Everything About Duration

What is duration?

Essentially duration estimates a bond’s sensitivity to interest rate movements. It incorporates a bond’s yield, coupon and maturity into a single data point, which is intended to illustrate how much influence a change in interest rates would exert on a bond or bond portfolio. Fundamentally duration calculates a bond’s expected price change for every percentage point movement in interest rates. For example, if interest rates were to move up 1%, a bond with a duration of five years would expect to see its price decline by 5%. The higher the duration, the more sensitive a bond, or bond portfolio, is likely to be to interest rate movements.

Duration types

While duration is widely viewed as a key metric in fixed income analysis, a variety of duration methods are used to calculate different forms of the measure.  Macaulay duration was the first form of duration and basically calculates how long it will take to an investor to earn their investment back. However the type usually referred to these days is modified duration, which is a version of the Macaulay model but accounts for changing interest rates

How do a bond’s characteristics impact duration?

Duration is driven by the nature and rate of a bond’s coupon, its time until maturity and its yield characteristics. There are five basic factors which are needed to calculate duration. These include:

  • Type of coupons
  • Size of the coupon payments
  • Frequency of the coupons
  • Maturity
  • Yield to maturity

With these five components, the price of most bonds can be calculated by discounting the bond’s future cash flows to the present value. From there, duration can be calculated by observing the percentage change in a bond’s price as interest rates change.

Type of coupons

A move in interest rates above the stated coupon rate of a bond should lead to a discounted price of that security. Floating-rate securities will generally have lower durations as a result of their interest rate ‘reset’ structure. In other words, the coupon of floating rate securities is usually pegged to a market interest rate, such as LIBOR or EURIBOR, which effectively allows the bondholder to catch up to current rates within a shorter time period than longer maturity, fixed coupon bonds. As a result, floating rate bonds with variable coupons will generally have lower durations compared to theifixed coupon counterparts.

Size of the coupon payments

 A higher coupon rate allows a bondholder to receive more of their loan back via interest payments, making the final principal payment a smaller relative portion of the overall bond cash flows, thus lowering duration. 

Frequency of the coupon payments

More frequent coupon payments (for example semi-annual versus annual), means the shorter the timeframe until the loan is received back, which again lowers duration.

Maturity

If a bond has a longer maturity, one would expect the duration of that bond to be higher. This is because the final return of principal is pushed further out into the future, making those longer-dated payments more sensitive to changes in interest rates.

Yield to maturity

The sensitivity of a bond’s price to changes in interest rates also depends on its yield to maturity i.e. the total return anticipated from a bond if it is held until the end of its lifespan. A bond with a high yield to maturity should display less interest rate sensitivity (i.e. duration) compared to a bond with a lower yield to maturity, all other features being equal. A bond with a poor credit rating will generally have a higher yield to maturity than one with an excellent rating. Therefore, bonds with lacklustre credit ratings typically display lower duration than bonds with robust credit ratings.

Bond portfolio duration

The duration of a bond portfolio is calculated by taking the weighted average duration of each of the underlying holdings. This should give investors a general idea of how their fund would react to interest rate movements.

However because a fund can house a large number of securities, it can make the overall duration number for the portfolio unreliable - and this is because of the yield curve - the measure which takes account of all maturities in the bond market. For instance, when there is a so-called parallel shift in the yield curve, yields in the bond market move in tandem across all maturities.

In such a scenario, the shape of the yield curve, doesn’t fundamentally alter and the overall duration of a bond fund should be an adequate measure to quantify the relation between changes in interest rates and the value of the portfolio. However a non-parallel shift means that yields of various maturities do not change by the same amount. Here the curve can notably change - by either steepening or flattening. This  ultimately makes the overall duration number, used to quantify the relationship between the value of the fund and changes in interest rates, for a bond portfolio inadequate

One way around this is to use key rate durations, which measure the sensitivity of a bond portfolio to a 1% change in the yield for a given maturity. Key rate durations can quantify any yield curve shift as they calculate the spot durations of each of the 11 key maturities along the yield curve. In essence, key rate durations allow the duration of a portfolio to be calculated for a one-percentage point change in interest rates, at any point of the yield curve e.g. the three-year maturity-point, while holding the other maturities constant.

Ultimately, while duration can be a valuable metric in evaluating a bond’s interest rate sensitivity, it is just one of the many factors to consider when investing in a fixed income security or in a bond portfolio. When evaluating either a bond or bond portfolio, it is critical that investors do not examine a single duration number in isolation but rather in the context of all the other risks and characteristics that make up the investment. Always remember that past performance should never be viewed as a guide to future returns.

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