If Jacobs enters into a $10 million 4-year annual-pay floating-rate equity swap based on 1-year LIBOR and the total return on the S&P 500 Index, what is the value of the remaining 3-year swap to the floating-rate payer after one year if the index has increased from 1,054 to 1,103 and the LIBOR term structure is as given below? LIBOR 1-year: 4.1% 2-year: 4.7% 3-year: 5.3% A) 0. B) $48,935. C) $9,583.

I remember this question. The idea is that a floating rate side and the equity side both reset after making a payment. So, technically you cannot value either side. What they have not made very clear in the question is that we are on the reset date. Since we are on the reset date, the value is going to be zero. Since both of them are essentially floating payments, the only time we will know what the value of the swap is will be on the reset date and no other date.

You can value an equity swap at any time, just as with any other type of swap.

The value is the present value of what you will receive minus the present value of what you will pay. The present value of the equity side is easy: it’s the equity return since the last payment plus the notional. The present value of the floating side is also easy; it’s the next coupon payment plus the notional discounted at the LIBOR rate to the next payment date.

Suppose that the notional is $10,000,000, the payments are semiannual,6-month LIBOR reset to 4% at the last payment date, it’s three months till the next payment date, 3-month LIBOR is 3%, and the equity return since the last payment is 4%. Then the PV of the equity leg is $10,000,000 × 1.04 = $10,400,000 and the PV of the floating leg is $10,000,000 × (1 + 4% / 2) / (1 + 3% / 2) = $10,049,261. The value of the swap is $350,739 to the floating-rate payer and −$350,739 to the equity payer.

LOL, no wonder I got that question wrong. Okay so we dont exactly need to have the value of the equity index at the end of the period, we can just use the last recorded equity value+the notional to get to the current value. Is this correct? But IIRC, the question that OP mentioned had the answer = 0. According to them, we were on the reset date so the value = 0. So what happens as soon as it resets? Does the value of the floating side also become 0? I know the equity side will go back to 0.

Yes: when a payment is made, the value of the floating leg always returns to the notional, and the value of the equity leg always returns to the notional.

i think i know where i got the weird idea from haha… why you simply divided the “denominator” (3 month Libor by 2) and the below answer each denominator was unannulaized differently i.e. 270 libor multiplied by 270/360, and the 90 day Libor by 90/360 and not simply convert it to semi annual bases . hope im making sense.

Consider a fixed-for-fixed 1-year $100,000 semiannual currency swap with rates of 5.2% in USD and 4.8% in CHF, originated when the exchange rate is $0.34. 90 days later, the exchange rate is $0.35 and the term structure is:

90 days

270 days

LIBOR

5.2%

5.6%

Swiss

4.8%

5.4%

What is the value of the swap to the USD payer?

$2,719.

The present value of the fixed payments on one CHF is

0.02372 + 0.98414 = 1.00786.

At the current exchange rate the value is 1.00786 × 0.35 = USD 0.35275.

The notional amount is 100,000/0.34 = 294,118 CHF so the dollar value of the CHF payments is 0.35275 × 294,118 = $103,750.

let me try to explain my weird thought and hope it make sense haha .

in your example, the Numerator, LIBOR rate was divided by 2 to get the semi annual payments (180/360 or /2) which i agree with.

since 3 months (90 days) past, the 3 months Libor was used to discount the payment ,and i also agree with that part.

the weird stuff kick in here. the part where the denominator multiplied by 180/360 (/2) and not 90/360 (/4) to count for the three months (90 days) that passed.

you calculated the PV of the floating leg as $10,000,000 × (1 + 4% / 2) / (1 + 3% / 2) = $10,049,261.

i thought : $10,000 X (1+4% *(180/360))/ 1+3%*(90/360) because 90 days had past already

i thought we always need to bring back to it’s original raw figure , so we need to multiply 3 months Libor by 90/360 like the example i encountered above.

I also share this thought with theprodigy. We have to discount the value of the floating leg to PV. In S2000’s example, It’s 3-month into the next payment date so we have to discount it 3-month back using the 3-month LIBOR rate, thus have to divide the 3-month LIBOR by 4, not 2 right? Can somebody clear this up?