Question

In: Economics

Suppose there are 3 bonds with the following characteristics. There is a 1-year Treasury bond with...

Suppose there are 3 bonds with the following characteristics. There is a 1-year Treasury bond with a face value of $1000, a 8% coupon rate, and the yield to maturity is 8%. There is a 2-year treasury bond with a face value of $1000, a 15% coupon rate, and the yield to maturity is 8%. There is also a 3-year treasury bond with $1000 face value, a 5% coupon rate, and the yield to maturity is 8%.

a) Based on expectations theory, what is the expected 1-year interest rate next year and what is the expected 1-year interest rate 2-years from now?

b) What is the shape of the yield curve right based on these bonds?

c) What does expectations theory predict should happen to short-term and long-term interest rates based on the information from these bonds?

d) Briefly explain, does your answers from part a) fit with the answer to part c)?

Solutions

Expert Solution

a)

Expectations Theory:

Investor would want a two year security to offer a return that is similar to the anticipated return from investing into two consecutive one year securities.

( 1 + i2 ) ^ 2 = ( 1 + i1 ) * ( 1 + rex)

(1 + 8%) ^ 2 = ( 1+ 8%) * (1 + rex )

1 + rex = 1 + 8%

rex = 8% ( expected 1-year interest rate next year)

( 1 + i3 ) ^ 3 = ( 1 + i2 )^2  * ( 1 + rex2)

(1 + 8%) ^ 3 = ( 1+ 8%)^2 * (1 + rex2 )

1 + rex2 = 1 + 8%

rex2 = 8% ( expected 1-year interest rate 2 year from now)

b)

Since the 1-year Treasury bond, 2-year treasury bond & 3-year treasury bond all have a common yield of 8%, the yield curve is flat irrespective of the duration of holding.

c)

Yield curve is flat.

Expectation is that interest rates will rise.

Savers or investors will invest in short term securities, because they can invest in long term securities when the interest rates rise.

Hence surplus in short term money, which will drive interest rates down at the short end.

Borrowers or issuer of securities will prefer to flat long term securities, as they can lock in at the current low rates.

This reduces demand for short term funds and will drive interest rates down at short end.

Hence, the yield curve would pivot upwards.

d)

The answer of part a does not fit to the answer for part c as the expected rate of interest is flat there at 8%.

This is because the given yield curve is flat and our expectation is that the yield curve will be pivoted upwards. Hence, there exists some limitations.


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