Question

Two years ago you acquired a 10 year zero coupon bond,$1000 par value bond at 12% YTM.Recently you sood this bond at 8% YTM. Using a semi-annual compounding,compute the annualized horizon for this investment.

Answer 1

Solution:

Annualized horizon return is the total annual return received on a bond made over a horizon period. It measures the rate of return if the bond is being sold prior to its maturity. In terms of a zero-coupon bond, the horizon return will be calculated as follows:

Interest = $\frac{12\%\;annually}{2\;interest \;payments\;per\;year} =6\%$

Semi-annual periods = 2 interest payments per year $\times$ 10 years = 20 semi-annual periods

Purchase price = Face value $\times$ PVF of 6$\%$ = 1000 $\times$ 0.31180 = 311.80

 

After 2 years, the selling price will be calculated as follows:

Interest = $\frac{8\%\;annually}{2\;interest \;payments\;per\;year} =4\%$

Semi-annual periods = 2 interest payments per year $\times$ 8 years = 16 semi-annual periods

Selling price = Face value$\times$PVF of 4$\%$ = 1000 $\times$0.53391 = 533.91