Spread Duration Explained

Spread duration is the sensitivity of a security’s price to changes in its credit spread. A security’s credit spread is the difference between the yield-to-maturity of the security itself and the yield of a benchmark rate (treasury or other government bond).

Spread duration can also be used to examine whole sectors or asset classes, such as all corporate bonds or all mortgage bonds.

Understanding Spread Duration

Spread duration will equal the percentage change in a security’s price when credit spreads change by 1%. A portfolio’s spread duration will equal the weighted-average spread duration of each of the securities within the portfolio.

Recall that modified duration measures the percentage change in a security or portfolio’s price when Treasury yields change by 1%.

For all securities other than Treasuries, the spread duration is equivalent to modified duration. Both a change in the credit spread of 1% or a change in Treasury yields of 1% will cause an equivalent change in yield-to-maturity of a non-treasury (and the same corresponding impact on price).

The outcome (change in price) is the same in either scenario, so spread duration and modified duration are the same.

Logically, the spread duration of a Treasury is zero. Treasuries will have the same yield-to-maturity regardless of the spread between treasuries and corporates.

Said another way, Treasuries themselves have no credit spread because they are the benchmark. Therefore, a change in credit spreads cannot influence a Treasury’s price.

How to Calculate in a Portfolio

The spread duration of a portfolio of securities will be the (market-value) weighted-average of the spread durations for each individual security, including Treasuries.

For example, you have a portfolio with:

• $10M market value of 9-year Treasury Notes, with a modified duration of 7 years
• $20M market value of a 7-year corporate bond with a modified duration of 5 years
• $30M market value of a 2-year corporate with a modified duration of 1.8 years

The spread duration of the portfolio is:

($10M/$60M) × 0 years + ($20M/$60M) × 5 years + ($30M/$60M) × 1.8 years

= 2.57 years

For comparison, the modified duration of the portfolio is:

($10M/$60M) × 7 years + ($20M/$60M) × 5 years + ($30M/$60M) × 1.8 years

= 3.73 years