Risk of Ruin For Dummies

A good percentage of  traders and investors get ruined because they are deceived into believing that they can be profitable in the longer term even if they are wrong more often than they are right provided they win multiples of what they lose, on the average. This is like playing Russian roulette with money. Understanding the simple math included in this post should be a top priority of anyone who plans to take risks in the markets. 

If trading and investing were that easy, everyone would be rich. But, unfortunately, markets do not like frequent losers and eventually ruin them.  For example, there is this investor who follows an analyst who is wrong 70% of the time but he makes 4 times as much as he loses when he wins.  The investor puts at risk 20% of his capital each time he follows a call from the analyst. It is easy to calculate that the probability of 5 consecutive losers that will wipe out the capital of the investor is equal to:

P(5 consecutive losers) = (1 – 0.30)^5 = 0.17 or 17%

i.e. the investor chances of losing his capital are 1 in 6, essentially a dummy playing a game of Russian roulette.

Playing with risk percent

Of course, the probability of ruin can be decreased significantly if the risk percent is decreased significantly. However, as the mathematics show, the potential for profit decreases proportionally. Here is an example:

Capital: $100K
Stock price: $100
Case 1: Risk percent: 20%  Case 2: Risk percent: 5%
Stop loss: 20%

Based on the above parameters, for Case 1 we calculate that the number of shares is equal to 1,000.  Now, if the risk percent is lowered to 5%, as in Case 2, the number of shares drops to 250.  Thus, the potential for profit drops proportionally.  

Playing with the stop-loss

One could decrease the stop-loss to 5% in the above example, in Case 2, to allow the same number of shares, i.e. 1,000, as in Case 1. But now, this is turning into a short-term trading timing game. If the stop is set too tight, the probability of it getting hit before the profit target is a lot higher. This is because, in order to make 4 times as much as the potential loss, the stop-loss must be set at $95 but the profit target at $120. Naturally, a $5 stop (5% of the price) may be hit before a $20 profit target (20% of the price) unless the timing of the trade is appropriate. Otherwise, the 30% win rate will not be maintained and it will be lower, probably 20% or even less. As a result, the probability of ruin will be adversely affected. You get the picture.

Mathematics is ruthless

Let us take a look at this problem from a strict mathematical perspective. If the average win to average loss ratio is 3, i.e. one makes three times as much as he loses on the average, then the minimum win rate for theoretical break even is when the profit factor is 1 or

pf = 1 = w x r/(1-w) => 3w = 1-w => w = 0.25 or 25%

where w is the win rate and r is the ratio of average win to average loss.

Thus, in order to just break even, the analyst who victimizes dummies must be actually right more than 1 out of 4 times. Now, and this is the fun part, in order to realize a respectable profit factor equal to 1.5, the same calculation gives:

pf = 1.5 = w x r/(1-w) => 3w = 1.5-1.5xw => w = 0.33 or 33%

i.e. one out of every three trades must be a winner. Even if r is 4, i.e. 4 times as much is made than lost on the average, the win rate to accomplish pf = 1.5 is calculated equal to 27%, which is more than one winner in every 4 trades.  

Next time someone promises high trading or investment returns although he is wrong more often than he is right, which is true for more than 95% of analysts, and his method is not short-term, medium frequency, trading but requires staying in the market for an extended period of time, like weeks or months, be aware that the probability of ruin is too high unless the risk percent is set very low, in the order of  5% or less, something that diminishes any potential for profit accumulation. Even then, someone can win the lotto and get ruined because of a long streak of losers.

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