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CHAPTER 5: INTRODUCTION TO RISK, RETURN, AND
THE HISTORICAL RECORD
CHAPTER 5: INTRODUCTION TO RISK, RETURN, AND
THE HISTORICAL RECORD
PROBLEM SETS
1. The Fisher equation predicts that the nominal rate will equal the equilibrium
real rate plus the expected inflation rate. Hence, if the inflation rate increases
from 3% to 5% while there is no change in the real rate, then the nominal rate
2. If we assume that the distribution of returns remains reasonably stable over
the entire history, then a longer sample period (i.e., a larger sample) increases
the precision of the estimate of the expected rate of return; this is a
3. The true statements are (c) and (e). The explanations follow.
Statement (c): Let
= the annual standard deviation of the risky
investments and
1
= the standard deviation of the first investment alternative
over the two-year period. Then:
2
1
Therefore, the annualized standard deviation for the first investment
alternative is equal to:
2
2
1
5-1
4. For the money market fund, your holding-period return for the next year
depends on the level of 30-day interest rates each month when the fund rolls
over maturing securities. The one-year savings deposit offers a 7.5% holding
period return for the year. If you forecast that the rate on money market
5. a. If businesses reduce their capital spending, then they are likely to
b. Increased household saving will shift the supply of funds curve to the
right and cause real interest rates to fall.
c. Open market purchases of U.S. Treasury securities by the Federal
Reserve Board are equivalent to an increase in the supply of funds (a
5-2
CHAPTER 5: INTRODUCTION TO RISK, RETURN, AND
THE HISTORICAL RECORD
6. a. The “Inflation-Plus” CD is the safer investment because it guarantees the
b. The expected return depends on the expected rate of inflation over the next
c. If you expect the rate of inflation to be 3% over the next year, then the
conventional CD offers you an expected real rate of return of 2%, which is
d. No. We cannot assume that the entire difference between the risk-free
nominal rate (on conventional CDs) of 5% and the real risk-free rate (on
The mean is unchanged, but the standard deviation has increased, as the
probabilities of the high and low returns have increased.
8. Probability distribution of price and one-year holding period return for a
30-year U.S. Treasury bond (which will have 29 years to maturity at
year-end):
Economy Probability YTM Price
Capital
Gain
Coupon
Interest HPR
5-3
CHAPTER 5: INTRODUCTION TO RISK, RETURN, AND
THE HISTORICAL RECORD
10. (a) With probability 0.9544, the value of a normally distributed
12.
(01/1928-06/1970)
Small Big
Low 2 High Low 2 High
(07/1970-12/2012)
Small Big
Low 2 High Low 2 High
Average 0.91% 1.33% 1.46% 0.93% 1.02% 1.13%
5-4
CHAPTER 5: INTRODUCTION TO RISK, RETURN, AND
THE HISTORICAL RECORD
13. a
nominal nominal
real
10.80 0.70
1 0.0588, 5.88%
1 1 1.70
r r i
r or
i i
+ - -
= - = = =
+ +
b.
nominal
.80 .70 .10
real
r i r- = - = »
Clearly, the approximation gives a real HPR that is too high.
14. From Table 5.2, the average real rate on T-bills has been 0.56%.
b. Expected return on Big/Value:
c. The risk premium on stocks remains unchanged. A premium, the
difference between two rates, is a real value, unaffected by inflation.
15. Real interest rates are expected to rise. The investment activity will shift
16. a. Probability distribution of the HPR on the stock market and put:
STOCK PUT
State of the
Economy Probability
Ending Price
+ Dividend HPR Ending Value HPR
Excellent
0.25
$ 131.00
31.00%
$ 0.00
100%
Good 0.45 114.00 14.00 $ 0.00
100
Poor 0.25 93.25 −6.75 $ 20.25 68.75
Crash 0.05 48.00
52.00
$ 64.00 433.33
Remember that the cost of the index fund is $100 per share, and the cost
of the put option is $12.
b. The cost of one share of the index fund plus a put option is $112. The
probability distribution of the HPR on the portfolio is:
State of the
Economy Probability
Ending Price
+ Put +
Dividend HPR
Excellent
0.25
$ 131.00
17.0%
= (131 112)/112
Good 0.45 114.00 1.8
= (114 112)/112
5-5
CHAPTER 5: INTRODUCTION TO RISK, RETURN, AND
THE HISTORICAL RECORD
c. Buying the put option guarantees the investor a minimum HPR of 0.0%
17. The probability distribution of the dollar return on CD plus call option is:
State of the
Economy Probability
Ending Value
of CD
Ending Value
of Call
Combined
Value
Excellent
0.25
$ 114.00
$16.50
$130.50
Good 0.45 114.00 0.00 114.00
Poor 0.25 114.00 0.00 114.00
Crash 0.05 114.00 0.00 114.00
18.
b. With a per quarter yield of 2%, the annual yield is
❑❑
= 1.0824, or
c. The appropriate formula is
❑❑()❑()❑❑❑()
, where
()❑
❑❑❑
. Using
d. The expected value of the excess return will grow by 120 months (12
months over a 10-year horizon). Therefore the excess return will be 120 ×
CFA PROBLEMS
5-6
CHAPTER 5: INTRODUCTION TO RISK, RETURN, AND
THE HISTORICAL RECORD
1. The expected dollar return on the investment in equities is $18,000 (0.6 × $50,000 + 0.4
4. X 2 = [0.2 × (– 20 – 20)2] + [0.5 × (18 – 20)2] + [0.3 × (50 – 20)2] = 592
6. The probability that the economy will be neutral is 0.50, or 50%. Given a
neutral economy, the stock will experience poor performance 30% of the
time. The probability of both poor stock performance and a neutral economy
is therefore:
5-7
