have been?
8. Suppose that the expected asset returns of XYZ shock are consistent with what the APT would
predict for a well-diversified portfolio. Assume that there are 2 risk-factors, Industrial Production
(IP), and Inflation (Inflat). XYZ industries has  IP  2 and  INFLAT  3 . In addition, IP  2%
and INFLAT  1% where  denotes the prices of risk for each of the factors. If the risk-free rate
is 5%, then what is the required rate of return in XYZ industries?
9. Which security should sell at a greater price? Explain briefly in each case.
a. A 6- month European call option with a strike price of $60 or a 6-month European call on
the same stock with a strike price of $55?
b. A 20-year Treasury bond with a 6.5% coupon rate or a 20-year Treasury bond with a
7.5% coupon rate?
c. An American call option on a dividend-paying stock with a strike price of $20 or a
European call option on that same stock at the same strike price and the same maturity?
10. Suppose that the risk free interest rate is 10 percent. Consider the following possible
configurations of prices of European options and current share prices on a non-dividend paying
stock with a maturity of one year hence. Say if they are possible or impossible. For those that are
impossible, please say why.
(a)
Strike Price
Value
Call Option
60
-3
Put Option
60
10
Stock
62
(b)
Strike Price
Value
Call Option
60
33
Put Option
60
10
Stock
32
(c)
Strike Price
Value
Call Option
60
3
Put Option
60
10
Stock
58
(d)
Strike Price
Value
Call Option
60
13
Put Option
60
10
Stock
60
2 Solutions
1. Suppose that the stock price rises for the first six months. At that point, the investor could buy a call
option, which pays off $3 in state (a) and nothing otherwise. The investor could alternatively buy a share
and borrow $50. In scenario (b), the portfolio is worthless; in scenario (a) it is worth $5. The portfolio
costs $2. Hence the call option is worth $1.20. If the stock price falls for the first six months, the call
option is worthless. Now go back to the start. The investor could buy a call option which pays of $1.20 if
stock prices rise and nothing otherwise. Or t.he investor could buy a share and borrow $48. If stock
prices fall, the portfolio is worthless; if they rise it is worth $4. The portfolio costs $2. Hence the call
option is with $0.60.
2. From the Black-Scholes formula, d1  0.1 , d 2  0.1 and the price of the put option is $7.96.
3. B, C, D, A.
4. The dividend of the stock satisfies 40 
D
meaning that the dividend is $5.20. If the covariance
0.13
doubles, then so must the risk premium. So the expected return on the stock must rise to 19%. And that
means that the price must fall to
5.20
or $27.37.
0.19
5. The expected return is
.25 (54/55 - 1) + .40 (64/55 - 1) + .35 (74/55 - 1) = 18.18%.
Similarly the standard deviation is 13.97%.
6. Covered interest parity holds that the forward-spot is an arbitrage relationship that says:
St * (1  Rt )  Ft (1  Rt* )
Uncovered interest parity is not an arbitrage relationship and says that
Et ( St 1 )(1  Rt* )  St (1  Rt )
Under the example given, the forward rate would have to be 1.31*
1.0025
 1.297
1.0125
7. Initially, the price of the bond is $1092.46. After one year, it is $1123.01. The holding period return is
1123.01  100  1092.46
 11.95%
1092.46
8. It is 0.05  (2 * 0.02)  (3 * 0.01)  12%
9. The call option with a strike price of $55.
The bond with a 7.5% coupon rate.
3 The American option.
10 They are all impossible
(a) Violates C  0
(b) Violates C  S0
X
X
60
 58 
 3.45
(as S0 
1  rf
1.1
1  rf
X
 13  54.54  67.54
(d) Violates Put-Call parity. C 
1  rf
(c) Violates C  S0 
P  S0  10  60  70
4