Money Management
■ (^) When R/r > 1, the favorable impact of edge kicks in earlier for small %r in
fixed sizing systems
■ (^) When R/r > 1, the favorable impact of edge kicks in later for larger %r in fixed
sizing systems
■ (^) When R/r > 1, the favorable impact of edge kicks in earlier for small %r in
dynamic sizing systems
■ (^) When R/r > 1, the favorable impact of edge kicks in later for larger %r in
dynamic sizing systems
It is also found that for a typical system with a two‐to‐one R/r ratio setup with
a %risk of around 1%r and %win of 40 percent, a small edge can take anywhere
from to 300 to 600 trades before it begins to impact the system favorably. From
both these findings, the trader, in order to position him - or herself with the highest
probability of being profitable over the longer term, should:
- Trade with the smallest %risk per trade possible
- Allow the system sufficient time and trades to allow any edge and trade ad-
vantage to kick in - Conduct backtests with at least 500 data points in order to see the effects of
any edge in the system
effect of tradesizing on linear and geometric
expectancy
Let us now compare two setups with equal settings except for an increase in
tradesize.- For Fixed‐Sizing Systems:
Lin Exp = (R × win ratio) − (r × loss ratio)
a. For R/r →2:1 and %win = 50 percent:
Lin Exp = ($2 × 0.5) − ($1 × 0.5) = $0.5 (positive expectancy)
b. For R/r →2:1 and %win = 50 percent with Tradesize doubled:
Lin Exp = ($4 × 0.5) − ($2 × 0.5) = $1 (positive expectancy)
Therefore increasing tradesize actually increases expectancy if it is > $0 - For Dynamic Sizing Systems:
Return Ratio = (Reward Ratio)wins × (Risk Ratio)losses
Geometric Expectancy = Return Ratio (1/T)
a. For R/r ∼ 2:1, %win = 50 percent, %risk = 1 percent, wins = 26, losses = 49:
Return Ratio = (1.02)^26 × (0.99)^49 = 1.022
Geometric Expectancy = Return Ratio (1/T) = 1.022(1/75)
= 1.00029 (i.e., >1)
(We do not actually need to calculate the geometric expectancy to see if
we have made or lost capital. If the Return Ratio is greater than one, then the
geometric expectancy will also be greater than one. Values above one indicate
positive expectancy and values below one indicate negative expectancy.)
b. For R/r ∼ 2:1, %win = 50 percent, %risk = 5 percent, wins = 26, losses = 49:
Return Ratio = (1.10)^26 × (0.95)^49 = 0.9653