1. Not To Be Naïve about Duration
The duration D we have been discussing also known as Macaulay duration.
First derivative of price-yield curve is
and is known as modified duration. Found in %ΔPB formula.
Convexity is second derivative of price-yield curve. Is a complicated expression (not studied here).
10/27

2. Managing Interest Rate Risk (a)
Duration is the holding period for which reinvestment risk exactly offsets price risk. Designed to give investor the YTM that was in effect at time bond purchased.
A way duration is used: If have a $5 million liability 7.5 years from now, buy a bond (or a portfolio of bonds) today that has a duration of 7.5 years. Then sell at the 7.5 year mark.
10/31

3. Example 18: Rebalancing Bond Portfolio
Consider the $20,000 portfolio ($4,000 in D = 5, $10,000 in D = 7, $6,000 in D = 9) of Example 17.
How much in D = 9 bonds should be sold, and how much in D = 5 bonds should be purchased, to reduce Portfolio D to 6.80?

4. Eliminating Interest Rate Risk (b)
Zero-coupon approach (best way). Buy high quality “zeros” with maturity equal to desired holding period. Locks in YTM. No reinvestment risk because no coupons payments, no price risk when held to maturity.
Duration matching (next best way). Selecting a portfolio of bonds whose duration matches desired holding period. Theoretically perfect, but only approximately perfect in real world as per footnote 8 on p. 162.
Maturity matching (don’t use). That is, selecting bonds with terms to maturity equal to desired holding period. Don’t use. Doesn’t work for eliminating interest rate risk.