One trade

For one trade the expectancy is a theoretical value, as it assumes probabilities for losing and winning. There is only one practical outcome, which is statistically insignificant, and you cannot calculate the expectancy without assuming ex-ante probabilities.

The R-multiple depends a bit on the mechanics of the trade. If you enter long for 2 contracts with a logical stop of -10 ticks, a 1st profit target of + 10 ticks with adjustment to breakeven, and a second profit target of +20 ticks, the outcome for a random market after a larger number of trades would be close to:

-10 ticks = 50%
+10 ticks = 25% (first contract)
+20 ticks = 12.5% (second contract splits between 0 and 20 ticks)
+- 0 ticks = 12.5%

The weighted reward-to-risk is (0.125*20 + 0.125*0 + 0.25*10)/ 0.5*10 = 5:5 = 1:1 Reward-to-risk is needed to calculate the edge of a trading system. The edge is the expectancy.

Expectancy = Average winner * Winning percentage - Average Loser * Losing percentage or by requiring a positive expectancy this equation can be transformed to

(1) R-Multiple > 1/winning percentage - 1

Example: If your winning percentage is 40%, your R-Multiple required to breakeven would be 1/0.4 -1 = 1.5 This example is before transaction cost and slippage. This is the easy part.

Many similar trades

If you have a larger number of similar trades, you can calculate a statistically based expectancy. This is based on an ex post probability which is a result of the trades. Note the difference with one trade.

If you are trading an automated system, always using the same stop and the same profit targets, you can calculate the correct reward-to-risk ratio by empirically counting the number of outcomes for each of the four possible results (I stay with my no-slippage model). The relative frequency of the outcomes is an approximation of the probability, and you can again calculate the reward-to-risk ratio by comparing the added positive outcomes with the added negative outcomes:

(2) R-Multiple = (added $ of winning trades/ number of winning trades)/ (added $ of losing trades/ number of losing trades)

Many different trades

If there are many different trades, you may want to evaluate them. For technical and other reasons your risk will sometimes be 2.3%, sometimes 1.4% of your account. I think that Van Tharp wants to make these trades comparable by not using the $$ outcome, but the outcome measured in multiples of R.

This is a way of normalizing the position sizing of the trades. If an undisciplined trader doubles position size and luckily wins, this for sure affects his account. In this case Van K Tharp - as I understand him - does not want to take into account the unduly increased position size, so he measures the outcome in terms of R achieved.

Now, there is a catch.

Expectancy

The idea of calculating an average R-Multiple is mathematical nonsense. But it can be a valid educational concept. The expectancy can only be calculated by taking into account both winning percentage and R-Multiple. A scalper with a high winning percentage does not need high R-multiples, as he relies on a hihg winning percentage. The high winning percentage will even allow him to increase his position sizing, because the probability of a larger drawdown is reduced. The scalper may actually tolerate a higher risk per trade, without increasing the risk of ruin*).

So why does Van Tharp calculate R-multiples?

Psychological Barriers

Most beginning traders do not let their profits run, and achieve bad R-Multiples. You will find some journals here that show R-multiples < 1. It is psychologically easy to take a quick profit, and have a large loss every 5 trades. You are emotionally rewarded with 4 successes and only 1 failure! Van Tharp uses this method as a way to monitor the trader's performance to cope with loss aversion and not letting profits run.

It is an educational tool

And there is another reason to use this method. To complete evaluate a trader's edge you would need to know the winning percentage and the R-multiple. To get a good approximation for the winning percentage, you would need something like 100 trades if you search for statistical significance. So you cannot give the trader immediate feedback on his performance. The R-Mulitple can be used even after 1 trade and is significant. So it is a concept that can be used to train traders.

Why does he choose the median?

He could choose the arithmetic average, the geometric average, the median, the mode, etc. No importance, the median can be observed without calculating anything.

And the mathematics?

There is little valid mathematics in the books of Van K Tharp. If you are really intested in the subject you should start with "The Mathematics of Money Management" by Ralph Vince. Not an easy read though, but very important. I am slowly digging through this, interrupted again and again by other priorities.

*) not known by many traders: Let us assume two trading systems:

system 1: winning percentage 70%, R-Multiple = 2
system 2: winning percentage 42%, R-Multiple = 4

Both systems have the same expectancy of 1.1R (which is excellent, 0R stands for break-even). However, the first system has a better Sharpe Ratio, so you can actually trade it with a larger position sizing, without increasing your actual risk (measured in terms of max. drawdown).

Note that mathematics is in contradiction with the methods of Van Tharp.

Who is able to calculate the position sizing for the 1st system relative to the 2nd, so that the risk of ruin becomes equal?

fat tail
how do you calculate exp, based on w% and r-m?

"And the mathematics?

There is little valid mathematics in the books of Van K Tharp. If you are really intested in the subject you should start with "The Mathematics of Money Management" by Ralph Vince. Not an easy read though, but very important. I am slowly digging through this, interrupted again and again by other priorities.

*) not known by many traders: Let us assume two trading systems:

system 1: winning percentage 70%, R-Multiple = 2
system 2: winning percentage 42%, R-Multiple = 4

Both systems have the same expectancy of 1.1R (which is excellent, 0R stands for break-even). However, the first system has a better Sharpe Ratio, so you can actually trade it with a larger position sizing, without increasing your actual risk (measured in terms of max. drawdown). "

thanks

alejo

fat tail
how do you calculate exp, based on w% and r-m?

The expectancy is the average outcome per trade. Let us take the system 1 with a winning percentage of 70% and a R-Multiple of 2. Out of 100 trades you would expect 70 trades with a winning amount of 2R and 30 trades with a losing amount of R. Therefore the expectancy can be calculated as

E = (70 * 2 * R - 30 * R)/100 = 0.7 * 2 * R - 0.3 * R = 1.1 * R

This is the raw expectancy.

The real results are also affected by commission and slippage, therefore the net expectancy is lower than this amount.

The impact of commissions and slippage can be dramatic for scalpers, but barely affects swing traders or investors.

thanks fat tails

i was wondering how calculate the expectancy of this 2 possiblities:

1)
3lot
risk -3t
t1+1t 2lot
t2 +2t 1lot

2)

4lot
risk -3t
t1+1t 2lot
t2 +2t 1lot
t3 +3t 1 lot

Attachment 127519

is it ok that i have done?the first system 3lot exp is 2.8 and the second
2.75?

thanks

then the formula is :
Exp=R*W%-(1-W%)
??

You cannot calculate an expectancy without a winning percentage.

thanks, i have calculated first with random at 50% and then with my measures of %80

i have enclosed the new excell v2 with a yellow shadow area, where i have added the rewor, risk, and expectancy exp2, but i do not know if i did it right and why there s a difference between exp, and exp2
to clarify a little, in both strategy 3L and 4L, i split in two: fix and trail, in fix i let the stop loss at -3 always and the other i close it before when it become a loser trail it the stop to -2,-1 and be

thanks again for your time and your help

alejo

Attachment 127520

I do not understand your table, as I do not speak Spanish, maybe you can post it in the Spanish part of the forum.