Answer:
Step-by-step explanation:
Zero Coupon
N 8 30
PMT 0 5
YTM 9% 9%
PV (at 9%) $50.19 $58.91
PV (at 10%) $46.65 $52.87
Actual Loss -7.05% -10.25%
PV (at 8%) $54.03 $66.23
Actual Gain 7.65% 12.43%
Duration 7.06 7.04
Convexity 155.1 244.8
Predicted Loss -6.28% -5.82%
Predicted Gain 7.84% 8.26%
As the yield increases, the bond prices fall and vice versa. Hence, there will be a loss when yields rise and a gain when yields fall.
In order to calculate the actual gains and losses, we need to find the bond prices at yields 8%, 9% and 10% using PV formula. PV(rate, nper, pmt, fv, 0)
Predicted loss and gain can be calculated using following equation
% Change in bond price = - Duration x (change in yield) + 1/2 x Convexity x (change in yield)^2
When YTM = 10%, change in yield = +1% and when YTM = 8%, change in yield = -1%