# Equity Swap

Please add some comment. what is the rationale behind this formular.

Consider a semiannual equity swap based on an index at 985 and a fixed rate of 4.4%. 90 days after the initiation of the swap, the index is at 982 and London Interbank Offered Rate (LIBOR) is 4.6% for 90 days and 4.8% for 270 days. The value of the swap to the equity payer, based on a \$2 million notional value is closest to:

A) \$22,314. B) \$22,564. C) −\$22,564.

Your answer: A was incorrect. The correct answer was B) \$22,564.

−\$22,564 is the value to the fixed-rate payer, thus \$22,564 is the value to the equity return payer.

for god sake take time to read your book

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Equity index forwards are calculated using continuously compounded rates

ln(1.044) = 4.306%

ln(1.048) = 4.688%

Value at initiation is 985 * e^0.04306 = 1028.34

After 90 days

Value for the Equity Index return payer = 1028.38/e^(0.4688*270/365) = 1016.654

Value for the Fixed return payer = 982/1 (b/c no dividend yield) = 982

Difference = 11.287 * 2000 = 22.575 = close enough

no. you don’t need continuous compounding and this is a question about equity swaps, not equity forwards.

the equity payer receives the fixed-rate payments – so work out the PV of a \$44,000 payment in 90 days and \$2,044,000 in 270 days using the libor rates given (you need to unannualize them).

the equity payer is meant to ‘pay’ the % increase of the equity index but in this case the index has declined, so they receive money from this too, ie (3/985) * 2,000,000. Add these two together, you should get \$22,564.

Kiakaha,

You’re right. I misread the question but we’re still missing part of the question.

The first payment is from the fixed rate side is -44,000 - 6091 = -50,091 back by 0.9886 = 49,522

For the second payment, we need to calculate the value of the swap.

1+4.6%*(90/360) = 0.9886

1+4.8%*(270/360) = 0.9653

(1-0.9653)/(0.9886+0.9653)= 0.03475

1.03475*2,000,000 = 2,071,138 -2,044,000 = 26,195 discount back by 0.9653 = 26,195

Sum of the two is 23,326.

I guess my estimate of the equity retun pay side of the swap is wrong but I can’t recall what I’m missing.

Fixed rate payer is paying:

(\$44,000 * .9886) + (\$2,044,000 * .9653) = \$43,498 + \$1,973,073 = \$2,016,571. fixed rate payer is also paying the change in the index (because it declined) = \$2,000,000 * (3/985) = \$6,091

add them together, take off the principal and you get \$22,662. pretty sure the difference is just rounding.

so if you receive the equity leg and the equity leg decreases you should pay to the counterparty the fixed rate + the amount of decrease of the equity. so why doesnt the valuation in the book take that into account ?? bk 6 page 279/280 example 6, part B, why is the decline on the equity leg added to the market value ? it should be subtracted. because the pay fixed side needs to pay first the fixed amount and then receives a negative amount for the equity = they pay that also.

thank you

You agreed to pay the equity return and receive the 4.4% fixed. The equity return is 985/982=0.997, multiply that by \$2 milion, and you get -\$1,993,909 that you have to pay.

You receive the fixed in the manner Kiakaha explained, so you receive +\$2,016,473. The difference is +\$22,563.73.