Determinants of Interest Rates Q A PDF

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DETERMINANTS OF INTEREST RATES Problems 1. A particular security’s equilibrium rate of return is 8 percent. For all securities, the inflation risk premium is 1.75 percent and the real risk-free rate is 3.5 percent. The security’s liquidity risk premium is 0.25 percent and maturity risk premium is 0.85 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% = 1.75% + 3.5% + DRP + 0.25% + 0% + 0.85% Thus, DRP = 8% - 1.75% - 3.5% - 0.25% - 0% - 0.85% = 1.65% 2. REAL RISK-FREE RATE You read in The Wall Street Journal that 30-day T-bills are currently yielding 5.5%. Your brother-in-law, a broker a Safe and Sound Securities, has given you the following estimates of current interest rate premiums: • • • •

Inflation premium = 3.25% Liquidity premium = 0.6% Maturity risk premium = 1.8% Default risk premium = 2.15%

On the basis of these data, what is the real risk-free rate of return? Answer T-bill rate = r* + IP 5.5% = r* + 3.25% r* = 2.25%. 3. 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 3.25 percent. Your broker has determined the following information about economic activity and Moore Corporation bonds: Real Risk-Free Rate = 2.25% Default Risk Premium = 1.15% Liquidity Risk Premium = 0.50% Maturity Risk Premium = 1.75% a. What is the inflation premium? b. What is the fair interest rate on Moore Corporation 30-year bonds? Answer: a. IP = i* – RFR = 3.25% - 2.25% = 1.00% c. ij* = 1.00% + 2.25% + 1.15% + 0.50% + 1.75% = 6.65%

4.

A two-year Treasury security currently earns 1.94 percent. Over the next two years, the real risk-free rate is expected to be 1.00 percent per year and the inflation premium is expected to be 0.50 percent per year. Calculate the maturity risk premium on the two-year Treasury security. Answer: 1.94% = 0.50% + 1.00% + 0.00% + 0.00% + MP => MP = 1.94% - (0.50% + 1.00% + 0.00% + 0.00%) = 0.44%

5. Tom and Sue’s Flowers Inc.’s 15-year bonds are currently yielding a return of 8.25 percent. The expected inflation premium is 2.25 percent annually and the real risk-free rate is expected to be 3.50 percent annually over the next 15 years. The default risk premium on Tom and Sue’s Flowers’ bonds is 0.80 percent. The maturity risk premium is 0.75 percent on 5-year securities and increases by 0.04 percent for each additional year to maturity. Calculate the liquidity risk premium on Tom and Sue’s Flowers Inc.’s 15-year bonds. Answer: 8.25% = 2.25% + 3.50% + 0.80 + LRP + (0.75% + (0.04% x 10)) => LRP = 8.25% - (2.25% + 3.50% + 0.80% + (0.75% + (0.04% x 10))) = 0.55%

6.

Nikki G’s Corporation’s 10-year bonds are currently yielding a return of 6.05 percent. The expected inflation premium is 1.00 percent annually and the real risk-free rate is expected to be 2.10 percent annually over the next 10 years. The liquidity risk premium on Nikki G’s bonds is 0.25 percent. The maturity risk premium is 0.10 percent on 2-year securities and increases by 0.05 percent for each additional year to maturity. Calculate the default risk premium on Nikki G’s 10-year bonds. Answer: 6.05% = 1.00% + 2.10% + DRP + 0.25% + (0.10% + (0.05% × 8)) => DRP = 6.05% - (1.00% + 2.10% + 0.25% + (0.10% + (0.05% x 8))) = 2.20%

7. The current one-year Treasury-bill rate is 5.2 percent and the expected one-year rate 12 months from now is 5.8 percent. According to the unbiased expectations theory, what should be the current rate for a two-year Treasury security? Answer: 1R2 = [(1 + 0.052)(1 + 0.058)]1/2 - 1 = 5.50% 8. Suppose that the current one-year rate (one-year spot rate) and expected one-year T-bill rates over the following three years (i.e., years 2, 3, and 4, respectively) are as follows: 1R1 = 6%, E(2r1) = 7%, E(3r1) = 7.5%, E(4r1) = 7.85% Using the unbiased expectations theory, calculate the current (long-term) rates for one-, two-, three-, and four-year-maturity Treasury securities. Answer: . 1R1 = 6% 1R2

= [(1 + 0.06)(1 + 0.07)]1/2 - 1 = 6.499% 1R3 = [(1 + 0.06)(1 + 0.07)(1 + 0.075)]1/3 - 1 = 6.832% 1R4 = [(1 + 0.06)(1 + 0.07)(1 + 0.075)(1 + 0.0785)]1/4 - 1 = 7.085%...