# Chapter 37 EOC Question 5 (Pg 168 of Book 5)

In the solution to question 5, it says that when interest rates increase, the NPV of cash flows is negative and the investor never recovers from the increased interest rate he faces on the overpayment of the 1st swap payment. When interest rates decrease, the NPV is positive because the investor gets a favourable interest rate on the loan he needs to take to finance the first overpayment. What I do not understand here is why does the investor need to take a loan to finance the first overpayment in either scenario? Any ideas?

It shall be the opportunity cost (interest rate) of the loan implicitly incorporated in the forward/futures/swap prices.

It is the opportunity cost. Investor could have used this money to reduce his borrowing or to invest somewhere.

The question 5 is asking “What happens to the value of your swap position?”. But the NPV calculation includes a short forward. Why?

Please refer to P.145 In table 1, the dealer is taking a position of “receive fixed price / paying floating price”, so he needs to hedge by LONG forwards. In Q5, he takes opposite position, so he needs to hedge by SHORT forwards.

But I don’t know why the dealer is taking a position of “receive fixed price / paying floating price” and is taking a opposite position in Q5. Anyone else can help ?

Thanks. It’s a continuation of question 3&4. IMO, the aggregate duration of the combined “portfolio”(swap + short forward) is positive. When the interest rate goes up, the PV(netCF) decreases. When interest rate goes down, PV(netCF) increases. So, the natural hedge(using short forward) does not fully hedge the position. ----------------------------------------------------------------------------- I have done an exercise. You are free to verify it. I change the forward prices for 1 year, 2 year, and 3year to \$22, 21, and 20; and change the 1-year, 2-year and 3-year effective annual interest rates to 7%, 6.5% and 6%. If the interest rate increases by 50 basis points, PV(netCF)=0.0082. A positive change instead of negative change in Q5. In this case, the aggregate duration is negative.

I think it is using the forward to hedge the risk due to the oil price changes. The interest rate risk still exists since the aggregate duration from this natural hedge is not zero.

Does LONG a swap" mean “pay receive fixed price (or I/R)/receive floating price (or I/R)” ?

Correction Does LONG a swap mean “pay fixed price (or I/R)/receive floating price (or I/R)” and SHORT a swap mean “receive fixed price / paying floating price” ?

I think you are right, but I haven’t seen it in CFAI curriculum.

AMA Wrote: ------------------------------------------------------- > Correction > Does LONG a swap mean “pay fixed price (or > I/R)/receive floating price (or I/R)” and SHORT a > swap mean “receive fixed price / paying floating > price” ? You are right. Although I avoid using terms like that since it adds to the never ending confusion http://www.contingencyanalysis.com/archive/archive99-2/00000161.htm

OK, then the questions can be answered.