Thursday, January 7, 2010

Expected Value Of A Position

Let me run this past you. I want to try to find the expected dollar pay off of trades using the expected probabilities of expiring worthless. Let's take the IWO GOOG trade listed at the bottom of this post for example. The odds of expiring worthless and collecting the $510 are .7168 x $510 = +365. However, I need the odds of expiring at or below the long put to get that expected loss. The expected loss isn't (1 - .7168), that is just the odds of losing something more than $1. In my mind this is a somewhat simple game. If implied volatilities hold true to the bell curve over the long-term, all you have to do is enter trades that have a positive expected payout. We already know the bell curve works for random probabilities, the question is going to be, what is the historical correlation of 30-day implied volatility versus actual outcomes over this time. I think the guy I emailed at the CBOE will know this information. What are your thoughts?
I liken this to playing roulette. If there are 38 numbers on the wheel and they were paying 39:1, you take that bet all day long and just have a big enough bankroll to wait for the odds to play themselves out over time. Since implied vol isn't a discrete random variable like the numbers on a roulette wheel, I would like to know it's historical accuracy. What are your thoughts? Do you agree that as long as the implied vol is accurate over the long run that all you would have to do is find positive expected payouts and then play enough of them over time to spread out the risk?


IWO Trade Idea for GOOG

SELL -2 VERTICAL GOOG 100 FEB 10 570/560 PUT @2.55 LMT

Return: 510

Risk: 1490

Return on Risk: 34.22%

Prob of expiring: 71.68%

Prob of touching: 55%

2 comments:

  1. So this is what I came up with for the expected return:
    Premium Collected: $2.55 * 2 * 100 = $510
    Max Loss : ($10-$2.55)*100 = $1,490
    Probability of worthless at expiry : =71.68%
    Probability of Touching : =55%
    Probability of loss (Set lower price slice from breakeven to 560 in TOS) : 4.3%

    So the formula would be (510*.7168)+(1490*(.043*.55)) = 365.56 – 35.23 = $330.32
    Do you agree with my method?
    Thanks

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  2. When IWO put this trade alert out. I took a look at it and liked it. The only thing that I did not like is the price action that I was seeing in GOOG. Recently GOOG released its own smartphone and there was a bit of sell the news that was going on. So I decided that I would put the trade on when I saw GOOG find a bid for support. The trade alert came out when Goog was trading at $603. I watched the tape on and off as well as the hourly chart. Finally I saw bids supporting the price at $592.65 and I executed 1 of these vertical spreads for $3. My plan was to add another if it went lower and I estimated that it could had went as low as the 50 day MA. Today it did trade as low as $588 in the pre-market and then the buyers came in and it rose very quickly back above $600. So I missed my opportunity to add another, but I am now comfortably in the money.

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