Probability and asymmetric outcomes
Stock72,
In your earlier posts you used to say that you are gambling only and not trading and cite 50% probability number. Don’t know where you got that number, but it sounds as if it is taken straight away from tossing of an unbiased coin.
Well, when tossing a coin you only have one variable and without external influences (of unpredictable variables) on the coin, the distribution of the outcome is uniform and thus you would estimate 50% probability of getting one side of the coin. But, in the stock market, you have lot more variables and to add on that unfairness (like you see now how govt.’s policies favor certain sectors of the market) and on top of that you have these variables’ properties like variance and mean, themselves varying with time.
When you are looking at the outcomes of your own trading, you still have more than two outcomes – profit and loss. Those are the magnitude of the profit/loss and the holding time period. If you are not looking at simple random buy and sell decisions, then you have conditional probabilities arising with your buy and sell decisions dependent on the stock price movement patterns, technical indicators, fundamental factors, news, rumors, events etc. Even if you just fix your profit and loss and keep trading in a tight window, you still have time. Time makes this thing very different from gambling in general in a casino. Life too is like that. Lot of wonderful lessons market teaches us in a short span of time which life would take its life to teach us (though life has its own position to teach certain things that market can’t teach).
In the gambling casino outcomes are fixed. But not in the stock market. That is the beauty of the stock market. Its potential is always untold and unlimited despite what the history has shown. Actually in a casino the probability is tailored to be beneficial for the casino and lesser odds for the gambler. Still in history, there were professional gamblers who had gone to greater lengths (one guy had build electronic devices like spy devices, in those amateur electronic days). Still there was the outcome that these people were given bitter experiences to not visit the casinos ever again and also upon multiple visits to throw them out of casino with the help of security guards. And it was like a crime to gamble counting cards. How in the hell would any professional trader like that case? How can you expect to blindly gamble with extremely limited odds? That’s why casinos are only supposed to be for pure fun and not for serious professions.
Most of the time, I noticed, people look at the odds of outcomes but not the outcomes themselves when applying probability on events with random outcomes. I was recently reading this book “Fooled by Randomeness” which nicely presents this case of skewness and asymmetry in trading profits/losses. The book makes an amazing reading and is one of the smartest books of all time (Kudos to Taleb). I used to think about asymmetry but never thought about skewness of probabilities (odds) and also never theorized on my most successful trades as to their reliability and repeatability. On the outset it was difficult for me to logically understand how some successful trades happen but I could only do those based on emotions and gut feels. Let me present this case of “skewness of odds and asymmetric outcomes”.
Imagine you are presented with an event (say next day’s stock price movement) where the probability of a 1% move up is 70% and that of a 5% move down is 30%. Which direction would you bet? Will buy call options or put options? Or will you sell the options? This kind of scenario occurs really in stocks. Later on that.
If you go by probability alone, you would buy call options or bet on up move looking for a more certain 1% gain. Would anyone go for shorting for 5% gain though probability is low?
Here the author shows how to arrive at the other decision. By calculating expectation which includes the value of outcome along with its odds. Look at below calculation.
Expectation on up move: 0.7*1=0.7
Expectation on down move: -0.3*5=-1.5
Total expectation = -0.8
What this means is that when the odds are skewed and outcomes are asymmetric, you should be looking at total expectation and not on individual probabilities or outcomes alone.
It goes like this. Tomorrow anything can happen in the market. As that is only one sample of an event. You are betting on up-move and say, it moves up, then you would make 1% gain. Now let us consider the other outcome which is a move down costing you 5% loss. Though its probability is less, a 5% loss will erode your capital significantly than you could cover through consecutive bets on the up-move in more number of bets.
Now consider the other case where you bet on down move. In case it moves up, you lose only 1% and in the other case you gain 5%. When you do more of these kind of bets, you see that you will gain on average as earlier calculation showed net expectation favorable to down move bets.
Last Wednesday, the day before the country wide Bandh, we had this case in context. The probability that the market would move down on the next day was high and it moved down 50 points. But the upside potential was higher though for the short term, probability was low. Higher because the market had a long term bear market (due to GDP coming down in last two years) and just getting relief in the form of reforms. And it doesn’t matter for the stock market index who gains money in a capitalist democracy, only total GDP number matters. What happened on Friday? Nifty gained 140 points (150 intra-day)! Now you could say that at the hindsight we can calculate these easily and match the equations. I will present other realities of stock price movements with skewness and asymmetry.
If you are looking at the stocks, for this case, look at those at 52 week highs. How do they move? You would notice that they move fast up in a short period of time, say 1 or 2 or 3 or 5 days and most of the time they are stuck in a range. It is as though you cannot predict when they move up and when they do and you miss it, you feel being cheated after having watched it not make any move for so many days. How do you position yourselves to take advantage of such a move? Apply this expectation based calculation. Its probability of a big percentage (10% or 20%) up move is less (as rarely it goes up). But when it does (and repeatedly once in a quarter or so), you will see the results. Combine this with pyramiding for scalability; you have a sustainable trading strategy. That’s what I do now.
Why stocks, even look at NIFTY since it was rising from 4800 levels of June, you should notice a characteristic of bull moves. The market moved in small range and small down range moves most of the time, but very less number of days it moved fast up 100 points or so. And only 4 times it moved 100 after 100 points in a clear trend. I can discount the ferocious up move of June as before deciding a trend reversal we need to notice one such move. Remember “there is nothing more bullish than a market that rises on strong momentum” by Gary Smith and correlate it with the 20% circuit limit of Sensex in 2009 May 18 (which I named as white Monday opposite of black Mondays in downtrends) and how the stocks gained to great heights after this ferocious trend reversal move. You see that you could be right (and big time at that) if you just kept buying CE options of Nifty once every month. In case you lost in one of the month, what’s that loss. A 100 point move on Nifty is a 3x on an out of money option. Your gain is dependent on how much stop loss you are willing to take, here the stop loss is the option price itself. Even if you did more trades per month say 2 or 4, on same CE options (say out of money that were available for 50/-) and waited for 150 point move till expiry, you would’ve had lot more gains (triples/quadruples) which would’ve netted you gains after discounting expired option losses.
Now this is the way to decide directions. Probabilities don’t matter. It’s the possibility itself. Imagine those onsets of bear markets, dot-com crash. Prior to that lot of money could be consistently made, then when the crash starts it’s a big gain to the PE option buyers.
Taking the same cases, you would avoid selling options. Even though a statistical study points that 85% of all options expire. Well, not all those buy for profiting on option itself, but some as insurance to their stock holding. And some do too much trading to lose, each trade costs money (mistake losses, brokerages and taxes). In Indian markets no such concept is there. Options are given to us suckers to lose money not as insurance. We cannot exercise. Can we? That doesn’t matter for this topic now. What happens is, if you keep on selling options you would make consistent stream of income. Remember, everyone gets their chance to be right in the stock market at one time or the other. Once option sellers recognize this opportunity of consistent money making when markets are moving in a range, they keep at it, until one quarter market breaks out of the range and moves decisively. We all have known about breakout patterns (assuming some trading experience). The longer it takes in a range, the greater the intensity of the ensuing decisive move. Which means, the more the option sellers milk from options, the more they increase they risk to blow up.
This is the way to perceive risk. You don’t see loss as an opposite of profit so you can cancel them in your books. Do you think you are okay dying soon so that you would anyway take another life and that cancels the death effect? No it won’t. So you take insurance. You know that it is money (premium) that doesn’t come back. But death is such a one time event that changes everything when it happens despite the lowest probability. The premium price of courses varies with probability as probability is higher for people with more age and for people with diseases, etc.
What happens with each rare, big time event is that, market will be there but participants will change. Market will be there, companies will change. I didn’t hear about stocks like AP Paper Mills, Hyderabad Ind, AGCNET etc. during 2007-2008. Now I don’t bother checking stocks like Torrent Power, Adlabsfilm, RNRL, the stocks of the 2007 cycle. If we don’t account for rare, unpredictable big impact events that can happen at unspecified time, then we won’t survive the market cycles.
Owing to SIP power that jobbers have they sure have the chance to keep trading all the time. But still that is not the way to go. You could be losing 13 Lakhs in one cycle and then another 13 in second cycle and so on. Your networth may not change much, as you have continuous supply of capital. What if, you had rather not looked at constant gains but gaining from the rare events that are of huge potential and molded your strategy to lose less from high probability events? Yet at the same time jobbers have the advantage to use it to their advantage to replenish their capital with small losses all the time, which anyway cancel with SIP inflows, and great life-altering gains after the rare market events like great crashes or great persistent bull markets. Jan'12 persistent market move was one such rare event but its potential was very easy to understand.
I will write about how to apply this for options trading later. Also how stop loss in equity dimension relates to options and how selling options relates to a certain corresponding activity in equity. Also on systems created based on historical samples, as a single rare event may totally negate a system. Is your system robust for a rare event?