Un cierto “apogeo” de los mapuches

12

RISK OF RUIN

I hesitate even to bring up this subject in a book that is focused on providing practical money management knowledge and applications. I often receive calls from wannabe know-it-alls who will discuss a method so intelligently and then bring up the subject of risk of ruin. Basically, my reaction is “who cares!” Risk of ruin has absolutely zero practical application in trading. Running through the calcula- tions to determine the risk of ruin on any particular method is also completely useless. Unlike most other applications contained in this book, there is no call to action with the risk of ruin. It just “is.” It is a statistic that is there. There is a statistic for just about every possi- ble dotted and crossed “t” in the realm of trading. Most are use- less. We might look at them and say, wow, I didn’t know that. But beyond enticing a wow from us, they have no further value. Such is the case with risk of ruin.

So, if it is worthless as a statistic, then why even mention it in the book? My purpose is to convince you that you should not devote any time or energy to this risk. By devoting this portion of the book to it, I hope to correct some misunderstandings of the subject. I hope to save those who are stat heads some valuable time in the future. For those of you who have never heard of risk of ruin, you might do your- self good not even to read this chapter. However, I am quite sure cu- riosity won’t let you do that.

The definition of risk of ruin is the probability that the account will draw down to a state where no further trading can take place. An example is trading a $5,000 account in the bond market that has a margin requirement of $3,000 per contract. If the $5,000 account draws down to below $3,000, the account is ruined and trading the

bond market must cease. The risk-of-ruin calculations take into con- sideration the sequence of wins and losses as they occur and recalcu- late the risk of ruin based on the sum of those wins and losses. The greater the account over the $3,000 margin requirement, the lower the risk of ruin. (This is a rough example, but it is as close to practi- cal as we will get.)

The only place I have seen an extensive discussion on this subject is in Ralph Vince’s book Portfolio Management Formulas. If for some reason, the reader wants to grasp the math behind this statistic, I suggest going to that book. The present chapter uses only the most simple math examples to generally illustrate how risk of ruin works and why it is useless. To illustrate what risk of ruin is, we will refer back to the illustration of the coin-flipping game where we risked 25 percent of the entire $100 stake without decreasing the size of the next bet after a losing flip. That example had us risking $25 on the next four flips regardless of winning or losing. For our $100 account to be ruined (i.e., left with nothing else to bet or for that matter be rendered so low that we are unable to continue betting), we would have to lose four times in a row.

We can easily calculate the risk of ruin in this scenario. For the first three trades, the risk of ruin is zero. It is impossible, assuming that the numbers and rules cannot be altered, that we draw the ac- count down so far that we cannot take the fourth trade. However, once we take into account the possibility of the fourth trade, the risk of ruin becomes 6.25 percent for the next four trades. Starting with $100 in the account, prior to making any bets, there are 16 possible combinations of wins and losses. However, only one possible combi- nation will render the account ruined. That combination is: Loss, Loss, Loss, Loss.

Any other combination of wins and losses will not render the ac- count ruined. Therefore, our risk of ruin, prior to betting, is 6.25 per- cent. = However, something interesting happens; this risk of ruin can never get any smaller with this situation. Even if the bet- ting yields 100 wins in a row, the fact that 25 percent of the account is being bet without a $ decrease during losing trades will never take the account away from the possibility of being ruined on the next four flips of the coin. Further, as soon as one losing flip is incurred the risk of ruin immediately jumps to 12.5 percent because there only eight possible outcomes of the next three flips. Only one of those outcomes can render the account ruined: Loss, Loss, Loss. No other outcome will render the account ruined within the next three trades.

174 RISK OF RUIN RISK OF RUIN 175 If the second trade is a loss, the risk of ruin immediately jumps to 25

percent. If the third trade is a loss, there is a 50 percent chance that the next trade will be a losing trade and therefore a ruined account. If there are three trades in a row that are losers and the fourth trade is a winner, it will not start the process all over. Instead, since total

risk of ruin can always occur within four flips of the coin in this sit- uation, it simply drops the fifth trade back off the record and re- places it with the win. In this situation, the trade scenario is as follows: Loss, Loss, Loss, Win.

Recall that every time we lost, we lost $1 for every $1 being bet, but we won $2 for every $1 being bet on winning flips. If the preced- ing sequence were the outcome of the first four flips of the coin, our account would have gone from $100 to $75 to $50 to $25 and then back up to $75 after the winning trade. Since 25 percent of $75 is less than the original $25 we started to bet with (no decrease), our next bet is still going to be $25. Therefore, our risk of ruin drops back to 12.5 percent over the next three trades (i.e., it would only take three losers in a row to render the account ruined).

This scenario does not give you a good understanding of the whole picture, though. The more trades you take into consideration, the higher the probability of ruin becomes. In the example, we came across another scenario that would render the account ruined by tak- ing in a sequence of seven trades instead of four: Loss, Loss, Loss, Win, Loss, Loss, Loss. This scenario would render the account ruined. The account would go from $100 to 0:

$100 75 50 25 75 50 25 0

In fact, the more trades that are taken into consideration, the more probable it is for risk of ruin. Taking into consideration six trades instead of only four, prior to any of those trades being taken, the probability of ruin increases from 6.25 percent to 9.375 percent.

At seven trades, the probability moves to 12.5 percent and includes the additional sequence besides the four losses in a row that will yield the account ruined.

I used this example because it is not a real-life option for real-life traders. The reason it is not a real-life option for traders is that the real risk of ruin is real great. How many needed to see the risk-of- ruin numbers to decide not to trade this ludicrous scenario?

If a trader applying the risk of ruin to trading places the account where there is anything but an absolute fraction of a fraction of a chance that the account will go into a ruinous state, the account is too small. This is the only use for the risk of ruin and it is not the stat but whether it even exists within the confines of trading. It did not take a genius to figure out that trading a bond system where the margin is $3,000 with a $5,000 account places the account at risk to ruin in 99.9 percent of the situations.

The question then arises, what if a trader has only $5,000 to trade with. What then? Isn’t the risk-of-ruin calculation important to better determine which method or markets to trade in that situation? In the- ory, maybe. However, there is one thing wrong with the entire risk-of- ruin calculation. It truly has no effect on future trading. You can run the risk-of-ruin calculation on a particular situation and come up with a risk of ruin of say, 28 percent. Then, you can run the risk of ruin on another situation and calculate a 23 percent risk-of-ruin prob- ability. Which one will you decide to trade? It is obvious isn’t it? The 23 percent risk-of-ruin situation should be the one. So you start trad- ing and as soon as you start trading, the thing goes into a

and you are ruined. Meanwhile, the method with the 28 percent calcu- lation went on a nice run and would have lowered the risk of ruin to only 10 percent because of the increased capital in the account.

In this scenario, the risk-of-ruin calculation didn’t help you at all because the calculation can only take into consideration past trades. It is somewhat like optimization (see Chapter 14) or optimal f (see Chapter 5). The whole calculation is based on past data. One small deviation from that past data and the calculations are way off. Fur- ther, the calculation is taking into account a long history of past trades. If you were to take the worst year of trade statistics instead of the entire history, you might find that the risk of ruin for those sta- tistics was 50 percent for your current situation now. Bottom line when dealing with these types of numbers is that it is all a gamble. Traders will do far better using a little common sense and logic when looking at trading methods with small accounts.

176 RISK OF RUIN

On a side note, my suggestion for small accounts would be to stick to trades that, in and of themselves, have a high probability of making money. This does not involve system trading. It involves disparity in certain market situations. It involves unique opportunities that don’t come up often. For example, in January 1997, the price of platinum came down and actually dipped below the price of gold. Without get- ting into the fundamentals of this opportunity, suffice it to say this is a rare thing. Platinum trades at an average of $50 to $100 per ounce more than gold. To take advantage of this, you simply buy platinum and sell the gold (actually, you buy 2 platinum as it only trades in 50 oz. contracts compared with 100 oz. contracts for gold).

There are other rare opportunities like this that small accounts can trade with little risk and high probability of winning as well as profit opportunity. I certainly don’t need a risk-of-ruin calculation comparison when trying to decide to take trades like this or to trade an overnight bond system with a of $3,000 in a $5,000 ac- count. A little common sense and logic will carry you farther than the risk-of-ruin calculations.

13