Index futures price

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afranks1

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March mock, AM, set 7 q 4, vignette says:
Evaluate futures contract on S&P MidCap 400 index that expires in 145 days. Annual risk free rate is 3.5% and index today is at 840. The accumulated value of dividends reinvested over the life of the futures contract is expected to be $3.15 per contract.
Question asks for S&PMidCap 400 index futures price assuming 365 day year, answer has: 840 x 1.035^(145/365)
Why do they not use the formula given for a futures price on an equity index of:
spot x e^ [(continuously compounded risk free - continuously compounded dividend yield) x (145/365)]
 
afranks1 wrote:
March mock, AM, set 7 q 4, vignette says:
Evaluate futures contract on S&P MidCap 400 index that expires in 145 days. Annual risk free rate is 3.5% and index today is at 840. The accumulated value of dividends reinvested over the life of the futures contract is expected to be $3.15 per contract.
Question asks for S&PMidCap 400 index futures price assuming 365 day year, answer has: 840 x 1.035^(145/365)
Why do they not use the formula given for a futures price on an equity index of:
spot x e^ [(continuously compounded risk free - continuously compounded dividend yield) x (145/365)]
Click to expand...
I think the key thing here is marked in bold. The accumulated value of dividend is stated over the life of the futures contract (i.e. not for a full year). Because of this, we do not need to make any adjustment to the FV of the dividend.
 
The formula should actually look like this: 840*(1+0,035)^145/365 - 3,15. That is what they have in the updated mock.
 
But since we are dealing with an equity index, why are we not using the continuously compounded formula?
spot x e^ [(continuously compounded risk free - continuously compounded dividend yield) x T]
 
Because they are using the future value version of the formula and subtracting off the future value of the already continuously compounded reinvestment return on dividends ($3.15)
 
I had the same question as you when I did this question, not sure why are they not using the continuously compounded risk free rate - but I came to an answer that is closest to the correct answer. I thought this answer is a bit inconsistent as well.
 
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