Spot-Future parity in KOSPI 200

G

gbentor

Hi all,

Sorry if this is a newbish question...

I'm trying to implent the Spot-Future parity equation on the KOSPI 200, but for some reason always getting a big difference (about 1.5%). I can't figure out what I'm doing wrong...
Risk-free interest rate is 1.25%, and I'm looking at futures expiring in 81 days. Current spot price is about 261.93, therefore my equation should be:

Future = 261.93*e^(0.0125*(81/365)) = 262.65

but futures are currently trading for much less, at about 258. Obviously there is no arbitrage that big, so I'm defintely missing a variable...
Could it be dividends? maybe something else?

Any help would be appreciated
 
gbentor said:
Hi all,

Sorry if this is a newbish question...

I'm trying to implent the Spot-Future parity equation on the KOSPI 200, but for some reason always getting a big difference (about 1.5%). I can't figure out what I'm doing wrong...
Risk-free interest rate is 1.25%, and I'm looking at futures expiring in 81 days. Current spot price is about 261.93, therefore my equation should be:

Future = 261.93*e^(0.0125*(81/365)) = 262.65

but futures are currently trading for much less, at about 258. Obviously there is no arbitrage that big, so I'm defintely missing a variable...
Could it be dividends? maybe something else?

Any help would be appreciated
More...

There is a small mistake and a big mistake in your calculation. The small mistake is using risk free; should be whatever you could earn if you lent out the stock.

The big mistake is dividends which are responsible for about 3 points extra (yield is about 4.8% or 1.1% over 81 days; in reality it depends on the timing of dividends over the year)

GAT
 
globalarbtrader said:
There is a small mistake and a big mistake in your calculation. The small mistake is using risk free; should be whatever you could earn if you lent out the stock.

The big mistake is dividends which are responsible for about 3 points extra (yield is about 4.8% or 1.1% over 81 days; in reality it depends on the timing of dividends over the year)

GAT
More...

Cheers mate!
I figuered it had something to do with the dividends, but I'm not so sure on how to evaluate them. I can add the change in the index over the last year (adjusted to the maturity time), and it really gives me a much closer results, but that's not really the dividends, is it?
So how do I calculate the dividends, in respect to their timing?
 
gbentor said:
Cheers mate!
I figuered it had something to do with the dividends, but I'm not so sure on how to evaluate them. I can add the change in the index over the last year (adjusted to the maturity time), and it really gives me a much closer results, but that's not really the dividends, is it?
So how do I calculate the dividends, in respect to their timing?
More...

Well the easiest thing to do is infer from the futures price...

Otherwise you'd need a schedule of all the firms in the index with their ex-divi and divi payment dates, and expected amounts. Good luck with that, especially for Korea.

Perhaps if you'd share why you want to do this I could offer some more helpful advice?

GAT
 
Yep, liek GAT says... you have to make assumptions about future dividends of the underlying stocks to check it... but why bother?
You will also run into issues with how dividends are taxed as well... do you take full dividends or nett?
And officially you might have to account for heavy short stock rates as well... during GFC the uptick rule and no shorting of financials made the futures trade at a discount because the EFP accounted for that....
 
JackRab is right.
- Also consider stocks that are in halts due to corporate actions, and their implied re-open price.
- Stocks to likely be dropped from the index at any re-balance prior to the futures expiry.

** But forgetting dividends is your main error. If you're arb-ing this, you need to discount each dividend cash flow prior to futures expiry, back to today .. using your carry funding cost.
 
Thanks everyone, you've been very helpful!

The reason I'm trying to figure it out is for a small study I'm conducting, trying to better understand the difference between the market cap method calculation and the calculation based on the spot-future parity equation. It could be a complete waste of time, but for now it's only for study purposes.

So if I understand correctly, It is practically impossible for me to continuously calculate the spot price that way using an algorithm, because it's impossible to implant the variables affecting the dividends into that algorithm?
Does it mean that the spot-future parity is useless in regard to indices and may only be calculated in commodities/stock/forex?
 
You just need to do the work to get divided estimates for all stocks in the index - then do the reasonably simple math to calc the index basket present value.

All index trading / program trading / basket trading desks do this, and update it every day.

* fine detail would be calculating the funding u pay on the futures margin, and the effective delta that gives you as the variation margin changes this $ funding. But. That's an issue for the details guys among us. Delta on a delta one hedged index arb book. Yes.
 
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