Question

Molly is an aggressive bond trader who likes to speculate on interest rate swings. Market interest rates are currently at 10.0% , but she expects them to fall 8.0% within a year. As a result, Molly is thinking about buying either a 25-year, zero-coupon bond or a 20-year, 8.5% bond. (both bonds have $1000 par value and carry the same agency rating.) Assuming that Molly wants to maximize capital gains, which of the two issues should she select? What if she wants to maximize the total return (interest income and capital gains) from her investment? Why did one issue provide better capital gains than the other? Based on the duration of each bond, which one should be more price volatile?

The capital gain of the zero-coupon bond is $______

Answer 1

Rate	ZCB	CB
10%	$92.30	$872.30
8%	$157.70	$1,048.02
Cap Gains	70.86%	20.14%

Let's calculate the price of both bond today with 10% rate and a year later with 8% rate using PV function on a calculator

For ZCB, N = 25 or 24, PMT = 0, I/Y = 10% or 8%, FV = 1000 => Compute PV = $92.30 and $157.70

For Coupon Bond, N = 20 or 19, PMT = 8.5% x 1000 = 85, I/Y = 10% or 8%, FV = 1000 => Compute PV = $872.30 and $1,048.02

Capital gains for zero coupon = 157.70 / 92.30 - 1 = 70.86%

Select zero coupon bond as it has higher capital gains.