Barbican Consulting Limited

# Duration - how it's used

**Duration - How it's Used**

Duration measures interest rate risk. Duration can therefore be used to control this risk. In the following "duration" refers to modified duration.

**Portfolio managers**

How would a fund manager use duration? He (or his investment committee) would target the duration for the investment portfolio.

The duration of the portfolio would need to suit the investment horizon. If 10 years is considered too risky and 1 year does not appropriately reflect the risk appetite the duration target could be set between 3 years and 5 years. What is the effect of this target?

The duration target allows the manager to take risk within the minimum and maximum duration levels. If the manager expected interest rates to fall he would increase the portfolio duration within the limits imposed. This increased level of risk would increase the opportunity to benefit from expectations.

But because there is a target duration for the portfolio if the manager anticipated rising interest rates the best he can do is to minimise the portfolio duration. Minimising duration will reduce risk but will not entirely eliminate it. If interest rates rise losses would still be incurred albeit those losses would be smaller than those that would be incurred with a longer duration portfolio.

**Dealers**

Dealers can use duration in order to calculate hedge ratios.

Suppose a dealer buys $10m of 3 year bonds and then decides to hedge the risk by selling 5 year bonds:

What is the hedge ratio? That depends on the duration of the two bonds.

If the duration of the 3 year bond was 2.72 years and the duration of a 5 year bond was 4.33 years, then the 3 year bond would lose $2,720 for a 1 basis point increase in interest rates and the 5 year bond would lose $4,330 for a similar increase in rates.

The hedge ratio is therefore $2,720/$4,330 = 0.6282

To hedge the purchase of $10m of the 3 year bond the dealer would need to sell $10 x $2,720/$4,330 = $6.2m of the 5 year bond. The two positions would have equal and opposite basis point values.

If interest rates rose by one basis point the 3 year bond would lose $2,720 this would be offset by a profit of $2,720 arising from the $6.2m 5 year short position.

This works for small parallel movements in the yield curve only. Non-parallel changes in the yield curve would lead to overall hedging losses or gains for the dealer.

Duration is not constant for all levels of interest rates.

At different yields the duration of a 5 year with a 5% coupon is as follows:

Interest rate Duration

1% 4.59

5% 4.55

10% 4.49

15% 4.43

20% 4.36

It means that when the yield falls this bond becomes more price sensitive to changes in interest rates. When the yield increases it becomes less sensitive. The bond is said to have "convexity".

This means if a dealer is reliant on hedge ratios calculated using duration these will change when yields change. The hedge ratio needs to be altered or rebalanced by the dealer. Whilst this may seem trivial, dealers that hedge large portfolios should frequently consider their hedge ratios.

*First Published by Barbican Consulting 2010*