Using the Yield Curve to Estimate Future Interest Rates You can calculate the yi

Question

Using the Yield Curve to Estimate Future Interest Rates You can calculate the yield curve, given inflation and maturity-related risks. Looking at the yield curve, you can use the information embedded in it to estimate the market's expectations regarding future inflation, risk, and short-term interest rates. The___________________theory states that the shape of the yield curve depends on investors' expectations about future interest rates. The theory assumes that bond traders establish bond prices and interest rates strictly on the basis of expectations for future interest rates and that they are indifferent to maturity because they don't view long-term bonds as being riskier than short-term bonds. For example, assume that you had a 1-ycar T-bond that yields 1.6% and a 2-year T-bond that yields 2.05%. From this information you could determine what the yield on a 1-year T-bond one year from now would be. Investors with a 2-ycar horizon could invest in the 2-year T-bond or they could invest in a 1-year T-bond today and a 1-year T-bond one year from today. Both options should yield the same result if the market is in equilibrium: otherwise, investors would buy and sell securities until the market was in equilibrium. Quantitative Problem: Today, interest rates on 1-year T-bonds yield 1.6%, interest rates on 2-ycar T-bonds yield 2.05%, and interest rates on 3-year T-bonds yield 3.7%. If the pure expectations theory is correct, what is the yield on 1-year T-bonds one year from now? Be sure to use a geometric average in your calculations. Round your answer to four decimal places. Do not round intermediate calculations._______% If the pure expectations theory is correct, what is the yield on 2-year T-bonds one year from now? Be sure to use a geometric average in your calculations. Round your answer to four decimal places. Do not round intermediate calculations._______% If the pure expectations theory is correct, what is the yield on 1-ycar T-bonds two years from now? Be sure to use a geometric average in your calculations. Round your answer to four decimal places. Do not round intermediate calculations._______%

Explanation / Answer

Pure expectations theory states that the shape of the yield curve depends on the investor's expectation about future risk interests.

Interest rate =

1 yr = 1.6%

2 yr = 2.05

3 yr = 3.7%

To do the calculation, first add 1 to the one year bond's interest rate,

0.016+ 1 = 1.016

Next, we take this result and square it:

1.016^ 2 = 1.0322

The next step is to divide this number by the current year's one-year interest rate plus one.

1.0322/ 0.016+1 = 1.0322/ 1.016 = 1.016

The final step is to subtract 1 from that last calculation,

1.016- 1 = 0.016 = 1.6%

B)

To do the calculation, first add 1 to the two-year bond's interest rate.

1 + 0.0205 = 1.0205

Next, we take this result and square it:

1.0205^ 2 = 1.0414

The next step is to divide this number by the current year's one-year interest rate plus one.

1.0414/ (1+ 0.016) = 1.0414 / 1.016 = 1.025

The final step is to subtract 1 from that last calculation,

1.025 – 1 = 0.025 which is equal to =2.5%

C) To do the calculation, first add 1 to the three year bond's interest rate,

0.037+ 1 = 1.037

Next, we take this result and square it:

1.037^ 2 = 1.0754

The next step is to divide this number by the current year's one-year interest rate plus one.

1.0754/ 0.016+1 = 1.0754/ 1.016 = 1.059

The final step is to subtract 1 from that last calculation, giving us the predicted one-year interest rate

1.059- 1 = 0.059 = 5.85%

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