Module 58: Yield Based Bond Convexity and Porfolio Properties

Question 1

What’s the issue with duration?

Answer 1

Duration measures the linear effect of a yield change on bond price (a first order effect), whereas the relationship is convex
- For larger changes in yield duration is insufficient

Question 2

What does convexity mean for price computation

Answer 2

For a yield drop: Duration underestimates the price rise
For a yield increase: Duration overestimates the price rise

Question 3

How do you compute convexity

Answer 3

Convexity Adjustment: 1/2 x Annual Convexity x (change in yield)^2
Convexity of single cash flow: t x (t+1) / (1+YTM/periodicity(^2

Question 4

What are the factors affecting convexity?

Answer 4

Higher Time to Maturity: Higher Convexity
Larger Coupon: Lower Convexity
High Yield: Lower Duration
The more dispersion of cash flows: More convexity

Question 5

How do you calculate approximate conveity??

Answer 5

PV(-) + PV (+) - 2PV0 / (Change in YTM)^2 * PV0

Question 6

Why do investors like convex bonds?

Answer 6

If yields change substantially, then a more convex bond will have a higher price increase if bonds fall, and will have a less severe price drop if yields go up

Question 7

How do you compute Money Convexity, and then working that to estimate the change in price of bond?

Answer 7

Money Convexity: Annualised Convexity x PV(full)
Change in yield: -(MonDuration x change in yield) + (1/2 x MoneyConvexity x change in yield)

Question 8

How do you work out total convexity using cash flows?

Answer 8

1. Write out cash flows
2. Discount cash flows back to present values
3. PV of each cash flow as a percentage of it’s the total PV
4. Find the convexity of each cash flow doing t x (t+1) / 2
5. Multiply the weight amount of each cash flow by the convexity of it’s corresponding cash flow
6. add all the amounts together

If there’s non annual coupons:
Convexity needs to be divided by perodicity(SQUARED)

Question 9

How do you calculate portfolio duration?

Answer 9

Weight of each bond1 * Duration of bond1 + Weight of each bond2 * Duration of bond2

Question 10

How do you calculate Weights of bonds?

Answer 10

Full price of the bond / Divided by total value of the portfolio.
% change in full price: -ModDuration x (change in yield) + (1/2 x Annual Convexity x change in yield^2)