Answer to Question #131468 in Financial Math for bonolo

Question

You have been provided with the following options.
a. A 10-year, R1000 face value, 10 percent coupon bond with semiannual interest
payments.
b. A 10-year, R1000 face value, 10 percent coupon bond with annual interest
payments.
c. A 10-year, R1000 face value, zero coupon bond.
d. A 10-year R100 annuity.
(3 points) Determine which one poses the highest price risk.

Answer 1

Solution

Investors holing bonds encounter changing interest rates which challenge the generation of desired income. However, for annuities, owners do not have that risk because payments are guaranteed for life. The price of a bond is given by: Price = Face value/(1 + interest rate) ^{number of years} while the future price of an annuity is given by Price=Amount*[(1+interest rate)^{number of years}  −1]/interest rate. As the price of the bond increase(decrease), the interest rates decrease(increase) with increase as investors become disenchanted looking for better rates. Comparing the bonds with annual and semi-annual payments, rising rates erode semiannual bonds prices less than they do annual bonds because of the compounding effect. On the other hand, prevailing lower interest rates tend to increase bond prices since buyers opt for bonds paying comparatively heroic rates. In other words, shorter accrual periods of semiannual bonds work against the bond’s rising price. Thus for this scenario, the 10-year, R1000 face value, 10 percent coupon bond with annual interest poses the highest price risk.