Book 4_Fixed_READING 60_YIELD-BASED BOND CONVEXITY AND PORTFOLIO PROPERTIES

Question 1

Convexity

Answer 1

refers to the curvature of a bond’s price-yield relationship

Question 2

The convexity of a single cash flow at period t

Answer 2

= t x (t+1)/(1+r)^2
t: period at which the cash flow occurs
r: periodic yield of the bond

Question 3

The convexity of a coupon-paying bond

Answer 3

• is the weighted average convexity of its cash flows. The weight is based on PV of cash-flow
• To annualize convexity for non-annual coupons, divide by periodicity squared (for example semi-annual, devide by 4)

Question 4

Convexity can be approximated using the following formula:

Answer 4

approximate convexity = (V- + V+ - 2Vo)/((deltaYTM)^2 * Vo)
V-: bond price if YTD decrease
V+: bond price if YTD increase
Vo: current price

Question 5

the percentage change in the full price of a bond

Answer 5

%change full bond price = -annual modified duration (delta YTD) + 1/2 annual convexity (delta YTD)^2

Question 6

The convexity effect to % bond price

Answer 6

1/2 annual convexity (delta YTD)^2

Question 7

Money convexity

Answer 7

stated in currency units and is sometimes expressed per 100 of bond value:
- money convexity = annual convexity × full price of bond position

Question 8

Using money duration and money convexity to directly estimate the change in price of a bond, this is the equation:

Answer 8

change full bond price = -(MoneyDur x deltaYTD) + (1/2 x MoneyCon x deltaYTD^2)

Question 9

There are two methods for calculating portfolio duration and convexity:

Answer 9

1. Calculate a single duration and convexity measure based on the aggregate cash flows of the bond portfolio.
2. Calculate the weighted average of durations of bonds in the portfolio. This method is used most often in practice, but it assumes a parallel shift of the yield curve.

Question 10

parallel shifts in Portfolio duration

Answer 10

the discount rate at each maturity changes by the same amount.