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Hedging using Duration

Hedging using Duration

Hedging using Duration

Interest rate movements can have a big impact on the value of financial instruments, especially bonds. An important concept to understand is modified duration. Even though it sounds like the maturity of a bond, it's a bit different.


Duration is the weighted average time until a bond's cash flows are received, adjusted for their present value.


A 3-year bond with a duration of 2.72 years would lose 2.72% of its value for a 1% increase in interest rates. A 5-year bond with a duration of 4.33 years would lose about 4.33% of its value for the same increase.

This means that longer-dated bonds are more sensitive to interest rate changes, which also makes them riskier. Here we'll explain how duration helps both portfolio managers and dealers manage risk.


Duration and Portfolio Management

Duration measures how sensitive a bond's price is to changes in interest rates. It's a key tool that helps fund managers manage risk and make sure their portfolios fit their risk tolerance and investment goals.


Setting Target Duration: Fund managers set a target duration based on their risk tolerance. For example, if a 10-year duration feels too risky but a 1-year duration is too conservative, they might choose a duration between 3 and 5 years to find a balance between risk and return.


Adjusting Portfolio Duration: Managers can adjust the duration of their portfolios depending on what they expect interest rates to do. If they think interest rates will go down, they might increase the duration to try to boost returns, since bond prices generally go up when rates fall. This happens because the fixed cash flows of a bond become more valuable when discount rates (interest rates) decrease.


On the other hand, if they think interest rates will go up, they might shorten the duration to limit losses. However, shortening the duration doesn’t eliminate interest rate risk. It only reduces potential losses compared to a longer-duration portfolio.


Duration in the Dealer's World

For dealers, duration is not only about managing risk—it also helps them figure out how to hedge against interest rate changes.


Hedge Ratio Explained: Let's look at an example. A 3-year bond has a duration of 2.72 years, and a 5-year bond has a duration of 4.33 years. If interest rates go up by 1 basis point (0.01%), the 3-year bond would lose £2,720, while the 5-year bond would lose £4,330. The hedge ratio between these two bonds is £2,720 / £4,330 = 0.6282.


To hedge a £10 million position in the 3-year bond, a dealer would need to sell about £6.2 million of the 5-year bond.


This way, gains and losses from interest rate changes balance out: if rates go up by one basis point, the loss on the 3-year bond is offset by a matching gain on the 5-year short position.


Scope of Hedging: These kinds of hedging techniques work well for small, parallel changes in the yield curve. However, bigger or uneven changes can lead to net gains or losses, which shows the limitations of this approach.


The Curveball: Convexity

While duration is a useful tool, it changes as interest rates change—a concept known as convexity. Convexity is important because it means a bond's sensitivity to further changes in interest rates depends on the level of interest rates.


For example, a 5-year bond with a 5% coupon has different durations depending on the interest rate:


  • At a 1% interest rate, its duration is 4.59 years.

  • At a 20% interest rate, its duration drops to 4.36 years.


This shows convexity—the way duration changes as interest rates change.


A bond's price sensitivity to interest rate changes isn’t a straight line; it’s curved, which affects hedging strategies.


For dealers, just relying on one duration measure can be risky, since the hedge ratio also changes with interest rate levels due to the non-linear relationship described by convexity.


This means regularly reassessing hedge ratios is important, especially for those managing large portfolios.


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