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The week's question
In December 2024, in the thread "Re: BRK: Why Not XOM?", BreckHutHigh asked the members: "What about the long road trips with kids?" This week it is put to everyone again. The button below opens the small thread re-asking it - read what others have said so far, then give your own answer as an ordinary reply.
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Investment Strategies / Mechanical Investing
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Author: mungofitch 🐝🐝🐝 GOLD
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Number: of 6132 
Subject: Re: OT: SPY vs SPX options and IV
Date: 07/29/24 3:59 PM
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The explanation that I came up seems correct but slightly unsettling: SPX, unlike SPY, has no shares and hence there's no arbitrage mechanism for SPX that keeps extrinsic value positive. I believe that to be a true statement, but feel like I'm missing something e.g. an expert might reply "that's true, but you neglected this".

They are both easily arbitraged, and in fact both can easily be arbitraged two ways: either with futures contracts or with actual stock.

I suspect (?) part of the issue may have to do with dividends and interest.

First, recall that index options are almost exactly like futures, in that they are both cash settled "side bets" on the level of the index at some future date. Not today.

When you buy an option on SPY, you are getting an option to buy an ETF which (for practical purposes) owns stock, and pays dividends, and incidentally can be exercised any time. Consequently the current fair price of SPY is the sum of the current prices of the shares it in effect owns, which is in effect the current index level.

Conversely when you trade futures or index options you are making a wager on the movement of the index number until some future time. The index itself does not pay dividends. Nor is it something you can buy, so it doesn't tie up your cash to make a wager long it.

The current fair price of a futures contract is therefore the "current price of the stocks" number (=the current index value), PLUS the amount of short term interest till expiry on the nominal value, MINUS the anticipated dividends whose ex-dates are prior to expiry. If today's dividend yield equals the current interest rate, then the futures will trade at the index level, but as that is generally not true, there is normally a gap except on expiration day. So, the price of SPY tracks the index, but the prices of wagers on a future index value (futures and index options) don't quite. Consequently an option for one wager even at an equivalent strike should not be expected to have the same price as the matching option wager on the other.

This is a real effect, but it's not large. The longer till expiry, the bigger the gap. e.g., for March futures, the gap between current index level and current futures contract quote right now is 173 points, almost 3.2%.

Jim

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