Question

a one year zero coupon treasury bond yields 3.82% and a two year zero coupon treasury yields 5.37%. what is the expected 1 year interest rate 1 year from now, assuming no-arbitrage pricing and no liquidity premium?

Answer 1

To calculate the expected 1-year interest rate 1 year from now, we can use the concept of no-arbitrage pricing. By equating the present value of the two-year zero coupon bond to the present value of the one-year zero coupon bond compounded at the expected 1-year interest rate, we can solve for the interest rate.

Step-by-step explanation:

To calculate the expected 1-year interest rate 1 year from now, we can use the concept of no-arbitrage pricing. Let's assume that the 1-year interest rate 1 year from now is x%. If we invest $1000 in the one-year zero coupon treasury bond, we will receive $1000*(1+x/100) after one year. Similarly, if we invest $1000 in the two-year zero coupon treasury bond, we will receive $1000*(1+5.37/100)^2 = $1000*1.109 - $1109 after two years.

Using the no-arbitrage principle, the present value of the two-year zero coupon bond should be equal to the present value of the one-year zero coupon bond compounded at the expected 1-year interest rate (1+x/100). Mathematically, this can be expressed as:

$1000*1/(1+x/100) = $1000*(1+5.37/100)^2

Simplifying the equation, we get:

1/(1+x/100) = (1+5.37/100)^2

By solving for x, we can find the expected 1-year interest rate 1 year from now.