Fixed Income Refresher

Question 1

Macaulay Duration

Answer 1

• Macaulay Duration

By reinvesting coupons, the time to realize the initial market discount rate on a bond should be shorter than the full maturity of the bond. The Macaulay duration is a measure of weighted average time to the receipt of the interest and principle payments that realize the original YTM. A Macaulay duration of 7 for a 10-year, 4% YTM bond means that at current market rates, it will be 7 years until the 4% YTM is achieved.

Only time Macaulay Duration is equal to maturity is with a zero coupon bond.

Question 2

Modified Duration

Answer 2

• When rates decrease by a large amount duration will underestimate the price increase.
• When rates increase by a large amount duration will overestimate the price decrease.