CFAI Derivatives EOC Q


Can someone please help me with question 9 of the CFAI pricing and valuation of fwd commitments? (using schwesers terminology of pricing the fixed side and floating side).

I understand that the floating side is worth $1 (assuming $1 FV) because we’re at a coupon date, but i’m struggling to work out the fixed side. i tried discounting coupons of 3% (with $1 FV) but i didnt get the right answer.


There are two years left in the swap

  • Year 1 has a PVF of .990099
  • Year 2 has a PVF of .977876

The Fixed side pays 3% and the equilibrium rate is 1%, So we would get the PV per dollar as (3%-2%)(Sum of PV Factors)

Multiply this by the notional and you’re done.

Always think of the value of the swap as the present value of the differences in payments.

It looks like your method is valuing the original swap and then closing out the position with the available 1% swap. Since when is this the way we value swaps?

Shouldnt it be:

Floating value = $1, since we’re at a payment date.

Fixed value = 0.03 * (0.990099 + 0.9977876) + 1 * 0.997786 = 1.057422598

Therefore receive floating = (1 - 1.057422698) * 50mil

= -2,871,134.9


The way to calculate it is taking the Present value of the difference between the Forward price you locked in, and the forward price you would lock in if you were to start a new contract today.

The bank locked in at 3%, when the current equilibrium rate is 1%. I made a typing error in my first calculation, it should be :

(3%-_ 1% _)(Sum of PV Factors)

The swap is going to have a negative value since you COULD BE paying 1%, but instead you are LOCKED in at 3%. The value will be the present value of the additional interest you are paying due to the difference between the locked in rate and the equilibrium rate.

This problem is pretty much identical to Blue Box #14 and it uses Formula #14. Take a look at that blue box it should help

"Thus, the value of a fixed rate swap at some future point in Time t is simply the sum of the present value of the difference in fixed swap rates times the stated notional amount (denoted NA), or (Equation 14)"

Oh yeah, and maybe this will answer this question : "We now turn to interest rate swap valuation. Following a similar pattern as forward contracts, Exhibit 18 shows the cash flows for a receive-fixed interest rate swap initiated at Time 0 but that needs to be valued at Time t expressed per unit of the underlying currency. We achieve this valuation through entering an offsetting swap—receive-floating, pay-fixed. The floating sides offset, leaving only the difference in the fixed rates."

According to schweser:

“At any payment date, the market value of a swap (to the fixed-rate payer) is the difference between the value of a floating-rate bond and the value of a fixed-rate bond.”

This is very different to valuing your original swap (diff(floating,fix)) - value of contract used to close out contract (diff(floating,fix))

Is schweser wrong, or am i not understanding correctly?


I just remembered you don’t even need to know this haha.

Log in to your Kaplan account and check the Errata. It tells you to ignore pages 142-145 in the Derivatives section, and also adds the same formula I used for valuing swaps.

hahaha just saw the eratta!

Thank you for your time :slight_smile:

Goodluck for the last 1.5months!

The worst part is I saw the errata after spending a decent chunk of time figuring those 3 pages out haha.

Good luck to you as well

Could you please be more clear?

Did they cancel the example where they valuate the fixed side and the floating side by discounting all the cashflows to today?

if yes why?

I have schweser 2016 and I noticed that swaps were valuated in a completely different manner (more complicated) compared to CFAI 2017 and as ejs190 said, the idea was:

“At any payment date, the market value of a swap (to the fixed-rate payer) is the difference between the value of a floating-rate bond and the value of a fixed-rate bond.”

But I suppose this is due to the fact that in 2016 also swaps between payment dates were evaluated, not in 2017.

In the CFAI 2017 regarding the formula: V=NA(FSo-FSt)*SumPV they say:

The examples illustrated here show swap valuation only on a payment date. If a swap is being valued between payment dates, some adjustments are necessary. We do not pursue this topic here. --> Does this mean that in the 2017 curriculum we don’t have to valuate swaps between payment dates?

Is this the reason why Schweser cancelled those pages?