Sunday, January 23, 2011

The Art of Asymmetric Arbitrage

I am engaged in this constant game of probabilities, evaluating asymmetry between the price of a given asset or its derivative and its risk. Money is made in the capital markets by first correctly identifying such an asset (believe me, no mean task) but even tougher is executing your strategy. Ofcourse I am not alone in this, knowingly or unknowingly the whole world is engaged in this activity, in case of equity markets the "fundamental analyst" who finds value in every other stock is a typical example, although he/she may not be aware of this. When that analyst says that the price of a stock is 20% cheaper than its fundamental value (never understood what this means in a world of unknowns.. anyways) he is pricing that asset with the underlying risk of earnings, interest rates and time so basically three unknowns.. meaning he is claiming to be a visionary who can see the future values of these 3 components and I always wonder why we call Heisenberg a genius when he was not able to see even one. Saying that a stock has 20% upside potential in the next one year, simply means he/she is mispricing risk..... why well because first in normal circumstances the whole world is looking at that stock and chances are that it is being fairly priced and for a 20% upside potential (again questionable) there is no reason to bet a 100% downside!!! The most sure way of making money in capital markets is arbitrage. Ofcourse you don't get too many arbitrage opportunities though. The reason is that in normal arbitrages like Put Call Parity, Cash Future arbitrage etc. both the price and the risks are known accurately. What I am going to discuss is called asymmetric arbitrage. Since early 1900 when Bachelier wrote his paper it is an established fact that markets are not normal, infact in this world full of traders the asset prices have the tendency of becoming absolutely depressed to be maniacally priced...... The reason, well the conditioning of human mind is such that it thinks linearly and not just in markets but in leading the lifestyle as well. 

Let me pick a simple example... let us say there are two rooms one of which has the probability of gold deposits. In Room A the probability is 90% and in Room B the probability is 1% and 9% chance that someone made a fool of you. To search for gold in Room B you have to pay an X amount and to search in Room A you have to pay a 70X amount. Which one would you choose? Well I think the answer to this are just 2 either I choose Room B or I choose nothing. The reason is simple since the probability of finding gold in Room A is so skewed towards it will attract too many people and so in essence my probability of finding gold in that room is actually not 90% but more closer to 0%!!! because I am not just playing against the static game but also the against the probability of one of those millions finding the gold. This is exactly where the market presents an arbitrage opportunity because the the real risk is hidden beneath the headline. When it becomes so obvious that a stock is going to go much much higher or lower the returns on the side of the crowd become highly negatively skewed. Again let me explain by taking an example... Let's say that I go to see a show in which the anchor throws gold coins at random intervals, the show has a ticket price X; now this news spreads and lots of people want to see this show, two things would happen either I share my seat with someone and thus reducing the chance of catching that golden coin by k times or pay a much higher price for the ticket and in turn for sure reducing my potential benefit, because no-one can evaluate the crowd it is impossible to fathom the potential reduction in rewards and so we observe maniac prices somewhere and depressed prices elsewhere. Evaluating such situations in markets and taking the opposite side of the trade is what I call "The Asymmetric Arbitrage". So let me reiterate the point of this arbitrage... Since the payoff of a specific trade is so skewed on one side that it ends up attracting so many market participants who thereby by their sheer force of numbers reduce the payoff to such an extent that the opposite end of the trade becomes more attractive.

Now another way  to look at a stock price from the prism of asymmetry is that the stock price is a sum of buying a call option on the Earnings of a company and selling a call option on the interest rate. The multiple you pay over earnings is proportional to the time for which you have bought and sold the options. Now since generally in a low interest rate environment the volatility in interest rates is less than earnings (except probably in hyper inflationary period) and the returns from business more than the interest rate the price of the call is more than the price of sold call option. If I give you an option of taking 100000 dollars now or toss a coin and if it comes heads take 200000 dollars else nothing, which option would you choose. Similarly if a risk free rate on some deposits is 10% and a PE on some stock in excess 20 which means that even for an ROE of 30% my next year return on paid equity is 5%, followed by 6.5%, 8.75%, 11.35%. My point is that would you take the 1 lakh dollars now or wait for the toss in this case approx. 10 years of unexpectedness (ofcourse there could always be positive surprises in stocks.. what I call the randomchalice price). The point that I am trying to drive is that in an easy liquidity environment when interest rates are artificially too low the sold leg of your stock (i.e. call option on interest rate) becomes too cheap and the call option on earnings of your stock becomes too expensive (as earnings are high) which essentially means you are sitting exactly on the other end of the asymmetric arbitrage by selling the bargain call and buying the maniacally overpriced put and since arbitrage is a sure way to make money.. If I extend this argument further in this case of de-arbitrage it is a sure way to loose money as just explained above.