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Fixed income > LM 4: Fixed Income Risk & Return > Flashcards

LM 4: Fixed Income Risk & Return Flashcards

1
Q

What are the three sources of return for a fixed-rate bond? RRC

A
  1. Receipt of coupon payments and principal on scheduled dates
  2. Reinvestment of coupon payments
  3. Capital gains or losses
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2
Q

What is constant yield to price trajectory?

A

the path that a bond’s price will follow as it approaches maturity if the YTM remains constant.

bonds trading at a premium will eventually go down to par and bonds trading at a discount will eventually go up to par.

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3
Q

What is a bond carrying value?

A

the current price of a bond

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4
Q

How do you tell if a bond is selling at a discount or premium with coupon rate and ytm?

A

if the coupon rate is less than YTM it is trading at a discount

if the coupon rate is more than YTM it is trading at a premium

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5
Q

What is the bond carrying value formula for a bond purchased at a discount and one purchased at a premium?

A

bond at discount: bond carrying value = bond purchase price + amortized amount of discount

bond at premium: bond carrying value = bond purchase price + amortized amount of premium

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6
Q

What is a capital gain on a bond vs a capital loss?

A

capital gain: if the bond is sold at a price above the price trajectory

capital loss: if a bond is sold at a price below the price trajectory

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7
Q

What is total return and formula?

A

total return is the sum of reinvested coupon payments and the sale price

total return = (sum of bond payments + last year coupon + par value)

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8
Q

What is the interest on interest (reinvestment income) formula?

A

total return - par value - total coupon payments = interest on interest

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9
Q

What is horizon yield and formula?

A

internal rate of return on a bond over the investor holding period

horizon yield = ((future value (total return)/ initial price) ^ (1/n)) -1

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10
Q

What is Macaulay’s duration?

A

weighted average time to maturity of cash flows. where the weights are the present value of cash flows

it is the weighted average number of years that an investor must maintain a position in the bond until the present value of the bond’s cash flows equals the amount paid for the bond

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11
Q

What are the steps to the macualay duration?

A
  1. get cash flow for each period (for the last period add the par value)
  2. discount cash flow back to get PV
  3. add up all PVs of different time periods to get price of bond
  4. divide the PV of each period / total price of all PV (to get the weight)
  5. times each period with each weight, and add together all the different periods weight and period.
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12
Q

What is the difference between price risk and reinvestment risk?

A

price risk: risk of a decline in the value of a security

reinvestment risk: the possibility that an investor will be unable to reinvest cash flows received from an investment, such as coupon payments or interest, at a rate comparable to their current rate of return.

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13
Q

How can an investor ensure their exposure to price risk and reinvestment risk offset each other?

A

by setting the bond portfolio’s Macaulay duration to match their investment horizon

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14
Q

What is the duration gap and formula?

A

an imbalance between the investment horizon and Macaulay duration is called the duration gap

Duration gap= Macaulay’s duration − Investment horizon

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15
Q

What are the 3 characteristics if Macaulay’s duration is greater than the investment horizon?

A
  1. positive duration gap
  2. price risk dominates
  3. exposure to rising interest rates
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16
Q

What are the 3 characteristics if the investment horizon is greater than Macaulay’s duration?

A
  1. Negative duration gap
  2. Reinvestment risk dominates
  3. Exposure to falling interest rates
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17
Q

What is duration?

A

% change in bond price to a 1% change in interest rate. The higher the duration, the more sensitive the bond is to changes in interest rates.

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18
Q

Which 2 categories does duration statistics fall into?

A
  1. yield duration
  2. curve duration
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19
Q

What is the difference between yield duration and curve duration?

A

Yield duration measures the sensitivity of a bond’s price to its own YTM

Curve duration measures sensitivity to changes in a benchmark yield curve, such as spot rates for zero-coupon government bonds of various maturities

20
Q

What is modified duration?

A

estimate of the percentage price change for a bond given a 1% change in its yield to maturity.

eg. a 1% increase in YTM will decrease the full price of the bond by 2.668% if the modified duration is 2.668%

21
Q

What is modified duration formula?

A

modified duration = MacDur / (1 + R/ periodicity)

r = rate per period
macdur = Macaulay duration

22
Q

What is the formula used to estimate the percentage change in a bonds price given change in its YTM (aka another formula for modified duration)?

A

% change PV bond = -AnnModDur * % change in yield

% chance in yield = annual change difference of the yield to maturity
AnnModDur = annual modified duration

23
Q

What is approx modified duration formula?

A

ApproxModDur =(PV−)−(PV+ ) / (2)(ΔYield)(PV0)

(PV+) = price of the bond if YTM increases
(PV-) = price of the bond if YTM decreases
ΔYield = change in yield
(PV 0) = current price of bond

24
Q

What is the approx Macaulay duration formula?

A

ApproxMacDur=
ApproxModDur×(1+r)

r = annual yield to maturity

25
Q

What is money duration and formula?

A

measure of the price change in currency units rather than percentage terms

MoneyDur= AnnModDur×PVFull

PV full = current price of the bond

26
Q

What is the formula for change in bond price in terms of money duration?

A

% change in bonds price = -money duration * ΔYield

ΔYield = change in yield

27
Q

What is the price value of a basis point and formula?

A

currency value of the price change for a 1 basis point change in yield

PVBP = {(PV-)-(PV+)} /2

(PV+) = price of the bond if YTM increases
(PV-) = price of the bond if YTM decreases

28
Q

What is the basis point value formula?

A

BPV = moneydur * basis point percentage (BPP * 100)

100 basis points = 1%

29
Q

What are the 2 rules for yield duration of a zero coupon bond and a perpetual bond?

A
  1. zero coupon bond: Macaulay duration = time to maturity
  2. perpetual bond: Macaulay duration formula for perpetual bonds = 1+r/r
30
Q

Describe the 4 relationships of duration with key bond futures. CYTF

A

coupon rate: inverse (lower coupon rate higher duration)

yield to maturity: inverse (highest discount rate lower duration)

time to maturity: direct (duration increases when time to maturity increases)

fraction of coupon period elapsed: inverse (increase in Macaulay’s tT formula leads to a decrease in duration)

31
Q

What is bond convexity?

A

bond’s convexity measures the sensitivity of a bond’s duration to changes in yield

32
Q

What is the formula used to estimate the percentage change in a bond’s price with a first-order effect and second-order effect?

A

% change PV bond = {-AnnModDur * ΔYield} + [1/2 * AnnConvexity * (ΔYield)^2]

ΔYield = annual change difference of the yield to maturity
AnnModDur = annual modified duration

33
Q

What is approximate convexity formula?

A

approximate convexity =(PV−)+(PV+ ) - [2(PV0)] / ((ΔYield)^2)(PV0)

(PV+) = price of the bond if YTM increases
(PV-) = price of the bond if YTM decreases
ΔYield = change in yield
(PV 0) = current price of bond

34
Q

What are the 2 benefits of more convex bonds?

A
  1. experience greater price appreciate when interest rates fall
  2. price will depreciate at a lower rate when interest rates rise
35
Q

What 4 factors will cause the convexity to be higher?

A
  1. a longer time to maturity
  2. a lower coupon rate
  3. a lower yield-to-maturity
  4. more dispersed cash flows
36
Q

Whats the formula for calculating money convexity?

A

MoneyConv= AnnualConvexity ×PVFull

PV full = current price of the bond

37
Q

What is the formula for change in bond price in terms of money convexity?

A

change in bonds price = [-money duration * ΔYield] + [1/2 * moneyconv * (ΔYield)^2]

ΔYield = change in yield

38
Q

What is effective duration?

A

Effective duration is a curve duration statistic that measures the sensitivity of the bond price relative to the benchmark yield (rather than the bond’s YTM).

39
Q

What is the effective duration formula?

A

EffDur=((PV−)− (PV+)) / ((2)(ΔCurve)(PV0))

40
Q

When must you use effective duration?

A

effective duration is useful for bonds with embedded options

41
Q

What is the effective convexity formula?

A

effective convexity =(PV−)+(PV+ ) - [2(PV0)] / ((ΔCurve)^2)(PV0)

(PV+) = price of the bond if YTM increases
(PV-) = price of the bond if YTM decreases
ΔCurve = change in benchmark yield
(PV 0) = current price of bond

42
Q

What is the formula for change in the price of a bond with the first order effect and second order effect derived from effective duration and effective convexity?

A

change in bonds price = [-EffDur* ΔCurve] + [1/2 * EffCon * (ΔCurve)^2]

ΔCurve = change in benchmark yield
EffDur = effective duration
EffCon = effective convexity

43
Q

What is the difference between analytical duration and empirical duration?

A

Analytical duration approximates the effect of changes in benchmark yields on bond prices by assuming that the government bond yields and spreads are independent and uncorrelated variables.

empirical duration refers to constructing statistical models using historical data to estimate duration.

44
Q

What is approximate modified duration of a portfolio?

A

((modified duration A * market price A) + (modified duration B * market price B)) / total market price of portfolio

45
Q

What is the relationship between Macaulay duration for lower coupon bonds vs higher coupon bonds?

A

Macaulay duration is higher for a low-coupon bond (discount bonds) trading at a discount than for a high-coupon bond trading at a premium. (Inverse, lower coupon, high Macaulay. High coupon, lower Macaulay.)

46
Q

What is the formula for convexity adjustment?

A

it’s the second order effect

(1/2 * convexity * (% change in yield ^2))

Fixed income (6 decks)

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