Maria Juarez is a professional tennis player, and your firm manages her money. S
ID: 2683568 • Letter: M
Question
Maria Juarez is a professional tennis player, and your firm manages her money. She has asked you to give her information about what determines the level of various interest rate. Your boss has prepared some questions for you to consider.
a) What are the four most fundamental factors that affect the cost of money, or the general level of interest rate, in the economy?
b) What is the real risk-free rate of interst (r*)and the nominal risk-free rate (r RF)? How are these two rates measured?
c) Define the term inflation premium(IP), default risk premium (DRP), liquidity premium (LP),and the maturity risk premium(MRP). Which of premium is included in determining the interst rate on (1)Short term U.S Treasury securities, (2)Long term U.S Treasury securities, (3)short term corporate securities, (4) long term coporate securities? Explain how the premiums would vary over time and among the different securities listed.
d) What is the term structure of interest rate? What is the yield curve?
e)Suppose most investors expect the inflation rate to be 5% next year, 6% the following year, and 8% thereafter. The real risk free rate is 3%. The maturity risk primium is zero for bonds that mature in 1 year or less and 0.1% for 2 years bonds; then the MRP increases by 0.1% per year thereafter for 20 years, after which it is stable. What is the interest on 1-,10-, and 20-year treasury bonds? Draw a yield curve with these data. What factor can explain why this constructed yield curve is upward-sloping?
f) At any give time, how would the yield curve facing a 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 illustrat your answer.
g) What is the pure expectations theory? What does the pure expectation theory imply about the term structure of interest rate?
Explanation / Answer
The four most fundamental factors affecting the cost of money are
(1) production opportunities,
(2) time preferences for consumption,
(3) risk, and (4) inflation.
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r = r* + IP + DRP + LP + MRP.
rRF = r* + IP.
The real risk-free rate, r*, is the rate that would exist on defaultfree securities in the absence of inflation.
The nominal risk-free rate, rRF, 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.
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The real risk-free rate, r*, is estimated by subtracting the expected rate of inflation from the rate on short-term treasury securities. It is generally assumed that r* is in the range of 1 to 4
percentage points. The T-bond rate is used as a proxy for the longterm 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.
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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.
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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 doshorter-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