Many of the ideas used by the investment community are adopted from the horse track and casino betting communities. Much of the failure that has dogged the investment community is due to rocket scientist PhDs misunderstanding the successful models of plebeian punters.
The use of betting as an example is not an endorsement, it is simply that this is where the mathematics was first developed and can be illustrated most lucidly. It is also how it is taught at investment firms on Wall Street.
To understand how the securities markets work you have to look no further than the horse bookies. Bookies take the bets from the bettors. This is the first point that the public begins to misunderstand how betting, and therefore investing, works.
There are two potential misunderstandings: the first is assuming that each horse has a uniform probability of winning, ie they are all just as likely to win. The second misunderstanding is assuming that the bookie offers one-to-one payout odds, ie pays $1 for each $1 that is bet. Grasping the significance of these statements is the key to successful investing.
The bookie, equivalent to the investment bank or broker, will always make money. Always. They do this because they do not set payout odds, depending on which horse they think will win, but on how people bet.
To understand the rest of this article you need to understand some notation from probability. Odds of one to four, written 1:4, means that there is a 1/5 or 20 per cent probability of winning. Similarly 1:9 means 1/10 or 10 per cent chance of winning. Payout odds are the same: 3:1 means that if you win you get $3 for each $1 you bet or invested, with the original dollar being returned.
Consider a two-horse race between Shadowfax, which has odds of 1:3 of winning, and Mr Ed, which has odds of 3:1 of winning. Many people would assume that the bookie should pay 3:1 on Shadowfax and 1:3 on Mr Ed. This would quickly lead to the bookie going bankrupt.
The issue to realise is that it does not matter what the probabilities are for winning. What matters is how people bet, because if half the money bets that Shadowfax wins, then it would be a very bad idea to offer 3:1 odds. If total bets are $100 in this scenario, then a bookie will pay out to the winners their $50 bet plus $150 in payoff, while the bookie will keep the $50 from the losing bets on Mr Ed. This a net loss of $150. Not good.
What a bookie wants to do is to match his assets (cash from bets) with his contingent liabilities (payouts to winning bettors). This is no different from a bank matching its assets and liabilities, a function so vital that they have a committee of senior executives named ALCO to oversee this function, which is managed by the bank’s treasury.
Using the previous example of half the money bet on each horse then the correct odds for the bookie to offer are 1:1 on each horse. That way, regardless of which horse wins, the bookie will not lose money. As another example, if two-thirds of the money bets on Mr Ed and one-third on Shadowfax, then the bookies would offer 1:2 on Mr Ed and 2:1 on Shadowfax. That way whichever wins, the bookie loses no money.
This is exactly how brokers, market makers and investment banks trade, although they shave the odds a bit to make money. The treasury of a bank uses the money markets. They get calls from other banks and corporate treasuries looking to buy and sell money, in the form of deposits. The bank treasury will quote an interest rate at which it is willing to borrow dollars, say 1 per cent, and an interest rate at which it is willing to lend dollars, say 2 per cent. It comes up with these numbers not based on where it thinks interest rates are going, but solely based on where current supply and demand are. This methodology is also how the intelligent investor makes money.
Here is the key to successful investing. It is not to maximise return. In the horse betting example this would be equivalent to betting on the horse with the highest payout odds. Neither is it to minimise your risk. In the horse betting example this would be equivalent to betting on the horse with lowest probability of losing. The key is to pick the horse with the biggest gap between payoff odds and winning probability.
In the example of Shadowfax having a 25 per cent chance of winning and Mr Ed having a 75 per cent chance of winning if the odds being offered on Shadow fax were 4:1 (as opposed to the 3:1 that the winning probabilities dictate) and therefore those on Mr Ed were 1:4 (as opposed to 1:3) then the correct investment to make is on Shadowfax.
The Investor’s Edge in Action
Now that we have introduced the idea of a payout — win odds gap, we will look at how it can be used.
Consider two Emiratis freshly returned from studying in the US. Khaled picked up an ability to play poker, believing that it will help him learn bluffing and betting strategies for a life in investing. Saleh focused on his academics, including probability and statistics.
Khaled, now an experienced poker player, asks Saleh if he would like to play this game. Saleh, understanding the rules but never having played, accepts. At first blush things might look grim for Saleh.
Poker usually requires that the players put up the same amount of money, called the ante. This is a mistake since Khaled is a much better player. Saleh, a neophyte poker player but an avid mathematician points out that it would only be fair to have odds involved, e.g. $1 from Saleh equals $100 from Khaled. This is not an unknown concept in games. Notably, golf has a handicap system to help level the playing field.
Khaled, who knows that he is at least 1,000 times better than Saleh, accepts the 100:1 payout odds on him. This is his fatal mistake.
On the day of the game Saleh seems to be in the position of having a 100:1 payoff but a 1:1,000 chance of winning. This is an improvement from the original 1:1 payoff with a 1:1,000 winning odds, but it is still a negative gap.
Here is the magic, the magic that is so difficult to develop, but when you have it, it seems to simple and you will win, not every time, not even the majority of the time, but enough times to trigger the payoff odds.
The magic is to now improve the winning odds. The target is to get it down to at least the payoff odds, ie from 1:1,000 to 1:100 or better. But how?
In this scenario, it is to bet everything on every hand. You see, if you bet everything on a single hand then all skill goes out the window. Bluffing is useless. Calculating probabilities is useless. Counting cards is useless. The key is that it is useless for both players. In this case the winning odds are even (1:1)!
Most people would belittle forcing a 1:1 winning strategy. It is not sexy. The genius of Saleh is not that he selected a strategy that gave him 1:1 odds of winning. The genius was that he understood that it was better than 1:1,000 odds of winning. When you add the fact that he had negotiated 100:1 payoff odds, Saleh has now transformed a massive negative gap to a large positive gap and, well, there you go.
It is important to understand the potentially counter-intuitive lesson here: selecting a strategy of betting everything seems like the height of insanity, bet it can make sense if it means altering your win odds to a point that creates a positive gap with your payout odds.
The second lesson is that moving payout odds is critically important. Normally, an investor cannot do this by negotiating, as Saleh did (trading the human element). But they can do it using leverage, the easiest way to move payout odds. Just make sure you know what you are doing.
The startling result of applying this analysis to investing is that if you do not know how to invest then the best strategy if you unwisely choose to do so is to invest everything in a single trade. This is not advice, it is a logical conclusion.
This revelation helps explain the many proprietary traders and hedge funds that seem to lose spectacular amounts of money. They know full well that they have no idea how to invest and so they bet big. It is easier when it is other people’s money. If they get lucky then they will become rich and famous. If not they go get another job or new clients.
Investment size, Risk of Ruin and the Kelly Criterion
To recap, we have covered when to invest, when the payout — win odds are positive, and worked through a completely fictional example. The next step is examining how much to invest and this is related to the likelihood of losing all your money, frequently called ruin.
Consider the following example: two people, Khaled and Saleh, are similar in terms of retirement needs, say $100 each. They also have both received a monetary gift, Khaled got $1 and Saleh $2. Each day they each make an investment that at the end of the day will result in either a profit of $1 with probability 60 per cent or a loss of $1 with probability 40 per cent.
The question is: what is the probability that they will reach their target of $100, or conversely, that they will lose everything? The math is a little involved, but can be found on the internet under the name “Gambler’s Ruin.” The interesting result is that Khaled has a 67 per cent of losing all his money, or ruin, and Saleh has only a 44 per cent chance of ruin.
Why are these results interesting? It shows that even when there is a good chance of profit (60 per cent), that starting with too little of an initial investment has an extremely high probability of ruin. Incidentally, this is one of the reasons most start ups go bust, there is not enough cash kept in reserve, it is all poured into the business on day one.
What if Tarek joins this game, but he starts with $5? Well, his risk of ruin is a low 13 per cent.
These ideas are mathematically complex, but they are critical to understanding why so many investment strategies seem to make sense but end up failing.
Basically, even when a strategy can result in a profit, even a large one, the path to this profit can, and usually does, involve a number of losses. The investor who has not grasped this idea will lose their shirt as they invest far too large an amount given their balance sheets.
So the question becomes how much should a person invest? The method that is famous by far is the Kelly Criterion. Again, the math is a little convoluted, but it basically formalises the earlier discussion on how successful investors make their investment decisions based the gap between the payout odds and the winning odds.
Continuing the example from earlier, consider a two horse race whereby the first horse, Shadowfax, has 1:3 odds of winning and the second horse Mr. Ed has 3:1 win odds. If the payout odds offered on Shadowfax were 4:1 (as opposed to the 3:1 that the winning probabilities dictate) and therefore those on Mr. Ed are 1:4 then the discussion showed that the correct bet to make is on Shadowfax. What is left is to decide what percentage of one’s bankroll should be wagered.
Kelly looked at this problem and decided that the best way to tackle it is to consider a betting strategy that maximised the growth rate of winnings. After some mathematical black magic, the gap is basically defined as a ratio of the payoff odds to the winning odds. From there Kelly derives the optimal amount to bet is a ratio of the odds gap divided by the payout odds. For the example above this comes out to 6.25 per cent of the bankroll.
If you are confused think of it in these terms: Finding an investment edge is just the beginning of the battle. Developing strategies to determine how much to invest on each trade and how to avoid the risk of ruin even on a positive expected return are just as important. Unfortunately there is too much emphasis on the first issue and not enough understanding of the latter two issues.
The Kelly Criterion is useful in terms of understanding how to think about things but it is deeply flawed. As an example, if there is an investment that leads to a profit of $1 for each $1 invested with a probability of 95 per cent and a loss of $1 for each $1 invested 5 per cent of the time it looks like a great investment. The Kelly Criterion proscribes investing 90 per cent of your cash each time. The problem with this is that if you lose on the first round, it will take 8 more investment rounds, all of which need to win, to make back your capital. Now imagine that these investments have a one year horizon. Not good.
Developing an Investment Strategy: Trading in the Real World
The Kelly Criterion was introduced as the most famous formula for answering the question of how much to invest and then subsequently shown to be too volatile. Now we will delve into why and also took at an effective strategy.
The heart of the problem with the Kelly Criterion is the following behaviour investment return behaviour: a 100 per cent profit is reversed by a 50 per cent loss and a 50 per cent loss requires a 100 per cent profit to make up for it.
What this means is that if you make a -20 per cent loss and then make +20 per cent return you are still going to have a loss of -4 per cent.
The investment professionals will point out that they use the logarithm of returns. It is not necessary to understand what that means other than that this implies that investments are more likely to lose money than to make money.
A simple example of why the logarithm of returns is an academic fiction considers two cases of a $100 investment either losing $50 or returning $50. In the case of the loss, the normal return percentage would be -50 per cent. The log return would be -69 per cent. On the other hand a $50 profit would be a normal return of +50 per cent but a log return of only +41 per cent.
If you would like to believe that losing $50 creates a different return percentage than earning a profit of $50, then you need read no further. This section is not for you.
So what does it mean to an investor if they need larger positive returns to offset smaller losses, e.g. +100 per cent vs -50 per cent? The first immediate issue is that if prices, and hence returns, move dramatically and/or often (this is called high volatility) then clearly a strategy based on pure luck on its profit and loss will result in a net loss. Returning +50 per cent on a $100 initial investment followed by -50 per cent will result in a net position of $75, or a -25 per cent loss! Do it again, returning +50 per cent then losing -50 per cent results in a net position of $56!
This behaviour of total return to a symmetrical (equal up or down) increase in volatility is called being short gamma. You do not need to understand the mathematics behind this just the behaviour: short gamma is similar to selling insurance or selling options. You get paid an amount up front and every time something happens, you lose money.
Lesson number one is that, in simple terms, investing is not zero sum. An average investor, e.g. one who gets it right half the time, will not break even but will lose money. The more volatile the markets, the greater the amount he will lose even though he is right half the time.
Lesson number two, therefore, is that if you are investing in conventional securities such as equities or real estate, find something that is low volatility because you are naturally short gamma. Think Adnic and not Emaar (notes: the author owns shares of Adnic. The author has in the past traded shares of Emaar and may do so in the future.)
Lesson number two and a half is that the famous “cut your losses short and let your winners run” should be re-examined in terms of the structural changes to the portfolio that it engenders, ie it increases the short gamma position. There is something to be said that the structural behaviour of a portfolio is just as important as position management.
Lesson number three is to deploy a strategy to mitigate this inherent challenge. A simple one is popularly known as the portfolio rebalancing strategy. In this, the investments are bought and sold to bring them back to the original percentages within the portfolio.
For example consider an investor who wants to invest half his money in Adnic and half in Emaar. After one year, Adnic is up 10 per cent and Emaar has doubled. The resulting weightings would be Adnic 35 per cent of the portfolio and Emaar 65 per cent. The investor then sells shares in Emaar and buys shares in Adnic to bring the portfolio back to 50 per cent each.
This strategy became famous based on the idea that maintaining a constant mix of securities or assets made good sense. The real reason it does well is that it offsets the short gamma position described above. Buy selling more volatile stocks and reinvesting in lower volatility stocks this strategy mimics buying a put option and hence reverses the short gamma position.
For the option savvy reader, this is a delta one long gamma strategy. This is the best way to sell (not short) excess volatility in a long only market.
This article is not meant to be a primer on investing but really to provide insight to an institutional investment process. The departure from the relatively lighter reading of this column is more a reflection of the large gap between perceived investment philosophies and successful investment philosophies.
Sabah Al Binali is an active investor and entrepreneurial leader. You can read more of his thoughts at al-binali.com
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