On of the questions in Schweser for chapter 51 is as follows and it has me baffled.
A bank entered into a $5,000,000, 1-year equity swap with quarterly payments 300 days ago. The bank agreed to pay an annual fixed rate of 4% and received the return on an international equity index. The index was trading at 3,000 at the end of the third quarter, 30 days ago. The current 60-day LIBOR rate is 3.6%, the discount factor is 0.9940, and the index is now at 3,150. The value of the swap to the bank is closest to:
The Answer is:
value of fixed-rate side = 0.9940x$5,050,000=$5,019,700
value of index return side =(3150/3000)(5,000,000)=$5,250,000
value of swap to bank = $5,250,000 – $5,019,700 = $230,300
My question is in the value of a fixed-rate side where did they get $5,050,000? I thought it would have been $5,000,000.
The answer compares values by calculating the PV of both the fixed-rate side, and the index-return side.
In the index-return side, it takes the value of the index from the last swap payment (i.e. end of third quarter) and calculates its present value:
(Present Index / Index 30 Days Ago) * (Capital)
In the fixed-rate side, it takes the future value of the swap (at final payout, 60 days from now) and back-calculates its present value. You have to include the final payout when valuing the swap because it’s not paid out yet, hence the $50,000:
(60-Day Discount Factor)*(Capital + Final Payout)
= 0.9940 * ($5,000,000 + 1%*($5,000,000) )
= 0.9940 * ($5,050,000)
Why a 1% final payout? Because it’s a swap with 4% fixed rate at quarterly payouts, so you’ll get a payout each quarter at 1%.
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