Tuesday, December 14, 2010

Chapter 4

Chapter 4
The Financial Environment:
Markets, Institutions, and Interest Rates


SOLUTIONS TO END-OF-CHAPTER PROBLEMS



4-1 k* = 3%; I1 = 2%; I2 = 4%; I3 = 4%; MRP = 0; kT2 = ?; kT3 = ?

k = k* + IP + DRP + LP + MRP.

Since these are Treasury securities, DRP = LP = 0.

kT2 = k* + IP2.
IP2 = (2% + 4%)/2 = 3%.
kT2 = 3% + 3% = 6%.

kT3 = k* + IP3.
IP3 = (2% + 4% + 4%)/3 = 3.33%.
kT3 = 3% + 3.33% = 6.33%.


4-2 kT10 = 6%; kC10 = 8%; LP = 0.5%; DRP = ?

k = k* + IP + DRP + LP + MRP.

kT10 = 6% = k* + IP + MRP; DRP = LP = 0.

kC10 = 8% = k* + IP + DRP + 0.5% + MRP.

Because both bonds are 10-year bonds the inflation premium and maturity risk premium on both bonds are equal. The only difference between them is the liquidity and default risk premiums.

kC10 = 8% = k* + IP + MRP + 0.5% + DRP. But we know from above that k* + IP + MRP = 6%; therefore,

kC10 = 8% = 6% + 0.5% + DRP
1.5% = DRP.


4-3 kT1 = 5%; 1kT1 = 6%; kT2 = ?

kT2 = = 5.5%.


4-4 k* = 3%; IP = 3%; kT2 = 6.2%; MRP2 = ?

kT2 = k* + IP + MRP = 6.2%
kT2 = 3% + 3% + MRP = 6.2%
MRP = 0.2%.

4-5 Let x equal the yield on 2-year securities 4 years from now:

7.5% = [(4)(7%) + 2x]/6
0.45 = 0.28 + 2x
x = 0.085 or 8.5%.


4-6 k = k* + IP + MRP + DRP + LP.
k* = 0.03.
IP = [0.03 + 0.04 + (5)(0.035)]/7 = 0.035.
MRP = 0.0005(6) = 0.003.
DRP = 0.
LP = 0.

kT7 = 0.03 + 0.035 + 0.003 = 0.068 = 6.8%.


4-7 a. k1 = 3%, and

k2 = = 4.5%,

Solving for k1 in Year 2, 1k1, we obtain

1k1 = (4.5% × 2) - 3% = 6%.

b. For riskless bonds under the expectations theory, the interest rate for a bond of any maturity is kn = k* + average inflation over n years. If k* = 1%, we can solve for IPn:

Year 1: k1 = 1% + I1 = 3%;
I1 = expected inflation = 3% - 1% = 2%.

Year 2: k1 = 1% + I2 = 6%;
I2 = expected inflation = 6% - 1% = 5%.

Note also that the average inflation rate is (2% + 5%)/2 = 3.5%, which, when added to k* = 1%, produces the yield on a 2-year bond, 4.5 percent. Therefore, all of our results are consistent.

Alternative solution: Solve for the inflation rates in Year 1 and Year 2 first:

kRF = k* + IP.

Year 1: 3% = 1% + IP1; IP1 = 2%, thus I1 = 2%.

Year 2: 4.5% = 1% + IP2; IP2 = 3.5%.

IP2 = (I1 + I2)/2
3.5% = (2% + I2)/2
I2 = 5%.

Then solve for the yield on the one-year bond in the second year:
Year 2: k1 = 1% + 5% = 6%.


4-8 k* = 2%; MRP = 0%; k1 = 5%; k2 = 7%; 1k1 = ?

1k1 represents the one-year rate on a bond one year from now (Year 2).

k2 =
7% =
9% = 1k1.

1k1 = k* + I2
9% = 2% + I2
7% = I2.

The average interest rate during the 2-year period differs from the 1-year interest rate expected for Year 2 because of the inflation rate reflected in the two interest rates. The inflation rate reflected in the interest rate on any security is the average rate of inflation expected over the security’s life.


4-9 Basic relevant equations:

kt = k* + IPt + DRPt + MRPt + LPt.

But here IP is the only premium, so kt = k* + IPt.

IPt = Avg. inflation = (I1 + I2 + ...)/N.

We know that I1 = IP1 = 3% and k* = 2%. Therefore,

kT1 = 2% + 3% = 5%. kT3 = k1 + 2% = 5% + 2% = 7%. But,

kT3 = k* + IP3 = 2% + IP3 = 7%, so

IP3 = 7% - 2% = 5%.

We also know that It = Constant after t = 1.

We can set up this table:

k* I Avg. I = IPt k = k* + IPt
1 2 3 3%/1 = 3% 5%
2 2 I (3% + I)/2 = IP2
3 2 I (3% + I + I)/3 = IP3 k3 = 7%, so IP3 = 7% - 2% = 5%.

IP3 = (3% + 2I)/3 = 5%
2I = 12%
I = 6%.


4-10 kC8 = k* + IP8 + MRP8 + DRP8 + LP8
8.3% = 2.5% + (2.8%  4 + 3.75%  4)/8 + 0.0% + DRP8 + 0.75%
8.3% = 2.5% + 3.275% + 0.0% + DRP8 + 0.75%
8.3% = 6.525% + DRP8
DRP8 = 1.775%.


4-11 T-bill rate = k* + IP
5.5% = k* + 3.25%
k* = 2.25%.


4-12 We’re given all the components to determine the yield on the Cartwright bonds except the default risk premium (DRP) and MRP. Calculate the MRP as 0.1%(5 - 1) = 0.4%. Now, we can solve for the DRP as follows:
7.75% = 2.3% + 2.5% + 0.4% + 1.0% + DRP, or DRP = 1.55%.


4-13 First, calculate the inflation premiums for the next three and five years, respectively. They are IP3 = (2.5% + 3.2% + 3.6%)/3 = 3.1% and IP5 = (2.5% + 3.2% + 3.6% + 3.6% + 3.6%)/5 = 3.3%. The real risk-free rate is given as 2.75%. Since the default and liquidity premiums are zero on Treasury bonds, we can now solve for the default risk premium. Thus, 6.25% = 2.75% + 3.1% + MRP3, or MRP3 = 0.4%. Similarly, 6.8% = 2.75% + 3.3% + MRP5, or MRP5 = 0.75%. Thus, MRP5 – MRP3 = 0.75% - 0.40% = 0.35%.


4-14 a. Real
Years to Risk-Free
Maturity Rate (k*) IP** MRP kT = k* + IP + MRP
1 2% 7.00% 0.2% 9.20%
2 2 6.00 0.4 8.40
3 2 5.00 0.6 7.60
4 2 4.50 0.8 7.30
5 2 4.20 1.0 7.20
10 2 3.60 1.0 6.60
20 2 3.30 1.0 6.30


**The computation of the inflation premium is as follows:


Expected Average
Year Inflation Expected Inflation
1 7% 7.00%
2 5 6.00
3 3 5.00
4 3 4.50
5 3 4.20
10 3 3.60
20 3 3.30

For example, the calculation for 3 years is as follows:



Thus, the yield curve would be as follows:






















b. The interest rate on the Exxon Mobil bonds has the same components as the Treasury securities, except that the Exxon Mobil bonds have default risk, so a default risk premium must be included. Therefore,

kExxon Mobil = k* + IP + MRP + DRP.


For a strong company such as Exxon Mobil, the default risk premium is virtually zero for short-term bonds. However, as time to maturity increases, the probability of default, although still small, is suffi-cient to warrant a default premium. Thus, the yield risk curve for the Exxon Mobil bonds will rise above the yield curve for the Treasury securities. In the graph, the default risk premium was assumed to be 1.0 percentage point on the 20-year Exxon Mobil bonds. The return should equal 6.3% + 1% = 7.3%.

c. Exelon bonds would have significantly more default risk than either Treasury securities or Exxon Mobil bonds, and the risk of default would increase over time due to possible financial deterioration. In this example, the default risk premium was assumed to be 1.0 percentage point on the 1-year Exelon bonds and 2.0 percentage points on the
20-year bonds. The 20-year return should equal 6.3% + 2% = 8.3%.


4-15 Term Rate
6 months 5.1%
1 year 5.5
2 years 5.6
3 years 5.7
4 years 5.8
5 years 6.0
10 years 6.1
20 years 6.5
30 years 6.3





4-16 a. The average rate of inflation for the 5-year period is calculated as:

= (0.13 + 0.09 + 0.07 + 0.06 + 0.06)/5 = 8.20%.

b. k = k* + IPAvg. = 2% + 8.2% = 10.20%.


c. Here is the general situation:

Arithmetic
1-Year Average Maturity Estimated
Expected Expected Risk Interest
Year Inflation Inflation k* Premium Rates
1 13% 13.0% 2% 0.1% 15.1%
2 9 11.0 2 0.2 13.2
3 7 9.7 2 0.3 12.0
5 6 8.2 2 0.5 10.7
. . . . . .
. . . . . .
. . . . . .
10 6 7.1 2 1.0 10.1
20 6 6.6 2 2.0 10.6


d. The “normal” yield curve is upward sloping because, in “normal” times, inflation is not expected to trend either up or down, so IP is the same for debt of all maturities, but the MRP increases with years, so the yield curve slopes up. During a recession, the yield curve typically slopes up especially steeply, because inflation and consequently short-term interest rates are currently low, yet people expect inflation and interest rates to rise as the economy comes out of the recession.

e. If inflation rates are expected to be constant, then the expectations theory holds that the yield curve should be hori¬zontal. However, in this event it is likely that maturity risk premiums would be applied to long-term bonds because of the greater risks of holding long-term rather than short-term bonds:

















If maturity risk premiums were added to the yield curve in Part e above, then the yield curve would be more nearly normal; that is, the long-term end of the curve would be raised. (The yield curve shown in this answer is upward sloping; the yield curve shown in Part c is downward sloping.)

SPREADSHEET PROBLEM



4-17 The detailed solution for the spreadsheet problem is available both on the instructor’s resource CD-ROM and on the instructor’s side of South-Western’s web site, http://brigham.swlearning.com.


INTEGRATED CASE



Smyth Barry & Company
Financial Markets, Institutions, and Interest Rates

4-18 ASSUME THAT YOU RECENTLY GRADUATED WITH A DEGREE IN FINANCE AND HAVE JUST REPORTED TO WORK AS AN INVESTMENT ADVISOR AT THE BROKERAGE FIRM OF SMYTH BARRY & CO. YOUR FIRST ASSIGNMENT IS TO EXPLAIN THE NATURE OF THE U.S. FINANCIAL MARKETS TO MICHELLE VARGA, A PROFESSIONAL TENNIS PLAYER WHO HAS JUST COME TO THE UNITED STATES FROM MEXICO. VARGA IS A HIGHLY RANKED TENNIS PLAYER WHO EXPECTS TO INVEST SUBSTANTIAL AMOUNTS OF MONEY THROUGH SMYTH BARRY. SHE IS ALSO VERY BRIGHT, AND, THEREFORE, SHE WOULD LIKE TO UNDERSTAND IN GENERAL TERMS WHAT WILL HAPPEN TO HER MONEY. YOUR BOSS HAS DEVELOPED THE FOLLOWING SET OF QUESTIONS THAT YOU MUST ASK AND ANSWER TO EXPLAIN THE U.S. FINANCIAL SYSTEM TO VARGA.

A. WHAT IS A MARKET? DIFFERENTIATE BETWEEN THE FOLLOWING TYPES OF MARKETS: PHYSICAL ASSET VS. FINANCIAL MARKETS, SPOT VS. FUTURES MARKETS, MONEY VS. CAPITAL MARKETS, PRIMARY VS. SECONDARY MARKETS, AND PUBLIC VS. PRIVATE MARKETS.

ANSWER: [SHOW S4-1 THROUGH S4-3 HERE.] A MARKET IS ONE IN WHICH ASSETS ARE BOUGHT AND SOLD. THERE ARE MANY DIFFERENT TYPES OF FINANCIAL MARKETS, EACH ONE DEALING WITH A DIFFERENT TYPE OF FINANCIAL ASSET, SERVING A DIFFERENT SET OF CUSTOMERS, OR OPERATING IN A DIFFERENT PART OF THE COUNTRY. FINANCIAL MARKETS DIFFER FROM PHYSICAL ASSET MARKETS IN THAT REAL, OR TANGIBLE, ASSETS SUCH AS MACHINERY, REAL ESTATE, AND AGRICULTURAL PRODUCTS ARE TRADED IN THE PHYSICAL ASSET MARKETS, BUT FINANCIAL SECURITIES REPRESENTING CLAIMS ON ASSETS ARE TRADED IN THE FINANCIAL MARKETS. SPOT MARKETS ARE MARKETS IN WHICH ASSETS ARE BOUGHT OR SOLD FOR “ON-THE-SPOT” DELIVERY, WHILE FUTURES MARKETS ARE MARKETS IN WHICH PARTICIPANTS AGREE TODAY TO BUY OR SELL AN ASSET AT SOME FUTURE DATE.
MONEY MARKETS ARE THE MARKETS IN WHICH DEBT SECURITIES WITH MATURITIES OF LESS THAN ONE YEAR ARE TRADED. NEW YORK, LONDON, AND TOKYO ARE MAJOR MONEY MARKET CENTERS. LONGER-TERM SECURITIES, INCLUDING STOCKS AND BONDS, ARE TRADED IN THE CAPITAL MARKETS. THE NEW YORK STOCK EXCHANGE IS AN EXAMPLE OF A CAPITAL MARKET, WHILE THE NEW YORK COMMERCIAL PAPER AND TREASURY BILL MARKETS ARE MONEY MARKETS.
PRIMARY MARKETS ARE MARKETS IN WHICH CORPORATIONS RAISE CAPITAL BY ISSUING NEW SECURITIES, WHILE SECONDARY MARKETS ARE MARKETS IN WHICH SECURITIES AND OTHER FINANCIAL ASSETS ARE TRADED AMONG INVESTORS AFTER THEY HAVE BEEN ISSUED BY CORPORATIONS. PRIVATE MARKETS, WHERE TRANSACTIONS ARE WORKED OUT DIRECTLY BETWEEN TWO PARTIES, ARE DIFFERENTIATED FROM PUBLIC MARKETS, WHERE STANDARDIZED CONTRACTS ARE TRADED ON ORGANIZED EXCHANGES.


B. WHAT IS AN INITIAL PUBLIC OFFERING (IPO) MARKET?

ANSWER: THE INITIAL PUBLIC OFFERING (IPO) MARKET IS A SUBSET OF THE PRIMARY MARKET. HERE FIRMS “GO PUBLIC” BY OFFERING SHARES TO THE PUBLIC FOR THE FIRST TIME.



C. IF APPLE COMPUTER DECIDED TO ISSUE ADDITIONAL COMMON STOCK, AND VARGA PURCHASED 100 SHARES OF THIS STOCK FROM MERRILL LYNCH, THE UNDERWRITER, WOULD THIS TRANSACTION BE A PRIMARY MARKET TRANSACTION OR A SECONDARY MARKET TRANSACTION? WOULD IT MAKE A DIFFERENCE IF VARGA PURCHASED PREVIOUSLY OUTSTANDING APPLE STOCK IN THE DEALER MARKET?

ANSWER: IF VARGA PURCHASED NEWLY ISSUED APPLE STOCK, THIS WOULD CONSTITUTE A PRIMARY MARKET TRANSACTION, WITH MERRILL LYNCH ACTING AS AN INVESTMENT BANKER IN THE TRANSACTION. IF VARGA PURCHASED “USED” STOCK, THEN THE TRANSACTION WOULD BE IN THE SECONDARY MARKET.


D. DESCRIBE THE THREE PRIMARY WAYS IN WHICH CAPITAL IS TRANSFERRED BETWEEN SAVERS AND BORROWERS.

ANSWER: [SHOW S4-4 AND S4-5 HERE.] TRANSFERS OF CAPITAL CAN BE MADE (1) BY DIRECT TRANSFER OF MONEY AND SECURITIES, (2) THROUGH AN INVESTMENT BANKING HOUSE, OR (3) THROUGH A FINANCIAL INTERMEDIARY. IN A DIRECT TRANSFER, A BUSINESS SELLS ITS STOCKS OR BONDS DIRECTLY TO INVESTORS (SAVERS), WITHOUT GOING THROUGH ANY TYPE OF INSTITUTION. THE BUSINESS BORROWER RECEIVES DOLLARS FROM THE SAVERS, AND THE SAVERS RECEIVE SECURITIES (BONDS OR STOCK) IN RETURN.
IF THE TRANSFER IS MADE THROUGH AN INVESTMENT BANKING HOUSE, THE INVESTMENT BANK SERVES AS A MIDDLEMAN. THE BUSINESS SELLS ITS SECURITIES TO THE INVESTMENT BANK, WHICH IN TURN SELLS THEM TO THE SAVERS. ALTHOUGH THE SECURITIES ARE SOLD TWICE, THE TWO SALES CONSTITUTE ONE COMPLETE TRANSACTION IN THE PRIMARY MARKET.
IF THE TRANSFER IS MADE THROUGH A FINANCIAL INTERMEDIARY, SAVERS INVEST FUNDS WITH THE INTERMEDIARY, WHICH THEN ISSUES ITS OWN SECURITIES IN EXCHANGE. BANKS ARE ONE TYPE OF INTERMEDIARY, RECEIVING DOLLARS FROM MANY SMALL SAVERS AND THEN LENDING THESE DOLLARS TO BORROWERS TO PURCHASE HOMES, AUTOMOBILES, VACATIONS, AND SO ON, AND ALSO TO BUSINESSES AND GOVERNMENT UNITS. THE SAVERS RECEIVE A CERTIFICATE OF DEPOSIT OR SOME OTHER INSTRUMENT IN EXCHANGE FOR THE FUNDS DEPOSITED WITH THE BANK. MUTUAL FUNDS, INSURANCE COMPANIES, AND PENSION FUNDS ARE OTHER TYPES OF INTERMEDIARIES.



E. WHAT ARE THE TWO LEADING STOCK MARKETS? DESCRIBE THE TWO BASIC TYPES OF STOCK MARKETS.

ANSWER: [SHOW S4-6 HERE.] THE TWO LEADING STOCK MARKETS TODAY ARE THE NEW YORK STOCK EXCHANGE AND THE NASDAQ STOCK MARKET. THERE ARE JUST TWO BASIC TYPES OF STOCK MARKETS: (1) PHYSICAL LOCATION EXCHANGES, WHICH INCLUDE THE NEW YORK STOCK EXCHANGE (NYSE), THE AMERICAN STOCK EXCHANGE (AMEX), AND SEVERAL REGIONAL STOCK EXCHANGES, AND (2) ELECTRONIC DEALER-BASED MARKETS THAT INCLUDE THE NASDAQ STOCK MARKET, THE LESS FORMAL OVER-THE-COUNTER MARKET, AND THE RECENTLY DEVELOPED ELECTRONIC COMMUNICATIONS NETWORKS (ECNs).
THE PHYSICAL LOCATION EXCHANGES ARE FORMAL ORGANIZATIONS HAVING TANGIBLE, PHYSICAL LOCATIONS AND TRADING IN DESIGNATED SECURITIES. THERE ARE EXCHANGES FOR STOCKS, BONDS, COMMODITIES, FUTURES, AND OPTIONS. THE PHYSICAL LOCATION EXCHANGES ARE CONDUCTED AS AUCTION MARKETS WITH SECURITIES GOING TO THE HIGHEST BIDDER. BUYERS AND SELLERS PLACE ORDERS WITH THEIR BROKERS WHO THEN EXECUTE THOSE ORDERS BY MATCHING BUYERS AND SELLERS, ALTHOUGH SPECIALISTS ASSIST IN PROVIDING CONTINUITY TO THE MARKETS.
THE ELECTRONIC DEALER-BASED MARKET IS MADE UP OF HUNDREDS OF BROKERS AND DEALERS AROUND THE COUNTRY WHO ARE CONNECTED ELECTRONICALLY BY TELEPHONES AND COMPUTERS. THE DEALER-BASED MARKET FACILITATES TRADING OF SECURITIES THAT ARE NOT LISTED ON A PHYSICAL LOCATION EXCHANGE. A DEALER MARKET IS DEFINED TO INCLUDE ALL FACILITIES THAT ARE NEEDED TO CONDUCT SECURITY TRANSACTIONS NOT MADE ON THE PHYSICAL LOCATION EXCHANGES. THESE FACILITIES INCLUDE (1) THE RELATIVELY FEW DEALERS WHO HOLD INVENTORIES OF THESE SECURITIES AND WHO ARE SAID TO MAKE A MARKET IN THESE SECURITIES; (2) THE THOUSANDS OF BROKERS WHO ACT AS AGENTS IN BRINGING THE DEALERS TOGETHER WITH INVESTORS; AND (3) THE COMPUTERS, TERMINALS, AND ELECTRONIC NETWORKS THAT PROVIDE A COMMUNICATION LINK BETWEEN DEALERS AND BROKERS. DEALERS CONTINUOUSLY POST A PRICE AT WHICH THEY ARE WILLING TO BUY THE STOCK (THE BID PRICE) AND A PRICE AT WHICH THEY ARE WILLING TO SELL THE STOCK (THE ASK PRICE). THE ASK PRICE IS ALWAYS HIGHER THAN THE BID PRICE, AND THE DIFFERENCE (OR “BID-ASK SPREAD”) REPRESENTS THE DEALER’S MARKUP, OR PROFIT.


F. WHAT DO WE CALL THE PRICE THAT A BORROWER MUST PAY FOR DEBT CAPITAL? WHAT IS THE PRICE OF EQUITY CAPITAL? WHAT ARE THE FOUR MOST FUNDAMENTAL FACTORS THAT AFFECT THE COST OF MONEY, OR THE GENERAL LEVEL OF INTEREST RATES, IN THE ECONOMY?

ANSWER: [SHOW S4-7 AND S4-8 HERE.] THE INTEREST RATE IS THE PRICE PAID FOR BORROWED CAPITAL, WHILE THE RETURN ON EQUITY CAPITAL COMES IN THE FORM OF DIVIDENDS PLUS CAPITAL GAINS. THE RETURN THAT INVESTORS REQUIRE ON CAPITAL DEPENDS ON (1) PRODUCTION OPPORTUNITIES, (2) TIME PREFERENCES FOR CONSUMPTION, (3) RISK, AND (4) INFLATION.
PRODUCTION OPPORTUNITIES REFER TO THE RETURNS THAT ARE AVAILABLE FROM INVESTMENT IN PRODUCTIVE ASSETS: THE MORE PRODUCTIVE A PRODUCER FIRM BELIEVES ITS ASSETS WILL BE, THE MORE IT WILL BE WILLING TO PAY FOR THE CAPITAL NECESSARY TO ACQUIRE THOSE ASSETS.
TIME PREFERENCE FOR CONSUMPTION REFERS TO CONSUMERS’ PREFERENCES FOR CURRENT CONSUMPTION VERSUS SAVINGS FOR FUTURE CONSUMPTION: CONSUMERS WITH LOW PREFERENCES FOR CURRENT CONSUMPTION WILL BE WILLING TO LEND AT A LOWER RATE THAN CONSUMERS WITH A HIGH PREFERENCE FOR CURRENT CONSUMPTION.
INFLATION REFERS TO THE TENDENCY OF PRICES TO RISE, AND THE HIGHER THE EXPECTED RATE OF INFLATION, THE LARGER THE REQUIRED RATE OF RETURN.
RISK, IN A MONEY AND CAPITAL MARKET CONTEXT, REFERS TO THE CHANCE THAT A LOAN WILL NOT BE REPAID AS PROMISED--THE HIGHER THE PERCEIVED DEFAULT RISK, THE HIGHER THE REQUIRED RATE OF RETURN.
RISK IS ALSO LINKED TO THE MATURITY AND LIQUIDITY OF A SECURITY. THE LONGER THE MATURITY AND THE LESS LIQUID (MARKETABLE) THE SECURITY, THE HIGHER THE REQUIRED RATE OF RETURN, OTHER THINGS CONSTANT.
THE PRECEDING DISCUSSION RELATED TO THE GENERAL LEVEL OF MONEY COSTS, BUT THE LEVEL OF INTEREST RATES WILL ALSO BE INFLUENCED BY SUCH THINGS AS FED POLICY, FISCAL AND FOREIGN TRADE DEFICITS, AND THE LEVEL OF ECONOMIC ACTIVITY. ALSO, INDIVIDUAL SECURITIES WILL HAVE HIGHER YIELDS THAN THE RISK-FREE RATE BECAUSE OF THE ADDITION OF VARIOUS PREMIUMS AS DISCUSSED BELOW.


G. WHAT IS THE REAL RISK-FREE RATE OF INTEREST (k*) AND THE NOMINAL RISK-FREE RATE (kRF)? HOW ARE THESE TWO RATES MEASURED?

ANSWER: [SHOW S4-9 AND S4-10 HERE.] KEEP THESE EQUATIONS IN MIND AS WE DISCUSS INTEREST RATES. WE WILL DEFINE THE TERMS AS WE GO ALONG:

k = k* + IP + DRP + LP + MRP.

kRF = k* + IP.

THE REAL RISK-FREE RATE, k*, IS THE RATE THAT WOULD EXIST ON DEFAULT-FREE SECURITIES IN THE ABSENCE OF INFLATION.
THE NOMINAL RISK-FREE RATE, kRF, IS EQUAL TO THE REAL RISK-FREE RATE PLUS AN INFLATION PREMIUM, WHICH IS EQUAL TO THE AVERAGE RATE OF INFLATION EXPECTED OVER THE LIFE OF THE SECURITY.

THERE IS NO TRULY RISKLESS SECURITY, BUT THE CLOSEST THING IS A SHORT-TERM U.S. TREASURY BILL (T-BILL), WHICH IS FREE OF MOST RISKS. THE REAL RISK-FREE RATE, k*, IS ESTIMATED BY SUBTRACTING THE EXPECTED RATE OF INFLATION FROM THE RATE ON SHORT-TERM TREASURY SECURITIES. IT IS GENERALLY ASSUMED THAT k* IS IN THE RANGE OF 1 TO 4 PERCENTAGE POINTS. THE T-BOND RATE IS USED AS A PROXY FOR THE LONG-TERM RISK-FREE RATE. HOWEVER, WE KNOW THAT ALL LONG-TERM BONDS CONTAIN INTEREST RATE RISK, SO THE T-BOND RATE IS NOT REALLY RISKLESS. IT IS, HOWEVER, FREE OF DEFAULT RISK.


H. DEFINE THE TERMS INFLATION PREMIUM (IP), DEFAULT RISK PREMIUM (DRP), LIQUIDITY PREMIUM (LP), AND MATURITY RISK PREMIUM (MRP). WHICH OF THESE PREMIUMS IS INCLUDED WHEN DETERMINING THE INTEREST RATE ON
(1) SHORT-TERM U.S. TREASURY SECURITIES, (2) LONG-TERM U.S. TREASURY SECURITIES, (3) SHORT-TERM CORPORATE SECURITIES, AND (4) LONG-TERM CORPORATE SECURITIES? EXPLAIN HOW THE PREMIUMS WOULD VARY OVER TIME AND AMONG THE DIFFERENT SECURITIES LISTED ABOVE.

ANSWER: [SHOW S4-11 HERE.] THE INFLATION PREMIUM (IP) IS A PREMIUM ADDED TO THE REAL RISK-FREE RATE OF INTEREST TO COMPENSATE FOR EXPECTED INFLATION.
THE DEFAULT RISK PREMIUM (DRP) IS A PREMIUM BASED ON THE PROBABILITY THAT THE ISSUER WILL DEFAULT ON THE LOAN, AND IT IS MEASURED BY THE DIFFERENCE BETWEEN THE INTEREST RATE ON A U.S. TREASURY BOND AND A CORPORATE BOND OF EQUAL MATURITY AND MARKETABILITY.
A LIQUID ASSET IS ONE THAT CAN BE SOLD AT A PREDICTABLE PRICE ON SHORT NOTICE; A LIQUIDITY PREMIUM IS ADDED TO THE RATE OF INTEREST ON SECURITIES THAT ARE NOT LIQUID.
THE MATURITY RISK PREMIUM (MRP) IS A PREMIUM THAT REFLECTS INTEREST RATE RISK; LONGER-TERM SECURITIES HAVE MORE INTEREST RATE RISK (THE RISK OF CAPITAL LOSS DUE TO RISING INTEREST RATES) THAN DO SHORTER-TERM SECURITIES, AND THE MRP IS ADDED TO REFLECT THIS RISK.

1. SHORT-TERM TREASURY SECURITIES INCLUDE ONLY AN INFLATION PREMIUM.

2. LONG-TERM TREASURY SECURITIES CONTAIN AN INFLATION PREMIUM PLUS A MATURITY RISK PREMIUM. NOTE THAT THE INFLATION PREMIUM ADDED TO LONG-TERM SECURITIES WILL DIFFER FROM THAT FOR SHORT-TERM SECURITIES UNLESS THE RATE OF INFLATION IS EXPECTED TO REMAIN CONSTANT.


3. THE RATE ON SHORT-TERM CORPORATE SECURITIES IS EQUAL TO THE REAL RISK-FREE RATE PLUS PREMIUMS FOR INFLATION, DEFAULT RISK, AND LIQUIDITY. THE SIZE OF THE DEFAULT AND LIQUIDITY PREMIUMS WILL VARY DEPENDING ON THE FINANCIAL STRENGTH OF THE ISSUING CORPORATION AND ITS DEGREE OF LIQUIDITY, WITH LARGER CORPORATIONS GENERALLY HAVING GREATER LIQUIDITY BECAUSE OF MORE ACTIVE TRADING.

4. THE RATE FOR LONG-TERM CORPORATE SECURITIES ALSO INCLUDES A PREMIUM FOR MATURITY RISK. THUS, LONG-TERM CORPORATE SECURITIES GENERALLY CARRY THE HIGHEST YIELDS OF THESE FOUR TYPES OF SECURITIES.


I. WHAT IS THE TERM STRUCTURE OF INTEREST RATES? WHAT IS A YIELD CURVE?

ANSWER: [SHOW S4-12 HERE. S4-12 SHOWS A RECENT (OCTOBER 2002) TREASURY YIELD CURVE.] THE TERM STRUCTURE OF INTEREST RATES IS THE RELATIONSHIP BETWEEN INTEREST RATES, OR YIELDS, AND MATURITIES OF SECURITIES. WHEN THIS RELATIONSHIP IS GRAPHED, THE RESULTING CURVE IS CALLED A YIELD CURVE. (SKETCH OUT A YIELD CURVE ON THE BOARD.)























J. SUPPOSE MOST INVESTORS EXPECT THE INFLATION RATE TO BE 5 PERCENT NEXT YEAR, 6 PERCENT THE FOLLOWING YEAR, AND 8 PERCENT THEREAFTER. THE REAL RISK-FREE RATE IS 3 PERCENT. THE MATURITY RISK PREMIUM IS ZERO FOR BONDS THAT MATURE IN 1 YEAR OR LESS, 0.1 PERCENT FOR 2-YEAR BONDS, AND THEN THE MRP INCREASES BY 0.1 PERCENT PER YEAR THEREAFTER FOR 20 YEARS, AFTER WHICH IT IS STABLE. WHAT IS THE INTEREST RATE ON 1-YEAR, 10-YEAR, AND 20-YEAR TREASURY BONDS? DRAW A YIELD CURVE WITH THESE DATA. WHAT FACTORS CAN EXPLAIN WHY THIS CONSTRUCTED YIELD CURVE IS UPWARD SLOPING?

ANSWER: [SHOW S4-13 THROUGH S4-18 HERE.]

STEP 1: FIND THE AVERAGE EXPECTED INFLATION RATE OVER YEARS 1 TO 20:

YR 1: IP = 5.0%.

YR 10: IP = (5 + 6 + 8 + 8 + 8 + ... + 8)/10 = 7.5%.

YR 20: IP = (5 + 6 + 8 + 8 + ... + 8)/20 = 7.75%.

STEP 2: FIND THE MATURITY RISK PREMIUM IN EACH YEAR:

YR 1: MRP = 0.0%.

YR 10: MRP = 0.1%  9 = 0.9%.

YR 20: MRP = 0.1%  19 = 1.9%.

STEP 3: SUM THE IPs AND MRPs, AND ADD k* = 3%:

YR 1: kRF = 3% + 5.0% + 0.0% = 8.0%.

YR 10: kRF = 3% + 7.5% + 0.9% = 11.4%.

YR 20: kRF = 3% + 7.75% + 1.9% = 12.65%.

THE SHAPE OF THE YIELD CURVE DEPENDS PRIMARILY ON TWO FACTORS:
(1) EXPECTATIONS ABOUT FUTURE INFLATION AND (2) THE RELATIVE RISKINESS OF SECURITIES WITH DIFFERENT MATURITIES.
THE CONSTRUCTED YIELD CURVE IS UPWARD SLOPING. THIS IS DUE TO INCREASING EXPECTED INFLATION AND AN INCREASING MATURITY RISK PREMIUM.


K. AT ANY GIVEN TIME, HOW WOULD THE YIELD CURVE FACING AN AAA-RATED COMPANY COMPARE WITH THE YIELD CURVE FOR U.S. TREASURY SECURITIES? AT ANY GIVEN TIME, HOW WOULD THE YIELD CURVE FACING A BB-RATED COMPANY COMPARE WITH THE YIELD CURVE FOR U.S. TREASURY SECURITIES? DRAW A GRAPH TO ILLUSTRATE YOUR ANSWER.


ANSWER: [SHOW S4-19 THROUGH S4-20 HERE.] (CURVES FOR AAA-RATED AND BB-RATED SECURITIES HAVE BEEN ADDED TO DEMONSTRATE THAT RISKIER SECURITIES REQUIRE HIGHER RETURNS.) THE YIELD CURVE NORMALLY SLOPES UPWARD, INDICATING THAT SHORT-TERM INTEREST RATES ARE LOWER THAN LONG-TERM INTEREST RATES. YIELD CURVES CAN BE DRAWN FOR GOVERNMENT SECURITIES OR FOR THE SECURITIES OF ANY CORPORATION, BUT CORPORATE YIELD CURVES WILL ALWAYS LIE ABOVE GOVERNMENT YIELD CURVES, AND THE RISKIER THE CORPORATION, THE HIGHER ITS YIELD CURVE. THE SPREAD BETWEEN A CORPORATE YIELD CURVE AND THE TREASURY CURVE WIDENS AS THE CORPORATE BOND RATING DECREASES.


L. WHAT IS THE PURE EXPECTATIONS THEORY? WHAT DOES THE PURE EXPECTATIONS THEORY IMPLY ABOUT THE TERM STRUCTURE OF INTEREST RATES?

ANSWER: [SHOW S4-21 AND S4-22 HERE.] THE PURE EXPECTATIONS THEORY ASSUMES THAT INVESTORS ESTABLISH BOND PRICES AND INTEREST RATES STRICTLY ON THE BASIS OF EXPECTATIONS FOR INTEREST RATES. THIS MEANS THAT THEY ARE INDIFFERENT WITH RESPECT TO MATURITY IN THE SENSE THAT THEY DO NOT VIEW LONG-TERM BONDS AS BEING RISKIER THAN SHORT-TERM BONDS. IF THIS WERE TRUE, THEN THE MATURITY RISK PREMIUM WOULD BE ZERO, AND LONG-TERM INTEREST RATES WOULD SIMPLY BE A WEIGHTED AVERAGE OF CURRENT AND EXPECTED FUTURE SHORT-TERM INTEREST RATES. IF THE PURE EXPECTATIONS THEORY IS CORRECT, YOU CAN USE THE YIELD CURVE TO “BACK OUT” EXPECTED FUTURE INTEREST RATES.


M. SUPPOSE THAT YOU OBSERVE THE FOLLOWING TERM STRUCTURE FOR TREASURY SECURITIES:

MATURITY YIELD
1 YEAR 6.0%
2 YEARS 6.2
3 YEARS 6.4
4 YEARS 6.5
5 YEARS 6.5

ASSUME THAT THE PURE EXPECTATIONS THEORY OF THE TERM STRUCTURE IS CORRECT. (THIS IMPLIES THAT YOU CAN USE THE YIELD CURVE GIVEN ABOVE TO “BACK OUT” THE MARKET’S EXPECTATIONS ABOUT FUTURE INTEREST RATES.)
WHAT DOES THE MARKET EXPECT WILL BE THE INTEREST RATE ON 1-YEAR SECURITIES ONE YEAR FROM NOW? WHAT DOES THE MARKET EXPECT WILL BE THE INTEREST RATE ON 3-YEAR SECURITIES TWO YEARS FROM NOW?

ANSWER: [SHOW S4-23 THROUGH S4-27 HERE.] CALCULATION FOR k ON 1-YEAR SECURITIES ONE YEAR FROM NOW:

6.2% =
12.4% = 6.0% + X
6.4% = X.

ONE YEAR FROM NOW, 1-YEAR SECURITIES WILL YIELD 6.4%.
CALCULATION FOR k ON 3-YEAR SECURITIES TWO YEARS FROM NOW:

6.5% =
32.5% = 12.4% + 3X
20.1% = 3X
6.7% = X.

TWO YEARS FROM NOW, 3-YEAR SECURITIES WILL YIELD 6.7%.


N. FINALLY, VARGA IS ALSO INTERESTED IN INVESTING IN COUNTRIES OTHER THAN THE UNITED STATES. DESCRIBE THE VARIOUS TYPES OF RISKS THAT ARISE WHEN INVESTING OVERSEAS.

ANSWER: [SHOW S4-28 AND S4-29 HERE.] FIRST, VARGA SHOULD CONSIDER COUNTRY RISK, WHICH REFERS TO THE RISK THAT ARISES FROM INVESTING OR DOING BUSINESS IN A PARTICULAR COUNTRY. THIS RISK DEPENDS ON THE COUNTRY’S ECONOMIC, POLITICAL, AND SOCIAL ENVIRONMENT. COUNTRY RISK ALSO INCLUDES THE RISK THAT PROPERTY WILL BE EXPROPRIATED WITHOUT ADEQUATE COMPENSATION, AS WELL AS NEW HOST COUNTRY STIPULATIONS ABOUT LOCAL PRODUCTION, SOURCING OR HIRING PRACTICES, AND DAMAGE OR DESTRUCTION OF FACILITIES DUE TO INTERNAL STRIFE.
SECOND, VARGA SHOULD CONSIDER EXCHANGE RATE RISK. VARGA NEEDS TO KEEP IN MIND WHEN INVESTING OVERSEAS THAT MORE OFTEN THAN NOT THE SECURITY WILL BE DENOMINATED IN A CURRENCY OTHER THAN THE DOLLAR, WHICH MEANS THAT THE VALUE OF THE INVESTMENT WILL DEPEND ON WHAT HAPPENS TO EXCHANGE RATES. TWO FACTORS CAN LEAD TO EXCHANGE RATE FLUCTUATIONS. (1) CHANGES IN RELATIVE INFLATION WILL LEAD TO CHANGES IN EXCHANGE RATES. (2) AN INCREASE IN COUNTRY RISK WILL ALSO CAUSE THE COUNTRY’S CURRENCY TO FALL. CONSEQUENTLY, INFLATION RISK, COUNTRY RISK, AND EXCHANGE RATE RISK ARE ALL INTERRELATED.

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