LUBIN SCHOOL OF BUSINESS
Pace
University
Fin
652 Investment Analysis
Fall 1999
Prof. P.V.
Viswanath
1. (40 points) Read the following article from the Interactive Wall Street Journal of October 12, 1999 and answer these questions:
a) Explain to your friend (who is also in the MBA program, but who has not yet taken a finance course), what is happening in the bond and the stock markets using the Dividend Discount model (or the Dividend Growth model).
b) Since bond prices are also falling, there is no evidence of a flight to quality. Suppose, however, that in addition to the other news that investors got about the economy on Tuesday, investors also believed that the economic picture was becoming more uncertain, and overall riskier. What would you have expected to happen to stock prices and bond prices.
Stocks
Tumble As Dollar, Bonds Pressure Market
By ANDREW FRASER INTERACTIVE JOURNAL
Stocks tumbled Tuesday as concerns about rising interest rates outweighed optimism about corporate profits. Bond prices fell and the dollar weakened.
The Dow Jones Industrial Average fell 231.12 points, or 2.2%, to close at 10417.06  its secondworst point drop this year. The Nasdaq Composite Index, which closed at a record high Monday, retreated 43.52, or 1.5%, to 2872.43.
Other broader market indexes were lower. The Standard & Poor's 500stock index fell 22.17 to 1313.04, and the New York Stock Exchange Composite Index slipped 9.95 points to 603.38.
The focus for stock investors was on the weakening bond market and the falling dollar, despite expectations for a continued string of healthy corporate profits as thirdquarter reports begin to trickle in this week.
Bond prices fell, pushing longterm yields toward the year's high of 6.27%, as investors weighed the inflationary and monetarypolicy implications of rising commodity prices and upcoming economic data.
"It's the 28th chapter of the risinginterestrates story," said Tom Madden, chief investment officer for U.S./highyield equities at Federated Investors in Pittsburgh. "And the stock market is looking at the bond market."
The drop in bond prices  and to some extent the stock market  was aggravated by a decline in the dollar. A weaker dollar makes the returns on U.S. assets less attractive to foreign investors.
Bonds took a hit as investors back from a holiday Monday continued to worry about signs of rising inflationary pressure in last Friday's jobs data for September and anticipated more bad news in reports this week.
Investors fear that the coming reports on retail sales and wholesale prices will provide more evidence to support another interestrate increase by the Federal Reserve. The Fed has raised rates twice this year and said it is more likely than not to raise them again to keep inflation at bay.
Higher interest rates are a worry for stock investors because it could damp corporate earnings by raising borrowing costs.
Also adding to pressure on the bond and stock markets was a drop in the dollar against the yen and the euro. The yen was supported by the belief that the Bank of Japan won't ease rates at its monetarypolicy meeting Wednesday.
A weaker dollar also can prove inflationary by making imports more expensive.
Worries about inflation and higher interest rates aside, Scott Bleier, chief investment strategist at Prime Charter Ltd., said the stock market has now established a lower trading range more in line with profit expectations.
"There really is no reason to be making big bets on the upside considering the recent rally we have had anticipating good earnings for so many companies," Mr. Bleier said.
Mr. Bleier said besides rising yields in the bond market and the dollar's weakness, some investors also were demonstrating concerns about "perceived" year 2000 problems that could hurt corporate profits.
He said money will continue to flow out of bluechip companies and into Internetrelated companies.
Earnings on Monday helped to push the Nasdaq Composite to a record close of 2915.95 as investors embraced technology issues to the exclusion of nearly all other sectors.
2. (40 points) The Wall Street Journal quoted the following rates as of midafternoon, Oct. 12, 1999.
Maturity 
Days to maturity 
Bid 
Asked 
Change 
Yield 
Oct 28 '99 
16 
4.40 
4.32 
0.01 
4.39 
Nov 04 '99 
23 
4.44 
4.36 
0.07 
4.43 
You wish to invest $1 m. for 23 days, starting tomorrow. You can get a commitment from a securities trader that he will borrow any amount up to $1.2 m. from you at an effective annual rate of 4.47% per annum, provided you will deliver the money to him by the close of trading on Oct. 28, 1999, and provided the money does not have to be repaid until the close of trading on Nov. 4, 1999. Which of the two options should you choose?
a)
Invest in the Tbill maturing on Nov. 4, 1993 (remember that settlement
takes one day)
b)
Invest in the Tbill maturing Oct. 28, 1999 and then invest the proceeds
of the Tbill with the securities trader.
Which is the better deal?
3. (30 points) You’ve borrowed $20,000 on margin to buy shares in Disney, which is now selling at $25 per share (Source: http://finance.yahoo.com). Your account starts at the initial margin requirement of 50%. The maintenance margin is 35%. Two days later, the stock price falls to $22 per share. How much money have you lost? How low can Disney’s price fall before you receive a margin call?
Bonus: (5
points; I will be more strict with the assignment of partial credit for this
question) Here is some information on the daily range of prices for the last 10
trading days. If you were a
brokerage firm, and you were allowed by the SEC to set your own margin
requirements, how much margin would you require?
How would you go about determining this number?
Date 
Open 
High 
Low 
Close 
Diff between high and low 
Volume 
12Oct99 
25.25 
25.3125 
25 
25 
0.3125 
4531100 
11Oct99 
25.1875 
25.6875 
25.125 
25.25 
0.5625 
4959200 
8Oct99 
25.3125 
25.625 
25.1875 
25.3125 
0.4375 
4878900 
7Oct99 
25.8125 
26.125 
25.5 
25.625 
0.625 
6230100 
6Oct99 
25.0107 
25.8215 
25.0107 
25.572 
0.8108 
5468300 
5Oct99 
25.5096 
25.9462 
24.8236 
24.8859 
1.1226 
6786400 
4Oct99 
25.6344 
25.6344 
25.1978 
25.572 
0.4366 
3774300 
1Oct99 
25.4473 
25.572 
25.073 
25.3225 
0.499 
6351000 
30Sep99 
26.071 
26.1333 
25.073 
25.9462 
1.0603 
8990500 
29Sep99 
26.1957 
26.5699 
25.8839 
26.1333 
0.686 
5337600 
2. The investor wishes to buy the bills; hence, under the second option, the appropriate rate to use would be the ask rate; using the 4.32% banker's discount rate, we see that the price, P, would satisfy the equation 0.0432 = [(100P)/100](360/16). Hence, P = 99.808 per $100; so if the investor bought $1m. worth of bills, the payoff at the end of the 16 days would be $1m./0.99808 = $1,001,923.70. Reinvesting this amount for another 7 days at an effective annual rate of 4.47% per annum, he realizes (1,001,923.70)(1.0447)^{7/365} = $1,002,764.30.
Under the first option, the price he pays for the bill satisfies the equation 0.0436 = [(100P)/100](360/23); solving, we see P = 99.72144 per $100. Hence an investment of $1m. would yield $1m/0.9972144 = $1,002,793.30, which is larger. Hence the second option is preferable.
3. You borrowed $20,000; since the margin requirement is 50%, you must have bought stocks worth $40,000. Since they are selling at $25 a share, you must have bought 40,000/25 = 1600 shares. If prices drop by $3/share, you have lost 1600 x 3 = $4800. If the maintenance margin is 35%, then to obtain the price at which you will be subject to a margin call, we solve the equation 0.35 = (1600P20000)/1600P. Solving, we see that the price below which the investor will be subject to a margin call is P = 19.23.
Bonus: I would look at the volatility of the share prices. This would help me compute the amount that I, the broker, could lose while waiting for the customer to put up margin. That is, I would set my margin requirements by taking into account the probability that during the time that I was waiting for the customer to put up margin, the value of the securities that the customer had with me in his account would not drop below the amount of the loan.
1. The following information has been computed using data for Nov. 1994 to Oct. 1999 from http://chart.yahoo.com/d/:

Pfizer (PFE) 
WarnerLambert (WLA) 
Price of one share at the end of Oct. 1994 
74.125 
76.25 
Price at the end of Oct. 1999 adjusting for stock splits and assuming dividends are constantly reinvested in the stock 
511.33 
524.241 
Actual price of one share at the end of Oct. 1999 
39.6875 
79.8125 
Annualized Average Return (over the past five years) 
42.04% 
43.03% 
Standard deviation of returns over the past five years (annualized) 
87.81% 
94.06% 
Beta 
0.95 
0.88 
Correlation coefficient between R_{pfe} and R_{wla } 
0.47 

In addition, you have the business profiles for the two companies, as well as some historical information on the US stock market, as given below.
Business Profile for Pfizer:
Pfizer develops, manufactures and sells technology intensive products in three segments: Health Care, includes pharmaceuticals, bone and joint devices, and medical instruments and implants; Animal Health and Consumer Health Care. For the six months ended 7/4/99, total revenues rose 21% to $7.71 billion. Net income from continuing operations rose 37% to $1.54 billion. Results reflect increased alliance revenue and improvements in the business and product mix.
Business Profile for WarnerLambert:
WarnerLambert Company manufactures pharmaceuticals products (ethical, biologicals, capsules), consumer health care products (OTC, shaving, pet care) and confectionary products (chewing gums, breath mints, cough tablets). For the six months ended 6/30/99, net sales rose 23% to $6.16 billion. Net income rose 33% to $828.9 million. Revenues reflect increased unit volume growth and the inclusion of sales from acquisitions. Earnings reflect improved gross margins.
The arithmetic average return on the US stock market in excess of the 3month Tbill rate, computed over the period 19261990 is 8.41% per year.
For reasons only known to him, Mr. Sarkis Sarkisian is considering investing all his money in the two stocks described above.
a) What is the annualized fiveyear holding period return on each stock? (10 points)
b) If he wanted to minimize the variance of returns on his portfolio, how much would he invest in each one? (15 points)
c) If his coefficient of riskaversion were 3, how much would he invest in each one, assuming that he believes that the trend of the last five years is bound to continue? (15 points)
d) If he could also invest in 3month Tbills, which currently yield 5.2% (Source: http://www.bloomberg.com/markets/iyc.html), how much would invest in each of the three securities: PFE, WLA and Tbills? (15 points)
e) What is the expected return on a portfolio consisting of equal amounts in each of the three securities over the next year? Explain your results, including a justification of the numbers that you choose. (15 points)
2. Here is an excerpt from an article in Risk Management, "Making the most of the capital markets: Securitization," published in Aug 1999 under the byline of John J Kollar. Answer the questions that follow:
a. Using the CAPM as a guide, discuss how you would price the first bond for sale to US investors. Explain your steps. (20 points)
b. Who would buy these bonds, in your opinion? Again, explain your answer. Do not use more than one page. (10 points)
Next in Line
Recently, for the first time, a noninsurance company tapped the capital market to finance a natural hazard risk through catastrophelinked securities. According to various published reports, the Japanbased Oriental Land Company, owner and operator of Tokyo Disneyland, placed two $100 million catastrophe bonds with two Cayman Islandbased special purpose reinsurers to protect against earthquakes.
The first bond provides Oriental Land with up to $100 million in earthquake coverage. This is provided for a fiveyear period and the payment depends solely upon the magnitude, location and depth of an earthquake, regardless of actual property damage. The second transaction provides Oriental Land with a $100 million fully collateralized postearthquake financing facility. In that case, Oriental Land will issue a $100 million fiveyear bond to the reinsurer, with no obligation to pay any interest for the first three years.
Clearly, primary insurersand now selfinsuredscan use securitization to supplement traditional reinsurance. Reinsurers can also use securitization to supplement traditional retrocessionreinsurance for reinsurers. And, if and when the insurance market hardens, risk managers will want to explore the use of catastrophe risk securitization as a supplement or alternative to the more common methods of risk transfer.
Securitizing risk with capital market instruments is still relatively new. But is it an emerging trend in risk funding that innovative and alert risk managers will adopt? Or is it an unproven gambit that investors and risk managers want to assess from the sidelines before calling into play? As availability and cost improve, market demand is likely to create a place for securitization in the risk manager's risk transfer arsenal for reducing costs and increasing capacity.
1. (please check the numbers; the formulas are correct; the numbers may be off a little.)
a) The annualized average return over the last five years is (511.33/74.125)^{0.2} = 47.15% for PFE and 47.05% for WLA.
b) The formula is w_{pfe} = ; substituting, we find w_{pfe} = 39.17%; w_{wla} = 60.83%.
c) The formula is w_{pfe} = ; substituting, we find w_{pfe} = 56.087%; w_{wla} = 43.913%
d)
If Mr. Sarkisian could invest in the riskfree asset as well, then he
would choose to allocate his assets between the riskfree asset and the tangent
portfolio. The portfolio weights
for the tangent portfolio are given by
where the two assets are labelled D and E.
Hence, if we let D represent PFE and E represent WLA, and substitute, we
find w_{pfe} = 179080.82/327762.66 = 54.637%; w_{wla} = 45.363%.
The expected return on this portfolio would be (0.54637)(42.04) +
(0.45363)(43.03) = 42.489%.
The variance of returns on this portfolio = (0.54637)^{2}(87.81)^{2}+(0.45363)^{2}(94.06)^{2}+2(87.81)(94.06)(0.47)(0.54637)(0.45363)
= 6046.63; the standard deviation = 77.76%;
The optimal proportion to invest in this portfolio is given by the formula [E(r_{p})r_{f}]/[0.01Avar(r_{p})]
= (42.4895.2)/[0.01x3x6046.63] = 20.56%;
hence the proportion invested in the riskfree asset = 79.44%;
the proportion invested in PFE = (0.2056)(0.54637) = 11.23%, while the
proportion invested in WLA = (0.2056)(0.45363) = 9.33%
e)
If I believed that the experience of the last five years would be a
better estimate of the statistical behavior of stock returns for the next year,
I would use the corresponding numbers given in the table.
In this case, the expected return would be (42.04+43.03+5.2)/3 = 30.09%.
On the other hand, if I believed that the statistical behavior of market risk
premiums and stock returns probably hadn't changed over the last 65 years, I
would use all the information. In
this case, I would use the CAPM to conclude that the E(r_{pfe}) = 5.2 +
0.95(8.41) = 13.19% and E(r_{wla}) = 5.2 + 0.8(8.41) = 12.60%.
The expected return on an equally weighted portfolio would then be
10.33%.
2.
a.
I would first figure out the expected cash flows on the policy.
In order to do this, I would have to estimate the probability of
earthquakes of various magnitudes, locations and depths and multiply them by the
insurance payment for each earthquake type, as specified in the bond indenture.
I would then add up all these numbers.
I now need to estimate the required rate of return. This can be obtained by using the CAPM. For this, I need the beta of these bonds.
Since the payoffs on these bonds are probability uncorrelated with the
market, the required rate of return would be the riskfree rate.
Discounting the expected insurance payment by the riskfree rate, I would
have my estimated bond price.
b. Investors who need to diversify their portfolio could hold these bonds. Alternatively, investors who are in a position similar to Oriental Land, i.e. their cashflows would be negatively impacted by an earthquake could also hold these bonds (Keep in mind that Oriental Land is selling these bonds to the insurance company.)
The quiz is closed book.
Time allowed is 2 hours.
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.
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.
1) Consider the quotes on the following Treasury bonds and note, obtained from the Wall Street Journal (http://interactive.wsj.com/documents/tsyquote.htm) of Dec. 15, 1999:
Bond 
Coupon Rate 
Maturity
Month/Yr 
Bid 
Asked 
Chg 
Ask 
1 
5 1/4 
Nov 28 (Tbond) 
84:14 
84:16 
41 
6.44 
2 
6 1/8 
Nov 27 (Tbond) 
95:07 
95:09 
44 
6.49 
3 
6 1/2 
Nov 26 (Tbond) 
99:24 
99:26 
44 
6.51 
4 
7 1/2 
Nov 24 (Tbond) 
111:21 
111:25 
48 
6.54 
5 
5 3/4 
Nov 02 (Tnote) 
99:02 
99:04 
8 
6.08 
6 
5 5/8 
Nov 00 (Tnote) 
99:22 
99:24 
1 
5.89 
Treasury bonds usually mature on the 15^{th} of the month. Assume that today is Nov. 15^{th} for your computations, unless specifically instructed.
a. (15 points) Compute the duration of the bonds
maturing on Nov. 15, 2028, Nov. 15, 2024 and the note maturing on Nov. 15, 2002.
Use the following formula from Bodie, Kane and Marcus: _{
}
, where
c is the coupon rate per period
T is the number of payment periods
Y is the bond’s yield per payment period.
Keep in mind that coupon payments are made every six
months.
b. (15 points) Estimate the duration of the bonds maturing on Nov. 15, 2026 and Nov. 15, 2027 without using your calculator. Explain how you came up with your estimates. Points will be awarded primarily for your explanation.
Suppose you work for an insurance company that has the following expected payments:
Date 
Amount 
Nov. 15, 2020 
$20m. 
Nov. 15, 2001 
$40m. 
Nov. 15, 2010 
$40m. 
c. (15 points) Construct a portfolio of the bonds maturing on Nov. 15, 2028, Nov. 15, 2024 and the note maturing on Nov. 15, 2002 to immunize your company’s liabilities (i.e. ensure that the liabilities are fully funded in the event of small but parallel movements in the term structure.)
d. (15 points) Do you think your company’s
liabilities be fully funded if rates move in parallel, but rate changes are
large? Explain your answer.
If you think you will not be adequately protected, but you wished to
restrict yourself to the six bonds in the table above, how would you modify your
portfolio?
2. Here is some Tbill rate information from the Wall Street Journal of Dec. 15, 1999. Quotes are from midafternoon of Dec. 14, 1999. Treasury bill quotes are in hundredths, quoted in terms of a discount rate. Days to maturity are calculated from settlement date. All yields are based on a oneday settlement and calculated on the asked quote.
Maturity 
Days to Mat. 
Bid 
Asked 
Chg 
Ask Yield 
Dec 30 '99 
15 
4.87 
4.79 
+0.05 
4.87 
Jan 13 '00 
29 
5.29 
5.21 
0.05 
5.30 
Jan 27 '00 
43 
5.15 
5.11 
+0.01 
5.21 
Feb 10 '00 
57 
5.11 
5.07 
0.04 
5.18 
Feb 17 '00 
64 
5.09 
5.07 
+0.01 
5.19 
Source: Telerate/Cantor Fitzgerald. 
a.
Use the ask yields to compute the 2week forward rates 15 days ahead, 29
days ahead, and 43 days ahead. Express
the spot rate and the forward rates as effective annual yields.
Keep in mind that treasury bills are quoted using the bank discount
yield, r_{BD} =
(FVP)/FV)*(360/n), where n = no. of days to maturity calculated from settlement
date, FV is the face value of the bill, and P is the price of the bill.
Bill yields are computed according to the formula, r_{BEY}
=[(FVP)/P](365/n). All
yields are based on a oneday settlement. (15 points)
b.
Use the information from the previous question to make predictions for
2week Tbill rates, 15 days ahead, and 29 days ahead.
Assume an annualized liquidity premium of about 10 basis points for all
bills up to a maturity of 6 months. (10 points)
3. Read the following article from the Wall Street Journal of Oct. 4, 1999, and answer the following question (15 points):
How would you evaluate the previous financing strategy of Boeing and that of Airbus Industrie from the point of view of exposure to interest rate risk? What about the current financing strategy of Boeing? How could Boeing protect itself from interest rate risk under the new strategy?
Boeing
Overhauls Financing Operation, Heightening Rivalry With Its Lessors
Boeing Co., hoping to improve service and increase profit from the lucrative realm of lending and leasing, plans to overhaul its customerfinancing arm, according to company and industry executives.
The changes are worrying some leasingcompany buyers of Boeing commercial jets, who fear the manufacturer is becoming their competitor.
A major restructuring of the Boeing Capital Corp. financing unit is expected to be announced this week. That larger maneuver represents the latest effort by Chief Financial Officer Deborah Hopkins to unify and broaden Boeing's limited approach to financing purchases of jetliners, military aircraft and spacerelated projects.
While Seattlebased Boeing is a large corporation, with 1998 revenue topping $56 billion, the aerospace company's approach to backing its customers' purchases has been seen as more constrained than that of other big industrial producers.
In the jetliner business, Boeing's flexibility is seen by some carriers as lagging behind that of rival Airbus Industrie. The European consortium has been seen as more aggressive at times in rounding up financing, with loans of longer duration and lower interest rates. Until now, Boeing has mostly provided partial and "backstop" financing on commercialjet purchases, including guarantees of repayment. Those loans typically are sold over time to other lenders.
Boeing Capital Corp., originally acquired via a 1997 merger with McDonnell Douglas Corp., mostly purchases and leases used jets, business planes and equipment such as machine tools and trucks. Ultimately, that unit's portfolio of loans and investment, including about $1.57 billion for aircraft, is seen as growing during the next few years. One Boeing executive said that when that unit's holdings are combined with other commitments that rest directly on the parentcompany balance sheets, Boeing's total portfolio is about $6 billion.
A Boeing spokesman declined to comment. New Risks For all its promise, the latest move includes new risks for Boeing.
The transition already is unnerving some commercialaircraft lessors among the 20 companies that lease out more than 900 Boeing jets and 250 Airbus planes. Some buy new jets and actively manage their fleets. Those planes are often leased to airlines unwilling or unable to fund their own purchases, through "operating leases." Many lessors also make money by helping put together financing for new planes.
In recent weeks, Boeing executives have tried to assure some lessors that the manufacturer's financing unit doesn't plan to simply buy Boeing jets on speculation and place them with needy carriers.
Robert Genise, chief executive of the Seattlebased lessor Boullioun Aviation Services, said that after discussions with Boeing executives, he nonetheless sees "an obvious problem." Mr. Genise, whose company controls 61 newer Boeing jets and has orders for 96 more, said that lessors must now ask themselves, "'How can you buy aircraft from somebody who's now thinking about competing with you?"
Mr. Genise said that Boeing officials seem drawn to the lessors' strong profit margins, but "I'm not sure they really are focused on the risks," especially those of being an operating lessor.
Boeing executives said that as they develop a "full portfolio," the company will be a primary lender to some carriers and would offer operating leases in some cases. They said market growth could offset the impact on lessors, and they will work more closely with certain lessors to arrange financing.
Steven Hazy, president of Los Angeles based International Lease Finance Corp., said that after "extensive consultations" with Boeing officials, he doesn't see "a direct threat." Mr. Hazy, whose company is one of Boeing's biggest customers, said the jet maker needs more tools "to play catchup with Airbus." He expects much of Boeing's direct leasing to involve airlines already ordering Boeing planes.
Mr. Hazy, whose company is a unit of insurance company American International Group Inc., said he expects greater competitive impact on small and mediumsize lessors, because they do lower volumes of business, rely on profit from financing, and have reduced access to lowcost funds. He also predicted some impact on his largest competitor, the capital aviationservices unit of General Electric Co. GE is heavily involved in newaircraft financing and operates a large fleet of newer planes for leasing. A spokeswoman for the GE unit had no comment.
In discussing Boeing's plans, Mr. Hazy cautioned that Boeing must approach its new plans "carefully," because the plane maker needs to preserve funds for developing new lines of aircraft.
Credit: Staff Reporter of The Wall Street Journal
1. a. Using the formula, _{
}
, we can find the durations. Thus,
for the Nov. ’28 bond, we’d use values of y = .0644/2 or 0.0322, with c =
.0525/2, and T = 29x2 = 58. We find
Bond 
Duration 
Nov 28 (Tbond) 
31.654 half years or 15.827 years 
Nov 24 (Tbond) 
12.305 years 
Nov 02 (Tnote) 
2.797 years 
b. For the Nov. 26 and Nov. 27 bonds, I would simply interpolate between the known durations of the Nov. ’24 and Nov. ’28 bonds. The coupons for the Nov. ’26 and Nov. ’27 bonds are sufficiently similar, and in any case, are also between the coupons for the 2024 and 2028 bonds. Hence my estimates would be about 13.8 for the Nov. ’26 bond and 14.8 for the Nov. ’27 bond.
c. We first need to compute the duration of the liabilities. There are two ways of doing this. The usual way is to use the yield on the security portfolio used to immunize the liabilities. The second and more precise way is to estimate the term structure and to use the interest rate for each liability that would be appropriate for comparable traded bonds. Both methods are complicated. Hence, since the term structure is fairly flat, we assume that it is indeed flat, and use a discount rate of 6.5% to discount the liabilities. This gives us a present value of the liabilities of 20/(1.065)^{21} + 40/(1.065)^{2} + 40/1.065^{11}, which works out to 15.3295 + 35.266 + 20.0085 = $60.6044m.
The duration of the liability portfolio thus works out to (5.3295/60.6044)(21) + (35.266/60.6044)(2) + (20.0085/60.6044) = 6.6421 years.
Assuming a flat term structure, if the proportion of the immunizing portfolio invested in the Nov. ’28 bond is denoted by x, we solve the equation, 15.827x + 2.7969(1x) = 6.6421. Solving, we find x = 0.295, and 1x = 0.715, or 29.5% of $60.6044 is invested in the Nov. ’28 bond and 71.5% in the Nov. 02 note.
c. The dispersion of the cashflows in the liability portfolio is greater than those of the assets. Hence the portfolio would not be fully protected for large movements in the interest rate. Hence I would choose the Nov. ’00 note instead of the Nov. ’02 note, but I would keep the Nov. ’28 note.
2. a. Using the bondequivalent yield formula, the prices for the relevant bills can be established as given in the second column
Maturity 
Price 
Forward Rates 
Dec 30 '99 
0.9980 

Jan 13 '00 
0.9958 
5.922% (2 wk rate 15 days ahead) 
Jan 27 '00 
0.99389963 
5.1064% (2 wk rate 29 days ahead) 
Feb 10 '00 
0.9919756 
5.1816% (2 wk rate 43 days ahead) 
The forward rates can be computed as follows:
The 2week forward rate 15 days ahead is given by (0.9980/0.9958) =
1.0022093. Annualized, we get
(1.0022093)^{365/14} = 1.05922 or 5.922%.
The others are obtained in the same fashion, and given in the third
column.
b. The predicted future spot rates are simply the forward rates plus the liquidity premium, i.e. 5.922  0.10 or 5.822% for the 2week rate 15 days ahead, and 5.1064  0.1 or 5.0064% for the 2week rate 29 days ahead.
3.a. Boeing’s previous strategy gave them some credit exposure for the time that they held the loans, but the interest exposure was limited. Airbus Industries’ interest rate exposure was much greater given the greater duration of their loans.
The new financing strategy of Boeing’s would give them much more interest rate exposure.
They could manage this exposure in a couple of different ways: one, they could sell the loans as soon as possible; two, they could immunize the exposure, perhaps by holding bonds issued by the governments of the countries where the airlines are based (assuming that both have correlated amounts of country risk).