The following article is reprinted from
On the Edge,
the Interactive Data Fixed Income Analytics monthly newsletter
Back-to-Basics: Understanding Spread Duration
Teri Geske
Senior Vice President, Product Development
In other Back-to-Basics columns, we have discussed the risk measures, Vega (a measure of volatility risk), Prepayment Uncertainty and Zero Volatility Spread (ZVO). This month we examine the Risk Measure, Spread Duration.
Spread Duration is defined as the sensitivity of a bond’s price to a change in its option-adjusted spread (OAS). Recall that a bond’s OAS is the spread which, when added to the Treasury spot curve, equates the discounted present value of the security’s option-adjusted cash flows to its market price:
For corporate bonds with embedded options, OAS is derived using the BondEdge option model; for mortgage-backed securities a Monte Carlo simulation is employed. We can solve for the OAS implied by a given price, or solve for a price by specifying the desired OAS.
When considering the impact of a change in OAS on a bond’s price, an interesting difference between corporate bonds and mortgage-backed securities is observed. With mortgage-backed securities, a change in OAS does not necessarily alter the cash flows the investor expects to receive, as the homeowner’s prepayment option is unaffected by changes in the OAS demanded in the secondary market1 . Similarly, a change in OAS for an Adjustable Rate Mortgage has no impact on the evolution of its coupon rate and therefore would not impact the likelihood of encountering the ARM’s reset or lifetime caps. Therefore, Spread Duration for mortgage-backed securities measures the impact of discounting cash flows (along each path generated by the Monte Carlo analysis) at higher and lower rates. However, a change in the OAS of a callable (or puttable) corporate bond does affect the cash flows an investor would receive, as the corporate issuer who is long the call option (or the investor who is long the put) will make a decision whether or not to exercise the option on the basis of the bond’s price in the market. If OAS’s narrow sufficiently, a bond’s price could rise above its call price, causing the issuer to call the security. Thus a small change in the OAS of an “at-the-money” callable bond could mean the difference between receiving cash flows based on the maturity date or the call schedule.
Consistent with this observation, we see that the Spread Duration for a mortgage pass-through often resembles its Modified (Macaulay’s) duration. Modified duration measures the sensitivity of a bond’s price to a change in yield and a change in OAS would produce a change in yield, assuming no change in the bond’s cash flows. Spread Duration for a pass-through will not be exactly equal to modified duration, as Spread Duration is derived from a Monte Carlo analysis which uses vectors of monthly mortality rates to determine prepayments along each projected interest rate path, whereas modified duration uses the single set of cash flows generated by the lifetime PSA speed. The Spread Duration for a CMO may not be similar to its modified duration, as the deal structure may produce extreme variability in cash flows along different interest rate paths which the modified duration value does not capture.
In contrast, the Spread Duration for a corporate bond is directly related to its effective duration. This is because a given basis point change in a bond’s OAS produces exactly the same effect on the price as a change in interest rates would cause. Interactive Data Fixed Income Analytics computes Spread Duration using a +/-100bp change in OAS; therefore, Spread Duration precisely equals Effective Duration for corporate bonds. To estimate the impact of a smaller shift in OAS, the Spread Duration should be multiplied by the basis point shift in OAS/100. For example, the impact of a 20bp shift in OAS on a bond with a spread duration of 4.37 is estimated by [0.20 x 4.37] = 0.874%.
For a corporate bond with no embedded options, effective duration, modified duration and spread duration will all be the same. Why do we go to the trouble of calculating spread duration for corporate bonds when it is equal to effective duration? The benefit becomes clear when we consider a portfolio that contains both mortgage-backed securities and corporate bonds. The spread duration of the portfolio measures the portfolio’s sensitivity to a change in OAS’s across all security types, giving the portfolio manager important information about a portfolio’s risk profile which no other duration measure provides. When used along with Effective Duration and Convexity, Spread Duration and the other Risk Measures allow the portfolio manager to gain a clear understanding of the portfolio’s sensitivity to the various sources of risk in the marketplace.
1Nevertheless, one could argue that changes in MBS spreads could, in turn, affect the rates on new mortgage loans as mortgage originators would adjust their rates in response to the price obtained when selling new production into the secondary market.
