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Test 2 Solution Sketches
Note for multiple-choice questions: choose the closest answer.
Exam date: 29 February 2016
Econ 134A, John Hartman
1. Multiple choice
• The face value of a bond is $5,000. Annual coupons equal to 10% of
the face value will be paid once per year starting one year from today,
and the bond will mature 9 years from today. The bond currently sells
for $4,600. Which of the following must be true about the yield to
maturity?
• The price of a bond and the interest rate have an inverse relationship.
As price of the bond falls, the yield to maturity (effective interest rate)
must be increasing. So the YTM must be strictly greater than 10% (c).
2. Multiple choice
• A zero-coupon bond sells for $500 today and will pay a face value of $700
on the date of maturity 18 months from today. What is the effective annual
rate of return for this bond?
700
(1+𝑟)1.5
700
1.5
+ 𝑟) =
500
• 500 =
• (1
• 1+𝑟 =
•𝑟=
700
500
• (d) 25%
700
500
1
1.5
1
1.5
− 1 = 25.146%
3. CAPM
• Baby Blue Bird Ballet, Inc. has a known distribution, with a rate of return of 6% two-thirds of the
time, and 21% one-third of the time. A risk-free bond always has a 9% rate of return.
• What is the covariance of the rate of return for these two assets?
2
3
1
𝜎𝐵𝐵𝐵𝐵,𝑅𝑓 =
3
1
3
• 𝔼𝑅 = 0.06 + 0.21 = 0.11
•
0.06 + 0.11 0.09 − 0.09 + 0.06 − 0.11 0.09 − 0.09 + (0.21 −
4. CAPM
• Baby Blue Bird Ballet, Inc. has a known distribution, with a rate of return of
6% two-thirds of the time, and 21% one-third of the time. A risk-free bond
always has a 9% rate of return.
• What is the standard deviation of a portfolio with 50% of each asset?
2
• 𝜎𝐵𝐵𝐵𝐵
=
1
3
0.06 − 0.11
2
+ 0.06 − 0.11
2
+ 0.21 − 0.11
2 2
2
2
2
• 𝜎𝑝𝑜𝑟𝑡
= 𝑊𝐵𝐵𝐵𝐵
𝜎𝐵𝐵𝐵𝐵
+ 2𝑊𝐵𝐵𝐵𝐵 𝑊𝑅𝑓 𝜎𝐵𝐵𝐵𝐵,𝑅𝑓 + 𝑊𝑅𝑓
𝜎𝑅𝑓 =
0.5 2 0.005 + 0 + 0.5 2 0 = 0.00125
• 𝜎𝑝𝑜𝑟𝑡 =
2
𝜎𝑝𝑜𝑟𝑡
= 3.5355%
2
= 0.005
5. IRR
• A project has a cash inflow today,
a cash outflow one year from
today, and a cash inflow two years
from today. (Note that a cash
outflow means you have to pay
money and a cash inflow means
you receive money.) Two internal
rates are found, 13% and 40%.
Darryl is trying to determine
whether or not net present values
(NPVs) are positive for 5%, 20%,
and 60% discount rates. For which
of these three discount rates will
the NPV be positive?
• (e) 5% and 60% only
5%
60%
13%
40%
6. Free response
• A stock with a beta value of 3 will pay annual dividends on today’s
date starting one year from today. The first dividend will be $8 one
year from today, and the annual growth rate of the stock will be 20%
per year. The market rate of return is 25% and the risk-free rate of
return is 15%. What is the present value of the stock?
• 𝑑𝑖𝑠𝑐𝑜𝑢𝑛𝑡 𝑟𝑎𝑡𝑒 = 𝑅𝑓 + 𝛽 𝑟𝑖𝑠𝑘 𝑝𝑟𝑒𝑚𝑖𝑢𝑚 = 0.15 + 3(0.25 −
7. Free response CAPM statistics
• There are three known states of
the world, each with one-third
probability of occurring: Good,
Bad, and Ugly. When times are
Good, Stock X has a rate of
return of 40%, and stock Y has a
rate of return of 4%. When
times are Bad, Stock X has a rate
of return of 10% and Stock Y has
a rate of return of 3%. When
times are Ugly, Stock X has a
rate of return of –20% and Stock
Y has a rate of return of 20%.
What is the correlation of Stock
X and Y’s rate of return?
•
𝔼𝑅𝑥 =
1
3
0.4 + 0.1 − 0.2 = 0.1
•
𝔼𝑅𝑦 =
1
3
0.04 + 0.03 + 0.2 = 0.09
•
𝜎𝑥,𝑦 =
1
3
0.4 − 0.1 0.04 − 0.09 + 0.1 − 0.1 0.03 − 0.09 + −0.2 − 0.1 (0.02 −