Practical Position Sizing Based on the Risk Ratio

In the blogosphere and elsewhere one can find many articles about optimal position sizing and on maximizing equity growth via the use of fancy math, for example the Kelly ratio. Traders and investors should ignore such supposedly optimal methods of sizing positions primarily due to the fact that most of those who write about them are just trying to appear smart while not being aware of the dangers they pose due to the lack of real trading experience and knowledge of probability theory.

I have in the past written a few posts about the Kelly ratio and the misconceptions surrounding optimal position sizing methods. I will briefly only mention the fact that although the longer-term win rate may converge to a specific value, in the meantime it can stay very low for extended periods of time. During such low profitability periods, optimal trading methods based on calculation of average values of parameters may overestimate position size and cause excessive drawdown levels and for all practical purposes account ruin, although, in theory only, such methods do not reduce available capital to zero.

A sub-optimal but practical way of sizing positions is via the use of what I call the Risk Ratio. This is the ratio of maximum risk percent on available capital per position divided by the position stop-loss, expressed as a percentage of entry price

RR = Maximum capital risk percent/Stop-loss percent = Rc/Rs

For example, if Rc, the maximum risk percent on available capital, is equal to 2%, meaning that one is willing to risk on a particular trade  only 2% of current bankroll, and Rs, the percent stop-loss, is also 2%, meaning the a stop-loss is placed at 2% of the entry price, then RR = 1. In this case the position size is equal to available capital divided by the entry price.

The formula for position sizing is then as follows

N = C x RR/P =  (CxRc)/(PxRs)                 (1)

when N is the number of shares (rounded to an integer value), C is the available capital, RR is the risk ratio and P is the entry price.

Example

If one is willing to risk only 2% of account but the stop-loss is set at 4% because that is dictated by technical analysis or other factors, then RR = 0.5 and, as a result, according to formula (1), only half of the available capital will be used to buy shares.

Debunking some naive claims

Note that the number of shares given by formula (1) depends only on risk of loss and not on profit target objectives. Traders who mostly rely on technical analysis and especially chart patterns and for this reason have a low win rate but claim they make on the average multiples of what they lose are still constrained only by their loses for their position sizing.  This means that they may need to trade more frequently to accumulate the same wealth as a trader with a high win rate and equal risk and reward. To see this let us consider the two cases:

Case A: win rate = 30%, reward = 3, risk = 1 (usually a technical analysis type)

Case B: win rate = 70%,  reward =1, risk =1 (usually an algorithmic trader)

In case A the expectation is equal to

E1 = 0.3 x 3 – 0.7 x 1 = 0.20

In Case B the expectation is higher

E2 = 0.70 x 1 – 0.3 x 1 = 0.40

Since the total profit is equal to expectation times the number of trades, the trader in Case A must trade twice as frequently as trader B to make the same profit. But this is NOT the only problem here. The trader in Case A has a much higher probability of ruin due to the low win rate. Actually, it turns out that the ratio in the case of risk of ruin due to a streak of consecutive losers is about 70, meaning that the risk of ruin for same Rc is 70 times higher in Case A when 20% of the capital is risked on each position. The ratio exceeds 2 million when 2% risked is used. This debunks some naive claims that a low win rate combined with a high reward/risk are as or even more advantageous than high win rate with reward/risk close to one. Such arguments are usually motivated by ignorance of the mathematics and a misunderstanding of the trading process.

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