# Hedging with interest rate derivatives

This might be a stupid or basic concept for some of you, I'm new to the concept of hedging with interest rate derivatives, I understand how to hedge an equity portfolio but i'm struggling with the concept of hedging when it comes to liability hedging and DV01 hedging using Interest rate derivatives for example using Swaps and Swaptions, Can anyone breakdown this concept for me or show some examples ? thank you

I will work through a detailed example. I hope it helps.

Suppose for simplicity that you are trying to hedge the interest rate risk of one simplistic debt instrument. Suppose that the obligor owes you USD 10 million and promises to pay fixed 10% annual coupon, and to repay the principal in equal installments in years 4 through 7. So the cash flows look like this:

years 1, 2, 4: USD 1 million coupon (10 million principal × 10% coupon rate)

year 4: 3.5 = 1 million coupon again + 2.5 principal ; only 7.5 million principal remains

year 5: 3.25 = 0.75 coupon (7.5 principal × 10% coupon rate) + 2.5 principal ; only 5 million principal remains

year 6: 3 = 0.5 coupon (5 principal × 10% coupon rate) + 2.5 principal ; only 2.5 million principal remains

year 7: 2.75 = 0.25 coupon (2.5 principal × 10% coupon rate) + 2.5 principal ; no principal remains, the debt is all paid off.

(Annual coupons are common in some countries; in some the coupon would likely be paid several times a year; this does not matter.)

Suppose that you need to mark-to-market this instrument, i.e. to calculate a realistic estimate of what someone might pay for this instrument, a fair value. Assume, for simplicity, that you can't directly observe the price of the instrument in the market. You would use a model to calculate a risky discount factor for each of your cash flows. The discount factor would include the time value of money (as expressed by the swap curve - if the risk-free interest rates are positive, then \$1 in the future is worth less than \$1 now), the likelihood that the debtor won't pay as promised, the recovery assumption (what you might get from the debtor in this case), your own cost of financing, etc.

For this instrument, without a credit event, the discount factor of cash each flow is going to approach 1 as you get closer to its payment date ("pull to par").

What can go wrong (i.e. what are the risks that might cause your mark-to-market to decline)?

The risk-free interest rates can rise, so the value of \$1 in the future would decrease. This is the only risk that we want to hedge in this example.

The likelihood that the debtor won't pay as promised might increase. The debtor might not pay as promised. This is credit risk. We are not hedging it in this example.

Conversely, the risk-free rates might decline and/or the debtor's credit might improve to a point where they might borrow the money at lower interest and may want to prepay you early, so you will get your principal back sooner, but not the 10% annual interest. For this example, we assume that this can't happen, and won't hedge this risk either.

If you have multiple instruments to hedge, accounting rules may require you to keep track of the hedges for each one separately, but it's really not harder than viewing everything that you want to hedge as well as your existing hedges as one portfolio. Conversely you can look at the risks of each cash flow (it is sometimes useful to get a better feel for how much various cash flows contribute to the market risk).

Your interest rate hedging instruments, should be the ones with the tightest bid-offer spread for the given tenor. For the purpose of this exercise, we will assume that they are:

1 month and 3 month LIBOR

then exchange-traded Eurodeposit futures until 5 years

then IR swaps until 30 years.

(Some people might say that you should use ED futures for the first 10 years and then swaps only for longer maturities.)

Your swap curve is likely to be build from lots of instruments in addition to these, but you only care about the MTM changes from a small change in each hedging instrument. You assume that the sensitivities are linear (i.e. ignore any convexity).

Once you have the sensitivities of your existing portfolio and of a nominal notional of each hedging instrument, you can immediately read off the notionals of the hedging instruments that will give you a new portfolio whose MTM will not change when the swap curve moves.

The hedges may need to be dynamically adjusted as time goes by or as market conditions change. You should have tools to analyze the effectiveness of your hedges.

You should also have a tool called P&L explain (or P&L attribution analysis (PAA) or something similar) that will attribute your MTM changes (your "hypothetical" P&L before fees etc) to various market exposures, including interest rates.

If your exposure is fully hedged, then the MTM change attributable to IR changes should be very small. As a consequence, your MTM will be less volatile than it would be without hedging. But this MTM volatility reduction is not free. Every time you adjust a hedge, you pay bid-ask spread.

In a banking book (intended to be held to maturity), MTM volatility is not really a concern, hedging the interest rate risk is not worth the cost. (However you may be required to calculate the interest rate exposure anyway). In a trading book (available for sale), reducing the MTM volatility is sometimes worth the effort and the cost of hedging because you don't want find yourself unwinding these positions when the rates are up and your MTM is down.

• Thank you for your response, I started to see the picture of you trying to explain but I still don't understand why we would buy a swap or sell swap if we expect that our payment in year 2 bucket for example will increase or decrease ? Apr 14 '20 at 8:26
• I'll edit and walk through that part. I hope it helps. Apr 14 '20 at 12:42