Answer 3 568 Previous page The following information will be used for the next 7
ID: 2780404 • Letter: A
Question
Answer 3 568 Previous page The following information will be used for the next 7 questions An investor is considering investing in a 4 year, 8% coupon bon (semi-annual) that has a par value of $100. The yield on this bond is 10%, continuously compounded. Calculate the convexity of the bond, to 3 decimal places. Take all previous calculations to 3 decimal places to ensure accuracy Answer Previous page The following information will be used for the next 7 questions An investor is considering investing in a 4 year, 8% coupon bon (sem-annual of $100. The yield on this bond is 10%, continuously compounded that has a par value ious calculations, if there is a .5% change in the price of the bond, how imal nlaces)Explanation / Answer
Formula to calculate convexity
Convexity = {1/ P*(1+y) ^2}* [(CF*t)/ (1+y) ^t]*(t^2+t)
Where P = Bond price
y = Yield to maturity in decimal form
t = Maturity time period
CF=Cash flow at different time
Now we have following formula for calculation of bond’s Price
Price of Bond P = C* [1- 1/ (1+y) ^n] /y + M / (1+y) ^n
Where,
Price of the bond P =?
C = coupon payment = 8%/2 of $100 = $4 semiannual coupon
n = number of payments = 4 years *2 = 8
Yield to maturity Y =10% per annum or 10%/2 =5% semiannual but it is continuously compounded
Therefore the equivalent continuously compounded yield is
y = 2 ln[(1 + Y/2 )] = 2 ln(1.05) = 9.758% per year
And semiannual continuously compounded yield = y/2 =9.758%/2 =4.879%
M = value at maturity, or par value = $100
Now we have,
P= $4 * [1 – 1 / (1+4.879%) ^8] /4.879% + 100/ (1+4.879%) ^8
= $25.980 + $68.311
= $94.291
Price of the bond is $94.291
Now discounted cash flow calculation is as follows-
time (t)
Cash Flow (CF)
CF * t
(CF*t)/(1+y)^t
(t^2 +t)
[(CF*t)/(1+y)^t]*(t^2+t)
1
$4
$4
3.814
2
7.628
2
$4
$8
7.273
6
43.638
3
$4
$12
10.402
12
124.824
4
$4
$16
13.224
20
264.482
5
$4
$20
15.761
30
472.834
6
$4
$24
18.033
42
757.407
7
$4
$28
20.060
56
1123.379
8
$104
$832
568.349
72
40921.121
Sum
43715.312
Now putting all the values in convexity formula
Convexity = {1/ $94.291*(1+0.04879) ^2}*43,715.312
= 421.489
Therefore convexity of the bond is 421.489.
time (t)
Cash Flow (CF)
CF * t
(CF*t)/(1+y)^t
(t^2 +t)
[(CF*t)/(1+y)^t]*(t^2+t)
1
$4
$4
3.814
2
7.628
2
$4
$8
7.273
6
43.638
3
$4
$12
10.402
12
124.824
4
$4
$16
13.224
20
264.482
5
$4
$20
15.761
30
472.834
6
$4
$24
18.033
42
757.407
7
$4
$28
20.060
56
1123.379
8
$104
$832
568.349
72
40921.121
Sum
43715.312