# Practice Exam Test Question – Pricing and MTM of Interest Rate Swaps (IRS)

And now for the last and final part of our Practice Exam Test Question series on Pricing Interest Rate Swaps (IRS). In our first post we walked through the process of building a annualized forward curve and then extending it to semiannual rates.

In this post we will take the forward curve generated in the previous post and use it answer our Interest Rate Swaps (swap rate) and mark to market (valuation) questions.

Here is the projected zero and forward rates curve from our previous post, posted here for convenience. Before you proceed further please take a quick look at the interest rate swap pricing free study guide to review our approach and methodology.

## Mark to Market and Valuing an Interest Rate Swap – Practice Test Question and Partial solution

A client has recently entered into a 4.5 year floating rate loan for US$ 400,000,000? The loan will be effective six months from now and will use the following repayment schedule.

**Figure 1 Practice Exam Question – Notional Principal for pricing Interest Rate Swaps**

The client has asked for a quote for the an effective interest rate risk hedge that would offset the risk of rising interest rates.

**a) ****What would be the swap rate at cost or breakeven basis for this structure? **

**b) Would the client be paying fixed or receiving fixed**

**c) What would be the swap rate if the loan starts at time 2.5 with 10,000,000 and ends at time 3 with an outstanding principal of 10 million.**

Here is the output from our solution Excel Sheet. The approach is as per interest rate swap pricing free study guide. The projected forward rates are as per the results above and were driven in the projected forward rates using bootstrapping post. As you can see that the trick here was recognizing that we didn’t have a normal interest rate swap but a forward starting amortizing swap and then adjust the pricing approach accordingly.

a) The exact breakeven swap rate is **13.718%** and the breakeven value of each leg (fixed and floating) is **3.001609 **million.

b) Since the client is hedging a floating rate loan with this swap he will be paying a fixed rate and receiving the floating rate or simply **paying fixed**.

**Figure 2 The practice test question solution – the interest rate swap pricing, MTM and valuation grid **

c) This question is asking you to price a one step FRA or a Forward Rate Agreement. To solve it you should pick the row corresponding to tenor 2.5 and solve for a fixed rate that allows the present value of fixed and floating payments to completely offset each other. This fixed rate is **17.5732%. **If you understood the question intuitively you should be able to answer it without resorting to the below solution by simply looking at the applicable forward rate and using that as the breakeven rate.

**Figure 3 The practice test question – the FRA pricing, MTM and valuation grid**

### Common Interest Rate Swap pricing and valuation mistakes made by students in this question

- Not making the forward pricing adjustment for the forward starting interest rate swap
- Not using the correct notional amount. A number of students used a flat value of 400 million rather than the amortization schedule shared with the question above. Use the correct amortization schedule
- Not adjusting for the day count in the fixed as well as floating cash flows. Students often use the full rate when calculating semiannual payment, where as they should be using 180/360 or 182/365 * the relevant interest to account for the fact that the payment is a semiannual interest payment.
- Not using the correct applicable floating (forward rate)

**d) Six month later the interest rates term structure has changed as shown below. Taking the original Swap structure and assuming that the Swap was purchased at the original breakeven Swap rate, what is the MTM (Mark to Market value of the Swap). **

**Figure 4 Practice Exam question – Revised Interest Rate Yield Curve **

This question requires a simple re-application of the above process one more time. Here are the revised projected forward rates

**Figure 5 Revised projected forward rates **

The trick now is to remember that we have all moved 6 months forward in time and the IRS is effective now. Based on this assumption this is how the revised grid looks like. The IRS has a negative MTM because we had expected rates to go up and they have actually come down.

**Figure 6 Pricing, MTM, Valuing the IRS under the new term structure and yield curve **

Once again the biggest mistake students made here was not moving forward in time and pricing the IRS on an as is basis. The second biggest mistake was not using the updated curve and the old Swap Rate calculated from the earlier part of the question.