Expectancy Article

This article is one of the better explanations of expectancy I’ve seen:

Expectancy Article

The following is an excerpt from the above link which may stimulate some debate:

“Some people like to use the Sharpe Ratio to gauge the relative quality of one trading strategy compared to another. After extensive research, I have no choice but to conclude that the Sharpe ratio isn’t useful for objectively evaluating the merit of a system. It does have uses, but I do not agree that it should be used for determining overall merit.”

This also may be of interest:
Position sizing techniques

I am not affiliated with this company in any way.

I’d have to disagree with the article’s explanation and use of the Sharpe ratio. In the article, he compares the returns to drawdowns. That is technically not correct, because the Sharpe ratio compares the excess return over a T-bill and the standard deviation of returns of the strategy. Drawdowns happen when there are consecutive negative returns.

Therefore, it is correct to compare strategies with different return precentages and standard deviation of those returns. For example, System A returns 5% with standard deviation of 5% and System B returns 50% with sd 50%. We would be indifferent to invest with system A or B, because they have the same risk/reward characteristics.

In the article’s definition, expectancy does not account for risk in the way Sharpe does. Expectancy is just another name for the average. For example, take the following extreme example.

Average Win = 10,000; probability 51%
Average Loss = 10,000; probability 49%.

According to the article, there is positive expectancy. However, what was the initial capital? It makes a huge difference if the starting capital was 50,000 or 1 million. If the starting capital was 50,000, then the standard deviation of those returns is huge! But if the starting capital was 1 million, the standard deviation is much smaller. Therefore, if the starting capital was 50,000, then the sharpe ratio will be very small, because of the large sd. If the starting capital was 1 million, it would be much higher. The article scales the expectancy by the average loss, but that ignores the amount of capital risked. It just compares the expectancy with the average loss.

Further, we have to take into consideration the probability distribution of the wins and the losses. Because the average win and the average loss is just the arithmetic average, it is severely affected by the probability distribution. Therefore, there is potential that there are two systems with the same expectancy giving substantially different Sharpe ratios because of the difference of the return distributions.

The conclusion is that the Sharpe ratio is very useful in determining whether a system/strategy is useful. Expectancy, is also useful, but does not take into account the standard deviation of those returns. It only is useful in determining whether the strategy will generate a positive return in the long run.

Hi

for those of you using Amibroker for TA in addition to 123P, here’s my Van Tharp surrogate for volatilty based positionsizing.

I personally use this system ( slightly advanced version [;)] ) for all my trades since more than 3 years. If you like tinker around with the ATR periods or your personal risk tolerance.

I found not much added value when testing different ATR periods but maybe you see it in a different way.

I built first line of the formula at a time when true ATR was not available as a single function in AB .

The formulae calculate ATR on 2 period Simple MA and calculates the pivot point for the NEXT trading day ( p ) - from there 2 resistance ( r1 and r2 ) and two support levels ( s1 and s2 ) which also define the risk level.
Risk / stock in points is entry-price minus stop price.
Entry price is pivotpoint price + 0.5% of this price
Stop is s2 * 99% - this gives enough leeway even for most volatile stocks.

The final part of the formula is to assing the adequate amount of equity to a position according to :
a: underlyings shortterm volatilty
b: risk on overall equity with regard to the entry / stop levels.
In this case, I use 20K equity with a 2% risk per position.

Example :
entry price = 50
Stop price = 45
Risk = 5 points

Portfolio risk = 2% of 20K = 400 $
Positionsize = 400/5 = Position of 80 Stocks x 50$ = 4.000$
Hope you got the picture.

For use, just copy and place it in your AB trading system.
If you just need the values - use it exploration mode.
You need to assign extra lines in the exploration to see the values :

i.e :

Column5 = ((20000)2/100)/(p(100.5/100)-(s2*(99/100)))/10;
Column5Name = “Max Pos”;
Column5Format = 1;

// being Pivotpoint calculation, Support and Resistance;
p = (MA(O,2)+MA(H,2)+MA(L,2)+MA(C,2))/4;
r1 = (2p)-LLV(L,2);
s1 = (2
p)-HHV(H,2);
r2 = p +(r1 - s1);
s2 = p -(r1 - s1);

// being Positionsizing algorithm ;
PositionSize=((20000)2/100)/(p(100.5/100)-(s2*(99/100)));
// end of formula;

In addition, you can use the Commentary function in AB and the above formulae ( + some others ) to display a window for each chart with this content ( for a 20 K portfolio ):

Commentary window :

PIVOT POINTS, SUPPORT AND RESISTANCE

SYMBOL : ADRE
NAME : BLDRS Emerging M

DATE :05.01.2006


THESE POINTS ARE VALID FOR NEXT TRADING DAY

RESISTENCE POINT 2 : ----------------123.85

RESISTENCE POINT 1 : ----------------121.56

PIVOTPOINT -----------------------------------------120.67

SUPPORT POINT 1 : ----------------------118.38

SUPPORT POINT 2 : ----------------------117.49

ENTRY PRICE :----------------121.27

STOP PRICE :----------------116.31

PROFIT TARGET :----------------124.34

MAX POSITION :----------------20

TOTAL POS PRICE :---------------2,446

RISK REWARD RATIO :------------0.62

If you have any questions, pm me at sgfuchs@onlinehome.de

Good Luck


AB Chartwindow-main.doc (188 KB)

Privateer,

I also use volatility based position sizing. After reading Van Tharp’s book last year, I did some paper tracking with position sizes based on ATR(10). I compared it to the straight percentage-of-capital position size that P123 uses, and it definitely reduced the overall volatility of the portfolio. So I started using volatility-based position sizing for real trades about a month ago. So far, I’m happy with the results.

I risk 1.5% of total equity on each trade, and typically set my trailing stop at 5 x ATR(10). This was based on P123 sims using the ATR trailing stop formula. A stop of 5 x ATR usually came out with the best returns. So, for example, using $20,000 total equity, and assuming the ATR(10) is 50 cents:

5 x ATR(10) = $2.50
Amount risked = $20,000 x 0.015 = $300
Number of shares purchased = $300 / $2.50 = 120

As far as using pivit points for a target purchase price, I played around with that a little bit last year also, but it didn’t seem to improve my results any. I didn’t give it much of a chance, though. I abandoned it pretty quickly.

And as far as determining expectancy, I thought about that quite a bit. But if a system is designed and rigorously tested on P123, I didn’t see where calculating an expectancy was really necessary. Maybe I’m missing something.

Brian

Traderblues,

thanks for your comment - please see below the result of system test in AB WITH the pos. sizing as explained above and a second one with equal sized positions - same trading system and parameters :

With Privateer’s Van Tharp version :
These are the system stats ( pure technical , but on a list of about 1000 volume stocks ) when using a slightly different version ( my current one ) of the above mentioned system for positionsizing -
only long trades. Max. 10 positions.
5 day rebalancing , or stopped out by trading signals.

Notice the Exposure% and risk adjusted return. Altthough the system has only 30% winners, it still makes quite a bit of money with comparably low downside risk.

tested 01/01/05 - 01/05/06

Statistics
All trades Long trades
Initial capital 20000.00
Ending capital 48076.60
Net Profit 28076.60
Net Profit % 140.38 %
Exposure % 42.84 %
Net Risk Adjusted Return % 327.66 %
Annual Return % 139.24 %
Risk Adjusted Return % 324.98 %


All trades 106 (100.00 %)
Avg. Profit/Loss 258.99
Avg. Profit/Loss % 0.92 %
Avg. Bars Held 4.71


Winners 32 (30.19 %)
Total Profit 46025.71
Avg. Profit 1438.30
Avg. Profit % 6.90 %
Avg. Bars Held 7.22
Max. Consecutive 4
Largest win 7400.60

bars in largest win 20


Losers 74 (69.81 %)
Total Loss -18572.97
Avg. Loss -250.99
Avg. Loss % -1.66 %
Avg. Bars Held 3.62
Max. Consecutive 8
Largest loss -2567.33

bars in largest loss 7


Max. trade drawdown -5040.
Max. trade % drawdown -14.19 %
Max. system drawdown -6725.32
Max. system % drawdown -13.11 %
Recovery Factor 4.17
CAR/MaxDD 10.62
RAR/MaxDD 24.80
Profit Factor 2.48
Payoff Ratio 5.73
Standard Error 3058.51
Risk-Reward Ratio 11.14
Ulcer Index 7.12
Ulcer Performance Index 18.80
Sharpe Ratio of trades 1.19
K-Ratio 0.20

With equal weighted positions :
Same sytem but with equal-weighted positions
( 10% of equity ).
Statistics
All trades Long trades
Initial capital 20000.00
Ending capital 20380.43
Net Profit 380.43
Net Profit % 1.90 %
Exposure % 21.11
Net Risk Adjusted Return % 9.01 %
Annual Return % 1.89 %
Risk Adjusted Return % 8.96 %


All trades 322 (100%)
Avg. Profit/Loss -0.30
Avg. Profit/Loss % -0.01
Avg. Bars Held 4.50


Winners 116 (36.02 %)
Total Profit 6071.01
Avg. Profit 52.34
Avg. Profit % 2.82 %
Avg. Bars Held 6.41
Max. Consecutive 6
Largest win 428.00

bars in largest win 8


Losers 206 (63.98 %)
Total Loss -6167.66
Avg. Loss -29.94
Avg. Loss % -1.59 %
Avg. Bars Held 3.43
Max. Consecutive 21
Largest loss -311.07

bars in largest loss 2


Max. trade drawdown -311.07
Max. trade % drawdown -15.64 %
Max. system drawdown -834.46
Max. system % drawdown -3.99 %
Recovery Factor 0.46
CAR/MaxDD 0.47
RAR/MaxDD 2.25
Profit Factor 0.98
Payoff Ratio 1.75
Standard Error 212.68
Risk-Reward Ratio 5.65
Ulcer Index 2.12
Ulcer Performance Index -1.65
Sharpe Ratio of trades -0.20
K-Ratio 0.10

Brian, aside from these two simple examples, which demonstrate the impact of positionsizing fairly well,

let me just briefly explain about the profit-target / pivotpoint idea I use in determining my initial position in stock :

Obviously these points are changing every day due to volatility and hence the positionsize on one day might be different then for the next day. However - when I get a buy signal ( either in AB or through weekly rebalancing in p123 ) I want to act the next day. So I need some kind of determination of positionsize - this has to be seen with regard to my overall risk management rules for the portfolio.

I know that p123 fairs well with more or less equalweighted positions in backtests, but knowing also the impact of the pos. sizing rules as explained above on almost any system I’ve tested so far, I want to use my system for the initial determination of the positionsize.

I also explained at another thread, that I do scale in and scale out of some positions. Using this system helps me, because it gives every day a recommendation, how large a position should be and not to violate my risk rules.

Of course, I’m not adjusting my positions every other day, but as long as a trade lasts, I check variations in the size. If the become too large compared to the initial position, I need to do something about it by either reducing or increasing my exposure to a certain stock.

I know - sounds complicated, but it is not , and it creates ( at least for me ) some added value.

regards
Stefan