Question

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Suppose most investors expect the inflation rate to be 5% next year, 6% the following year,...

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 MPR increased by 0.1% 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?

Expert Solution

Solution 1)

Maturity risk premium (MRP) for 1-year bond = 0%

Maturity risk premium (MRP) for 2-year bond = 0.1%

It is given that the Maturity risk premium (MRP) will increase by 0.1% per year thereafter for 20 years

Therefore, Maturity risk premium (MRP) for 10-year bond = 0.1*9 = 0.9%

Maturity risk premium (MRP) for 20-year bond = 0.1*19 = 1.9%

Inflation rate during year 1 = 5%

Inflation rate during year 2 = 6%

Inflation rate during and after year 3 = 8%

Thus, Average inflation rate for 10 year bond = (5% + 6% + 8*8%)/10 = 75%/10 = 7.5%

Average inflation rate for 20 year bond = (5% + 6% + 18*8%)/20 = 155%/20 = 7.75%

Risk-free rate = 3%

Interest rate = Real risk-free rate + Inflation premium + Default risk premium + Liquidity premium + Market Risk Premium

Since the bonds are treasury bonds, hence, these bonds are supposed to have zero default rates. Thus, the default risk premium = 0 for these bonds

Also, since these are treasury bonds, hence, these bonds have high liquidity, hence, the liquidity premium would be zero.

Thus, putting these values in the above equation, we get,

Interest rate = Real risk-free rate + Inflation premium + Market Risk Premium

The interest rate for 1-year bond = 3% + 5% + 0 = 8%

The interest rate for 10-year bond = 3% + 7.5% + 0.9% = 11.4%

The interest rate for 20-year bond = 3% + 7.75% + 1.9% = 12.65%

Solution 2) Since the interest rates are increasing with an increase in maturity, thus, the yield curve is upward sloping.

Solution 3) Reasons for upward yield curve:

a) The increasing maturity risk premium of the bonds with the increase in maturity

b) The increasing inflation risk premium of the bonds with the increase in maturity.

jeff jeffy answered 1 year ago

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