Question

You observe the 12-month and 18-month zero coupon rates for U.S. Treasury securities are 1.95% and 2.25%, respectively. Assuming arbitrage free markets and no friction costs, the implied 6-month rate in 12 months’ time should be closest to:

Answer 1

Answer:

semiannual 1.42%

yearly          2.85%

Explanation:

Those are annual rate so we need to determinate the 6-month rate

The annual rate times the semiannual rate will be equal to the 18 months rate

$(1+0.0195)(1+r)=(1.0225)^{3/2}$

$\frac{1.0225^{3/2} }{1.0195} - 1 = r$

r = 0.01416296  = 1.42%

If we want to express it annually:

1.0142^2 - 1 = r  = 2.85%

<em />