CHAPTER 8
1.      i, iii and iv.
2.      b. The promised yield on AAA-rated bonds is higher than on A-rated bonds
3.      b = 15/10 = 1.5
4.      The stock would be worth only $5.20/.19 = $27.37.
5.      NPV       = 15.64      b = 40.55 / 10 = 4.055
6.      a.      False.  b = 0 implies E(r) = rf, not zero.   b.     False.     c.     False.
7.      a.      bA  =     2.00          bD  =     .70
         b.      E(rA) = .5(2 + 32)    = 17%           E(rB) = .5(3.5 + 14) =   8.75%
         c.      The SML is determined by the market expected return of .5(20 + 5) = 12.5%, with a beta of 1, and the bill return of  8% with a beta of zero.  The equation for the security market line is:  E(r) = 8 + b(12.5 – 8).
        d.      The aggressive stock has a fair expected return of:  E(rA) = 17%  and the expected return by the analyst also is 17%.  Thus its alpha is zero.  Similarly, the required return on the defensive stock is: E(rD) = 11.15%, but the analyst’s expected return on D is only 8.75%, and hence,   aD = –2.4%.     The points for each stock plot on the graph as indicated above.
         e.      The hurdle rate is determined by the project beta, .7, not by the firm’s beta.  The correct discount rate is 11.15%, the  fair rate of return on stock D.
8.      Not possible.  Portfolio A has a higher beta than B, but its expected return is lower.
9.      Possible.    10.    Not possible.   11.    Not possible  12.    Not possible.   13.    Not possible
14.    Possible.    15.    P1 = $109
16.    The difference, $6944.44, is the amount you will overpay if you erroneously assumed that beta is zero rather than 1.           If the cash flow lasts only one year:   a difference of $78.47.
         For any n year cash flow the difference is: 1,000 ´ Annuity factor(8%, n)  –  1,000 ´ Annuity factor(18%, n)
17.    b = –2/10 = –.2
18.    a.      To tell which investor was a better predictor of individual stocks we look at their abnormal return, which is the ex-post alpha, that is, the abnormal return is the difference between the actual return and that predicted by the SML.  Without information about the parameters of this equation (risk-free rate and market rate of return) we cannot tell which one is more  accurate.
         b.   a1 = 19 – [6 + 1.5(14 – 6)]  =  19 – 18 = 1%
               a2 = 16 – [6 + 1(14 – 6)]  =  16 – 14 = 2%
         Here, the second investor has the larger abnormal return and thus he appears to be a more accurate predictor.  By making better predictions the second investor appears to have tilted his portfolio toward underpriced stocks.
         c.    a1 =19 – [3 + 1.5(15 – 3)] = 19 – 21 = –2%
               a2 = 16 – [3+ 1(15 – 3)] = 16 – 15 = 1%
         Here, not only does the second investor appear to be a better predictor, but the first investor's predictions appear  valueless (or worse).
19.    a.      The expected rate of return is 12%.
         b.     The portfolio's fair return is the risk-free rate, 5%.
         c.      The stock must be underpriced.
20.    a.       Hence A is desirable and B isn’t.
         b.       Portfolio A would be a good substitute for the S&P 500.
21.    H is an arbitrage portfolio.
23.             rf = 6%
24.    a.      The expected dollar return is $60,000 and the standard deviation of dollar returns is $134,164.    b.      If n = 50 stocks, the standard deviation of dollar returns is $84,853.
                  Similarly, if n = 100 stocks, the standard deviation of dollar returns is $60,000.
25.    Any pattern of returns can be "explained" if we are free to choose an indefinitely large number of explanatory factors.  If a theory of asset pricing is to have value, it must explain returns using a reasonably limited number of explanatory variables
     (systematic factors).
26.    The APT factors must correlate with major sources of uncertainty, i.e., sources of uncertainty that are of concern to many investors.  Researchers should investigate factors that correlate with uncertainty in consumption and investment opportunities.  GDP, the inflation rate, and interest rates, are among the factors that can be expected to determine risk premiums.  In particular, industrial production (IP) is a good indicator of changes in the business cycle.  Thus, IP is a candidate for a factor that is highly correlated with uncertainties that have to do with investment and consumption opportunities in the economy.
27.    -revised estimate  =  14  +  [1 x 1  +  .4 x 1] = 15.4%
28.    The expected return-beta relationship is:  E(rp) = 7 + 4.47bp1 + 11.86bp2

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)