CHAPTER 9
1. The statements consistent with efficient
markets are (i) and (iii).
2. Zero. 3.
c. 4. c. This is
a classic filter rule which should not work in an efficient market.
5. b. This is the definition
of an efficient market.
6. d. 7.
c. 8. No 9.
No.
10. While positive beta stocks will respond well
to favorable new information about the economy’s progress through the
business cycle, they should not show abnormal
returns around already anticipated events
11. Expected rates of return will differ because
of differential risk premiums.
12. The market responds positively to new news. If
the eventual recovery is anticipated, then the recovery already is reflected
in stock prices. Only a better-than-expected recovery should affect stock
prices.
13. Over the long haul, there is an expected upward
drift in stock prices based on their fair expected rates of return. The
fair expected return over any single day is very small (e.g., 12% per year
is only about .03% per day), so that on any day the price is virtually
equally likely to rise or fall. However, over longer periods, the small
expected daily returns cumulate, and upward moves are indeed more likely
than downward ones.
14. Buy. 15. Assumptions
supporting passive management are a. informational efficiency
b. primacy of diversification
motives
16. a. The grandson is recommending taking
advantage of (i) the small firm in January anomaly and (ii) the weekend
anomaly.
b. (i)
Concentration of assets in stocks having very similar attributes may expose
the portfolio to more risk than is desirable. The strategy limits
diversification potential.
(ii) Even if the study results are correct as described, each such study
covers a specific time period. There is no assurance that future time periods
would yield similar results.
(iii) After the results of the studies became publicly known, investment
decisions might nullify these relationships. If these firms in fact offered
investment bargains, their prices may be bid up to reflect the now-known
opportunity.
17. a. Consistent. Half of managers should
beat the market based on pure luck in any year.
b. Inconsistent
c. Consistent. d.
Inconsistent e.
Inconsistent
18. Implicit in the dollar-cost averaging strategy
is the notion that stock prices fluctuate around a “normal” level.
19. No
20. The market may have anticipated even greater
earnings. Compared to prior expectations, the announcement was a
disappointment.
21. The low P/E effect and small size effect could
be used to enhance portfolio performance if one could expect them to persist
in the future. However, concentration in these stocks would lead
to departures from efficient diversification. In this case, beta
would no longer be an adequate descriptor of portfolio risk because non-systematic
risk would remain in the portfolio.
22. Reasons to avoid the strategy: a.
You might believe that these effects will no longer work now that they
are widely known.
b. You
might decide that too much diversification must be sacrificed to exploit
these effects.
c. The
level of risk resulting from a low P/E, small capitalization emphasis might
be inappropriate. d. You might decide that these
"effects" are in fact a reward for bearing risk of a nature not fully captured
by the beta of the stock. In other words, it may be that the
abnormal returns on these strategies would not appear so high if we could
more accurately risk-adjust performance.
CHAPTER 10
1. a.
Effective annual rate on 3-month T-bill is .10 or 10%
b.
Effective annual interest rate is .1025 or 10.25%
Therefore, the coupon bond has the higher effective annual rate.
2. an annual coupon of 8.16%.
3. The bond callable at 105 should sell
at a lower price because the call provision is more valuable to the firm.
Therefore, its YTM should be higher.
4. Lower. As time passes, the bond
price, which now must be above par value, will approach par.
5. True. 6.
C. 7.
Uncertain.
8. If the yield curve is upward sloping,
you cannot conclude that investors expect short-term interest rates to
rise because the rising slope could either be due to expectations of future
increases in rates or due to the demand of investors of a risk premium
on long-term bonds. In fact the yield curve can be upward sloping even
in the absence of any expectations of future increases in rates.
9. a.
Current price: $1052.42 Price 6 months from
now: $1044.52
b. Rate
of return = .04 or 4% per six months
10. a. Bond equivalent yield to maturity
= 8.52%. Effective annual yield to maturity = .087
= 8.7% b. The bond equivalent
yield to maturity is 8%. Effective annual yield to maturity
= .0816 = 8.16% c. Bond equivalent yield
to maturity = 7.52%, or 3.76% on a semi-annual basis.
Effective annual yield to maturity = .0766 = 7.66%
11. The resulting yields for the
three bonds are:
Bond Price
Bond equivalent yield = Effective annual yield
$ 950
8.53%
$1000
8.00%
$1050
7.51%
All else equal, annual payments make the bonds less attractive to the investor,
since more time elapses before payments are received. If the bond
price is no lower when the payments are made annually, the bond's yield
to maturity must be lower.
12.
Remember that the convention is to use semi-annual periods:
Maturity
Maturity
Semi annual
Bond equivalent yield
Price
(years)
(half-years)
YTM
to maturity
$400
20
40
2.317% 4.634%
$500
20
40
1.748% 3.496%
$500
10
20
3.526% 7.052%
$376.89
10
20
5%
10.000%
$456.39
10
20
4%
8.000%
$400
11.68
23.36
4%
8.000%
14. The invoice price is the reported price plus accrued
interest, or $1003.51.
15. The bond must be selling below par value.
16. The coupon rate must be below 9%.
17. The price schedule is as follows:
Remaining Constant yield value
Imputed interest
Year
Maturity, T 1000/(1.08)T
(Increase in constant yield value)
0 (now)
20 years 214.55
1
19
231.71
17.16
2
18
250.25
18.54
19
1
925.93
20
0
1000.00
74.07
18. Total taxable income is $40 + $14.60 = $54.60.
19. a. HPR = .195 = 19.5%
b. Tax
on explicit plus implicit interest in first year = .40 ´ ($50 + $6.43)
= $22.57
Tax on capital gain = .30 ´ $81.40 = $24.42
Total taxes = $22.57 + $24.42 = $46.99
c. After
tax HPR.129 = 12.9%
d. r =
.1297 = 12.97%
e. r =
.0847 = 8.47%
20. a. Yield to call is 3.368% semiannually:
b. Yield
to call is 2.976%. With a lower call price, the yield to call is
lower.
c. Yield
to call is 3.031% semiannually
21. The expected yield to maturity would be only
8.526%.
22. The realized compound yield to maturity will
be a function of r as given in the following table:
r Total proceeds
Realized YTM = – 1
--- -----------
-----------------------------
8% $1208
– 1 = .0991 = 9.91%
10% $1210
– 1 = .1000 = 10.00%
12% $1212
– 1 = .1009 = 10.09%
23. Zero coupon bonds provide no coupons to
be reinvested. Therefore, the final value of the investor's proceeds
from the bond are independent of the rate at which coupons could be reinvested
(if they were paid). There is no reinvestment rate uncertainty
with zeros.
24. The invoice price is $1036.25
25. i. The ABC debt is a larger issue and therefore
may sell with more liquidity.
ii.
An option to extend the term from 10 years to 20 years is favorable if
interest rates in 10 years are lower than today’s. In contrast, if interest
rates are rising, the investor can present the bond for payment and reinvest
the money for better returns.
iii. In
the event of trouble, the ABC debt is a more senior claim. It has
more underlying security in the form of a first claim against real property.
iv. The
call feature on the XYZ bonds makes the ABC bonds relatively more attractive
since ABC bonds cannot be called from the investor.
v. The
XYZ bond has a sinking fund requiring XYZ to retire part of the issue each
year. Since most sinking funds give the firm the option to retire
this amount at the lower of par or market value, the sinking fund can work
to the detriment of bondholders.
26. a. The fixed rate note therefore
will have a greater price range.
b. Floating
rate notes may not sell at par for any of the several reasons:
The yield spread between 1-year Treasury bills and other money market instruments
of comparable maturity could be wider than when the bond was issued.
The credit standing of the firm may have eroded relative to Treasury securities
which have no credit risk. Therefore, the 2% premium would become
insufficient to sustain the issue at par. The coupon increases are
implemented with a lag, i.e., once every year. During a period of
rising interest rates, even this brief lag will be reflected in the price
of the security. c.
The risk of call is low d.
Call risk is currently low.
e. This
is the coupon rate that would be needed for a newly-issued 15-year maturity
bond to sell at par. f. “yield-to-recoupon
date” is a more meaningful measure of return.
27. a. The yield on the par bond equals
its coupon rate, 8.75%.
b. The
4% bond will offer a greater expected return.
c.
Implicit call protection is offered in the sense that any likely fall in
yields would not be nearly enough to make the firm consider calling the
bond. In this sense, the call feature is almost irrelevant.
28. Market conversion price =
$583.24 Conversion premium = 191.76
29. a. The call provision requires the
firm to offer a higher coupon (or higher promised yield to maturity) on
the bond to compensate the investor for the firm's option to call back
the bond at a specified price if interest rate falls sufficiently. Investors
are willing to grant this valuable option to the issuer, but only for a
price that reflects the possibility that the bond will be called.
That price is the higher promised yield at which they are willing to buy
the bond.
b. The
call option will reduce the expected life of the bond. If interest
rates fall substantially and the likelihood of call increases, investors
will begin to treat the bond as if it will "mature" and be paid off at
the call date, not at the stated maturity date. On the other hand
if rates rise, the bond must be paid off at the maturity date, not later.
This asymmetry means that the expected life of the bond will be less than
the stated maturity.
c. The
advantage of a callable bond is the higher coupon (and a higher promised
yield to maturity) when the bond is issued. If the bond turns out
not to be called, then one will earn a higher realized compound yield on
a callable bond issued at par than a non-callable bond issued at par on
the same date. The disadvantage of the callable bond is the risk
of call. If rates fall and the bond is called, the investor will
receive the call price and will have to reinvest the proceeds at now-lower
interest rates than the yield to maturity at which the bond originally
was issued. In this event, the firm's savings in interest payments
is the investor's loss.
30. a. f = .1001 = 10.01%
b. The best guess would be 10.01%.
c. The
best guess would be less than 10.01%.
31. The top row must be the spot rates.
32. a. (4) b.
(2) c. (2) c. (3)
e. (2) is the only correct choice. f. (1
+ .12/4)4 = 1.1255. Choice (3) is correct. g.
(3) h. (2) i. (3) j.
(3) k. (4) l.
(4)