(R46) Understanding Fixed-Income Risk and Return Flashcards

1
Q

Three sources of return from bonds and associated risk

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

Capital gain vs. capital loss

A

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

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3
Q

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

A

Higher reinvestment of coupon but results in capital loss

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4
Q

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

A

Lower reinvestment of coupon but results in capital gain

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5
Q

Carrying value =

A

Purchase price + amortized discount

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6
Q

Duration

A

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

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7
Q

Yield Duration

A

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

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8
Q

Curve Duration

A

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)

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9
Q

Macauley Duration

A

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.

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10
Q

Modified Duration Formula if MacDur is known

A

ModDur = MacDur/ (1+r)

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11
Q

Modified Duration definition

A

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

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12
Q

% Change in Full Price of Bond =

A

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

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13
Q

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

A

[(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

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14
Q

Effective Duration definition

A

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)

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15
Q

Effective Duration formula

A

[(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

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16
Q

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

A

When rates increase, full price of bond decreases

17
Q

Key Rate duration

A

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

18
Q

What happens to interest rate risk when duration increases?

A

Interest rate risk increases

19
Q

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

A

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

20
Q

Calculate the duration of a portfolio

A

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

21
Q

Portfolio Duration

A

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

22
Q

Money Duration of a Bond

A

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

23
Q

Money Duration formula

A

AnnModDur x PVfull

24
Q

$ Change in full price of bond =

A

-MoneyDur x change in yield

25
Q

Price Value of a basis point

A

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%

26
Q

Price value of a basis point (PVBP) formula

A

[(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

27
Q

Change in PV due to duration - primary effect

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

A

xxx

28
Q

When is a convexity adjustment required?

A

For large changes in basis points

29
Q

Approximate convexity Formula

A

[(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

30
Q

Convexity adjustment formula

A

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

31
Q

Yield Volatility

A

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

32
Q

Duration Gap formula

A

MacDur - investment horizon

33
Q

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

A

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