Book 4_Fixed_READING 61_CURVE-BASED AND EMPIRICAL FIXED-INCOME RISK MEASURES

Question 1

Because bonds with embedded options have uncertain cash flows, they do not have a single well-defined yield

Answer 1

Therefore, effective duration and effective convexity must be calculated with respect to shifts in the benchmark curve rather than the bond’s yield for bonds with embedded options.

Question 2

Effective duration

Answer 2

is a linear estimate of the percentage change in a bond’s price that would result from a 1% change in the benchmark yield curve:
- Effective duration = (V_ - V+)/ (2Vo x ∆Curve)

Question 3

Effective convexity

Answer 3

= (V_ + V+ - 2Vo)/(Vo x ∆Curve^2 )

Question 4

Callable bonds and MBS

Answer 4

may exhibit negative convexity at low yields

Question 5

The expected price change for a bond with respect to an expected ∆Curve

Answer 5

Change in full bond price = -EffDur x (∆Curve) + 1/2 x EffCox x (∆Curve)^2

Question 6

Key rate duration

Answer 6

is a measure of the price sensitivity of a bond or a bond portfolio to a change in yield for a specific maturity while other yields remain the same

Question 7

The key rate duration of a cash flow in a portfolio

Answer 7

• The cash flow’s modified duration multiplied by its weight in the portfolio
  = modified duration x weight
• The effect on the overall portfolio is the sum of these individual effects

Question 8

analytical durations

Answer 8

The duration measures we have introduced so far, based on mathematical analysis

Question 9

Macaulay, modified, and effective duration

Answer 9

are examples of analytical duration

Question 10

Empirical duration

Answer 10

• is estimated from historical data using models.
• may be lower than analytical duration in interest rate environments where the assumptions underlying analytical duration may not hold, such as for credit risky bonds in a flight-to-quality scenario