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Determinants of Interest Rates Q A
Accountancy (1BSA)
Miriam College
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DETERMINANTS OF INTEREST RATES
Problems
- A particular security’s equilibrium rate of return is 8 percent. For all securities, the inflation risk premium is 1 percent and the real risk-free rate is 3 percent. The security’s liquidity risk premium is 0 percent and maturity risk premium is 0 percent. The security has no special covenants. Calculate the security’s default risk premium.
Answer: The fair interest rate on a financial security is calculated as
r = r* + IP +DRP +LRP + MRP i* = IP + RFR + DRP + LRP + SCP + MRP 8% = 1% + 3% + DRP + 0% + 0% + 0%
Thus, DRP = 8% - 1% - 3% - 0% - 0% - 0% = 1%
- REAL RISK-FREE RATE You read in The Wall Street Journal that 30-day T-bills are currently yielding 5%. Your brother-in-law, a broker a Safe and Sound Securities, has given you the following estimates of current interest rate premiums:
- Inflation premium = 3%
- Liquidity premium = 0%
- Maturity risk premium = 1%
- Default risk premium = 2%
On the basis of these data, what is the real risk-free rate of return?
Answer T- b i l l r a t e = r * + I P 5% = r* + 3% r* = 2%.
- You are considering an investment in 30-year bonds issued by Moore Corporation. The bonds have no special covenants. The Wall Street Journal reports that 1-year T-bills are currently earning 3 percent. Your broker has determined the following information about economic activity and Moore Corporation bonds:
Real Risk-Free Rate = 2% Default Risk Premium = 1% Liquidity Risk Premium = 0% Maturity Risk Premium = 1%
a. What is the inflation premium? b. What is the fair interest rate on Moore Corporation 30-year bonds?
Answer: a. IP = i* – RFR = 3% - 2% = 1%
c. ij* = 1% + 2% + 1% + 0% + 1% = 6%
- A two-year Treasury security currently earns 1 percent. Over the next two years, the real risk-free rate is expected to be 1 percent per year and the inflation premium is expected to be 0 percent per year. Calculate the maturity risk premium on the two-year Treasury security.
Answer: 1% = 0% + 1% + 0% + 0% + MP => MP = 1% - (0% + 1% + 0% + 0%) = 0%
- Tom and Sue’s Flowers Inc.’s 15-year bonds are currently yielding a return of 8 percent. The expected inflation premium is 2 percent annually and the real risk-free rate is expected to be 3 percent annually over the next 15 years. The default risk premium on Tom and Sue’s Flowers’ bonds is 0 percent. The maturity risk premium is 0 percent on 5-year securities and increases by 0 percent for each additional year to maturity. Calculate the liquidity risk premium on Tom and Sue’s Flowers Inc.’s 15-year bonds.
Answer: 8% = 2% + 3% + 0 + LRP + (0% + (0% x 10)) => LRP = 8% - (2% + 3% + 0% + (0% + (0% x 10))) = 0%
- Nikki G’s Corporation’s 10-year bonds are currently yielding a return of 6 percent. The expected inflation premium is 1 percent annually and the real risk-free rate is expected to be 2 percent annually over the next 10 years. The liquidity risk premium on Nikki G’s bonds is 0 percent. The maturity risk premium is 0 percent on 2-year securities and increases by 0 percent for each additional year to maturity. Calculate the default risk premium on Nikki G’s 10-year bonds.
Answer: 6% = 1% + 2% + DRP + 0% + (0% + (0% × 8)) => DRP = 6% - (1% + 2% + 0% + (0% + (0% x 8))) = 2%
- The current one-year Treasury-bill rate is 5 percent and the expected one-year rate 12 months from now is 5 percent. According to the unbiased expectations theory, what should be the current rate for a two-year Treasury security?
Answer: 1 R 2 = [(1 + 0)(1 + 0)]1/2 - 1 = 5%
- Suppose that the current one-year rate (one-year spot rate) and expected one-year T-bill rates over the following three years (i., years 2, 3, and 4, respectively) are as follows:
1 R 1 = 6%, E( 2 r 1 ) = 7%, E( 3 r 1 ) = 7%, E( 4 r 1 ) = 7%
Using the unbiased expectations theory, calculate the current (long-term) rates for one-, two-, three-, and four-year-maturity Treasury securities.
Answer: . 1 R 1 = 6%
1 R 2 = [(1 + 0)(1 + 0)]1/2 - 1 = 6% 1 R 3 = [(1 + 0)(1 + 0)(1 + 0)]1/3 - 1 = 6% 1 R 4 = [(1 + 0)(1 + 0)(1 + 0)(1 + 0)]1/4 - 1 = 7%
- The real risk-free rate is 3%. Inflation is expected to be 2% this year and 4% during the next 2 years. Assume that the maturity risk premium is zero. What is the yield on 2-year Treasury securities? What is the yield on 3-year Treasury securities?
Answer r* = 3%; I 1 = 2%; I 2 = 4%; I 3 = 4%; MRP = 0; rT2 = ?; rT3 =?
r = r* + IP + DRP + LP + MRP.
Since these are Treasury securities, DRP = LP = 0.
rT2 = r * + I P 2. IP 2 = (2% + 4%)/2 = 3%. rT2 = 3 % + 3 % = 6 %.
rT3 = r * + I P 3. IP 3 = (2% + 4% + 4%)/3 = 3%. rT3 = 3 % + 3. 3 3 % = 6. 3 3 %.
- One year Treasury securities yield 5%. The market anticipates that 1 year from now, 1-year Treasury securities will yield 6%. If the pure expectations theory is correct, what is the yield today for 2-year Treasury securities?
Answer rT1 = 5%; 1 rT1 = 6%; rT2 =?
( 1 + rT2) 2 = (1)(1) ( 1 + rT2) 2 = 1. 1 + rT2 = 1. rT2 = 5%.
- The real risk-free rate, r*, is 2%. Inflation is expected to average 2% a year for the next 4 years, after which time inflation is expected to average 3% a year. Assume that there is no maturity risk premium. An 8-year corporate bond has a yield of 8%, which includes a liquidity premium of 0%. What is its default risk premium?
Answer rC8 = r* + IP 8 + MRP 8 + DRP 8 + LP 8 8% = 2% + (2% × 4 + 3% × 4)/8 + 0% + DRP 8 + 0% 8% = 2% + 3% + 0% + DRP 8 + 0% 8% = 6% + DRP 8 DRP 8 = 1. 7 7 5 %.
Determinants of Interest Rates Q A
Course: Accountancy (1BSA)
University: Miriam College
