Must Read for Traders and Investors
Most finance textbooks emphasise the virtues of diversification: by diversifying your investments you can minimise your losses. But a high degree of diversification also ensures only average investment performance. The maestros of the investment world have all made their money by playing the game differently. Unlike the small investor who makes small and frequent bets, the maestros make infrequent but big bets. It is not as if they love risk. They make these big bets only when they perceive that the downside risk to them is minuscule and the upside potential very high.
Take a couple of examples. After the salad oil crisis hit American Express in 1963, Warren Buffett calculated that this was only a temporary crisis, and that so long as customers’ faith in American Express’s traveller cheques remained intact, the company would recover from this setback. He wagered $7 million, effectively 40 per cent of his fund on this single investment.
Similarly, in 1992, George Soros calculated that the British pound would be devalued even though UK’s Chancellor of the Exchequer kept insisting till the very last that a devaluation was not in the offing. Soros bet $10 billion on this single wager through leveraging, (Quantum Fund’s worth then was $7 billion). Though we might think that Soros acted like a risk junkie, in reality this master investor calculated that in case things didn’t pan out the way he thought they would, his loss wouldn’t exceed 4 per cent.
How much to bet
What the above two examples underline is the need to invest only when the stock market offers us very high odds of winning. For any investment that we are considering, we also need to think about the probability of different outcomes. And finally, investors must know the optimum amount of their total funds that they should bet on a particular investment. The Kelly formula offers the answer to the last question.
The Kelly f ormula can be defined as = edge/odds. For simple bets with two outcomes, such as tossing a coin, the formula is: f = (bp – q)/b where, f is the fraction of your funds you should bet; b is the net odds received on a bet (odds are quoted as “b to 1”); p is the probability of winning; and q is the probability of losing.
Imagine that someone offers you a bet wherein you will be paid Rs 4 if the coin shows head; and Re 1 if the coin shows tail. Here b=4; p=0.5; and q=0.5. f = (4*0.5 – 0.5)/4 = 1.5/4 = 0.375.
According to Kelly formula, the maximum you should bet is 37.5 per cent of your funds.
Now, investments are not dual but multiple outcome bets, with each outcome having a different probability. Suppose you are analysing a stock and you believe that your returns from it would be as follows: 80 per cent probability that the stock will rise 200 per cent; 15 per cent that it will rise 100 per cent; and 5 per cent that you will lose all the m oney (-100 per cent return). Instead of doing the calculations yourself, visit this web page: www.cisiova.com/betsizing.asp which has a calculator for the Kelly formula. In the first column, fill the outcome name (in our example, write: one, two, and three); in the second column, fill expected returns (here, 200, 100 and -100); in the third column fill the probability (here, 80, 15, and 5). Click on the calculate button. The answer we get is 92.2 per cent. This is the maximum percentage of your funds you should bet on this investment.
Most investors tend to be conservative, deploying a smaller percentage of funds than the formula suggests, and rightly so. After all, investors can never predict the probability of various outcomes with complete certainty. Hence, some degree of conservatism is advisable. Above all, what using the Kelly formula does is reinforce the habit of thinking probabilistically about our investments.