(R46) Understanding Fixed-Income Risk and Return

Question 1

Three sources of return from bonds and associated risk

Answer 1

1. Coupon payments (Credit Risk)
2. Reinvestment of coupon payments (Interest Rate Risk)
3. Capital Gain/Loss (Interest Rate Risk)

Question 2

Capital gain vs. capital loss

Answer 2

Gain: bond is sold above carrying value
Loss: bond is sold below carrying value

Question 3

If rates increase, what happens to the reinvestment of coupon and does it result in capital gain or loss?

Answer 3

Higher reinvestment of coupon but results in capital loss

Question 4

If rates decrease, what happens to the reinvestment of coupon and does it result in capital gain or loss?

Answer 4

Lower reinvestment of coupon but results in capital gain

Question 5

Carrying value =

Answer 5

Purchase price + amortized discount

Question 6

Duration

Answer 6

Measures the sensitivity of the bond’s full price to changes in interest rate;
Represents approximate amount of time a bond would have to be held for the YTM to be realized

Question 7

Yield Duration

Answer 7

The sensitivity of the bond price with respect to its own YTM (Macauley, modified, money, & price value for a basis point)

Question 8

Curve Duration

Answer 8

The sensitivity of the bond price (or the market value of a financial asset or liability) with respect to a benchmark yield curve; used with complex bonds such as embedded options (Effective Duration)

Question 9

Macauley Duration

Answer 9

The approximate amount of time a bond would have to be held for the market discount rate at purchase to be realized if there is a single change in interest rate. It indicates the point in time when the coupon reinvestment and price effects of a change in yield-to-maturity offset each other.

Question 10

Modified Duration Formula if MacDur is known

Answer 10

ModDur = MacDur/ (1+r)

Question 11

Modified Duration definition

Answer 11

Measures the percentage price change for a bond given a change in its YTM

Question 12

% Change in Full Price of Bond =

Answer 12

-AnnModDur x change in yield; this is a linear estimate and requires a convexity adjustment

Question 13

Modified Duration Formula if Macdur is unknown (Approx ModDur) =

Answer 13

[(PV-) - (PV+)] / (2 x change in yield x PVo)
PV- is the PV of bond with a decrease in rate
PV+ is the PV of bond with a decrease in rate
PVo is the original PV of bond

Question 14

Effective Duration definition

Answer 14

Linear estimate of the percentage change in a bond’s price that would result from a 1% change in the benchmark yield curve. (used for complex bonds with embedded options such as callable bonds)

Question 15

Effective Duration formula

Answer 15

[(PV-) - (PV+)] / (2 x change in curve x PVo)
PV- is the PV of bond with a decrease in rate
PV+ is the PV of bond with a decrease in rate
PVo is the original PV of bond

Question 16

What happens to full price of bond when rates increase and decrease?

Answer 16

When rates increase, full price of bond decreases

Question 17

Key Rate duration

Answer 17

Duration at a specific maturity on the yield curve; Key rate duration must be be used to estimate % change in portfolio value for a non-parallel shift in the yield curve; You get a different key rate duration for each maturity. The sum of all key rate durations equal the effective duration

Question 18

What happens to interest rate risk when duration increases?

Answer 18

Interest rate risk increases

Question 19

What happens to duration with changes in TTM, coupon, and YTM

Answer 19

If TTM increases, duration increases
If Coupon decreases, duration increases
If YTM decreases, duration increases

Question 20

Calculate the duration of a portfolio

Answer 20

= ModDur (weight 1) + ModDur (weight 2) + ModDur (weight n)

Question 21

Portfolio Duration

Answer 21

Percentage change in portfolio value for a 1% change in yield, only for parallel shifts of the yield curve.

Question 22

Money Duration of a Bond

Answer 22

Measure of price change in terms of currency; Money duration is stated in currency units and is sometimes expressed per 100 of par value.

Question 23

Money Duration formula

Answer 23

AnnModDur x PVfull

Question 24

$ Change in full price of bond =

Answer 24

-MoneyDur x change in yield

Question 25

Price Value of a basis point

Answer 25

The price value of a basis point is the change in the value of a bond, expressed in currency units, for a change in YTM of one basis point, or 0.01%

Question 26

Price value of a basis point (PVBP) formula

Answer 26

[(PV-) - (PV+)] / 2
PV- is the PV of bond with a decrease in rate
PV+ is the PV of bond with a decrease in rate

Question 27

Change in PV due to duration - primary effect

Change in PV due to convexity - secondary effect (only for large changes in basis points)

Answer 27

xxx

Question 28

When is a convexity adjustment required?

Answer 28

For large changes in basis points

Question 29

Approximate convexity Formula

Answer 29

[(PV-) + (PV+) - (2PVo)] / (PVo x change in yield squared)
PV- is the PV of bond with a decrease in rate
PV+ is the PV of bond with a decrease in rate
PVo is the original PV of bond

Question 30

Convexity adjustment formula

Answer 30

1/2 (Ann. Convexity) x change in yield squared

Question 31

Yield Volatility

Answer 31

Number of basis points change; As TTM increases, the yield volatility decreases.

Question 32

Duration Gap formula

Answer 32

MacDur - investment horizon

Question 33

How does coupon re-investment risk compare to market price risk if duration gap is less than 0 or greater than 0?

Answer 33

Re-investment risk dominates market price risk if less than 0; market price risk dominations re-investment risk if greater than 0.