Question

13. Current prices for US Treasury, zero-coupon bonds (each with face values of $1000), are as follows:

• A 6-month zero coupon is currently selling for $986.3.
• A 12-month zero coupon is currently selling for $965.38.
• An 18-month zero coupon is currently selling for $941.1.
• A 24-month zero coupon is currently selling for $912.07.

All YTM’s come from US Treasury, zero-coupon bonds.

Determine the YTM for each bond, and then plot as much of the yield curve as you can.

After you finish constructing the yield curve, report the YTM (as an effective annual rate) for the 18-month zero-coupon bond.

Express your answer as a decimal, not as a percent, using at least four significant digits.

Answer 1

Answer:

Zero coupon bonds is an instrument which issued on discount and redem on face value and there is no series on interest payment.

So in order to calculate YTM (yield to maturity) of zero coupon bonds,

the formula is,

YTM = [(Face value / Current pricce of bond) ^ (1 / Years to maturity) ] - 1

Now in our case YTM of 6-month bond,

YTM = [(1000 / 986.3) ^ (1 / 0.5)] - 1

YTM = 2.8% or in decimal 0.0279

Now YTM in case of 12-month bond,

YTM = [(1000 / 965.38) ^(1 / 1)] -1

YTM = 3.59% or in decimal 0.0358

Now YTM in case of 18-month bond,

YTM = [(1000 / 941.1) ^(1 / 1.5)] -1

YTM = 4.13% or in decimal 0.0413

Now YTM in case of 24-month bond,

YTM = [( 1000 / 912.07) ^ (1 / 2)] - 1

YTM = 4.7% or in decimal 0.4709

Now graph of yield curve is given below

X-axis is months and Y-axis is YTM in (%).

YTM on 18-month bond is 0.0413.