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A ten-year Treasury security with 2-1/8 percent coupons, its price is (P = 98.39) and its yield is (y=2.306 ). I would like to compute its convexity. Here is how I did it.
Note that the yield is annual yield, so the semiannual interest rate is ( y/2).
Each coupon is paid semi-annually and is (C = 100 ×2.125/100/2= 1.0625.)
The convexity (by the formula given at Chapter 3 Section 3.7 Convexity of Investment Science by Luenberger) is
(
\begin{align*}
Convexity
&= \frac{1}{P(1+y/2)^2} (
\frac{100+C}{(1+y/2)^{20}} (20^2+20)/2^2
+ \sum_{t=1}^{19} \frac{C}{(1+y/2)^t} (t^2+t)/2^2)
\\&= \frac{1}{98.39 \times (1+0.02306/2)^2} (
\frac{100+1.0625}{(1+0.02306/2)^{20}} (20^2+20)/2^2
+ \sum_{t=1}^{19} \frac{1.0625}{(1+0.02306/2)^t} (t^2+t)/2^2)
\\&= 89.75947
\end{align*}
)
But the solution is 94.18. Where am I wrong? Thanks for help!
Note that the yield is annual yield, so the semiannual interest rate is ( y/2).
Each coupon is paid semi-annually and is (C = 100 ×2.125/100/2= 1.0625.)
The convexity (by the formula given at Chapter 3 Section 3.7 Convexity of Investment Science by Luenberger) is
(
\begin{align*}
Convexity
&= \frac{1}{P(1+y/2)^2} (
\frac{100+C}{(1+y/2)^{20}} (20^2+20)/2^2
+ \sum_{t=1}^{19} \frac{C}{(1+y/2)^t} (t^2+t)/2^2)
\\&= \frac{1}{98.39 \times (1+0.02306/2)^2} (
\frac{100+1.0625}{(1+0.02306/2)^{20}} (20^2+20)/2^2
+ \sum_{t=1}^{19} \frac{1.0625}{(1+0.02306/2)^t} (t^2+t)/2^2)
\\&= 89.75947
\end{align*}
)
But the solution is 94.18. Where am I wrong? Thanks for help!
