Library/CFA (Chartered Financial Analyst)/JuiceNotes 2024 Fixed Income/Yield-Based Bond Duration Measures and Properties

Yield-Based Bond Duration Measures and Properties

50 questions available

Sources of Return and Duration Types5 min
Fixed-rate bond investors derive return from coupons, principal repayment, and reinvestment income. Interest rate risk comprises market price risk and reinvestment risk, which act in opposite directions depending on the investment horizon. Three main duration types are discussed: Macaulay (time-based), Modified (yield sensitivity), and Effective (for embedded options).

Key Points

  • Sources of return: Coupons, Reinvestment, Capital Gains/Losses.
  • Macaulay Duration: Weighted average time to cash flows.
  • Modified Duration: Percentage price change for a unit change in yield.
  • Effective Duration: Required for bonds with embedded options.
Factors Affecting Duration and Calculations6 min
Duration is influenced by the bond's characteristics. Longer maturity increases duration, while higher coupons and higher yields decrease duration. The text provides formulas for calculating Modified Duration using price shifts and defines Money Duration and PVBP for estimating absolute price changes.

Key Points

  • Duration increases with Maturity.
  • Duration decreases with higher Coupon Rate.
  • Duration decreases with higher YTM.
  • Money Duration = Modified Duration * Full Price.
  • PVBP measures price change for 1 basis point shift.
Specific Instrument Durations4 min
Certain bonds have unique duration properties. Zero-coupon bonds have a Macaulay duration equal to their maturity. Perpetual bonds have a duration based purely on yield. Floating-rate notes have very low duration, approximately equal to the time remaining until the next interest rate reset.

Key Points

  • Zero-Coupon Bond Macaulay Duration = Time to Maturity.
  • Perpetual Bond Macaulay Duration = (1 + r) / r.
  • Floating-Rate Note Duration = (Time to Reset) / (Total Period).

Questions

Question 1

Which of the following is NOT one of the three sources of return for a fixed-rate bond investor?

View answer and explanation
Question 2

For an investor's yield-to-maturity at purchase to equal their realized rate of return, which assumption must hold?

View answer and explanation
Question 3

Uncertainty about the price at which a bond can be sold prior to maturity is best described as:

View answer and explanation
Question 4

If an investor has a shorter investment horizon, which risk is dominant?

View answer and explanation
Question 5

Macaulay duration is best defined as:

View answer and explanation
Question 6

If a bond pays coupons semiannually, how is the annualized Macaulay duration obtained?

View answer and explanation
Question 7

Modified duration is primarily used to measure:

View answer and explanation
Question 8

Which duration measure is most appropriate for bonds with embedded options like callable bonds?

View answer and explanation
Question 9

Calculate the approximate Modified Duration if a bond price drops from 100 to 98 when the yield rises by 50 basis points, and rises to 102 when the yield falls by 50 basis points.

View answer and explanation
Question 10

What is the relationship between Macaulay duration and Modified duration for an annual coupon bond?

View answer and explanation
Question 11

How does the duration of a bond typically react to an increase in maturity, holding other factors constant?

View answer and explanation
Question 12

How does an increase in the coupon rate affect a bond's duration?

View answer and explanation
Question 13

How does an increase in the Yield-to-Maturity (YTM) affect a bond's duration?

View answer and explanation
Question 14

For a callable bond, how does duration compare to a non-callable bond when yields are low?

View answer and explanation
Question 15

Money Duration is defined as:

View answer and explanation
Question 16

A bond has a Modified Duration of 6 and a full price of 1050. What is the Money Duration?

View answer and explanation
Question 17

The Price Value of a Basis Point (PVBP) represents the change in bond price for what magnitude of yield change?

View answer and explanation
Question 18

If the Money Duration of a bond is 6300, what is the estimated change in the bond price for a 0.5 percent change in yield?

View answer and explanation
Question 19

What is the Macaulay duration of a zero-coupon bond?

View answer and explanation
Question 20

What is the Macaulay duration of a perpetual bond with yield r?

View answer and explanation
Question 21

Which bond has a Macaulay duration equal to (T - t) / T, where T is the time between resets?

View answer and explanation
Question 22

Why do floating-rate instruments generally offer low interest rate risk to investors?

View answer and explanation
Question 23

If a bond's modified duration is 5.0, what is the approximate percentage change in price for a 1 percent increase in yield?

View answer and explanation
Question 24

What is the key difference between Modified Duration and Effective Duration regarding cash flows?

View answer and explanation
Question 25

For a Putable bond, how does duration behave when yields are high?

View answer and explanation
Question 26

Optionality of a bond will generally _________ the duration compared to an option-free bond.

View answer and explanation
Question 27

Which duration metric calculates the percentage change in the full price of a bond?

View answer and explanation
Question 28

If a bond has a Money Duration of 5000 and the yield changes by +0.01% (1 basis point), what is the change in price?

View answer and explanation
Question 29

In the formula for approximate Modified Duration, V_minus refers to:

View answer and explanation
Question 30

Which risk balances coupon reinvestment gain/loss against price loss/gain for a one-time parallel shift?

View answer and explanation
Question 31

Generally, the 'price risk' of a bond is higher when:

View answer and explanation
Question 32

Reinvestment risk matters more when:

View answer and explanation
Question 33

The difference between Macaulay duration and the investment horizon is known as the:

View answer and explanation
Question 34

If the Duration Gap is positive (Macaulay Duration > Investment Horizon), the investor is primarily exposed to:

View answer and explanation
Question 35

If a zero-coupon bond has 10 years to maturity and a yield of 10%, what is its Modified Duration?

View answer and explanation
Question 36

For a floating-rate note with a 180-day coupon period and 57 days elapsed since the last reset, what is the approximate Macaulay duration?

View answer and explanation
Question 37

What is the primary reason floating-rate instruments are useful in portfolio management?

View answer and explanation
Question 38

Which bond type always has a Macaulay duration equal to its time-to-maturity?

View answer and explanation
Question 39

Calculate the PVBP for a bond with a Money Duration of 450,000.

View answer and explanation
Question 40

If yield volatility is high, which duration measure is most critical for a callable bond?

View answer and explanation
Question 41

A bond's full price is 100. Its Modified Duration is 8. If the yield rises by 50 bps, the price is expected to:

View answer and explanation
Question 42

Why is the duration of a perpetuity not infinite?

View answer and explanation
Question 43

Which bond has the highest interest rate risk (duration), assuming equal yields and coupons?

View answer and explanation
Question 44

Which bond has the highest interest rate risk (duration), assuming equal maturity and yield?

View answer and explanation
Question 45

In the context of Money Duration, the term 'Dollar Duration' is synonymous with:

View answer and explanation
Question 46

If a bond's price increases by 4 when yield falls by 1%, what is the Modified Duration approx?

View answer and explanation
Question 47

What does a PVBP of 0.625 imply?

View answer and explanation
Question 48

For a fixed-rate bond, reinvestment risk is strictly:

View answer and explanation
Question 49

In the formula used for calculating Modified Duration from prices (V-, V+, V0), the divisor includes '2 * V0 * Delta_Yield'. Why is the factor '2' included?

View answer and explanation
Question 50

Which bond property leads to 'negative convexity' behavior where duration falls as yields fall?

View answer and explanation