Twitter poll on expectancy

Trading Journal

I had put a poll on twitter yesterday with options to choose from various combinations of Winrate and Risk:Reward(RR)

Here is the twitter link:

44% of the voters chose Option 4, 32% of the voters chose Option1, followed by Option 2 and Option3 respectively.

Before getting into the groove of things, I would like to elucidate a bit about ‘Expectancy’ of a system. This term was coined by Van Tharp and here it is:

Expectancy = (Win rate x Average winner) – (Loss rate x Average loser)

If we insert this formula with the numbers given in the poll, We get the following –

Expectancy of System 1 = (0.5×2.2) – (0.5×1) = 1.1 – 0.5 = 0.6

Expectancy of System 2 = (0.7×1.2) – (0.3×1) = 0.84 – 0.3 = 0.54

Expectancy of System 3 (I meant to give the RR of system 3 as 1:0.8 but gave it as 0.8:1 – we will stick to what was given in the poll)
= (0.8×1) – (0.2×0.8) = 0.8 – 0.16 = 0.64

Expectancy of System 4 = (0.35×4) – (0.65×1) = 0.75

So, what is this expectancy? Expectancy is how much one can expect to make on the average over many trades. Expectancy is best stated in terms of how much you can make per rupee you risk. Tharp talks in terms of R-multiples but let us just focus on it in layman terms.

If someone risks 1% per trade and their system expectancy is 0.5, it just means that over a large sample of trades, he is expected to make 0.5% (1% x 0.5) per trade. So, if he has 100 trades in a year, he is expected to make (100×0.5%) 50% that year.

Surface level analysis of the poll results

1. It is quite obvious from the above calculation that higher the expectancy, greater is your chances of making money in the markets. So, as a new trader, it is pretty easy to select the option # 4 from the choices. No brainer there.

2. Few people pointed out that Option 1 is better as it is easy on psychology of the trader. It is true to an extent but if one is striving for better risk adjusted returns, option 4 is the obvious choice again (especially for a pure trend follower). Different people, different choices 😊

3. Some people take profits on the way and they would have naturally gravitate towards a better winrate system with lesser R:R. The traders who trail profits will almost always have a lower WR but better RR system in hand.

4. As I always advocate that there are various ways to skin the cat, nothing is right or wrong here. We just need to pick what is comfortable for us. But, if one has to analyse logically, it is option 4. On a side note, one comment mentioned that we need to find system that have a expectancy like the choices mentioned 😊. Fair enough !!

5. The traders who are new to the market gets enamored by the high winrate for a very simple reason – typically, they don’t want to take losses (Forget about newcomers – even the experienced lot do not like to take losses). Their mind can never get around in accepting the losses. So, they naturally gravitate towards high winrate as high WR typically means more number of winners than losers. But, what they forget is the other side of the coin – the Risk:Reward. They lose more when they lose and win less when they win. This has many statistical implications. We will see that in detail in the next section of this post.

6. Winrate and Risk:Reward should be seen together. They are like peas and carrots, day and night – always go together. This is why I like this expectancy as it nicely clubs both the parameters to give a logical view of the system in hand.

7. Few people have voted for option 3 as they feel high winrate can give them the psychological comfort – again, this is just another way of telling that ‘I don’t want to take losses’. As some great trader mentioned. ‘avoiding losses in trading is like you want to breathe in but don’t want to breathe out’. But if it works for you, great !!

In-depth analysis of the poll

1. Most of the stock market strategies employ trend following concept and the pure essence of trend following is to let the profits run. So, the detailed analysis is based on that assumption.

2. First let us dissect what High Winrate really means. Typically, a high WR system will have low Risk:Reward (compare to a low WR with same expectancy). This is a given. But, this also means that the average loser of a high WR system is usually larger than a low WR system(assuming the timeframe and expectancy are the same). In a trend following system, high WR is usually achieved by giving so much room for the market to catch the trend. Statistically, bigger SL will have a huge drawdown potential (am talking about maximum drawdown) and if the max DD is high, it is very difficult to proceed with the system for two important reasons –

a) The recovery factor will be high – meaning the number of trades it takes to get back to equity high(again) will be more and the problem exasperates if someone is trading higher timeframe. People grossly underestimate time drawdown – but it is a different topic altogether

b) Compounding can be a big problem for a system with larger max DD for obvious reasons

3. When a system has a bigger SL (again assumption is that we are talking about pure trend following systems with trailing stoplosses) like a moving average crossover system, the time the market spends between the entry point and stoploss is huge. This has so many psychological ramifications –

a) It can create havoc to our mind as it will feel that we are always in loss (even though it is not realized). One can draw analogy with an investor who enters a stock and the stock is underwater for 2-3 years. It is a very tough phase for that investor if he is still holding it.

b) It can force a trader to make mistakes (not following the plan) and just letting the emotions take the driver seat (how many of us have heard this ‘ I felt uncomfortable in the trade and got out but only to see the market moving in my favor again’). So, wider SL is a fertile ground for all these mishaps in the thought process.

On the other hand,if WR is less with smaller average losses, it will diminish the active trade time in grey area (between entry and SL) and give us a big advantage mentally.

4. Lesser WR and higher RR generally means smaller losses (compared to high WR and low RR/same expectancy system) and consequently, a trader can be well equipped for the proverbial series of losses in a row. One can place large number of bets or trades before we reach out max limit. So taking randomness into account, we give ourselves a fair chance to be in the game. Not to mention, these smaller SLs will also cap the maximum DD and will keep it nicely in control.

The below picture shows the 95% probability of losing streaks for various winrates. Even a 50% winrate system can have 16 losses in a row over 5000 trades. It is not a question of how but it is a question of when.

Workshop

5. On the flip side, Low WR and high RR will never have even distribution of profits as the system will turn positive only with large profits. If one misses those trades, then the performance would be pretty dismal.

6. The interesting thing is that most of us would feel better with a system that produces more winning trades than losers. The vast majority of people would have a lot of trouble with the 4th system (even though it has the best statistical advantage compared to other systems) because of our natural tendency to want to be right all of the time.

7. As I always say ‘there is nothing right or wrong’ in the markets. We just need to choose what is comfortable for us. The battlecry is ‘how to find the one that is comfortable for us?’. Very simple – try them all with minimum size. Your mind will naturally cling towards the one that is comfortable for you 😊

Happy trading !!

Law of Large numbers and its implication in Trading

Trading Journal

Besides loving to trade and playing cricket, I am an ardent subscriber to the statistical concept – the law of large numbers. According to probability theory, the law of large numbers is a theorem that describes the result of performing the same experiment a large number of times. Moreover, the average of the results obtained from a large number of trials should be close to the expected value, and will tend to become closer as more trials are performed.

Let us look at some illustrations first before talking about its implications in trading.

Law of Large numbers and Coin toss

Law of large numbers is best illustrated by the example of a coin flip, which has a 50% chance of landing on heads. If we flip the coin twice, we have almost exactly equal chances of any scenario happening: heads twice, tails twice, or evenly split. The probability of getting 5 heads and 5 tails on ten flips is just 8% but that probability keeps increasing as we increase the sample size. If one flips the coin 100 times, the probability of getting 50 heads and 50 tails (P=0.5) increases to 70% and so on.

Below is a depiction of the Law of Large Numbers in action, for 1000 trials –

Workshop

As one can see, the more the sample size (trials) is, the probability of getting equal number of heads/tails increases.

Law of large numbers and casinos

Coin flips are interesting theoretically, but the Law of Large numbers has a number of practical implications in the real world as well.

A famous example is Casinos – who can forget the ringing sound of slot machines/clamoring laughters sound in the craps table of Casino halls. Casinos live and die by the law of large numbers. Each game has a house edge built into it, representing the average loss over the initial bet. Some sample edges are –

* Blackjack – 0.75%
* Baccarat – 1.2%
* Craps – 1.4%
* Roulette – 5%
* Slot machines – 5-10%

Over longer time frames, it becomes increasingly likely that the house edge will represent the casino’s profit margin.

Law of large numbers and trading

When it comes to trading, many misinterpret(in a negative way) this law of large numbers. They think that the more they trade, they would have more losses which leads to account blow-up. If a traders’ methodology has a statistical ‘edge’, and if he does not change the underlying parameters on the way, it is better for a trader to let the law of large numbers to work in his/her favor.

Trading decisions may appear to be binary – either buy or sell or up or down, but they are not. There are a critical variables which must be accounted for, such as how much am willing to lose/how to trail the profits, or in other words, what is the risk/reward of the trade and how do I manage the trade. So, there is something other than chance that comes into play when trading, and that is skill and technique.

It stands to reason then, that the better your skills and technique, the more you should trade. While Law of large numbers is important because it “guarantees” stable long-term results for random events, it follows that it is also important that our sample of trades is large enough to maximize the number of successful outcomes from our skillful trades and therefore maximize your earning potential. So, if it sounds so simple, why does traders do not allow this law to work for themselves? Why do they jump ships on the way(changing trading systems)?

Think about this for a second. The trader starts trading their plan with all good intentions. Things may or may not go well straight away, but sooner or later as the markets behavior ebbs and flows with/against the strategy’s strengths and weaknesses, losing trades will inevitably occur. At this point of time, the trader gets scared. They don’t like to give money back to the market, so they decide to try and modify the system to filter out trades like that last losing one. They begin to add indicators to charts, coming up with new ever more convoluted combinations, furiously testing to see what cuts out the most bad signals while leaving in place the good ones. A few times round this loop and suddenly, their chart starts to resemble something a seismologist might be more used to seeing than a price chart 🙂 As a result, again, the loop starts – they never let ‘law of large numbers’ to work as they dont stick around with one idea. Law of large numbers will be rendered meaningless if we keep changing the rules on the way.

Law of large numbers and behavioral difficulties

To let the law of large numbers work for us, we need to put trade after trade, over and over again without changing the underlying parameters. Just like onerously bolting on wheels on an automobile assembly line, making a series of trades can be very tedious. It may be hard to maintain self-control at times. It is understandable. We are human, and humans have a strong primal urge to seek out drama and action.

The kind of person who is attracted to trading is not the person who prefers tedium to excitement. This is the raw fact. If we are a trader, we’re probably the kind of person who has shunned a mundane 9-to-5 job for a more unconventional, adventurous profession (many come to trading for this reason). The excitement of working as a full time, active trader appeals to us. We thrive on the uncertainty and endless possibilities. What attracts us to trading, however, may also be a reason for our downfall, unless we are careful. We may be the kind of person who gets bored easily. It is quite possible that the long hours of self-control required to make a profit may be difficult to maintain. This is why many crave for action in the markets. So, eventually, they put on trades that is not part of their plan. It is exactly at this juncture, we break the ‘law of large numbers’ as it assumes that we do the same kind of trades(based on a definite idea) day in/day out. Essentially, we never stick around (or stick around with the same idea) for law of large numbers to work.

How to gain from Law of large numbers

It would be prudent if a trader(new and experienced alike) does the following –

1. Create a trading plan
2. Backtest the plan with large sample size (never fall victim to small sample skewing)
3. Determine your risk based on backtesting parameters
4. Create a money management plan
5. Stick to the plan to let the law of large numbers work

Final thoughts

It is illogical to subscribe to the theory that ” you’re only as good as your last trade. ” If you are going to trade for a living, there is no last trade, only the next trade. Whether, our last trade was a winner or a loser, it has absolutely no bearing on the outcome of our next trade.

Unlike gambling, a winning streak by a trader will NOT eventually be overcome by the parameters of the game, unless he somehow convinces himself that this is his inevitable outcome. Trading is not gambling where the house has the edge (let us not focus on the broker’s commission and negative sum game for a moment). Trading is a performance based activity that requires skill, technique, experience and above all, practice. Most important though, the trader must have the right attitude, focus, patience, and self-confidence, and then the trader will be the one who possesses the edge – not the other way around 🙂

Happy trading !!