No matter how the forward rate of interest is ultimately realized, the value of each component in the hedged position changes precisely in the same offsetting way. This is because the net cash flows are zero.

Online, consider the following position. Suppose you have 100 units of Security 1 which is a 3-year coupon bond that makes annual coupon payments equal to 5% of $1,000. In addition, suppose you have 0 units of four zero-coupon bonds with maturities ranging from 1 - 4 years. In the Duration subject of Bond Tutor, if not already shown, select "Set Position" under Example 6.2.1.

In the above grid you should verify that column 2, titled Sec 1, is equivalent to a 3-year coupon bond that makes annual coupon payments of 5% relative to a face value equal to $1000.

Column 3, titled Sec 2, is equivalent to a 1-year zero coupon bond with face value equal to $1,000.  Similarly for Sec 3 (2-year zero coupon bond) and Sec 4 (three year zero coupon bond).

Next observe from this grid you can create the synthetic (i.e., cash matched) equivalent of 20 units of the coupon bond from a position of 1 Security 2 + 1 Security 3 + 21 Security 4 which is equivalent to 20 coupon bonds (Security 1).

In this example, your original position is long 100 coupon bonds.  This position benefits from a decrease in interest rates and is hurt from an increase in rates.   The above graph reflects this decreasing position value (Y-axis) as rates increase (X-axis).

Next you can verify that the cash matching solution works by entering the offsetting synthetic position directly into the cells corresponding to units (i.e., -5 Security 2, -5 Security 3 and -105 Security 3, or alternatively, selecting "Cash Match" under Example 6.2.1 to get:

Now the position is completely hedged against interest rate risk and appears as the horizontal line as follows:

That is, the net value of the position and its synthetic opposite equals zero.

In general, you do not want to eliminate all risk but instead alter your exposure profile to some preferred profile. For example, suppose you predict that yield curve volatility is likely to reduce such that the yield curve will remain around the current rates. Online, you can explore different exposure profiles to find profiles that best meet your predictions.

In the following calculator, select "Set Position" under Example 6.2.2:

In the position illustrated above, a shift in either direction decreases this position's value, but you gain if the yield curve remains constant.

By changing the units you hold of each security, you can experiment with creating different exposure profiles, those that benefit from a rise in rates, those that benefit from a fall in rates, and so on.

Cash matching works because it hedges every possible dimension for a shift in the yield curve. That is, if there are 50 different cash flow dates, then there are 49 possible forward rate changes that can result in new yield curves that affect the value of the underlying position. The complexity of applying cash matching should be obvious. To hedge a large underlying position, cash matching is an immense undertaking.

At the other end of the spectrum is the concept of duration, which reduces the problem of hedging interest rate risk to one dimension. The value and limitations of duration are underscored by the important bond immunization theorem developed in the next topic.

The advantage of managing interest rate risk using duration is simplicity (and thus lower transaction costs), because only one number needs to be managed and the hedge is easily constructed. The disadvantage of this approach is that reducing the problem to one dimension means that it provides an approximation. That is, it rests upon the underlying assumptions of the bond immunization theorem.

In the next topic, you will see how you can apply Cash Matching to a zero coupon bond problem.