Morton & Handley Case Study
a. What are the four most fundamental factors that affect the cost of money, or the general level of interest rates, in the economy? The four most fundamental factors that affect the cost of money are production opportunities, time of consumption, risk, and inflation. The interest rate given to savers is based on: the rate of return on invested capital, savers time preferences for current versus future consumption, the riskiness of the loan, the expected future rate of inflation. High inflation and high risk will result in high-interest rates.
b. What is the real risk-free rate of interest and the nominal risk-free rate? How are these two rates measured? The real risk-free rate of interest is the rate that would exist on default-free securities when there is no inflation. The nominal risk-free rate is equal to the real risk-free rate plus an inflation premium. The inflation premium is equal to the average expected inflation rate over the life of the security into the rate they charge. These rates are measured in percentages. 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. Inflation premium is a premium added to the real risk-free rate of interest to compensate for potential inflation.
The default risk premium is a premium based on the probability that the person who issues the loan will not follow through; this is measured with the difference between the U. S. interest rate on a Treasury bond and a corp. bond of equal maturity and marketability. A liquid asset can be sold at a predicted price in a short amount of time. A liquidity premium is added to the rate of interest on securities that are not liquid. The maturity risk premium reflects the interest rate risk. Long-term securities have more interest rate risk than short-term securities and the maturity risk premium is added to represent the risk. Short term long term treasury securities include an inflation premium. Long-term treasury securities also contain a maturity risk premium. Short-term rates on corporate securities are equal to the real-risk free rate plus premiums for inflation, liquidity, and default risk. Premiums will alter based on the financial strength of the company and the degree of liquidity. Long term rates on corporate securities include a premium for maturity risk. Corporate securities typically yield the greatest gains out of the four types of securities. What is the term structure of interest rates? What is a yield curve?
The term structure of interest rates is the relationship between interest rates, or yields, and maturities of securities. A yield curve shows the relationship between bond yields and maturities.
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 premium is zero for bonds that mature in 1 year or less and 0. 1% for 2-year bonds; then the MRP increases by 0. % per year thereafter for 20 years, after which it is stable. What is the interest rate on 1-, 10-, and 20-year Treasury bonds? Draw a yield curve with these data. What factors can explain why this constructed yield curve is upward sloping? The average expected inflation rate over year 1 to year 20
Yr. 1: Interest Premium= 5%
Yr. 10: IP= (5+6+8+8+8+8+8+8+8+8)/10= 7. 5%
Yr. 20: IP= (5+6+8+8+8+8=8+8+8+8+8+8+8+8+8+8+8+8+8+8)/20 =7. 75%.
Maturity risk premium in each year:
Yr. 1: MRP= 0%
Yr. 10: MRP=. 1% x 9 = 0. 9%
Yr. 20: MRP= . 1% x 19 = 1. 9%.
Sum the IPs and MRPs, and add real risk-free rate: r*=3%
Yr. 1: rRF= 3%+5%+0%= 8%
Yr. 10: rRF= 3%+7. 5%+. 9%= 11. 4%
Yr. 20: rRF= 3%+7. 75%+1. 9%= 12. 65%.
The shape of the curve depends on the expectations about future inflation and the relative riskiness of securities with different maturities. In this situation, the yield curve would be sloping upward which is because of the expected increase in inflation and maturity risk premium.
f. 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. The AAA-rated curve, the BB-rated curve and the U. S. treasury curve are all parallel to each other. The BB-rated accumulates the most interest rate, then comes the AAA company and then the U. S. treasury. The yield normally slopes upward because short term interest rates are typically lower than long term interest rates. Corporate yield curves will always be above government yield curves. The riskier the corporation the higher the yield curve. The distance between the corporate yield curve and the treasury curve increases as the corporate bond’s rating decreases.
g. What is the pure expectations theory? What does the pure expectations theory imply about the term structure of interest rates? The pure expectations theory is the theory that investors establish bond prices and interest rates on the sole basis of expectations for interest rates. The term structure of interest rates describes the relationship between long and short term rates. The investors are indifferent about the maturity expectations of short-term and long-term bonds. Investors perceive long-term bonds to be riskier than short-term.
h. Suppose you observe the following term structure for Treasury securities: MaturityYield 1 year6% 2 yrs. 6. 2% 3 yrs. 6. 4% 4 yrs. 6. 5% 5 yrs. 6. 5% r on 1 yr. securities one year from now:
(1. 062)2= (1. 06)(1 + X) 1. 1278= (1. 06)(1 + X) 1. 1278/1. 06= 1 + X 6. 4%= X
**Securities will yield 6. 4% r on 3 yr. securities two years from now:
(1. 065)5= (1. 062)2(1 + X)3 (1. 065)5/(1. 062)2= (1 + X)3 1. 3701/1. 1278= (1 + X)3 (1. 2148)1/3 – 1= X 6. 7%= X.
Securities will yield 6. 7%.