Equity Swap Need Help!

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Rasec

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You enter into a 2yr equity swap in which it will receive the rate of return on the russell and will pay fixed 4.99%
with a notional of 100M
at Initiation the index is 757.09
in 100 days the index is 723.86
260- Libor:.0442; Disount factor = .9691
620- libor:.0499; Discount factor = .9209
the market value is?? I can’t seem to solve this :(
 
I haven’t really done many of these in a while but isn’t just a case of discounting all the cash flows for each side and calculating the difference
Equity side: (723.86/757.09 - 1) * 100M <<— discount this back to today. Note that this is a negative, so paying a negative mean you are receiving
Fixed pay side: There are 2 cash flows of 4.99% * 100M. Discount these using given discount factor and add up.
Now calc the difference of the discounted cash flows to get your answer (again, note that you’ll be subtracting a negative for the eqt return side, so really you’re adding them up)
The trick here might be to understand that the guy paying the fixed side is also paying for the equity side.
What’s the answer? I think this is how it’s done but not 100% on these.
 
The answer is -5,910,000
I don’t understand why we subtract 0.9209 from (723.86/757.09)? can you explain this?\
((723.86/757.09)-0.9209-.0499*(0.961+0.9209)) * 100,000,000 = -5,910,000
 
9209 is the discount factor for 620 days??? why are we subtracting this??? from the index return?
 
Rasec wrote:
The answer is -5,910,000
I don’t understand why we subtract 0.9209 from (723.86/757.09)? can you explain this?\
((723.86/757.09)-0.9209-.0499*(0.961+0.9209)) * 100,000,000 = -5,910,000
Click to expand...
First off, the wording/question is poorly setup. They don’t specify if 4.99% is the quarterly/annual/semiannual rate.
Actually, what is going is, they’re calculating the fixed rate at the day of marking to market. And the formula for that is = Original Fixed Rate * (X1 + X2) + X2.
So, Mark to Market Fixed Rate = 0.0499*(0.961+0.9209) + 0.9209
The above value is then subtracted from the return on the equity index. Hence, negative 0.9209.
 
I think where I went wrong is that I assumed the payoff at expiry for the eqt side was calculated simply by using today’s values. I think you need to calc the forward in order to do this. But then you just end up PV the forward, so really you don’t need to forward it all in the first place. I think what they are doing is just discounting the expected payoff which is something like this PV( FV(Eqt Retunrn) - 1), which is just (Eqt Return) - PV(1), which is EqtReturn - 0.9209 in this case. So it’s not that they are subtracting the DF, it just look like they are because they are discounting the 1 value used in the equation.
I need obviously need to review this. Thanks for bringing this up.
 
I have copied the actual problem: Can someone help me make sense of this index swap valuation problem!! Clever CFA!! I still don’t understand why they are not PV of floating leg - PV of fixed leg
: Equity swap to gain exposure to the Russell 2000 index. Springtree enters into a two-year equity swap in which it will receive the rate of return on the Russell 2000 Index and will pay a fixed interest rate equal to 4.99 percent. The swap has annual payments. The Russell 2000 Index is at 757.09 at the beginning of the swap and the notional principal of the swap is $100 million.
notional of 100M
at Initiation the index is 757.09
in 100 days the index is 723.86
260- Libor:.0442; Disount factor = .9691
620- libor:.0499; Discount factor = .9209
 
The question clearly states that 4.99% is the annual fixed rate.
Think of the inflows and outflows, Rasec. You have an obligation to pay a fixed rate of 4.99% (your outflow). And you have the right to receive the return on the equity index (your inflow).
There’s no need for you to even calculate the floating rate. Based on the inflows and outflows, try to answer your own question: “I still don’t understand why they are not PV of floating leg - PV of fixed leg”.
Per your statement “PV of floating leg” is your inflow while “PV of fixed leg” is your outflow, which is not entirely correct. You’re thinking in terms of other swaps and the concept of marking to market, which has nothing to do with the question at hand.
 
Try to break it down into steps.
Easiest part first, calculate the return on the Russel: 723.86/757.09 = 0.9561
Now calculate the PV of the fixed payments: The fixed rate is provided in the question as 4.99%. Multiply this by our discount factors to find the PV. Now bring the hypothetical notional principal of 1.0 back to PV as well. 0.0499(0.9691+0.9209)+1.0(0.9209) = 1.0152
We are paying fixed and receiving the return on the Russel so: (0.9561-1.0152)x$100M = - $5,910,000
 
Guys!!!
Thank you for your time!!! I means a lot :)




-rasec
 
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