Fixed Income Risk and Return

Question 1

What are the key sources of return for a bond?

When does a capital gain or loss occur?

What does changes in YTM cause?

Answer 1

Coupon and principal payments.
Reinvestment of coupon payments.
Capital gain or loss if bond is sold before maturity.

Changes in yield to maturity produce market price risk (uncertainty about a bond’s price) and reinvestment risk (uncertainty about income from reinvesting coupon payments). An increase (a decrease) in YTM decreases (increases) a bond’s price but increases (decreases) its reinvestment income.

Question 2

Explain and calculate Macaulay duration

Calculate Macaulay Duration

What can Macaulay duration be interpreted as?

What should you remember when calculating macaulay

Answer 2

Macaulay duration is the weighted average number of coupon periods until a bond’s scheduled cash flows.

Modified duration is a linear estimate of the percentage change in a bond’s price that would result from a 1% change in its YTM.

Calculate:

1: Take cash flow for period (e.g coupon, principal or coupon and principal)

2: take present value of cash flow (divide by ytm)

3: Calculate weight ( PVCF / FV)

4: Sum 1 x (0.weight 1) + 2 x (0.weight 2)

Macaulay duration may be interpreted as the investment horizon for which a bond’s market price risk and reinvestment risk just offset each other.

Remember:
1. %’s go in as decimal in the calculation
2. If its a semi annual pay bond, divide the result by 2 9adjust for periodicity)

Question 3

Define and Calculate Approximate modified duration.

What other calculation is this one similar to?

Answer 3

Modified duration is a linear estimate of the percentage change in a bond’s price that would result from a 1% change in its YTM

Calculate

V- - V+
/
2 x V0 x Change in YTM

Similar to effective duration

Question 4

Define and Calculate effective duration.

When should you use effective duration?

What other calculation is this one similar to?

Answer 4

Effective duration 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.

Calculate

V- - V+
/
2 x V0 x Change in Curve

Effective duration is the appropriate measure of interest rate risk for bonds with embedded options because changes in interest rates may change their future cash flows. Pricing models are used to determine the prices that would result from a given size change in the benchmark yield curve.

Question 5

What is key rate duration?

Answer 5

Key rate duration is a measure of the price sensitivity of a bond or a bond portfolio to a change in the spot rate for a specific maturity. We can use the key rate durations of a bond or portfolio to estimate its price sensitivity to changes in the shape of the yield curve.

Question 6

Explain the impact of an increase in the following factors on duration:

Maturity
Coupon Rate
YTM

Answer 6

Duration increases when maturity increases.
Duration decreases when the coupon rate increases.
Duration decreases when YTM increases.

Question 7

What are the two ways of calculating portfolio duration?

Answer 7

1. Calculate the weighted average number of periods until cash flows will be received using the portfolio’s IRR (its cash flow yield). This method is better theoretically but cannot be used for bonds with options.
2. Calculate the weighted average of durations of bonds in the portfolio (the method most often used). Portfolio duration is the percentage change in portfolio value for a 1% change in yield, only for parallel shifts of the yield curve.

Question 8

Calculate money duration

How is money duration stated?

Answer 8

money duration = annual modified duration × full price of bond position (or price per 100 of par)

as a currency

Question 9

What is one basis point equivalent to (percentage and decimal form)

25 basis points is what as decimal?

Answer 9

One basis point is equivalent to 0.01% (1/100th of a percent) or 0.0001 in decimal form.

0.0025

Question 10

Calculate the price value of a basis point

Answer 10

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%.

PVBP = [(V– − V+) / 2] × par value × 0.01

or
1. tweak up
2. tweak down
3. add together
4. divide by 2

Question 11

Define and Calculate Approximate Convexity

Answer 11

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

V- + V+ - 2V0
/
(Change in YTM2) x V0

Question 12

Define and Calculate Effective Convexity

Answer 12

V- + V+ - 2V0
/
(Change in Curve) x V0

Question 13

Calculate percentage change in bond full price

Answer 13

Step 1: (–annual modified duration) x Change in YTM
Step 2 0.5 x Annual convexity x Change in YTM squared
Step 3: Sum

Question 14

Explain the term structure of yield volatility (there is one key takeaway)

Answer 14

The term structure of yield volatility refers to the relationship between maturity and yield volatility.

Short-term yields may be more volatile than long-term yields. As a result, a short-term bond may have more price volatility than a longer-term bond with a higher duration.

Question 15

Explain the impact of YTM on price for the different investment horixons

What can the macaulay duration be interpreted as?

Wat is the conclusion if Horizon > MD or if Horizon < MD?

Answer 15

Over a short investment horizon, a change in YTM affects market price more than it affects reinvestment income.

Over a long investment horizon, a change in YTM affects reinvestment income more than it affects market price.

Macaulay duration may be interpreted as the investment horizon for which a bond’s market price risk and reinvestment risk just offset each other.

Horizon > MD - reinvestment risk
Horizon < MD - Price risk

Question 16

How do you calculate and interpret duration gap

Answer 16

duration gap = Macaulay duration − investment horizon

Price risk -> Macaulay Duration -> Reinvestment risk
(Positive) (negative)

Question 17

What are the different types of duration and when should they be used

Answer 17

Macaulay, modified, and effective duration are examples of analytical duration.

Empirical duration is estimated from historical data using models.

Empirical duration may differ from 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.

Question 18

explain bond spread to benchmark curve

Answer 18

A bond’s yield spread to the benchmark curve includes a premium for credit risk and a premium for illiquidity

Question 19

Given values for duration and convexity, the effect on the value of a bond from a given change in its yield spread (∆spread) can be estimated as:

Answer 19

–duration(∆spread) + ½ convexity(∆spread)2

Question 20

how do you calculate Macaulay and modified duration?

Answer 20

Macaulay

1. Calculate PV cash flows
2. Sum them
3. Calculate weights by dividing the pv of each cash flow by the total present value outstanding
4. multiply each cash flow by the period it is going to be recieved in
   sum

Modified duration

Divide macaulay by 1+ytm!