LUBIN SCHOOL OF BUSINESS
Pace
University
Fin
652 Investment Analysis
Fall 2000
Prof. P.V.
Viswanath
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)
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.
Late 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.
Later, 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 to Mat. |
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.)
3. Cisco Systems (CSCO) was trading at 51 1/8 at 4 p.m. on Tuesday, October 10 (http://finance.yahoo.com). However, Jan noticed from her favorite website (http://www.viwes.com/invest/shorts/query.cgi) 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. The following points are relevant:
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.
This suggests that manufacturing activity went up even though the index
still remains below 50.
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.
This suggests that corporate cashflow estimates probably aren't going up
to any great extent, if at all.
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.
This seems to indicate uncertainty.
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.
This very clearly indicates uncertainty.
The totality of the article indicates that the risk-free rate has increased; the level of uncertainty has increased as well. Consequently, the market risk premium probably went up as well. The required rate of return on stocks therefore must have gone up. On the other hand, there is no reason to believe that corporate cashflow estimates went up, either. Consequently, there is no reason to believe that the stock market went in the opposite direction to the bond market. Hence the stock market as a whole must have dropped.
2.a. r_{bey} = [(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
1. Read the article below and answer the following questions:
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 http://www.stockpoint.com. They all list their objective as objective growth.
3-year beta | Std. dev. (3 year) | R^{2} | |
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 http://www.stockpoint.com.Holdings | # of Shares | Market Value | % of Holdings | Beta | |
---|---|---|---|---|---|
1 | ARIBA INC COM (ARBA) | 1,230,750 | $ 218,304,000 | 12.61% | 2.8 (from http://www.hoovers.com) |
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 http://www.hoovers.com) |
5 | PHONE COM INC COM | 316,895 | $ 36,740,000 | 2.12% | 0.7 (from http://www.hoovers.com) |
6 | INTERWOVEN INC COM | 301,531 | $ 30,962,000 | 1.79% | 1.0 (from http://www.hoovers.com) |
7 | NETRO CORP COM | 625,000 | $ 30,811,000 | 1.78% | 6.7 (from http://www.hoovers.com) |
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 http://finance.yahoo.com) |
10 | TRANSWITCH CORP COM (TXCC) | 207,212 | $ 15,036,000 | 0.87% | 1.3 (from http://www.hoovers.com) |
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)
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 = R_{f} + b(E(R_{m}) - R_{f})], 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 w_{FGRWX} = 0.76
E(R_{tgt portfolio}) = (0.76)(81.52) + (0.24)(128.36) = 92.75%; Var(R_{tgt portfolio}) = (0.76^{2})(30.93^{2})+(0.24^{2})(54.98^{2}) + 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 R^{2}s, we see that VWEGX is least diversified. However, we could look at the unexplained variance, which is (1-R^{2})Var(R_{fund}). 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 w_{i} is the fund's percentage portfolio holdings for stock i, and b_{i} is the beta of stock i, the value-weighted average of the betas of the seven stocks is obtained as Sw_{i}b_{i}/Sw_{i}. Sw_{i }= 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.
Q. 1. Read the article below from the Wall Street Journal of December 18, 2000 and answer the following questions:
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(R_{i}) - R_{f} = b_{i} [E(R_{m}) - R_{f}], where R_{i} is the rate of return on any asset i, R_{m} is the rate of return on the market portfolio, b_{i} is the market beta of asset i, and R_{f} 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. 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(R_{long-bond}) = R_{1 yr. bond} + Bond Beta(Market Risk Premium). We also know from the definition of the liquidity premium that E(R_{long-bond}) - R_{1 yr. bond} = Liquidity Premium. Hence Liquidity Premium = Bond Beta(Market Risk Premium). However, we also know that the bond beta = -b_{r,m}(Duration), where b_{r,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 -b_{r,m}(Duration)(Market Risk Premium) = Liquidity Premium. Now, since the Market Risk Premium and the b_{r,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 r_{BEY} = 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).