CHP 6

An investor in Treasury securities expects inflation to be 1.65% in Year 1, 3% in Year 2, and 4.4% each year thereafter. Assume that the real risk-free rate is 2.1%, and that this rate will remain constant. Three-year Treasury securities yield 6.30%, while 5-year Treasury securities yield 8.30%. What is the difference in the maturity risk premiums (MRPs) on the two securities; that is, what is MRP5 - MRP3

First, calculate the inflation premiums for the next three and five years, respectively. They are IP3 = (1.65% + 3% + 4.4%)/3 = 3.02% and IP5 = (1.65% + 3% + 4.4% + 4.4% + 4.4%)/5 = 3.57% 6.3% = 2.1% + 3.02% + MRP3, or MRP3 = 1.18%. Similarly, 8.3% = 2.1% + 3.57% + MRP5, or MRP5 = 2.63%. Thus, MRP5 - MRP3 = 2.63% - 1.18% = 1.45%

Corporate yield curves are _____ than that of Treasury securities, though not necessarily parallel to the Treasury curve.

Higher

: Assume inflation is expected to be 5% next year, 6% the following year, and 8% thereafter, what is the one year inflation premium? 10 year inflation premium? And 20 year inflation premium?

IP10= (5%+6%+8%x8)/10=7.5% IP20= (5%+6%+8%x18)/20= 7.75%

Suppose the real risk-free rate is 2.50% and the future rate of inflation is expected to be constant at 4.10%. What rate of return would you expect on a 5-year Treasury security?

Step 1: r=r*+IP Step 2: MRP1= 0 MRP10= .1%(10-1)= .9% MRP20= .1(20-1)= 1.9% Step 3: r=r*+IP+MRP (exclude LP and DRP because its a treasury bond) r1= 3%+5%+0= 8% r10=3%+7.5%+.9= 11.4% r20= 3%+7.75+1.9%=12.65

You read in The Wall Street Journal that 30-day T-bills are currently yielding 5.7%. Your brother-in-law, a broker at Safe and Sound Securities, has given you the following estimates of current interest rate premiums: Inflation premium = 2.5% Liquidity premium = 0.4% Maturity risk premium = 1.55% Default risk premium = 2.45% On the basis of these data, what is the real risk-free rate of return? Round your answer to two decimal places.

T-bill rate = r* + IP 5.70% = r* + 2.50% r* = 3.20%.

Set up an amortization schedule for a $42,000 loan to be repaid in equal installments at the end of each of the next 3 years. The interest rate is 11% compounded annually.Round all answers to the nearest cent.

With a financial calculator, enter N = 3, I/YR = 11, PV = -42,000, and FV = 0, and solve for PMT = $17,186.95. Then go through the amortization procedure as described in your calculator manual to get the entries for the amortization table. FOr 2nd am fisrt time input p1=1 p1=2 values in year one and WE NEED TO SOLVE FOR BB FOR EVERY YEAR BUT YEAR 1 Repayment Remaining (Beg bal- princple=remaining

Yield Curve

a graph of the term structure

S-T Corporate

r* + IP + DRP + LP

L-T Corporate

r* + IP + DRP + LP + MRP

The real risk-free rate is 2.5%. Inflation is expected to be 2.25% this year and 4.25% during the next 2 years. Assume that the maturity risk premium is zero A .What is the yield on 2-year Treasury securities? Round your answer to two decimal places. B. What is the yield on 3-year Treasury securities? Round your answer to two decimal places.

r* = 2.5%; I1 = 2.25%; I2 = 4.25%; I3 = 4.25%; MRP = 0; rT2 = ?; rT3 = ? ****r = r* + IP + DRP + LP + MRP. ***Since these are Treasury securities, DRP = LP = 0. rT2 = r* + IP2. IP2 = (2.25% + 4.25%)/2 = 3.25%. rT2 = 2.5% + 3.25% = 5.75%. rT3 = r* + IP3. IP3 = (2.25% + 4.25% + 4.25%)/3 = 3.58%. rT3 = 2.5% + 3.58% = 6.08%

S-T Treasury

r= r* + IP

Term Structure

relationship between interest rates (or yields) and maturities.

Nominal Rates

the interest rate before taking inflation into account. It is the interest rate that is quoted on bonds and loans.

Inflation Premium (IP)

the currency's purchasing power is reduced by a rate known as the inflation rate. Inflation makes real dollars less valuable in the future and is factored into determining the nominal interest rate. The difference between Nominal interest rate and Inflation rate represents approximate real interest rate r - IP=

Real Rates

the interest rate adjusts for the inflation and gives the real rate of a bond or a loan. Formula: the real rate = the nominal rate - the inflation rate (the inflation premium)

As maturity becomes larger, MRP becomes?

larger, but inflation premium(IP) can be larger or smaller, so interest rate can be larger or smaller

L-T Treasury

r= r* + IP + MRP

The real risk-free rate, r*, is 2.05%. Inflation is expected to average 1.6% a year for the next 4 years, after which time inflation is expected to average 3.95% a year. Assume that there is no maturity risk premium. An 8-year corporate bond has a yield of 11.95%, which includes a liquidity premium of 0.6%. What is its default risk premium?

rCB = r* + IP8 + MRP8 + DRP8 + LP8 11.95% = 2.05% + (1.6% x 4 + 3.95% x 4)/8 + 0.0% + DRP8 + 0.6% 11.95% = 2.05% + 2.78% + 0.0% + DRP8 + 0.6% 11.95% = 5.43% + DRP8 DRP8 = 6.53%.

A 5-year Treasury bond has a 4.85% yield. A 10-year Treasury bond yields 6.2%, and a 10-year corporate bond yields 8.15%. The market expects that inflation will average 2.85% over the next 10 years (IP10 = 2.85%). Assume that there is no maturity risk premium (MRP = 0), and that the annual real risk-free rate, r*, will remain constant over the next 10 years. (Hint: Remember that the default risk premium and the liquidity premium are zero for Treasury securities: DRP = LP = 0). A 5-year corporate bond has the same default risk premium and liquidity premium as the 10-year corporate bond described above. What is the yield on this 5-year corporate bond?

rT5 = 4.85%; rT10 = 6.2%; rC10 = 8.15%; IP10 = 2.85%; MRP = 0. For Treasury securities, DRP = LP = 0. rT10 = r* + IP10 6.2% = r* + 2.85% r* = 3.35% rT5 = r* + IP5 4.85% = 3.35% + IP5 1.5 = IP5 rC10 = r* + IP10 + DRP10 + LP10 8.15% = 3.35% + 2.85% + DRP10 + LP10 1.95 = DRP10 + LP10 rC5 = 3.35% + 1.5% + DRP5 + LP5, but DRP5 + LP5 = DRP10 + LP10 = 1.95%. So, rC5 = 3.35% + 1.5% + 1.95% = 6.8%

Real Risk Free Rates r*

the risk-free rate after taking inflation into account. It assumes no risk or uncertainty, simply reflecting differences in timing: the preference to spend now/pay back later versus lend now/collect later. risk free rate is low in the first place, therefore real risk free rate can sometimes be negative, particularly in times of high inflation.

Risk Free Rates

the theoretical rate of return of an investment with zero risk. The risk-free rate represents the interest an investor would expect from an absolutely risk-free investment over a specified period of time. In theory, the risk-free rate is the minimum return an investor expects for any investment because he will not accept additional risk unless the potential rate of return is greater than the risk-free rate.

upward-sloping yield curve

upward slope due to an increase in expected inflation and increasing maturity risk premium.

The spread between corporate and Treasury yield curves...

widens as the corporate bond rating decreases.

Four factors affect the level of interest rates

¥ Production opportunities (r*) ¥ Time preferences for consumption (r*) ¥ Risk (DRP, LP, MRP) ¥ Expected inflation (IP)