Pace University
Fin 652 Investment Analysis
Fall 2000
Prof. P.V. Viswanath


Midterm I

1. The following article appeared on the WSJ Internet site on Oct. 3.  Assuming that the article was responding to current information, what do you think the WSJ was reporting regarding the stock market at that time on Oct. 3?  Use the information in the article and the theories described in class to explain your answer.  Your answer will be evaluated in the context of how well you use the information in the article and the understanding of the theories of interest rate determination that you demonstrate.  Other than that, it is irrelevant as to whether you actually remember what the stock market did on Oct. 3. (35 points)

Oil's Ascent Causes Bond Market to Slip

By JOHN PARRY, Dow Jones Newswires, Oct. 3, 2000

NEW YORK -- Soaring crude-oil prices that reignited worries about inflation in the U.S. sent the bond market mostly lower ahead of Tuesday's Federal Reserve policy makers' meeting, at which no shift in interest rates is expected.

The fall was sharpest in U.S. government securities with longer-dated yields, which narrowed the inversion of the yield curve. Some strategists say the curve could flip back to its normal state later this week.

Ten-year yield chartLate Monday, the price of the 10-year Treasury note was down 5/32 point, or $1.5625 for a note with $1,000 face value, at 99 12/32. Its yield rose to 5.816% from 5.795% late Friday, as yields move inversely to prices.

At the longer end of the Treasurys curve, the 30-year Treasury bond was at 104 14/32, down 18/32. Its yield rose to 5.921% from Friday's 5.882%.

Among Treasury securities with shorter maturities, the yield on the two-year note was unchanged on the session at 5.966%, while the yield on the five-year note fell to 5.833% from 5.841%.

"Energy [prices] were showing some renewed vigor, and that's weighing on the back end of the [Treasurys] curve," said Kevin Flanagan, fixed-income strategist at Morgan Stanley Dean Witter & Co. in New York.

Crude oil for November delivery in New York climbed $1.34 to $32.18 a barrel late Monday. The rise was due partly to news that European countries were unlikely to release strategic petroleum reserves for use and to violent clashes in the Middle East that are seen as a possible trigger for higher oil prices.

Bond-market participants will watch Tuesday's Federal Open Market Committee meeting carefully to see if policy makers refer specifically to energy prices. If in that regard the FOMC statement is "a little bit more hawkish," said Gemma Wright, director of market strategy at Barclays Capital in New York, that could intensify the already negative market sentiment about inflationary pressures.

This sentiment was driven Monday in part by uncertainty about violence on the West Bank and the Gaza Strip, which Ms. Wright said is "on the [bond] market's horizon." However, she added, "no one knows how extensive it is, or how to assess it yet," in terms of the possible longer-term impact on crude-oil prices.

Tuesday's FOMC meeting isn't likely to spring any fundamental surprises, strategists said. In a display of unanimity, all 25 primary dealer economists surveyed by Dow Jones Newswires and CNBC agreed that the FOMC is unlikely to change interest rates or to alter its statement of risks at the meeting.

"We don't think there's any debate about the move," with no change in interest rates expected, said Dana Johnson, head of research at Banc One Capital Markets Inc. in Chicago.

Treasury Yield CurveLater, however, some members of the FOMC may start debating whether to change the bias of risks, currently weighted toward inflation, in the accompanying statement, he said. That is unlikely to shift to a neutral bias until the U.S. unemployment rate is shown to be rising significantly, Mr. Johnson added.

Mr. Flanagan of Morgan Stanley Dean Witter said that depending on whether the next batch of first-tier economic data -- most notably the September U.S. employment report slated for release Friday -- confirm the U.S. economy is slowing, the yields of short-dated Treasurys could then fall below those of the long bond.

That shift would be based on market expectations that the Fed was contemplating cutting interest rates, but it would be "premature" to speculate about an imminent easing of monetary policy, Mr. Flanagan added.

"Inversion" means that yields of longer-dated Treasurys are lower than those of shorter-dated ones. The trend began in January, after the government indicated it would start a program to buy back $30 billion of mainly longer-dated Treasurys this year, pushing the long bond's price up and its yield down.

"One of the major forces causing the [Treasurys yield] curve to normalize is the expectation that the Fed may be finished and also that inflation may not be completely contained," said Mark MacQueen, executive vice president of Sage Advisory Services in Austin, Texas.

That outlook was keeping yields of shorter-dated U.S. government securities low but pushed up the yields of longer-dated securities, which are more vulnerable to inflation expectations.

Monday, many Treasury-market participants bought shorter-dated Treasurys and sold longer-dated Treasurys, noted Mr. Johnson of Banc One Capital Markets. That was driving the inverted yield curve between two-year and 30-year Treasurys toward disinversion.

There was good buying of five-year Treasury securities against longer-dated U.S. government securities, noted Ms. Wright of Barclays Capital.

One factor heightening worries about price pressures Monday, bond strategists said, was the prices-paid component of the National Association of Purchasing Management's September business index.

The main index rose to 49.9 from 49.5 in August; readings below 50 indicate a contraction of manufacturing activity. But the prices-paid index -- at 58.1, compared with August's level of 56.2 -- continued to indicate that factory prices are rising.

2. Treasury Quotes as of midafternoon Friday, October 6, 2000 from the WSJ.  Keep in mind that these rates are valid for immediate, with one day allowed for settlement (however, given that Monday is Yom Kippur and the markets are closed, settlement will take place on Tuesday).

Maturity Days
Bid Asked
Oct 12 '00 2 5.99 5.91
Oct 19 '00 9 5.83 5.75
Oct 26 '00 16 5.89 5.81
Nov 02 '00 23 5.92 5.84
Nov 09 '00 30 5.94 5.90
Nov 16 '00 37 5.92 5.88

Money Rates For Friday, October 6 (assume these are also midafternoon rates).  (also from the WSJ Internet edition)

COMMERCIAL PAPER: placed directly by General Electric Capital Corp.: 6.48% 30 to 37 days; 6.46% 38 to 67 days; 6.43% 68 to 96 days; 6.51% 97 to 121 days; 6.46% 122 to 160 days; 6.41% 161 to 201 days; 6.36% 202 to 239 days; 6.33% 240 to 270 days.

Suppose you have a million dollars to invest as of mid-afternoon Friday, Oct. 3, 2000 .  You wish to invest those million dollars for 37 days.  

  (Assume that commercial paper rates are quoted in bank-equivalent yields, and are ask quotes, and that Treasury quotes are banker's discount.)

  1. How much would you have on hand at the end of 37 days, if you invest in GEC Corp. commercial paper? (10 points)
  2. How much would you have on hand at the end of 30 days, if you invest in Treasury bills? (10 points)
  3. If you invested in Treasury bills for 30 days, and then invested the proceeds in another instrument for another 7 days, what rate of return would that second instrument have to yield, in order for you to have the same dollar amount in hand at the end of the 37 days, as if you had invested in 37 day GEC commercial paper?  Give your answer in bond-equivalent yield.  (Assume that settlement for the second instrument is immediate.) (10 points)

3. Cisco Systems (CSCO) was trading at 51 1/8 at 4 p.m. on Tuesday, October 10 (  However, Jan noticed from her favorite website ( that short interest in Cisco on September 15th was on the order of 52,002,242 shares.  As a ratio of average daily volume, it worked out to about 1.24%.  She felt that this was too large a number, and that the market was telling her that CSCO was bound to drop in price.  Hence she went to her broker and sold about 1000 shares of Cisco short; her broker, DB Alex. Brown requires initial margin of 50% for short sales of stock  Fortunately for Jan, the price had not changed, and the broker was able to sell shares for her at exactly 51 1/8. 

  1. If the broker's maintenance margin is 35%, how much can the price rise before Jan will face a margin call?  (15 points)
  2. If the broker's policy is that once a margin call is made, the account margin has to be brought up to the initial margin level, what amount will Jan have to deposit into her account if the price of CSCO rises to $65 before a margin call is made? (20 points)

Solutions to Midterm I:

1. The following points are relevant:

2.a. rbey = [(FV-P)/P](365/37), or 0.0648 = (FV/P - 1)(365/37).  Solving, we find that FV/P = 1.0065688.  Hence an investment of $1 million will result in a terminal value of $1,006,568.80 after 37 days.

b. 0.059 = (1-P/FV)(360/30); solving P/FV = 0.9950833.  If P = $1m., FV = $1,004,941.00

c. An investment of $1,004,941.00 must result in a terminal value of 1,006,568.80 after 7 days.  Hence the rate of return for the 7 days is 1,006,568.80/1,004,941.00.  To express this in bond-equivalent yield terms, we annualize it by multiplying by 365/7 to get 8.44629%

3. a. We use the formula Equity/Loan = 0.35, or (51.125x1000x1.5 - 1000P)/1000P = 0.35.  Solving, we get P = 56.8056

b. Again, using the same formula, but this time equating it to 0.5, we get [(51.125x1000x1.5 + x - 65000)/65000] = 0.5.  Solving, we find x = $20,812.50

Midterm II

1. Read the article below and answer the following questions:

  1. The article reports: "And over the long term, Alliance's strategy is to keep its business diversified."  Does diversification make sense for Alliance Capital?  Explain your answer in about one page. (25 points)
  2. "The stock is changing hands at about 48.69, about 14.5 times Zack's Investment Research 2001 earnings estimates of $3.35 per share -- a slight premium to its 13% long-term growth rate."  Use this information to estimate the required rate of return on Alliance.  If the return on the S&P 500 over the last three years was 16.5% (according to Yahoo), and the rate of return on 1 year T-bills is 6.19% according to, estimate Alliance's beta. (20 points)

Is It Time to Align with Alliance?

By ALLISON KRAMPF, Barron's Online, Nov. 6, 2000

In their heyday, mutual funds were the way to invest, before technology stocks and online trading seized the limelight.

Now, with the tech stock selloff, shares of mutual fund companies have taken off as investors have come to value asset managers -- and their takeover potential. The stocks have come so far that some analysts and fund managers say that too many funds are chasing too little money (see Weekday Trader, "Fund Stocks May Lose Street's Mutual Admiration," June 19).

But others say some asset managers could be good investments over the long term.

One favorite: New York City-based Alliance Capital Management.

Alliance, which has a market capitalization of $8.52 billion, acquired Sanford C. Bernstein, the renowned money manager for institutions and wealthy individuals, for $3.5 billion (approximately $1.5 billion in cash and 40.8 million newly issued shares). The deal closed last month.

But even before the Bernstein acquisition, Alliance was "an early player in the private, high-net-worth area," says John Riazzi, president and chief investment officer of Dean Investments.

And now, with nearly half a billion dollars under management, Alliance has the scale to be one of the major players among asset managers. It also gets fee income comprising almost 95% of the company's revenue.

"Alliance is seeing net inflows [of funds]," Riazzi says.

Riazzi, who holds 100,000 shares of Alliance, says he would add more at current levels of 48.69, about 14.5 times Zack's Investment Research 2001 earnings estimates of 3.35 per share. Currently, the stock is trading about 15% off its 52-week high of 56.688 hit in September. (It hit a low of 29.313 in January.)

And over the long term, Alliance's strategy is to keep its business diversified. The fund company is looking to broaden its product lines (it recently launched a global and international index management business) and to expand its fixed-income capabilities.

"Investors have focused on equities, but we want to make sure if the pendulum swings that we have a diverse and broad product line," Alliance CFO Robert Joseph tells Barron's Online.

Derek Izuel, portfolio manager with the Aim Global Trends Fund, likes several aspects of Alliance's business. "It is growing earnings steadily (in the mid-teens over the last few years) and it has a higher return on equity," estimated at 89.3% this year (three percentage points above its average of about 86.3% for the last four years), Izuel says.

Alliance has benefited from its emphasis on growth mutual funds over the last decade. But though growth funds have cooled in this year's market, that should not cause too much concern.

"Value funds have done better in this year's market, but that is only one year in the last eight," Izuel says. And, "if you look at demographic trends, the demand is for growth funds," Izuel adds.

(Sanford Bernstein is a value shop, so Alliance is not putting all its eggs in the growth basket.)

And Alliance does not seem to be suffering. With $9.2 billion in net inflows for the third quarter, "Alliance remains a leader across the mutual fund industry in attracting new money," says Prudential Securities' analyst John Hall.

Alliance's Joseph says that international expansion is still in the cards. Alliance has had a presence in Europe since the 1970s, and currently Alliance has 27 offices and affiliates and joint ventures in 20 different countries.

Meanwhile, the shares look attractively valued. "It is cheaper now [than at the beginning of the year, when it was trading at about 20x earnings] due to the choppiness of the equity markets, which have hurt most fund groups," says Jeff Hopson, an analyst at A.G. Edwards & Sons.

The stock is changing hands at about 48.69, about 14.5 times Zack's Investment Research 2001 earnings estimates of $3.35 per share -- a slight premium to its 13% long-term growth rate.

Earnings are expected to grow by 20% in 2000 and by 15% in 2001, according to Goldman Sachs.

Goldman analyst Richard Strauss rates Alliance Market Perform, with a price target at 60, a 25% premium over the current price. Strauss says more industry consolidation and continued fund flows into Alliance could boost its stock price.

Of course, since Alliance is 57% owned by AXA Group, the stock does not have the same takeover premium as many of its independent peers do.

"If there was the decision to buy the rest, AXA would pay some premium but it is not the same open bidding process," Riazzi points out. A.G. Edwards' Hopson speculates that parent AXA could acquire Alliance for around 58, a 20% premium to the current price.

But unlike other fund companies, Alliance's diversified earnings stream and solid fee income should help it prosper no matter what the market is doing. And investors who ally themselves with the company should benefit as well.

2. The following funds all have above a billion dollars in assets, and have been selected from a Fund Screener program at  They all list their objective as objective growth. 

  3-year beta Std. dev. (3 year) R2
Hartford Capital Appreciation A (ITHAX) 1.11 26.78% 0.50
Van Wagoner Emerging Growth (VWEGX) 1.36 54.98% 0.18
MFS Capital Opportunities A (MCOBX) 0.92 19.62% 0.65
MFS Capital Opportunities B (MCOFX) 0.92 19.64% 0.65
Fortis Growth Fund A (FGRWX) 0.9 30.93% 0.25

Stockpoint provides the following explanations of the terms used in the Table:

R-Square 3 year
Measures the correlation between the fund's performance and that of the broader market as measured by an approximate index. The calculation is done with 3 years of stored data.
Beta 3 year
A Statistical measure of fund's sensitivity to market fluctuations calculated with 3 years of stored data .It measures how far the fund has historically moved relative to similar moves in the index, discounting the risk-free rate of return of a three-month treasury bill.
Std. Deviation 3 year
Measures the variability of a fund's returns. The figure indicates the number of percentage points above or below the fund's average annual return within which any given annual return can be expected to fall two-thirds of the time. The calculation id done with 3 years of stored data.

The chart above shows the cumulative return two funds VWEGX and ITHAX starting from (more-or-less) the beginning of November.  For example, if you had invested $100 in ITHAX at the beginning of November, you would have had approximately $112 at the end of January 2000 and $118 at the end of April, $117 at the end of July and $120 at the end of October. 

The chart above shows the cumulative returns for Hartford Capital Appreciation (ITHAX) relative to the S&P 500. (The cumulative return for ITHAX from the beginning of November 1999 to the beginning of November 2000 is about 20%.)

a. Using the chart, visually estimate the beta of ITHAX. Now come up with an estimate of the beta of VWEGX, that would be consistent with your ITHAX beta estimate.  (10 points)

b. The correlation coefficient between the monthly returns of FGRWX and VWEGX, computed over the last twelve months, is 0.72.  If you were constructing a portfolio, how much would you invest in each fund?  Your portfolio can consist of investments in these two  as well as in 1 year T-bills, which earn 6.19%.  The expected return on FGRWX is 81.52%, while the expected return on VWEGX is 128.36%. (Source: Bloomberg). (35 points)

c. Which of the five funds in the table above is least diversified? (10 points) 

3 (additional question). Here are the top ten holdings of Van Wagoner Emerging Growth Fund (VWEGX), as reported at
Holdings # of Shares Market Value % of Holdings Beta
1 ARIBA INC COM (ARBA) 1,230,750 $ 218,304,000 12.61% 2.8 (from
2 COBALT NETWORKS INC COM (COBT) 648,648 $ 60,645,000 3.50% n.a.
3 ONHEALTH NETWORK CO COM (ONHN) 5,192,050 $ 46,404,000 2.68% n.a.
4 BLUESTONE SOFTWARE INC COM (BLSW) 416,075 $ 42,927,000 2.48% 3.1 (from
5 PHONE COM INC COM 316,895 $ 36,740,000 2.12% 0.7 (from
6 INTERWOVEN INC COM 301,531 $ 30,962,000 1.79% 1.0 (from
7 NETRO CORP COM 625,000 $ 30,811,000 1.78% 6.7 (from
8 PREVIEW SYS INC OC-COM (PRVW) 425,000 $ 22,819,000 1.32% n.a.
9 JDS UNIPHASE CORP COM (JDSU) 97,650 $ 15,752,000 0.91% 1.85 (from
10 TRANSWITCH CORP COM (TXCC) 207,212 $ 15,036,000 0.87% 1.3 (from

Assuming that the average beta for the stocks for which betas are not provided is equal to the average beta for the stocks for which betas have been provided above, estimate the beta of the Van Wagoner Emerging Growth Fund. (10 points)

Solutions to Midterm 2

1. a. Diversification for the sake of reducing the volatility of the stock return does not make sense because investors can diversify their own portfolios much more easily.  Diversification performed at the firm level is more expensive for at least two reasons: one, combining operations of two firms under one roof is operationally more difficult; two, investors can change their portfolio composition if they want to, for any reason, but the firm cannot easily undo an acquisition easily.  In this case, there is potential for confusion because the firm is an asset management firm.  However, when the writer of the article talks about the firm's diversification, he refers to the firm's diversifying in terms of the products it offers its clients, i.e. the different funds; he is not talking about offering diversified funds.  

It is, however, possible to make an argument for product line diversification.  If the firm believes that its clients are looking for a one-stop shop for all their investment needs, then the firm should offer a complete line of funds, i.e. product diversification.  Also, if its costs per fund would be lower, the greater the number of funds it offers.  This could be, for example, if there are economies of scale in managing funds.

b. Using a growth rate (of earnings) of 13%, if 3.35 is the earnings per share estimate for the coming year, the stock price formula (for a growing perpetuity) gives us: 48.69 = 3.35/(r-0.13), where r is the required rate of return.  Solving, we find r = 19.88%.

If we now use the CAPM [Required ROR = Rf + b(E(Rm) - Rf)], we have the relation 20.77 = 6.19 + b(16.5-6.19). Solving, b = 1.415.

2a. Eyeballing the chart, we see that the price movements for ITHAX are greater in amplitude relative to the price movements for the S&P 500.  Hence the beta is greater than 1; a reasonable estimate is 1.25. Similarly, from the second chart we see that the price movements of VWEGX are much greater than those of ITHAX.  Hence the beta of VWEGX relative to ITHAX could be estimated as 1.5, and hence the beta of VWEGX relative to the S&P 500 is (1.25)(1.5) = 1.875.

2b. We need to find the tangent portfolio first.  The formula for the tangent portfolio is:

; applying it to this case, we get

; hence wFGRWX = 0.76

E(Rtgt portfolio) = (0.76)(81.52) + (0.24)(128.36) = 92.75%; Var(Rtgt portfolio) = (0.762)(30.932)+(0.242)(54.982) + 2(0.76)(0.24)(0.72)(54.98)(30.93) = 1173.24.

The optimal combination of this tangent portfolio and the riskfree asset is given by the formula , where y* is the optimal amount in the tangent portfolio .  Plugging in the values, we get y* = [92.75-6.19]/[(0.01)(4)(1173.24)] = 1.8, i.e. 80% of the amount that the investor's equity is being borrowed at the T-bill rate.  Hence the proportion invested in VWEGX is (1.8)(0.24) = 0.432 or 43.2% and 1.8 - 0.432 = 1.368 or 136.8% in FGRWX.

2c.  Looking at the R2s, we see that VWEGX is least diversified.  However, we could look at the unexplained variance, which is (1-R2)Var(Rfund).  This works out to 358.58 for ITHAX, 2176.42 for VWEGX, 134.73 for MCOBX, 135.01 for MCOFX and 717.5 for FGRWX.  Hence on this score as well, VWEGX is the least diversified.

3. We have the beta values for seven of the firm's holdings.  If wi is the fund's percentage portfolio holdings for stock i, and bi is the beta of stock i, the value-weighted average of the betas of the seven stocks is obtained as Swibi/SwiSwi = 22.56; hence the value-weighted average works out to [(2.8)(12.61) + (3.1)(2.48) + (0.7)(2.12) + (1.0)(1.79) + (6.7)(1.78) + (1.85)(0.91) + (1.3)(0.87)]/22.56 = 2.006.  If we can assume that the average beta for the stocks for which betas are not provided is equal to the average beta for the stocks for which betas have been provided, then 2.006 is also the estimated beta of the fund.

Final Exam

Q. 1.  Read the article below from the Wall Street Journal of December 18, 2000 and answer the following questions:

  1. Estimate the duration of the 30 year bond. (10 points)
  2. Estimate the duration of the 10 year note. (10 points)
  3. Estimate the duration of the two-year note, assuming only for this purpose that a coupon of 6% is paid annually, and that the note is selling at par.  Use this duration estimate to come up with a fresh estimate of the yield of the two-year note, as of the end of trading on Friday, December 15, 2000.  (20 points)
  4. (Bonus question) Can you come up with a procedure to estimate the yield of the two-year note as of the end of trading on Friday, December 15, 2000, without making any assumptions about the note's duration? (10 points)

Treasurys Rise as Traders Await Fed Rate Action

NEW YORK -- Treasurys rose Monday as the market awaits Tuesday's meeting of Federal Reserve officials, with many hoping the central bank will announce an aggressive response to the slowing U.S. economy.

In afternoon trading in New York, the 10-year note was up 10/32, or $3.125 per $1,000 face value at 104 19/32. Its yield, which moves inversely to its price, fell to 5.131% from 5.172% late Friday.

The 30-year bond rose 9/32 to 112 14/32, yielding 5.401%, down from 5.418% late Friday. The two-year note gained 4/32 to 100 20/32, yielding 5.276%.

Monday's gains, though modest, extended a sharp advance over the past two weeks. The yield on the benchmark 10-year note has dropped to 5.13% from 5.53% on Dec. 4.

2.  (20 points) Suppose investors' horizons are the same and equal to 1 year.  Then, the CAPM would imply E(Ri) - Rf = bi [E(Rm) - Rf], where Ri is the rate of return on any asset i, Rm is the rate of return on the market portfolio, bi is the market beta of asset i, and Rf is the rate of return on a 1 year T-bill.  Use the definition of the liquidity premium (remember there are two different ways of expressing the liquidity premium), and the relationship between the beta of a bond and its duration to answer the following question:

3. Here is some information on Treasury bills from the Wall Street Journal Interactive edition.  The following information is also available on the website:

Treasury bond, note and bill quotes are from midafternoon. Colons in bond and note bid-and-asked quotes represent 32nds; 101:01 means 101 1/32. Net change in 32nds. Treasury bill quotes in hundredths, quoted in terms of a discount rate. Days to maturity calculated from settlement date. All yields are to maturity and based on the asked quote.

Maturity Days to Mat. Bid Asked Chg Ask Yield
Dec 28 '00 9 5.35 5.27 -0.12 5.35
Jan 04 '01 16 5.60 5.52 -0.08 5.61
Jan 11 '01 23 5.65 5.57 -0.08 5.67
  1. Compute the ask prices of the three bills.  (10 points)
  2. Compute the forward yields for the weeks ending Jan. 4, 2001 and Jan. 11, 2001. (10 points)
  3. Assuming a liquidity premium of 10 basis points annualized for the T-bill maturing Jan. 11, 2001, estimate the expected future 1-week rate for the week ending Jan. 11, 2001. (10 points)
  4. Assuming that your 1-week rate forecast for the week ending Jan. 11, 2001 is correct, can you use it to make abnormal profits?  If so, explain how.  If not, explain who could use such a forecast and for what purpose. (10 points)

Solution to Final Exam

1. a, b. The duration of a bond can be estimated as the negative of the ratio of the percentage price change to the percentage gross yield change, i.e. D = -(DP/P)/[Dy/(1+y)].  Applying this formula to the case of the 30 year bond and the 10 year bond, we have the durations as shown in the table below.  Note that prices have been converted from thirty-seconds to decimals.

New price change old price new yield change old yield Duration
30 yr bond 112.4375 0.28125 112.1563 5.401 -0.017 5.418 15.55016
10 yr note 104.59375 0.3125 104.2813 5.131 -0.041 5.172 7.687056

c. Assuming a coupon of 6%, and a price of par (of course, we have the true original price, which is 100 20/32 - 4/32, or 100.5, but we use a price of $100 for convenience), the duration can be computed using the formula ; this gives us (1.06/.06)[1-(1.06)-2] = 1.9433. 

We can now use the duration formula above to come up with the equation 1.9433 = - (4/32)/[(0.05276-x)/1+x], where x is the old yield (as of Friday close).  Solving, we find x = 5.34342.

d. We first start by assuming a trial value for the coupon.  This can be used to estimate a duration, which is then used to estimate the old yield (as in the c. above).  Once the old yield is available, it can, once again, be used to compute a duration, using the formula in the first part of c.  By iterating on this procedure, it should be possible to reach a point, where the duration computed changes very little from iteration to iteration (assuming the procedure converges). 

2. According to the CAPM, E(Rlong-bond) = R1 yr. bond + Bond Beta(Market Risk Premium).  We also know from the definition of the liquidity premium that E(Rlong-bond) - R1 yr. bond = Liquidity Premium.  Hence Liquidity Premium = Bond Beta(Market Risk Premium).  However, we also know that the bond beta = -br,m(Duration), where br,m is the sensitivity of interest rates to changes in the return on the market.  Since all interest rates move in parallel, there is only one such beta.  Putting the two equations together, we have -br,m(Duration)(Market Risk Premium) = Liquidity Premium.  Now, since the Market Risk Premium and the br,m are the same for all bonds, while the duration of each bond is different, it is clear that hte liquidity premium must also differ from bond to bond.

3. a. The ask prices can be computed from the definition of the bond equivalent yield, i.e. .  Plugging in rBEY = 0.0535, n = 9, and FV = 100, we can solve for the price of the first bill.  Following this approach, we compute the numbers given in the table below, in the second-to-last column. 

b. The forward yields are computed by simply taking the ratio of the prices of the relevant bonds.  For example, the 1 week forward yield nine days ahead is computed by taking the ratio of 99.8683 to 99.7547, which yields 1.001138.  We then deduct 1 from this, and multiply it by 365/7 to annualize it.  This gives us the forward yield of 5.9365%.  This is repeated for the second forward yield as well.  The answers are given in the last column.

Maturity Days to Mat. Bid Asked Chg Ask Yield Ask Price Forw yld
Dec 28 '00 9 5.35 5.27 -0.12 5.35 99.8683  
Jan 04 '01 16 5.6 5.52 -0.08 5.61 99.7547 0.059365
Jan 11 '01 23 5.65 5.57 -0.08 5.67 99.6440 0.057929

c. Since the forward rate is equal to the expected future spot rate plus the liquidity premium, we see that the expected future spot rate equals 5.7929 - 0.1 = 5.6929%.

d. Since this forecast is taken from the observed term structure, it is not possible to obtain abnormal profits from it (unless the investor has a better estimate of the liquidity premium).   However, it is possible for an intending borrower to use it to choose between borrowing now and borrowing later (assuming the value of borrowing is the same for this person between now and then).