Let us continue reviewing the modern methods of money management. All the methods described below are antimarthingale, i.e. they increase the risk size as capital size grows and decrease it as capital shrinks and involve risking a fixed fractional.
For instance, we have a maximal set drawdown in % of the capital. The method involves equaling the starting risk for the position to a fixed fraction of the set maximal drawdown:
Num_Lots = % Risk * (Capital – (1 – Max_%_Drawdown) *
Maximal_Capital) / starting_risk_per_unit_assets / 100.
If our current capital is $100 000, maximal reached capital $110 000 and maximal allowable drawdown 20%, we can risk a sum equal to 10% of the drawdown. Then our risk would be $1200 (10% * ($ 100 000 – 80% * $110 000)). Thus, if the risk per share is $0.1, we can buy 120 lots of 100 shares. If price changes were uninterrupted, transaction costs negligible, odd lots permitted and the traders’ timing perfect, then this method would guarantee tha drawdown never goes over the limit.
Another option of drawdown control is taking into account its maximal historical value
(with a fair reserve):
Num_contracts = Capital / (2 * Max_Drawdown + margin_per_contract)
Kelly’s method
This method defines the optimal percent of risk that should be employed to maximalise the “usefulness” function presented as logarithm of the capital. Relatively to gambling and further, to stock trading was developed by professor Edward Thorpe3.
In the trading game of doctors of sciences described in the previous article (where 60% of cases won and 40% lost the bet), the optimal bet according to Kelly is 20% of current capital. From Table 3 of that article we can see that the 50-percentile k-50 really reaches its maximum of 7940 when the stake is 20%. What’s not so smooth-looking is that 50% of drawdowns are over 79.09$ and the maximal drawdown reaches 99.43%. Are we willing to reach the maximal possible profit at the cost of losing 99% of the capital somewhere along the way? If we want to break the record of Larry Williams, then maybe so. As Ralph Vince explained that achievement: “He is one of the few persons really able to trade with fully optimal values and pass through the concomitant drawdowns” .
Kelly’ s method defines the percent of risk as^
Kelly%=%win – %loss * Avg_profit / Avg_loss
Hence we can estimate the position size:【交易知识www.irich.com.cn § macd.org.cn 收集整理】
Num_Lots = Kelly% * Capital / starting_risk_per_unity_of_assets
Thorpe recommends using % of risk within 0.5 * Kelly <= % risk < Kelly bounds. Table 1 shows the results that allow us to conclude that with risks 18% of Kelly and more our simple trading system is no longer profitable.
Table 1. Results of testing Kelly’s method
|
%risk* Kelly |
Net Profit |
Avg. profit/ Avg.loss |
Avg. trade |
Maximal drawdown |
Profit factor |
|
4 |
731586.50 |
1.8916 |
3870.828 |
-1004958 |
1.2445 |
|
6 |
1386439.00 |
1.728 |
7335.6561 |
-3618084 |
1.1368 |
|
8 |
1876666.00 |
1.6285 |
9929.4497 |
-9506103 |
1.0714 |
|
10 |
1814372.00 |
1.5704 |
9599.8519 |
-19437432 |
1.0332 |
|
12 |
1164496.00 |
1.5394 |
6161.3545 |
-31176880 |
1.0127 |
|
14 |
451504.00 |
1.5252 |
2388.9101 |
-42140292 |
1.0034 |
|
16 |
23984.00 |
1.5202 |
126.8995 |
-50536160 |
1.0001 |
|
18 |
-94656.00 |
1.5191 |
-500.8254 |
-61471408 |
0.9994 |
