LUBIN SCHOOL OF BUSINESS
Pace
University
Fin
652 Investment Analysis
Spring 1997
Prof. P.V.
Viswanath
· The exam is open book and open notes.
· Explain all your steps; correct answers without explanations may not be given any credit at all.
· Show all your computations and formulae. Make all your assumptions explicit. If your approach is correct, you will get some credit, even if your arithmetic answer is wrong. So concentrate on getting your logic right.
· Write legibly; I cannot guarantee any credit for what I cannot read, even if it is correct.
· If an answer contains two contradictory statements, you may get no credit for the answer, even if one of the statements is correct.
· If you answer a question, I have the discretion to award you some points, even if you are completely wrong. If you don't attempt the question at all, I can give you no points! So attempt every question.
· Each question is worth 25 points.
1. The Wall Street Journal of Feb. 28, 1997 carried the following report:
Mergers, Acquisitions Mania
Gives Investors More to Chew
McDonald's offer of 55-cent Big Macs was noteworthy, but hardly the only deal worth sinking your teeth into this week. From technology to corn products to hotels and beyond, the momentum of corporate mergers and acquisitions continued apace. And the factors behind the trend were explained in a week-long series in The Wall Street Journal titled "Amalgamating America."
a) On Friday, Cigna Corp. announced plans to acquire Healthsource Inc., which offers health maintenance organization coverage in 16 states, for about $1.45 billion. The deal demonstrates the movement by big health care insurance providers to team up to expand their base of subscribers so that they can command better deals from health-care providers and reduce costs. "Healthcare is their [Cigna] highest-return business," said Weston C. Hicks, senior research analyst with Sanford C. Bernstein. Michael A. Lewis, an insurance analyst with Dean Witter Reynolds, said Cigna is a well-capitalized player in the insurance industry that is increasing its emphasis on health care. He likened the move to Aetna Inc.'s shedding of its property casualty business and acquiring U.S. Healthcare Inc. "This is a natural fit for them," Mr. Lewis said . "Cigna has made it very clear that they are in a restructuring cycle."
b) Elsewhere this week, 3Com agreed to buy modem maker U.S. Robotics in a stock deal initially valued at $6.6 billion, the second-largest technology acquisition ever. Analysts called the deal an attempt by 3Com, a network-equipment maker, to challenge Cisco, the leader in that market.
c) CPC plans to spin off its corn-refining business to focus on its much larger packaged-food business.
d) Applied Magnetics launched a hostile takeover bid for rival Read-Rite valued at $36 a share in stock, or $1.7 billion. A combination would create a new leader among suppliers of recording heads for PC disk drives.
e) Buyout firm Texas Pacific Group agreed to acquire Del Monte Foods for at least $800 million.
f) In the talking stage, Hyatt Hotels said it plans to spend up to $1 billion within the next three years to acquire between 20 and 30 hotels.
g) And Raytheon said it will try to sell its appliance division. Analysts said the unit could bring $1 billion or more.
h) Kimberly-Clark said it would move to become a pure consumer-products business, exiting the cyclical pulp business by selling three mills.
What can you say about the effect of each transaction on the variance of returns on the common stock of the acquiring/divesting companies highlighted in the above list? Use no more than three sentences for each case.
2. The 1-year riskfree rate is 10%, and the expected return on the market for the following year is 14%. You ask a stockbroker what the firm's research department expects for these three stocks. The broker responds with the following information:
|
Stock |
Current Price |
Expected Price |
Expected Dividend (to be paid in 1 yr.) |
Beta |
|
Healthsource, Inc. |
22 |
24 |
0.75 |
0.85 |
|
K-Mart |
48 |
51 |
2.00 |
1.25 |
|
Mercury Financial Corp. |
37 |
40 |
1.25 |
-0.20 |
a) What actions would you take with regard to these stocks?
b) Plot the SML.
3. The market's expected return is 12%, whereas the risk-free return is considered to be 5%. We construct a portfolio in the following fashion:
|
|
A |
B |
C |
|
Beta |
1.2 |
0.9 |
1.8 |
|
Investment weight |
0.4 |
0.3 |
0.3 |
What is the beta of this portfolio, and what is its required rate of return according to the Capital Asset Pricing Model?
4. Bret Barakett has a margin account and deposits $50,000. Assuming the prevailing initial margin requirement is 40%, commissions are ignored, and Reebok is selling at $35 per share:
a) How many shares can Brett purchase using the maximum allowable margin?
b) What is Brett's profit/loss if the price of Reebok stock falls to $25?
c) If the maintenance margin is 30%, to what price can Reebok fall before Brett will receive a margin call?
d) How much additional money must Brett deposit if the stock price drops to $5 below the level computed in c) above, and he is required to bring up the actual margin on his account to the initial margin?
· This exam is a take-home exam, and is due in one week on April 24, 1997. No extensions of the deadline will be given. You may also drop off your exam in person. If I am not in, you may put the exam in my mailbox in the Goldstein building at Pleasantville.
· You can use all information that you have available to you. You may discuss the exam with fellow students in this class; however, you may not discuss it with anybody outside the class. In the final analysis, you are reponsible for the answers you give. The written answers must be formulated individually. No collaboration is permitted at this stage. If I deem it necessary, I can, at my discretion, can ask you for a follow-up oral answer to a question. You must be available during the week following the hand-in deadline to answer such questions.
· Explain all your steps; correct answers without explanations may not be given any credit at all.
· Show all your computations and formulae. Make all your assumptions explicit. If your approach is correct, you will get some credit, even if your arithmetic answer is wrong. So concentrate on getting your logic right.
· Write legibly.
1.
(40 points) Here is some information on Treasury Note And Bond Quotes (From
Cantor Fitzgerald Securities) as reported on the Wall Street Journal’s
Interactive Edition on Tuesday, April 15, 1997 as of 2 p.m.
The quotes are as of Midafternoon Monday 4/14/97 (Yields for Delivery 04/15/97)
|
Cusip No. |
Coupon |
Maturity |
Bid |
Ask |
Chg |
Yield |
|
912827P71 |
6 1/2 |
05/15/1997-N |
100.01 |
100.03 |
0 |
5.22 |
|
912827UW0 |
8 1/2 |
05/15/1997-N |
100.06 |
100.08 |
0 |
5.28 |
|
912827Q70 |
6 1/2 |
08/15/1997-N |
100.07 |
100.09 |
-1 |
5.59 |
|
912827VE9 |
8 5/8 |
08/15/1997-N |
100.29 |
100.31 |
-1 |
5.62 |
|
912827R79 |
7 3/8 |
11/15/1997-N |
100.24 |
100.26 |
0 |
5.92 |
|
912827VN9 |
8 7/8 |
11/15/1997-N |
101.19 |
101.21 |
0 |
5.93 |
|
912827S78 |
7 1/4 |
02/15/1998-N |
100.28 |
100.30 |
0 |
6.07 |
|
912827VW9 |
8 1/8 |
02/15/1998-N |
101.19 |
101.21 |
0 |
6.05 |
|
912827T77 |
6 1/8 |
05/15/1998-N |
99.29 |
99.31 |
0 |
6.15 |
|
912827WE8 |
9 |
05/15/1998-N |
102.27 |
102.29 |
-1 |
6.17 |
N=Note. WI=When Issued. IW=Inflation-indexed note, when issued. I= Inflation-indexed note. Representative and indicative over-the-counter quotations based on $1 millon or more. Yields are based on next day settlement and asked prices. For bonds callable before maturity, yields are computed to the earliest call date on issues quoted above par and to the maturity date on issues quoted below par.
a. Use as much of the above information as possible, and answer the following question:
What are the implied yields on zero-coupon bonds with maturities 5/15/97, 8/15/97, 11/15/97, 2/15/98 and 5/15/98? Explain in as much detail as necessary, how you reached your answer.
Here are the prices of Treasury-bills as of the same date:
U.S. Treasury Bill Quotes As of Midafternoon Monday 4/14/97 (Yields for Delivery 04/15/97)
|
Cusip No. |
Maturity |
Bid |
Ask |
Chg |
|
9127944J0 |
05/15/1997 |
5.19 |
5.15 |
0.03 |
|
9127945J9 |
08/14/1997 |
5.34 |
5.32 |
0.00 |
|
9127942W3 |
11/13/1997 |
5.52 |
5.50 |
0.00 |
|
9127944R2 |
02/05/1998 |
5.61 |
5.57 |
-0.04 |
|
9127944S0 |
03/05/1998 |
5.63 |
5.61 |
-0.01 |
|
9127944T8 |
04/02/1998 |
5.69 |
5.68 |
0.01 |
Representative and indicative over-the-counter quotations based on $1 million or more. Bills are quoted in terms of a discount rate. Yields are based on next day settlement and asked rates and are on a bond-equivalent basis. WI=When Issued.
b. What are the implied yields on these zero-coupon securities?
c. Do you perceive a systematic difference between the rates computed in part (a) above and the rates computed in part (b)? To what do you ascribe the difference, if any?
d. Assuming that the unbiased expectations holds, forecast the 3 month, 6 month, 9 month, and 1-year yields on zero-coupon securities, one month from now.
2. (40 points) A firm with a very high credit rating expects to issue 15 year bonds worth $1 million, one month from now. In order to protect itself against changes in the yield on 15-year bonds, it intends to hedge the proposed issue by selling 30-year T-bond futures contracts maturing one month from now. (A one-month maturity 30-year T-bond futures contract represents a contract to purchase a 30-year T-bond one month from now at the futures price.) If rates rise over the next month, the firm will realize a lower amount of money from the proposed issue. On the other hand, T-bond futures prices generally move in the same direction as the prices of actual T-bonds. Hence, the firm will probably make money on its futures position, since 30-year T-bond futures prices may be expected to drop as well, if prices of 15-year bonds drop. Since the firm's credit rating is very high, the CFO feels that it is reasonable to approximate the yield on the firm's debt by the corresponding yield on Treasury securities.
You have the following additional information:
· Currently, 9% coupon 15 year T-bonds are selling at par.
· The price of the 30-year T-bond futures contract is based on a 10% coupon non-callable T-bond. Assume that only such bonds can be delivered in satisfaction of the futures contract. Each futures contract requires the delivery of futures contracts with a face value of $1 million.
· The futures price is currently 100.
· The term structure of interest rates is likely to raise or fall by the same amount at all maturities over the next month.
· T-bonds pay coupons half-yearly.
For the purposes of the question, you may assume that the price sensitivity of T-bond futures contracts is equal to the price sensitivity of the corresponding T-bond selling at the futures price.
The
CFO would like an answer to the question of how many futures contracts to
sell. You realize that what you want is
find the number a
(also called the hedge ratio), such that
.
What is the correct
value of a?
3. (20 points) You are given the following information on the performance of Twentieth-Century Fund:
For the year ended Mar. 31, 1997, the fund manager invested his funds in three different asset classes in the proportions shown in the table below. Twentieth Century Fund is evaluated according to a given benchmark diversified portfolio, whose composition is also given below. In addition, returns on Twentieth-Century and on the benchmark portfolio for the different asset classes are provided in the table.
|
|
Investment Weights |
Returns |
||
|
Asset Class |
Actual |
Benchmark |
Actual |
Benchmark |
|
Stock |
0.50 |
0.60 |
9.7% |
8.6% |
|
Bonds |
0.38 |
0.30 |
9.10% |
9.2% |
|
Cash |
0.12 |
0.10 |
5.6% |
5.4% |
a) How much of the discrepancy between Twentieth Century's performance and that of the benchmark can be attributed to the difference in investment proportions across asset classes?
b) The choice of investment weights different from that of the diversified benchmark implies that the Twentieth-Century portfolio is less than perfectly diversified. For example, Twentieth-Century is overinvested in the bond sector, from the viewpoint of diversification. Consequently, even if the return on Twentieth-Century over the performance evaluation period is higher than the return on the benchmark portfolio, that may simply be compensation for holding a less-than-perfectly-diversified portfolio, and not abnormal returns. How might you adjust the performance of Twentieth-Century for the increased diversification?
1. a. Here are the cashflows on each coupon bond, and its invoice price:
These numbers have to be corrected because bond prices are quoted in 32nds, which I have not taken into account!
|
|
|
5/15/97 |
8/15/97 |
11/15/97 |
2/15/98 |
5/15/98 |
|
|
Quoted prices |
Invoice prices |
D2 |
D3 |
D4 |
D5 |
D6 |
Time to 1st coupon in fraction of yrs |
|
1000.2 |
1027.4 |
1032.5 |
0 |
0 |
0 |
0 |
1/12 |
|
1000.7 |
1036.2 |
1042.5 |
0 |
0 |
0 |
0 |
1/12 |
|
1000.8 |
1011.7 |
0 |
1032.5 |
0 |
0 |
0 |
4/12 |
|
1003 |
1017.5 |
0 |
1043.125 |
0 |
0 |
0 |
4/12 |
|
1002.5 |
1033.3 |
36.875 |
0 |
1036.875 |
0 |
0 |
1/12 |
|
1012 |
1049.1 |
44.375 |
0 |
1044.375 |
0 |
0 |
1/12 |
|
1002.9 |
1015.1 |
0 |
36.25 |
0 |
1036.25 |
0 |
4/12 |
|
1012 |
1025.6 |
0 |
40.625 |
0 |
1040.625 |
0 |
4/12 |
|
993 |
1018.6 |
30.625 |
0 |
30.625 |
0 |
1030.625 |
1/12 |
|
1022.8 |
1060.4 |
45 |
0 |
45 |
0 |
1045 |
1/12 |
We regress the bond invoice prices against the cash flows. Here are the results:
|
|
Coeffs |
Standard Error |
t Stat |
P-value |
Lower 95% |
Upper 95% |
Lower 95.0% |
Upper 95.0% |
Implied yield |
|
D2 |
0.994506 |
0.001153 |
862.2043 |
3.98E-14 |
0.991541 |
0.997471 |
0.991541 |
0.997471 |
0.068342 |
|
D3 |
0.977628 |
0.001153 |
847.8072 |
4.33E-14 |
0.974664 |
0.980592 |
0.974664 |
0.980592 |
0.070235 |
|
D4 |
0.961735 |
0.001151 |
835.6539 |
4.66E-14 |
0.958776 |
0.964693 |
0.958776 |
0.964693 |
0.069173 |
|
D5 |
0.94641 |
0.001153 |
820.6553 |
5.1E-14 |
0.943445 |
0.949374 |
0.943445 |
0.949374 |
0.068329 |
|
D6 |
0.930362 |
0.001155 |
805.7967 |
5.59E-14 |
0.927394 |
0.93333 |
0.927394 |
0.93333 |
0.068899 |
b. Here is the information on the zero-coupon bills, and their implied yields.
|
|
|
|
|
Zero Yields |
Yields from coupons |
||
|
Cusip No. |
Bid |
Ask |
Chg |
Yield (based on ask) |
Maturity |
Maturity |
Yield |
|
9127944J0 |
5.19 |
5.15 |
0.03 |
5.24 |
05/15/1997 |
5/15/97 |
6.83 |
|
9127945J9 |
5.34 |
5.32 |
0.00 |
5.49 |
08/14/1997 |
8/15/97 |
7.02 |
|
9127942W3 |
5.52 |
5.50 |
0.00 |
5.75 |
11/13/1997 |
11/15/97 |
6.92 |
|
9127944R2 |
5.61 |
5.57 |
-0.04 |
5.87 |
02/05/1998 |
2/15/98 |
6.83 |
|
9127944S0 |
5.63 |
5.61 |
-0.01 |
5.92 |
03/05/1998 |
|
|
|
9127944T8 |
5.69 |
5.68 |
0.01 |
6.01 |
04/02/1998 |
5/15/98 |
6.89 |
c. The differences may be due to the fact that the prices of the coupon bonds have tax implications different from those of the zero-coupon bonds. A simpler reason may be that the coupon bonds are less liquid and therefore require a higher yield. This is consistent with the fact that the furthest out zero-coupon bond computed zero-yield differs less from its corresponding coupon-bond computed zero-yield than the others.
d. We can use the implied strip yields generated from the coupon bonds to compute the forward rates:
|
Maturity |
Yield |
nonannualized gross rates |
nonannualized forward rates |
annualized forward rates, 1 mth ahead |
Maturity of forward contract |
|
5/15/97 |
6.83 |
1.005521 |
|
|
|
|
8/15/97 |
7.02 |
1.022873 |
1.017257 |
7.083408 |
3 month |
|
11/15/97 |
6.92 |
1.039803 |
1.034094 |
6.935007 |
6 months |
|
2/15/97 |
6.83 |
1.056601 |
1.0508 |
6.83 |
9 months |
|
5/15/97 |
6.89 |
1.074852 |
1.06895 |
6.895002 |
1 year |
2.
The futures price is 100, meaning that the underlying security can be purchased
at par. Since changes in the term
structure are assumed to be parallel, we can use the duration as a
measure. The firm effectively wishes to
issue 15 year T-bonds, which are now selling at par with a 9% coupon. The contract with which it wants to hedge is
on a 30-year T-bond selling currently at par, with a 10% coupon. The durations of these two instruments can
be computed using Rule 8 on p. 457. The
numbers are, respectively, 
= 17 half years for
the 15 year instrument and 
= 19.875 for the 30 year instrument. Hence the value of a = 17.02/19.875 =
0.8564. The face value of the futures
contract is the same as the face value of the bond issue, so no adjustment is
needed on that count. The CEO should
sell 0.8564 futures contracts.
3. a)(From Reilly and Brown, Investment Analysis and Portfolio Management, p. 1012).
The overall actual return is (0.50 x 0.097) + (0.38 x 0.091) + (0.12 x 0.056) = 8.98%
The benchmark overall return is (0.60 x 0.086) + (0.30 x 0.092) + (0.10 x 0.054) = 8.46%.
Thus the manager beat the benchmark by 52 basis points. The part of this 52 basis points that is due to the manager's allocation effect can be computed by multiplying the excess asset class weight by that class's relative investment performance:
[(-0.10) x (0.086-0.0846)] + [(0.08) x (0.092 - 0.0846)] + [(0.02) x (0.054-0.0846)] = -0.02%
This shows that if the manager had made just has market timing decisions (asset allocation) and not picked different securities than those represented in the benchmark, he would have lagged the benchmark by two basis points.
b) Using the Capital Market Line, one may argue that the required excess return on the investment portfolio should be equal to the excess return on the benchmark portfolio multiplied by the ratio of the standard deviation of the investment portfolio to that of the benchmark portfolio.