A portfolio manager wants to estimate the interest rate risk of a bond using dur
ID: 2733267 • Letter: A
Question
A portfolio manager wants to estimate the interest rate risk of a bond using duration. The current price of the bond is 106. A valuation model employed by the manager found that if interest rates decline by 25 basis points, the price will increase to 108.5 and if interest rates increase by the same number of basis points, the price will decline to 104.
a. What is the duration of this bond?
b. What is the convexity of this bond?
c. Using the duration and convexity measures calculated above, estimate by how much the value of this bond would change if interest rates increase by 50 basis points.
Estimated change using duration =
Convexity adjustment =
Total estimated percentage price change =
d. Using the duration and convexity measures calculated above, estimate by how much the value of this bond would change if interest rates decrease by 50 basis points.
Estimated change using duration =
Convexity adjustment =
Total estimated percentage price change =
e. Assume the bond portfolio manager purchased portfolio manager purchased $10 million in market in market value of the bond. Use the estimates above to determine the change in this portfolio value if interest rates increase by 50 basis points.
f. Assume the bond portfolio manager purchased portfolio manager purchased $10 million in market value of the bond. Use the estimates above to determine the change in this portfolio value if interest rates decrease by 50 basis points.
Explanation / Answer
duration of bond=(Price if yield decline - price if yield rise / 2(initial price)(change in yield in decimal)
initial price=106
if decline=108.5
if increase=104
change in yield=.25%*2=0.5%
Duration=4.245
2)Convexity=(v3+v2-2v1)/(2*v1)*(change in yield)^2
v1 bond price
v2 bond price when interest rate increased
v3 bond price when interest rate decreased
v1=106
v2=104
v3=108.5
change in yield=.5%
convexity=94.34
convexity adjustment formulae=C*changein yield^2*100
=377.35*.25%^2*100
=.2358
c)
Bond Price Change=(-Duration×Yield Change*100)+Convexity Adjustment
=(-4.245*.5%*100)+.2358
=1.89% increase
d)if decreases by 50 bps
Bond Price Change=(-Duration×Yield Change*100)+Convexity Adjustment
=(-4.245*-.5%*100)+.2358
=2.36% decrease
e)10mn*(1+1.89%)=10,189,000
f)10mn*(1-2.36%)=9,764,151
c)
Duration=(
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.