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The four horsemen of apocalyptic position sizing used by professional investors

4 horsemenDespite picking a fair share of good stocks, it is still tough to generate some consistent serious alpha. Picking the right stocks and exiting them well tells You how often You win. How much You win, however, is a function of how much You bet. Some professional investors pay surprisingly little attention to their bet sizes. Below are four algorithm often practiced by professionals that can

  • Four popular bet sizing algorithms used by professionals that have negative gain expectancy
  • Size does matter in the markets: 1$ or 100 will have a different outcome

 

When it comes to bet sizing, there are only two sizes: either too much, either too little. As a professional short-seller, position sizing is mission critical. Successful positions shrink. Not only do they contribute less and less, but they also tilt exposures (net & net Beta). To add insult to injury, they become less noticeable. On the other hand, unsuccessful positions balloon. They immediately hurt. So, I have spent years studying the science of bet sizing. I sought to learn from other investment professionals. It eventually dawned upon me that Long biased people rarely ask themselves the same questions. For them, bet sizing does not have the same degree of urgency. Worse even, it became apparent that some position sizing algorithms had outright negative expectancy, or nasty side effects that they were never even aware of.

Aral Sea Ships

Insufficient liquidity

Horseman 1: Liquidity. If You can’t get out, You don’t own stuff. Stuff owns You
Getting into a position is like buying a boat, or a second house. You can do that any day of the week. Now, selling a boat is tough (been there, done that). It may take time to build a position in a stock. Time is an expensive luxury few market participants can afford when they want to liquidate.So, no matter how attractive a story may be, if you can’t exit easily, just don’t enter.

Rule 1: don’t size your positions so that they may go Hotel California on You:
“You can check-out anytime You like, but You can never leave!”, Don Henley, Hotel California

 

 

Bernie-Madoff-mugshot

Example of long conviction

Horseman 2: High conviction: feel-good position sizing
Disclaimer: this position sizing is used by the greatest and the worst investors. The classic rationale is: “if You believe in something, then you should go big or go home”. What else is it but a feel good position sizing algorithm ? Risk is not quantified but subjectively assessed. The problem is mental accounting, or the constant emotional revisionism of the situation. Jack Welch said: “what can be measured can be improved”. If You can’t quantify your risk, then don’t expect improvement in consistent alpha generation capability.

The greatest investors also use conviction as a position sizing algorithm. The only difference is that they express conviction in units of risk. They quantify risk first and then put chips on the table according to their perception of the reward. If an idea does not pan out, risk can be parred down.

 

Horseman 3: Equal size: one-size-fits-all and the volatility roller coaster
This position sizing algorithm will not bring ruin, but it has negative side-effects that may prevent You from achieving your obejctives in terms of performance, attractiveness to investors and quality of life…

Equal weight is a form of laziness:
First, let’s look at the math behind equal weight. All trading systems boil down to their trading edge (Avg Win% * Win% – Avg Loss% *|Loss%|). Since all bets are equal, equal weight implicitly puts emphasis on the signal, and excludes the value of money management. In other words, stock picking has to be consistently above 50% to absorb losses and generate a profit. Unfortunately, no system works all the time. So, equal weight carries cyclicality in performance.

Ignoring volatility at the position sizing level invites volatility in the portfolio
Not all stocks have the same personality. Some are more volatile than others. For example, internet stocks tend to be much more turbulent than utilities. If all positions are sized equally, then the most volatile stocks will drive the volatility of the overall portfolio. Morality, ignoring volatility at the position sizing level will in turn invite volatility in the portfolio.

Horseman 4: Average down, martingale and the certainty of ruin
Rookie gamblers always come up with some elaborate scheme to break the casino. It is usually a variation on the theme of doubling down after each loss. They believe that the losing streak will end and they will recoup their losses. This position sizing algorithm is known as martingale. Let’s look at the math behind this algorithm

1. Adding to a losing position reduces the hit ratio
2. even if You had infinite capital, the most favourable outcome would be break-even. First, do You have infinite capital ? Second, any other outcome before the most favourable one carries an interesting probabilistic property called certainty of ruin
3. Doubling down means adding to losers. Resources have to come from somewhere, probably winning trades. Books written by successful market participants always emphasize “cut losers, ride winners”. Do You know any successful market guru who says “cut your winners, ride your losers ?”

In conclusion, there is a reason casinos have gold, marble, paintings from masters and gamblers declare bankruptcy. Double down on losers and You will go broke. One more thing about probabilities, it’s not about if, it’s about when.

Conclusion
Size does matter in the markets. Not paying enough attention to position sizing has consequences that range from unpleasant volatility to certainty of ruin. Position sizing is not a glamorous topic, but in highly competitive sport, every little bit of edge counts

Track record 2015 – 05 – 22

Nothing speaks louder than a track record. There is no shortage of interesting indicators, strategies, ideas, but in the end, we trust only one thing: track-record. Track record sheds a crude light over two things: robustness of the strategy and quality of execution. Here are the things I have committed to:
  • run this strategy live with real money: 3/4 of my life savings
  • publish the track record on our website
Week in review: May 22nd
Attached is a pdf of the track record:  Track Record 2015 – 05 – 22
Forex impact:
Cash deposits are held in Euro, GBP and JPY. Base currency is denominated in USD. Converting everything into USD would eliminate the currency risk. Forex is however one more tool in the toolbox. EUR and GBP trends have turned bullish against USD. This may juice up NAV growth. This week, it detracted -0.6% from performance.
Performance analysis:
Performance excluding Forex impact was +1.01% inception and month to date. It was +0.48% YTD, inclusive of Forex impact. Both Long and Short books have contributed. Portfolio is still in ramp-up phase. No open position has been either reduced or closed yet. Hit ratio is 32% and 67% on the Long and Short sides, respectively.
Risk:
Cumulative risk is -6.69% to the equity. Risk-per-trade remain below budget (-0.68%) at -0.24% and -0.3% on the Long and Short side, respectively.
Customised metrics measure risk. Sharpe, Sortino, Treynor are the right mathematical answers to the wrong question: volatility is not the enemy. Formulas of the Common Sense ratio, amygdala index and other risk measures will be disclosed in ulterior articles.
Exposures
Net exposure is +60%. Directionality is intentional. Correlation between ETFs is low. For example, correlation between uranium long and Dow Jones Transportation short is low. If securities were correlated, i-e constituents of an index, then relative instead of absolute series would be traded. This would collapse the net exposure to +/-20%.
Signals are taken as they appear. The vast majority of signals are longs for now. Short signals with expensive borrow (>5% ) are rejected.
Gross exposure is now +138%. It will rise as long as the quality of performance (measured by the amygdala index) warrants it. The amygdala index is an asynchronous version of the ulcer index.
Productivity
 A time-sheet keeps precise record of time and activities. This week, it took 2 hours 49 minutes to reconcile trades, process signals and trade. Friction can be further reduced.
Time invested to build the file is not recorded (approximately 29 hours 38 minutes), as it will be amortised over the lifetime of the spreadsheet.
Strategy synopsis
This strategy was developed on the short side in order to underperform the longest bear market in modern history: Japan equities. It follows a philosophy of essential simplicity: complexity is a form of laziness.
The strategy is composed of two modules: entry/exit signals and money management.
Signal Module
Entry and re-Entry conditions are simple. It is easy to get in, but hard to stay in. Entry is a choice, exit is a necessity
  1. Regime definition for all constituents in the universe
    1. Bullish: higher highs & higher lows
    2. Bearish: lower lows & lower highs
  2. Entry: “Buy on Weakness” (Bullish Weakness) and “Short on Strength” (Bearish Strength)
    1. Long: enter the day after a swing low has been recorded && dominant trend remains bullish, “Bullish weakness”
    2. Short: enter the day after a swing high has been recorded && dominant trend remains bearish, “Bearish Strength”
  3. Exits: There are three types of exits:
    1. Isometric staircase stop loss: all open positions are simultaneously closed. Stop Loss is calculated as the swing value +/- an allowance for volatility in Average True Range (ATR).
    2. Trend reversal: if a trend reverses from bullish to bearish, all Long open positions are closed. This is the highest possible point at which positions can be logically closed. Symmetrical rules apply on the short side when a trend reverses from bearish to bullish
    3. Risk reduction: our primary concern is risk. Every new position adds risk. So, the priority is to reduce. We have developed a proprietary adaptive exit threshold (AET) algorithm that optimizes the quantity to be closed, while reducing risk to near zero level
  4. Re-Entry: re-entries are allowed only after a partial exit has taken place. Re-entries are only possible along the trend
  5. Stock selection and order priority:
    1. Signals: every day, signals on ETFs, Forex and major indices are published on our website. Candidates come exclusively from that list. The exact same information is available to everyone, including myself.
    2. Priority: Candidates are ranked by position size: the bigger, the better. Borrow check happens before position sizing. Thin expensive borrow is an indication of how crowded trades are. All trades with borrowing fee above 5% are rejected. This is the only difference between Longs & Shorts.
Money Management
Money is made in the money management module. Risk is not an abstract debate over an investment thesis. Risk is a series of numbers, made visual so as to stay painfully compelling at all times. Our basic philosophy is: profits look big only to the extent that losses are kept small. Tomorrow’s reward cannot be predicted, but risk can be managed today. Our Alpha Secure proprietary position sizing algorithm responsively manages risk (per trade and in aggregate), exposures (Gross/Net), position sizes in real time.
  1. Alpha Secure: This proprietary position sizing algorithm is so impressive that the company was named after it. This tool weathers drawdowns and re-accelerate during winning streaks.
  2. Net exposure:
    • This is an absolute directional Long and Short model: both sides are expected to generate alpha. Directionality (Net +/-100%) is only tolerated because of the low correlation between constituents (ETFs). If the universe was composed of stocks within a index, we would run relative series and collapse net exposure to +/- 20%
    • Net exposure is a direct function of signal generation. For now, the vast majority of signals are bullish. I woke up -100% net short every day for 8 years. So, net exposure will go deeply net negative when needed.
  3. Gross exposure: Gross exposure will be limited to less than 400% so as to avoid margin calls. Gross exposure is a function of market’s money and the Alpha Secure algorithm
  4. Cash deposits: Cash is maintained in various currencies. Forex is another tool in the toolbox to increase equity
Objectives
When managers say “I want to make as much money as possible”, it usually means “I have no risk-control in place”. Expressing objectives in terms of absolute performance percentage points falls into the outcome bias trap. This is a process driven portfolio. Accordingly, objectives are expressed in risk metrics
  1. Reward to risk ratio above 3 for risk management
  2. Common Sense Ratio between 1.8 to 2.1 for robustness
  3. System will be deemed bankrupt if maximum drawdown reaches -20%.
Chart examples:
Charts published every day contain the same information as the ones traded, but presented in a different fashion.

The first chart shows over-imposition of the Buy/Sell strategy over the public chart. They contain rigorously the same information. The only difference is the order logic component, absent in the public display chart, so as not to constitute a Buy/Sell strategy.
  • Stop Loss is the dotted line below each swing Low
  • Numbers preceded by the # sign (for example:#7.6%) are a rudimentary position sizing algorithm that assumes -1% loss to the equity if a position was entered at the Close of the day when the signal happens and stopped at the lower dotted line on the Long side (upper dotted line on the short side)
  • The upper dotted line is a level at which closing half (50%) the position would ensure the trade breaks even thereafter
Black triangles symbolise entries. Stacked black triangles represent single entry but multiple/split exits
Red/Green inverted triangles symbolise exits. Stacked triangles represent final exits. In the example above, the four triangles show the final exit of 4 open positions. Trend reversed from bullish to bearish.
 This is the public version of the same chart. Numbers are rigorously the same. Any smart trader can figure out for herself. In fact, the public version has the advantage of giving free will back to traders. It leads itself to multiple permutations, free from the “mechanical” constraint of a systematic strategy. For example, sideways periods can be used to accumulate stocks, or stay out of the markets.
Below are examples on the short side, with both the “weaponized” and public versions of the same chart. Strategy is symmetrical. It was developed on the short side and then translated to the Long side.
 
The key to being successful on the short side is to take risk off the table. and top-up successful positions. This is exactly what this strategy does.
Charts stripped of Buy/Sell signals lend themselves to multiple combinations and permutations. For example, the three low dotted lines indicated a volatility adjusted inverse head and shoulder pattern: volatility abated and as a result, stop loss moved higher, a movement that preceded a trend reversal.
Call to action
Please opt-in on our website. You will receive daily/weekly signals on equity indices, ETFs and Forex. The same signals on ETFs go into the portfolio.
You will also receive research on money management, trading strategies and trading psychology.
In addition, You will receive codes on C#, free Excel files. Those tools and utilities are not available to non-subscribers.
http://alphasecurecapital.com/subscribe/

 

Track record ETF portfolio 2015 – 05 – 15

Nothing speaks louder than a track record. There is no shortage of interesting indicators, strategies, ideas, but in the end, we trust only one thing: track-record. Track record sheds a crude light over two things: robustness of the strategy and quality of execution.
In 2013 and 2014, I wanted to start a hedge fund out of this strategy. We gathered some interest, but we were not able to raise enough assets to make it a viable commercial proposition. Reason was simple: live track-record. The strategy had been running on paper for years, (my bonus was calculated out of it so it was serious), but my employer back then had no interest in seeding a product that would be radically different from their product line-up. Being a sushi chef in a steakhouse does not have a bright long term career prospect.
So, here are three things I have committed to, I will:
  • run this strategy live with real money
  • put 3/4 of my life savings in it
  • publish the track record on our website
Track record for the week-ended May 15th
Attached is a pdf of the track record. The portfolio is still in ramp-up phase. Large positive net exposure is due to the abundance of bullish signals across the investment universe.
Borrow can be thin and fairly expensive for some ETFs. As a results, 3 short candidates were rejected. Borrow ranged from 6% to 9%.
Strategy synopsis
This strategy was developed on the short side, in order to underperform the longest bear market in modern history: Japan equities. This is why it has many counterintuitive features that make sense in aggregate. It relies on three assumptions: persistence of trend, risk management, capital efficiency. If trends persist, then temporary weaknesses/strengths constitute high probability entry points on the Long and Short sides, respectively. It also means that as probabilities recede, risk increases. It is therefore prudent to reduce risk, as trades mature. Capital efficiency simply states that compounded resources put back in circulation should be consistently re-allocated to fresh positions. We assume we cannot predict the future and do not know which trades will be big winners, so we keep on fishing.
The strategy is composed of two modules: entry/exit signals and money management. It takes a bit of grit (> 3,762 hours) to simplify every element to its bare essence. The objective is to continuously invest in successful trends, while reducing risk along the way.
Signal Module
Entry and re-Entry conditions are simple. It is easy to get in, but hard to stay in. Exits, on the other hand, took hundreds of hours for a simple reason: the quality of exits determines the shape of the P&L distribution. Entry is a choice, exit is a necessity. The exit process has been simplified from 9 layers to 3.
  1. Regime definition for all constituents in the universe
    1. Bullish: higher highs & higher lows
    2. Bearish: lower lows & lower highs
  2. Entry: “Buy on Weakness” (Bullish Weakness) and “Short on Strength” (Bearish Strength)
    1. Long: enter the day after a swing low has been recorded && dominant trend is bullish, “Bullish weakness”
    2. Short: enter the day after a swing high has been recorded && dominant trend is bearish, “Bearish Strength”
  3. Exits: There are three types of exits:
    1. Stop Loss: isometric staircase stop loss: all open positions are closed. Stop Loss is calculated as the swing value +/- an allowance for volatility expressed in Average True Range (ATR).
    2. Trend reversal: if a trend reverses from bullish to bearish, all Long open positions are closed. This is the highest possible point at which positions can be logically closed. Symmetrical rules apply on the short side when a trend reverses from bearish to bullish
    3. Risk reduction: every new position carries risk to the equity. So, the priority is o reduce risk. We have developed a proprietary adaptive exit threshold (AET) algorithm that optimizes the quantity to be closed, while reducing risk to near zero level
  4. Re-Entry: re-entries are allowed only after a partial exit has taken place. Re-entries are only possible along the trend
  5. Stock selection and order priority:
    1. Signals: every day, signals on ETFs, Forex and major indices are published on our website. Candidates come exclusively from that list. The exact same information is available to everyone, including myself.
    2. Priority: Candidates are ranked by position size: the bigger, the better. Borrow check happens before position sizing. Thin expensive borrow is an indication of how crowded trades are. All trades with borrowing fee above 5% are rejected. This is the only difference between Longs & Shorts.
Money Management
Money is made in the money management module. Risk is an obsession. Risk is not an abstract debate over a thesis. Risk is a series of numbers, made visual so as to stay painfully compelling at all times. Our basic philosophy is: profits look big only to the extent that losses are kept small. Tomorrow’s reward cannot be predicted, but risk can be managed today. Our proprietary position sizing algorithm responsively manages risk (per trade and in aggregate), exposures, position sizes in real time.
  1. Alpha Secure: This proprietary position sizing algorithm is so impressive that the company was named after it. This is the best tool to weather drawdowns and re-accelerate during winning streaks.
  2. Net exposure:
    1. This is an absolute directional Long and Short model: both sides are expected to generate alpha. Directionality (+/-100%) is only tolerated because of the low correlation between constituents (ETFs). If the universe was composed of stocks within a index, we would run relative series and collapse net exposure to +/- 20%
    2. Net exposure is a direct function of signal generation. For now, the vast majority of signals are bullish. I woke up -100% net short every day for 8 years. So, net exposure will go deeply net negative when needed.
  3. Gross exposure: Gross exposure will be limited to less than 400% so as to avoid margin calls. Gross exposure is a function of market’s money and the Alpha Secure algorithm
  4. Cash deposits: Cash is maintained in various currencies. Forex is another tool in the toolbox to increase equity
Objectives
When managers say “I want to make as much money as possible”, it usually means “I have no risk-control in place”. Expressing objectives in terms of absolute performance percentage points fall into the outcome bias trap. This is a process driven portfolio. Accordingly, objectives are expressed in process metrics. Those are a) reward to risk above 3 for risk management, b) Common Sense Ratio between 1.8 to 2.1 for robustness, 3) trading edge of 0.5 to 1.5 for quality of performance. System will be considered bankrupt if maximum drawdown reaches -20%.
Chart examples:
Charts published every day contain the same information as the ones traded, but presented in a different fashion.

The first chart shows over-imposition of the Buy/Sell strategy over the public chart. They contain rigorously the same information. The only difference is the order logic component, absent in the public display chart, so as not to constitute a Buy/Sell strategy.
  • Stop Loss is the dotted line below each swing Low
  • Numbers preceded by the # sign (for example:#7.6%) are a rudimentary position sizing algorithm that assumes -1% loss to the equity if a position was entered at the Close of the day when the signal happens and stopped at the lower dotted line on the Long side (upper dotted line on the short side)
  • The upper dotted line is a level at which closing half (50%) the position would ensure the trade breaks even thereafter
Black triangles symbolise entries. Stacked black triangles represent single entry but multiple/split exits
Red/Green inverted triangles symbolise exits. Stacked triangles represent final exits. In the example above, the four triangles show the final exit of 4 open positions. Trend reversed from bullish to bearish.
 This is the public version of the same chart. Numbers are rigorously the same. Any smart trader can figure out for herself. In fact, the public version has the advantage of giving free will back to traders. It leads itself to multiple permutations, free from the “mechanical” constraint of a systematic strategy. For example, sideways periods can be used to accumulate stocks, or stay out of the markets.
Below are examples on the short side, with both the “weaponized” and public versions of the same chart. Strategy is symmetrical. It was developed on the short side and then translated to the Long side.
 
The key to being successful on the short side is to take risk off the table. and top-up successful positions. This is exactly what this strategy does.
Charts stripped of Buy/Sell signals lend themselves to multiple combinations and permutations. For example, the three low dotted lines indicated a volatility adjusted inverse head and shoulder pattern: volatility abated and as a result, stop loss moved higher, a movement that preceded a trend reversal.

 

3 reasons why selling futures is a not a hedge to the Long book

out_of_balance_-_Google_SearchIn the Long/Short equity space, managers find it difficult to find “good shorts”. So, they resort to selling futures in order to reduce the net exposure (Long – Short exposures). With low net exposure, volatility comes down, VAR is apparently low, so it is possible to leverage up again; problem solved, or not ? Selling futures solves only one of the five major hedges: gross, net, Beta, market capitalization, concentration. Selling futures is an implicit bullish bet on the market. It all works well, until it doesn’t. In this article, we will look at three reasons why selling futures is not an all-weather hedge to the short book. We will also look at other ways to hedge the short book.

On January 24th, 2006, the arrest of Horie-san, president of LiveDoor, sent the Japanese market into a tailspin. Despite our collective best efforts to reassure investors that we were properly hedged, our performance suffered. On the surface, it seemed like we had low net exposure, reasonable gross exposure (Long  + Abs(Short) exposures or leverage). Yet, we were caught like deers in the headlights, watching our performance inexorably sink day after day. The source of our problems to one big position in the short book: March 06 futures.
Selling futures is not a hedge for three reasons
  • Selling futures as a form hedge is an expensive form of laziness
  • Short futures is an implicit bet on market cap
  • Short futures is an implicit bullish bet on Beta
Selling futures as a form of hedge is an expensive form of laziness
Investors do not need to pay 2% & 20% for something they can do themselves. In fact, many investors are already natural hedgers. For example, insurance companies routinely trade futures and index options. Selling futures in lieu of single stocks unfortunately shows lack of skill in the Long/Short craft.
Some managers argue that net exposure management is an important tool in their arsenal. Managing net exposure is vital to deliver superior returns. When investors hear this, they understand “Beta jockey”. At 40%+ net Long, this is no longer a hedge, this is directionality. During the GFC, directional hedge funds did not bring the net to -30%, or at least -10% net Short. Net exposure continued continued to hover about +10/20%, sometimes neutral at best. Managers may have said they wanted to be positioned for the rebound, but in reality they were just scared. They did not know how to hedge and it was the wrong time to learn.
Hedging is a delicate craft that must be honed during bull markets. Those markets are more forgiving. As long as performance goes up, mistakes can be forgiven. When the going gets rough and patience of investors wears thin, hedging mistakes can be deadly.
There is one exception where selling futures as a hedge shows superior skill. When net exposure remains below +/-10% throughout the cycle, performance comes from the excess return over the index. This is as close as it will ever get to pure alpha in the equities world. This is a rare skill: managers understand they are not good at short-selling, so they concentrate on delivering excess returns, only partially juiced up by some residual market exposure. Managers who can deliver genuine excess returns deserve recognition and unsurprisingly see their AUM grow over time, survive and thrive through the thick or thin.
Long Stocks/Short future is an implicit bet on market cap and exchange
Managers like to invest in small/mid caps.  This is where the fun and the gold nuggets are. Small-mid caps tend to have better upside potential than large caps during bull markets. Besides, stories are interesting. It is easier to have access to senior management. Uncover a few 3-4 baggers and a new stock picking star is born.
On the other hand, futures are a reflection of the underlying large caps in the index. For example, Topix Core 30 accounts for more than half of Tokyo first section market capitalisation. So, performance of the index is driven by its top caps.
Then, selling futures and buying small-mid caps is an implicit bet on market cap: Long small/mid caps, Short large caps. It goes even one step further. It is often a bet on the exchange: small/mid caps are often listed on different sections of the exchange. So, it can take the form of Long Nasdaq/Short S&P 500, Long JSDA / Short Nikkei, Long Kosdaq / Short Kospi etc.
As usual, it all works well until it doesn’t. Small/Mid caps do better than large caps in bull markets. In bear markets however, small/mid caps fall faster and harder than large caps. This is what happened to us in 2006. Our Long book fell -4-5% everyday. Liquidity evaporated. We could not get out of stocks without pushing them even further down.  Meanwhile, our short book only fell by 2%, leaving a gap of -2-3% every day. Selling futures is an implicit bullish bet that works as long as the market stays bullish.
The psychological implications are even worse. As much as waiting for the first heart attack  is not recommended to start living a healthy lifestyle, waiting for a bear market is a bad time to start learning the discipline of short selling. Selling short is a muscle that atrophies when not flexed. Managers grow complacent during bull markets. They believe “good shorts” will be plenty available when the market turns bearish.
Unfortunately, bear markets are harder to trade. Volatility increases, volume drops, bid/ask spreads widen, borrow becomes harder to source and squeezes can be vicious. Small caps may drop and look like great shorts, but in practice, they are hard to sell short. Obvious shorts quickly become crowded and once they do, they rarely fall as fast as the market.
On top of this, investors are risk-adverse and prone quick to redeem. So, trying to learn a difficult skill in a tough environment, without being allowed the luxury to make mistakes is hardly a good recipe for a lasting business.
Long Stocks/Short future is an implicit bet on Beta
The index has a Beta of 1. Since futures are a reflection of the index, they have a beta of 1. Small/mid caps outperform the index during bull markets. They therefore have a Beta above 1. So, Long small/mid caps/Short futures is therefore an implicit bet on Beta.
The difficulty comes with the first derivative of Beta, or speed. When the drop comes, it is sudden and violent. In our 2006 “soft patch”, one investor noted that we had a beta of 1.5 on the way up and 3 on the way down, after which he proceeded to redeem his investment. The only way to manage the short book via futures is to turn Beta neutral to negative. All things being equal on the Long side, that means large negative net exposure, something that traditionally net long managers are not comfortable doing.
A classic solution is to replace small/mid caps on the Long side with Low Beta stocks such as utilities, pharmaceuticals, food stocks. Net Beta can be negative, or below while net exposure can stay marginally positive. It works, but this is a reactive move implemented only after the reality of bear market has settled in. That usually comes after a drawdown.
How to edge properly then ?
Are VIX options a real hedge ?
Every time there is an earthquake, earthquake insurance sales go up. They then peter out over the next few years. Every time the market tanks, VIX goes up and investors rush to buy VIX options. VIX options become rapidly expensive. Besides, VIX is the only true mean reverting asset class. Trading VIX options is therefore an expensive form of hedge, hardly profitable in bear markets.
Absolute versus relative series
Analysts often complain that  short ideas are hard to find in a bull market. This is true, but only if they look at absolute series. If one is to divide absolute prices by the closing price of the Index (relative series), then quite a different world starts to emerge. There is ample supply of underperformers out there, matched by an abundance of outperformers. This is however a paradigm shift. The objective is no longer to generate money in absolute terms. In fact, the true meaning of Long/Short is excess return over the index on the Long side and excess return over the inverse of the index on the short side.
All of a sudden, it becomes much easier to hedge the Long and Short side. Furthermore, competition is not as intense as in the absolute world. Shorts are not as crowded, because in absolute terms, they still look like they are going up, only slower the rest of the market. So, one would enter a short, knowing it would probably lose money in absolute terms. That is a challenging psychological hurdle. Years into it, It is still hard to intellectually reconcile positive performance, despite a full red inked absolute P&L column.
The main drawback of the relative series is the added complexity of calculation. Everything has to be divided by the index: charts, stop losses & target prices, risk management, even performance. The architectures of portfolio management systems radically differ. Imagine sending a limit order in absolute (try and send your favorite broker) a relative currency adjusted  but managing stop losses in relative terms. It takes time to getting used to it, but the reward is well worth the effort. Short and Long candidates are abundant. Volatility is much lower, which makes it more commercially attractive to investors. Institutional investors prefer low volatility consistent returns over highly volatile performance. For example, the largest hedge funds in the equity space do not shoot for the moon, they do want to beat the market, they just aim to deliver high teens performance year after year.
Conclusion
Selling short is a muscle that atrophies each time futures are sold in lieu of stocks. As much as waiting for a heart attach is not the best time to start exercising, waiting for the bear market is the wrong time to learn the discipline of selling short.  Investors are not dupe: they see through directionality and large futures positions on the short side. They have been there before and they did not like it then.
Shorts are plenty available all the time. They are just not going down in absolute terms but relative to the index. It implies a complete rethinking of both sides. It takes practice to learn but over the years investors have rewarded managers who deliver low volatility consistent returns from stocks on both sides of the book. As John F. Kennedy said, The time to repair the roof is when the sun is shining”.

Regardless of the Asset Class, There Are Only Two Types of Strategies

Finance is one industry where there is no shortage of creativity. There is always a new strategy, investment vehicle, or asset class. This alphabet soup is confusing, particularly when it comes to assessing risk and reward across asset classes. Yet, there is a simple universal way to classify strategies. They fall into two buckets: either mean reversion or trend following. Simply said, the exit policy determines the win rate, which then shapes the return distribution.

Summary

  • A powerful visual representation of style/gain expectancy: Call to Action: our commitment is to help people become better traders. if YOU want to visualise your style, opt-in and we will send YOU a portfolio diagnostic tool for free
  • Regardless of the asset class, there are only two types of strategies: mean reversion or trend following
  • Each strategy type has a specific risk profile, which require different risk metrics. Common Sense Ratio recaptures risk for all strategy types (Read this, it is important)
  • How to increase the win rate, gain expectancy and overall profitability depending on strategy type ?

I. The only two types of strategies: mean reversion or trend following

Over the years of patiently testing multiple algorithmic strategies, patterns in the return distribution repeated over and over. It eventually became apparent that strategies fall into two buckets: mean reversion or trend following. Attached are graphical representations of the gain expectancy of mean reversion and trend following strategies. The reason why the same patterns repeat themselves is simple: exit policy.

Market participants tend to treat exit as a single final event. Each trade is a binary event: either it is profitable or not. The accumulation shapes the return distribution. Hit ratio is then determined not by what we enter, but how we exit.

Charts below are return distributions for each strategy type. They are also visual representations of gain expectancy. One image speaks more than a thousand words. This representation changed my life. It permanently altered the way I perceive the markets. The game is about tilting gain expectancy: contain the left tail, moving the peak hit ratio to the right and elongating the right tail. This visual representation is a powerful tool. This is why we want to share it. We are committed to helping people build smarter trading habits. Sign-in to our newsletter (it’s free) and we will send you a portfolio diagnostic tool.

Mean reversion strategies compound small profits

Gain Expectancy - Classic Mean reversion

Death by knock-out: many small profits. a few knock-out blows

Mean reversion strategies compound multiple small profits. They rely on the premise that extremes eventually revert to the mean. They aim ato arbitraging small market inefficiencies. They often have low volatility  consistent performance. They perform well during established markets: bull, bear or sideways. They unfortunately perform poorly during regime changes. They also perform poorly during tail events. The key issue is to contain rare but devastating blow-ups.

 Mean reversion strategies characteristics are (see graphical representation):
  • Moderate to high turnover
  • High win rate: often above 50%. The shorter the duration, the higher the probability of success
  • Consistent small average profits: trades are closed around the mean
  • Low volatility consistent performance
  • Potentially devastating left tail losses: make a little bit of money every day and lose a fortune in one day
  • Long period of recovery after losses:
Examples of mean reversion strategies are
  • Short Gamma: sell OTM options so as to collect pennies in front of a steam roller
  • Pairs trading (non FX): bet on the convergence between two historically correlated securities
  • Value investing: Buy low PBR stocks and “undervalued” assets
  • Counter trend: sell short shooting stars and catch falling knives

Mean reversion strategies post modest but consistent profits. They cater to investors who would look for low volatility returns. Their challenge is the left tail, those infrequent big losses that will take a long time to recoup.

Trend following strategies have a few home-runs 
Gain Expectancy - Classic Trend Following

Death by a thousand cuts: many frogs, a few princes

Trend following strategies rely on the capital appreciation of a few big winners. Whether they follow stories, fundamentals, earnings or price momentum, stock pickers are trend followers. They may fail to appreciate being called trend followers, but their P&L distribution tells a different story.

Trend followers kiss a lot of frogs: they have a low hit ratio, often between 30% and 45%. Performance is cyclical. Styles come in and fall out of favor. Volatility is elevated. Performance can be underwhelming for long periods of time. The key issue is to contain losses during drawdowns.

 Trend following strategies share those common characteristics (see graphical representation):
  • Relatively low turnover
  • Low win rate: 30 to 40%: see chart
  • Big wins and lots of small losses: right tail on chart
  • Relatively higher volatility
  • Pronounced cyclicality: style comes in and goes out of favor
Example of trend following strategies are
  • CTA type systematic trend following,
  • Momentum: earnings momentum, news-flow, price momentum
  • GARP investing: growth at reasonable price
  • Buy & hope
 Trend following strategies post impressive but volatile performance. They can go through long periods of underwhelming performance, which take their toll on the emotional capital of managers. Their main challenge is to keep cumulative losses small. Profits only look big to the extent losses are kept small.
II. How to measure risk for each strategy type
Investors suffer from a “nice guy syndrome”: some young women genuinely say they want to marry a nice guy, but unconsciously react to so-called “bad boys”. Investors genuinely say they want returns, but in reality they do react to drawdowns. More specifically, they are susceptible to drawdowns in three ways:
  1. Magnitude: never lose more than what investors are willing to tolerate
  2. Frequency: lull investors to sleep. Clients will trade performance for low volatility: big money is fixed income, not stocks
  3. Period of recovery: never test the patience of investors.
There are two ways to lose a boxing match: either on points or by knock-out. Mean reversion strategies score until they get knocked out. Trend following strategies lose on points. Risk is not evenly distributed. Therefore, each strategy deserves its own set of risk metrics.
Risk metric for mean reversion strategies: knock-out
Knock-out

Knock-out

Mean reversion strategies have low volatility, consistent performance and high Sharpe ratio. On the surface, they are what investors look for. The problem is mean reverting strategies work well, until they don’t. Big losses are unpredictable. LTCM had a great Sharpe ratio, at least until October 15th, 1987… Risk is in the left tail. The best metric for mean reverting strategies is therefore: tail ratio. Tail ratio measures what happens at the ends of both tails:

Tail ratio  = percentile(returns, 95%) / percentile(returns, 5%)
For example, a ratio of 0.25 means that losses are four times as bad as profits. Turnover then becomes an important variable: the higher the turnover the shorter the period of recovery. The two ways a mean reversion strategy can survive is either by 1) containing the left tail or 2) increasing turnover.
Mean reversion strategies will test investors’ nerves on two things: magnitude of loss and period of recovery. For example,  some strategies such as fundamental pairs trading post constant, reassuring but modest profits like 0.5% a month. Then one day, they post losses of 3 to 5%. They lose in one month the gains of an entire year.
Investors often succumb to the sunk cost fallacy with mean reversion strategies. They believe that big losses are rare and that managers will eventually make them back. This bias ignores probabilities, particularly the theory of runs. It also ignores opportunity costs. The good news is that there is an optimal point below which it makes more sense to redeem than to stick with managers who experienced a severe loss. It is often referred to as optimal stopping. Whilst the formula can be complicated, a simple rule of thumb is to redeem if losses are below 0.4 of turnover.
On the other, trend following strategies have tail ratios ranging from 3 to 10. Winners are much bigger than losers. So, tail ratio is meaningless for trend followers.
Risk metric for trend following strategies: erosion
Trend following strategies have typically low win rates. Risk is therefore not in the tails, but in the aggregates: are a few winners big enough to compensate for the multitude of losers ? Measuring risk then boils down a simple ratio of profits over losses. The risk metric for trend following strategies is therefore:
Gain to Pain Ratio = Sum(profits) / Sum(losses)
Trend following strategies will test investors nerves on frequency of losses and period of recovery. Frequency of losses is another word for volatility. Trend following strategies are volatile, but semi-volatility (downside volatility) is low. They can also post lackluster performance for long periods. For example, mutual funds have built-in cyclicality. Even if they claim to beat the index, mutual funds still lose money during bear markets.
GPR does not apply to mean reversion strategies because blow-ups are unpredictable. GPR can stay high until it is torpedoed by one or two bad losses.
Combined risk metric: Common Sense Ratio
 
 “Common sense is not so common these days”, Voltaire, French freedom fighter
Managers rarely define themselves as adherents of either mean reversion or trend following. Even so, it still would not be easy to assess robustness. Besides, the more risk metrics we use, the more confusing it becomes. For example, some managers have great performance despite a bad Sharpe ratio, so the question is “which matters more in which context?”
Since both metrics outlined above can be expressed in a simple binary ratio, combining them makes sense. When this ratio was first to colleagues and friends in the HF world, comments sounded like “yep, common sense”, hence its imaginative name: Common Sense Ratio
                                                                     Common Sense Ratio = Tail ratio * Gain to Pain Ratio
                                                               Common Sense Ratio = [percentile(returns, 95%) * Sum(profits) ] / [percentile(returns, 5%) * Sum(losses)]
Above 1: make money, below 1: lose moneyCSR is much more powerful than either metric taken individually.
Example 1: GPR = 1.12, TR = 0.25, turnover = 2, CSR =  0.275
Let’s take a classic mean reversion strategy that generates 10% p.a. (GPR = 1.1). It has a moderate turnover of 1.5. Within a 24 months period, it will post a monthly drop of -4%, with a 95% probability. This is 5 times as big as the average profit, and roughly 4 times as bad as right tail profits (TR = 0.25). Common Sense Ratio is CSR = 0.25 *1.1 = 0.275.
On the surface, it may look like a modestly attractive strategy. In reality, the period of recovery combined with magnitude of loss imply that investors will have to be patient. In very simple terms, the CSR shows that returns are not attractive enough to justify investing in such strategies. Try this with a few low volatility strategies. Risk is not where You think it is.
Example 2: GPR = 0.98, TR = 3, turnover = 0.5, CSR = 2.94
Now, let’s take a strategy that loses 2% over a complete cycle (GPR = 0.98). Best winners are 3 times as big as worst losers (TR = 3). Turnover is low 0.5. You may think, why invest in a vehicle that loses money ? It does not make sense. Yet, You are invested in such vehicles: welcome to the average mutual fund. 80% of mutual funds lose roughly 2% to the benchmark. Every now and then, they outperform with a vengeance. The rest of the time they suck air. Morality: over time, mutual funds are poor investment vehicles if You stay invested through the cycle.
III. How to tilt the win rate, gain expectancy and overall profitability depending on your win rate
Gain Expectancy - Alpha SecureThe question boils down to: is it possible to combine the benefits of both strategy types without having the drawbacks of either one ? How can we generate a return distribution that would look like the one on the chart ? (*)
The whole game of investing is about generating a return distribution that would have the following characteristics:
  1. No left tail: small losses like a trend following strategy
  2. Long right tail: big wins like a trend following strategy
  3. High win rate: above 50% win rate like a mean reversion strategy

This type of strategy combines both short term compounding with long-term capital appreciation.

Investors following a mean reversion typically come in early and leave too early. The key is therefore to elongate the right tail. This is done through allowing a remainder to extend beyond the mean with a trailing stop loss.
  1. Set a stop loss (more on this in an upcoming article)
  2. When the trade means reverts, close half the position
  3. Set a trailing stop loss (not based on valuation) and close the trade once the stop loss is penetrated
Bottom line, markets can stay irrational longer than You think. When it stops making sense for You, it may start making sense for someone else. Ride their tail, but protect your downside.
If You are a trend follower, here is a simple game (game of 2 halves) that will mechanically improve your return distribution. We all know that making money is about cutting the losers and riding the winners. Here is an objective way to do it:
  1. Calculate your average contribution, divide it by 2
  2. Reduce by half every losing position below – half average contribution
  3. re-allocate the proceeds to winners
Bottom line, you have reduced losers and increased winners in a simple way (more in an upcoming article)
Conclusion
The  purpose of this article was to introduce a simple yet powerful way to reframe strategies independent of asset class. This enabled us to look at the merits and drawbacks of each type. We then looked at risk metrics that would best recapture their risk profile. We introduced a unified risk metric Common Sense Ratio that works across all asset classes. Finally, we looked at ways to tilt gain expectancy for each strategy type. Last but not least, if You want to know what your trading style, please subscribe and we will send You a diagnostic tool for free.
Preview of the next article:
The next article will deal with investor psychology. Short sellers have a unique perspective on investors psyche. We never sell short against buyers. We observe people who once held a position and are now processing grief. The next article will be about the psychology of grief adapted to the markets.
  1. Market regime: bear markets have several distinctive phases, with a measurable market signature
  2. You will never read an analyst report the same way again. You will learn to read emotions through language and back it up with numbers
  3. You will be better equipped to bottom fish for stocks
(*) : All above return distributions are derived from the same strategy. It has both mean reversion and trend following components. In order to draw a mean reversion strategy, the trend following component was switched off, and vice versa to build a TF distribution. Both components are normally switched on, third distribution

Is Stock Picking Overrated ?

Summary

  • If 80% of managers underperform their benchmark, we probably focus on the wrong thing. How about focusing on gain expectancy instead of stock picking ?
  • Signal module: how often we win (hit ratio) is not a function of what we enter (stock picking) but how we exit.
  • Money is made in the money management module: how much we win is a function of how much we bet (position sizing).
  • Psychology module: Great traders are not smarter, they have smarter trading habits

The finance industry is built on the cult of the stock picker. We have been conditioned to believe that entering the right stocks is the recipe to beat the markets. Year after year, we spare no effort, expenses, technology and time just to find that golden nugget. We never stop and ask ourselves whether it works in the first place. SPIVA gives an unapologetic report on active versus index investing. Every year, about 80% of managers underperform the market by a few percentage points, the equivalent of fees plus transaction costs of one time turnover. There are probably two reasons for this.

Firstly, Charles Ellis explained in his book “winning the losers game” that markets are dominated by institutional investors. The index is therefore the average of highly educated, intelligent, hard working and ferociously competitive people. So, outperforming the index comes down to beating a very high average.

Secondly, if , year after year, we try the same old “better sameness” just a little bit harder and expect different results, only to be humbled each time, we may have been focusing on the wrong thing in the first place. The answer may lie in an equation so simple it is often overlooked: Gain Expectancy.

But first, please understand that our objective is not to throw stones at active management from our modest glass house. We are committed to helping market participants build smarter trading habits. We provide simple yet powerful tools to nudge performance: resources, research, links, Excel files.

Enter Gain expectancy

Gain expectancy is just another fancy word for average profit. All strategies without exception boil down to this formula:

Gain Expectancy = Win rate% * Avg Win% – Loss rate% * |Avg Loss%|

Using this equation, we will examine what we believe to be the four components of any strategy in increasing order of importance: entry, exit, money management and psychology.

Entry Accounts for 5% of performance

Jesse-Owens-007

Finance is the only sport that hands out medals before the race

Finance is the only competitive sport where we expect medals to be handed out before the race. Market participants focus their energy on picking the right securities, but stock picking is the process that leads to entry. When we focus on stock picking, we just care about getting the best stocks to the starting blocks and assume they will do well thereafter. We overlook critical questions such as 1) what if they do not perform as expected, 2) how big we should be and more importantly 3) will we have the fortitude to stomach the ride ?

Stock picking is not irrelevant, it is overrated. There is no doubt that picking the right stocks increases our chance of success. The treasure hunt of stock picking is the most exciting aspect of the job. Ironically, entry is also the part that has the lowest impact on performance. Looking back at the gain expectancy formula, entry is just an ingredient of the win rate%, not the happy meal. After all, even the best ingredients will not necessarily turn into a succulent meal if there is no recipe. When everyone else is fixated on entry, paying a little more attention to other components may give us a critical edge.

In the coming articles, we will examine different types of entry techniques, common pitfalls and remedies. Everybody likes to buy on weakness and sell short on strength. But sometimes weakness is a symptom of a bigger problem and vice-versa on the short side, strength turns into bullishness.

Exit Accounts For 20% of Performance

jesse-owens

It’s not what we pick but how we exit that determines the hir ratio

We all have been shaken out of a position and then watched it rally without participating. The hit ratio is not determined by what we enter, but how we leave. Exit is a binary event: a trade is either profitable or not. The only time when win rate% can be calculated with absolute certainty is after positions are closed. Anytime before that is just paper profit. The quality of our exits determines the shape of our P&L distribution.

Before I embraced the sophistication of simplicity, I used to believe that a certain combination of factors would generate optimal performance. I was looking for a holy grail of some sort. The first epiphany came after a Monte Carlo optimization. One of the combinations made money 19 years out of 20, despite a win rate of 34%. Meanwhile, the highest win rate (67%) lost money 17 out of 20 years. The lesson was clear: “making money in the markets is not about trying to be right. It is about accepting one is wrong and move on”. There is one class of individuals to whom it should come easy: married men.

Would You drive a car without brakes ? Then, would You trust a strategy without a stop loss ? Market participants are often refractory to the idea of a stop loss. It is however the second most important component in any strategy. It has direct impact on 3 out of 4 variables of the gain expectancy: win rate%, loss rate%, Avg loss%. In addition, it has a direct impact on trading frequency and bet sizing. Profits look big only to the extent that losses are kept small.

Entry and exit constitute the signal module. They only determine the win rate. A trading system is like a car. The signal module is the engine. The money management is the transmission and psychology is the driver.

In the coming articles, we will examine the various types of exits and their influence on the P&L distribution.

Money management accounts for 25% of performance

Different Weight simulations SPX - Excel 2015-03-10

Same strategy, different bet sizing algorithms generate different outcomes

Money is made in the money management module. There is rampant confusion in our industry that associates alpha generation capability with high win rate. LTCM used to boast a win rate above 70%. Yet, their demise nearly took down the modern financial system. By contrast, William Eckhardt, the father of the Turtle Traders, claims a modest win rate of 35%. He has however achieved a remarkable annualized performance of 18% over a 36 year career. It is not how often we win but how much we make that ultimately determines our performance.

In a previous job, I used to run my algorithm across various portfolios. The objective was to help other managers better trade their positions 5bps at a time. Compound this over a year and this is the difference between 2nd quartile and top decile performance. The same stocks kept on reappearing in top ten bets. Managers exchange ideas and have access to the same research. There was a low dispersion of holdings, but there was a high disparity of performance. So, the difference that made the difference was obviously not stock picking: everybody owned the same stocks. The primary determinant of performance was bet sizing.

Looking back at the gain expectancy formula, bet sizing is the component that tells how much we make. It helps us achieve our investment objectives. It is also the most important component for market participants engaged in short selling activities.

In the coming articles, we will look at various position size algorithms, risk management tools so as to help You extract more alpha out of your ideas. We will look at specific techniques designed to help You clarify your objectives and achieve your goals.

Psychology Accounts For 50% of Performance

“If You don’t know who You are, this [markets] is an expensive place to find out”, Adam Smith

Habits

Great traders are not smarter, they have smarter trading habits

Unfortunately, bull markets have never boosted anybody’s IQ. We simply get overconfident during winning streaks and start gambling away. Then, during the ensuing losing streaks, we get depressed and take too little risk. In any case, we tend to abandon our discipline. Even systematic traders tend to tweak their models during losing streaks.

We have been conditioned to believe that willpower is the key to success. Unfortunately, willpower is a muscle that tires quickly, particularly under stress. For example, we all know that the key to performance is to cut losers and ride winners. So, we promise ourselves that we will reevaluate positions once stories change. Unfortunately, no plan has ever survived its collision with reality. If we leave this process to our willpower, it invariably turns into an internal debate, where our inner saboteur often convinces us to keep losers in the portfolio.  Inertia creeps in and the next thing we know, our portfolio has turned into a toxic waste junkyard. The problem is: every time we say “Yes” to a loser, we say “No” to a potential winner.

Market psychology is comprised of two parts. It is the ability to execute a trading plan through winning and losing streaks alike. It is also the inner game of investing: the inner alignment from deep subconscious beliefs to daily unconscious routines. “Watch your thoughts, they become words. Watch your words, they become actions. Watch your actions, they become habits. Watch your habits, they become character. Watch your character, for it becomes your destiny”, Mohandas Gandhi

There is a simple, but not easy, solution to change our psychological make-up. According to a 2002 research paper by Wendy Wood, we spend between 45% and 60% of waking time in habitual mode.  Interestingly enough, the study was conducted on young undergraduates, a segment of the population where habits are still highly malleable. Imagine how habitual our behavior can be after 10 years on the job. We probably learned for the first 2 years and then pushed the repeat button ever since.

Great traders are not smarter, they have smarter trading habits. They have developed and practiced profitable behaviors that have turned into trading rituals. The beauty of habits is that they bypass conscious decision process. They become effortless and emotionless over time. Under stress, we ditch elaborate plans and fall back to our habits. This is why installing smarter habits is critical: success is a habit and unfortunately, so is failure.

Fortunately, executing stop losses can be as emotionally intense as brushing teeth. This is a gradual process that starts, not with ruthlessly cutting losers, but with keeping a portion in the portfolio…  It starts small but the compounded effects are immense. The difference between sending a golf ball off course or close to the hole is one millimeter when hitting the ball. If smarter trading habits resulted in a gain as small as 0.02% per trade, the compounded effect over 100 trades would put us in the rare company of market gurus.

At ASC, We are committed to help You build healthier trading habits. In the coming articles, we will provide You with research from the fields of finance and medical sciences, resources exercises, links that will help You change your habits.

Conclusion

“We are what we repeatedly do. Excellence, then, is not an act, but a habit.”, Aristotle

If we want different results, then doing something different is probably a good start. Stock picking is not irrelevant, it is overrated. All it takes to nudge gain expectancy (i-e performance) is to redirect a small portion of our focus to the other components of the success formula.

Great traders are not smarter, they have smarter trading habits. We are committed to helping market participants form healthier trading habits. We will provide You with resources, links, exercises and an App on the Bloomberg portal.

Preview of the next article

  • In the next article, we will introduce a powerful visual representation of gain expectancy
  • Using this tool, we will reclassify strategies across all asset classes in two types
  • We will provide You with suitable risk measures risk for either type of strategy
  • We will introduce a new risk measure: Common Sense Ratio
  • We will provide You with a simple technique that dramatically improve your win rate %