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.
I need to go back and check, but I’ll try to do it based on some common sense… looks like the equity return is -0.3%, while the equity holder gets 2.2% return after 90 days. So, if you discount 0.022*$2m for 90 days minus the 0.3% * $2m loss on the equity portion, you get something close to $36k…which I don’t see in the answers choices!
equity payer: 982/985 - 1= -0.0003045 = -0.3045% LIBOR Fixed rate: 4.4% = 0.022 per 180 days 90 4.6 -> 1/(1+.046*90/360) = 0.9886 270 4.8 -> 1/(1+0.048*270/360) = 0.9652 Received Fixed = 0.022 * (0.9886+0.9652) + 0.9652 = 1.00818366 Pay Equity, receive Fixed = 982/985 - 1.00818366 = -0.01122935 for 2 Mill Notional = -22458 ~~ Choice B
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You got that backwards cpk. If the equity return is negative, the equity payer will not only receive the fixed payment but also receive extra based on the negative return. No way it has a negative value to the equity payer. I did get $22,564 though.
Answer is C. Its from Qbank. cpk, you rock man…I cant even attempt such questions and you get the answer to the last point… Editing my post, I see the reason why it is positive now…
What is the logic behind this calculation: “Received Fixed = 0.022 * (0.9886+0.9652) + 0.9652 = 1.00818366” Is there another more intuitive way to arrive at the value of the fixed instrument?
Its a semi-annual swap, so coupon payment will be made once in 6months. the swap is already 90 days in, thus first cpn payment will be made 90 days from now and 270 days from now. .9886 = discount factor for 90 days i.e. value of 1 dollar today, which will be paid 90 days from now .9652 = discount factor for 270 days i.e. value of 1 dollar today, which will be paid 270 days fron now. .022 is the cpn payment. If that helps…
it should be -ve value - so B is the answer… not C as u have written… please check.
I got choice C Equity Side = 982/985 = .996954 Fixed Side: .988631*.022 = .02175 .965251*1.022 = .98646 Total = 1.008236 Value of $1 notional = 1.008236 - .996954 = .011282 Value of $2 million notional = .011282*2000000 = 22564.1
I should also mention, this is a no excuses question. It’s as straightforward as it gets.
I choose C Equity value: 982/985 * 2,000,000 = 1,993,908.65 Fixed value You know the payment semi annually = 4.4% x 2,000,000 x 180/360 = 44,000 So we have two payments to be received, 1. 44,000 at 180 day and 2. 2,044,000 at 360 day So discount both of them till today 1. 44000/(1+0.046 x 90/360) = 43499.75 2. 2,044,000/(1+0.048 x 270/360) = 1,972,972.97 Add both of them = 2,016,472.72 Now since we are going to receive the fixed payment and make the equity payment, the answer is 2,016,472.72 - 1,993,908.65 = 22,564.07
edited: it is a repeat
It’ll be positive since it is an equity payer and (assuming fixed rate receiver) And since its not at the payoff for the equity index yet, so no payment is paid to for the equity index. But since the fixed rate payment can be calc’d, you can present valued the payment to that 90th day and calc the value (not the payoff of the swap). And if at the payoff the index is lower than the initial date then the equity payer (fixed rate receiver) will receive not only the fixed payment but also the difference of the index. (982/985) - 1 = -0.003 + the final fixed payment. (this logic… right?)
Looks easy after the fact! One problem I had was with the swap period…I don’t see how you all assumed it’s a one-year swap! Why stop at 270 days when you discount future coupons? Are you just guessing that since they didn’t provide other LIBOR rates, you stop there? If it were a 2-year swap, or 6-month swap, the fixed payment would be different…am I right on that? Another point is that if I sell you the return of my equity portfolio in exchange for 4.4% fixed return (which seems to be the situation here), and my portfolio’s value drops at year end, I get compensated for the drop *and* earn 4.4% interest! Sounds weird, doesn’t it? If my portfolio goes up 5%, I pay you 5% and you pay me 4.4%. Am I right again on that? If so, then what I have done is equivalent to buying a put on my portfolio *and* earning interest on my portfolio’s value as of beginning of year. Again, it sounds bizarre to me, as I’m getting a free put, and free interest…someone stop me please.
Answer is C as per the QBank.
Dreary Wrote: ------------------------------------------------------- > Looks easy after the fact! One problem I had was > with the swap period…I don’t see how you all > assumed it’s a one-year swap! Why stop at 270 > days when you discount future coupons? Are you > just guessing that since they didn’t provide other > LIBOR rates, you stop there? If it were a 2-year > swap, or 6-month swap, the fixed payment would be > different…am I right on that? YES YOU ARE RIGHT, based on answers I estimate 
that it is a 1y s/a swap and correct answer is C > > Another point is that if I sell you the return of > my equity portfolio in exchange for 4.4% fixed > return (which seems to be the situation here), and > my portfolio’s value drops at year end, I get > compensated for the drop *and* earn 4.4% interest! > Sounds weird, doesn’t it? If my portfolio goes > up 5%, I pay you 5% and you pay me 4.4%. Am I > right again on that? If so, then what I have done > is equivalent to buying a put on my portfolio > *and* earning interest on my portfolio’s value as > of beginning of year. Again, it sounds bizarre to > me, as I’m getting a free put, and free > interest…someone stop me please. NO YOU ARE WRONG you have portfolio and you inter into an equity swap: where you short-sell your portfolio and instead of it you invest into fixed-rate bond (if you split the swap into two legs) there is no option in there if portfolio price goes down, you earn on your short position in portfolio and you earn on your fixed rate bond (but you have you initial position in your portfolio where you lose) if portfolio price goes up, you lose on your short position in portfolio and you earn on your fixed rate bond (but you have you initial position in your portfolio where you lose) whatever happens to portfolio price you earn fixed interest and that is exactly what you wanted to achieve (get rid off the portfolio risk and receive fixed income, but without real selling of your portfolio)
Dreary , if they have more periods out , they have to provide more LIBOR forward rates too. So If they don’t give , you don’t ask ( the question ). Its a swap expiring after two payments
acer Wrote: ------------------------------------------------------- > 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. CF in time 0 = .044/2 = .022 Compute PV factors in 90 days: 1/(1+.046*.25), 1/(1+.048*.75) -> .9886, .9652 Compute CF to swap receiver: .022*(.9652+.9886)+.9652 = 1.0082 Index return = 982/985 Return to equity payer or the index payer = 1.0082 - 982/985 = 22491~22564 C.
Your “rounding” error is due to choosing the wrong Discount factor for the return of $1 . You calculated : .022*(.9652+.9886)+.9652 should be : 022*(.9652+.9886)+.9886
FIXED SIDE: Payment in 90 days = 44,000 Payment in 270 days = 2,044,000 PV of payment 1 = 43,499.75 PV of payment 2 = 1,972,972.97 Total PV of fixed payments = 2,016,472.73 EQUITY SIDE: Value = 982/985 x notional = 1,993,908.63 Value to equity side: equity payer pays equity, receives fixed: 2,016,472.73 - 1,993,908.63 = 22,564.10 Choice “C”. Anyone having trouble with swaps, i strongly recommend using my above layout. I can’t be bothered using all the fractions schweser presents…