9.2) Macaulay Duration Measure

Question 1

What is the Macaulay duration measure?

Answer 1

Duration is a measure of bond price sensitivity: Measures the bond price change when yield changes

Question 2

What is duration applied in? (2)

Answer 2

1)Trading strategies
2) Estimating price changes when yield changes

Question 3

how is duration applied in trading strategies? (2)

Answer 3

1) Simple trading decisions (Anticipation of interest rate changes)
2) Immunization (For insurance companies and even banks; Making a choice between best bond to buy to make a trading profit)

Question 4

How does weighted average time to maturity of a bond impact high and low duration?

Answer 4

o High duration – More risk
o Low duration – Less risk

Question 5

Duration is always ________ than time to maturity

Answer 5

lower

Question 6

True or false, If you do not want to be affected by interest rate changes you only hold the bond for its duration and sell it after that.

Answer 6

True

Question 7

When do you sell the bond?

Answer 7

o On the duration point price risk and interest rate risk intersect.
o Realize the initial return.

Question 8

What is the duration fromula?

Answer 8

Look at lecture example to make sense

Question 9

How is duration modified?

Answer 9

• Modified duration (D*) – To express the number as a percentage.
• 1% change in yield will result in the bond price changing by ##%

Question 10

How is duration applied? (2)

Answer 10

1. Trading Strategies
2. Applying the duration to estimate the price change

Question 11

How is price change estimated?

Answer 11

Question 12

Since duration represents a _________ relationship, the same % change in bond ______ will be applicable to an increase/decrease in the ______

Answer 12

linear
price
yield

Question 13

Why is the duration negative & what are the shortcomings of Duration? (1)

Answer 13

• Duration is not an accurate measures of bond price sensitivity(The estimate is not equal to the price when using it)

Question 14

What are the rules for duration?

Answer 14

The Macaulay duration of a zero-coupon bond equals it’s time to maturity. (There is only 1 cash flow which has a weighting of 1)

Question 15

What factors affect duration? (3)

Answer 15

1) A bond’s duration is higher when the coupon rate is lower. (↓ Coupon Rate ↑ Duration) - Inversely proportional
2) A bond’s duration generally increases with its time to maturity ↑Time to Maturity ↑ Duration) - Directly proportional
3) The Duration of a coupon bond is higher when the bond’s yield to maturity is lower (↓ TM ↑ Duration) - Inversely proportional

Same factors that affect price sensitivity

Question 17

What are the shortcut duration formulas used for (4)

Answer 17

• Perpetuity
• Annuity
• Coupon bond
• Par Coupon Bond

Question 18

What are the different versions of duration? (4)

Answer 18

1. Macaulay duration – Measures of sensitivity in terms of time
2. Modified duration – Measures of sensitivity as a percentage
3. Money duration – Measure of sensitivity in monetary terms
4. Price value of a basis point (PVBP) – Measure as a one basis point change

Question 19

What is an alternative approach to approximate the modified duration (AMD) DIRECTLY?

Answer 19

Question 20

How is the approximate Macaulay duration (AD) calculated?

Answer 20

from the approximate modified duration
(AMD).

Question 21

What are the shortcomings with duration as a measure of bond price sensitivity? (3)

Answer 21

* Inaccurate
o If it was accurate the lines would be equal
* Restrictive
o Accurate for small changes not large
o Is only accurate for small changes in yields, for large changes it underestimates.
* Underestimate
o Always underestimates

Question 22

Why does duration fail as a measure of bond price sensitivity?

Answer 22

• Duration assumes a linear relationship between price and yields
  o The relationship is not linear it is convex

Question 23

In conclusion what is duration?

Answer 23

Duration is the first linear approximation
o It is the rate of change in price for small changes in yield

Question 23

In conclusion what is convexity? (2)

Answer 23

Convexity is the second approximation
o It is the rate of change of the slope of the price-yield curve as a fraction of the bond’s
price.
o Measure the curvature of that line with which when added to duration gives us the
convexity

Question 24

What does high convexity imply? (2)

Answer 24

• A bond with high convexity: When yields increase, bond will experience lowest price appreciation. Vice versa
• Bond with high convexity always outperforms those with low convexity

Question 25

What must the bonds have in common in order to be comparable?

Answer 25

They must be comparable, duration must be equal