In May 2001, several months before the recession of 2001 ended, the interest rat

Question

In May 2001, several months before the recession of 2001 ended, the interest rate on one-year Treasury bonds was about 3.80 and the interest rate on two-year Treasury bonds was about 4.30.

a. Assuming no liquidity premium (expectations theory) what was the market expecting the one-year interest rate on a bond selling in May 2002 to be?

b. Assuming a liquidity premium (liquidity premium theory) of .05% what was the market expecting the one-year interest rate on a bond selling in May 2002 to be?

c. What general implication of the liquidity premium theory concerning the slope of the yield curve and expected interest rates does this example illustrate?

For a and b, I don't need to know how you got the answers, but "c" is the important part that I am struggling with. Thank you so much in advance!

Explanation / Answer

a)  the interest rate on one-year Treasury bonds was about 3.80

interest rate on two-year Treasury bonds was about 4.30 hence there was a probability that the market is providing an additional 0.5% for illiquidity as liquidity premium due to an additional year of maturity.

market expecting the one-year yield on a bond selling in May 2002 to be lesser than 4.3% as it would be maturing in the same year of 4.3% two year bond. But the price of the bond would be traded at a higher price after one year due to the premium it is offering.Hence the yield of the bond would be lesser but the interest rate or coupon it would be providing would be 4.3%.

b) Assuming a liquidity premium (liquidity premium theory) of .05% the market expecting the one-year interest rate on a bond selling in May 2002 to be= 4.3%-0.05%= 4.25%

c) the liquidity premium theory explicitly talks about paying a premium to the bond buyers for the illiquidity. Here, the bond was traded @ 4.3% when it had a maturity of 2 years.Now it got reduced to 1 year hence the liquidity is improved resulting in a loss of coupon rate due to higher or better liquidity i.e. 4.25% being 0.05% as the liquidity premium.

Coming to yield, whwn the tenure of the bond is reduced with lesser coupon rate, it has a double whammy. Due to lesser coupon rate, the demand of the bond would be less but the price of the bond would be at face value or at a discount whereas the two year bond maturing at the same year would be traded at a higher price. Hence the yield depends on the proportion of the following:

The change in the traded price and the change in the coupon rate. If the effect of coupon rate is more then the yield would increase due to lesser coupon rate whereas if the effect of trading price is dominant then the yield would decrease .

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