• Gold (and gold mining stocks) tend to be inversely correlated to stocks regardess of whether the prevalent fears concern inflationary or deflationary pressure;
• Dow/Gold ratio, coupled with simple trend-line analysis on a logarithmic scale (i.e. for long-term trend analysis), is a popular way to determine whether stocks or gold/commodities are a relatively more attractive investment. 

• Although the real estate and housing markets tend to move in line with inflationary and deflationary pressure, this is not always the case. 
• The surge in real estate values for a decade and a half from 1990 occurred amid low inflationary pressure and the fear of deflation occurring. 
• Instead, real estate and housing move according to a different cycle than the normal business cycle.

1. QE1 & QE2 pushed treasury yields, stocks and commodities higher throughout the life of the program. 
2. Operation twist, which involved selling short term securities and buying longer term ones to lower borrowing rates for mortgages and automobile purchases, pushed stocks higher but had a relatively muted impact on bond yields. It also contributed to the flattening of the yield curve.
3. Homebuilders responded particularly sharply (positively) to operation twist

• QE1 & QE2 caused the yield curve to steepen as a result of the rise in 10 year yields. 
• The yield curve dropped sharply during the third quarter of 2011 as a result of money pouring into treasury bonds to offset a weakening stock market.

1. Bond prices normally have an inverse relationship with commodity prices (due to their inverse relationship with inflation). 
2. Changes to the normal bond/commodity relationship are usually caused by action in stocks or the dollar. Specifically, central bank action to stem a fall in stock prices push interest rates lower (causing bond prices to rise) and the currency to depreciate. This is exactly what happened in 2007, at which point commodities started to rally due to a weakening in the USD

• Includes 19 commodities, all of which are traded on exchanges in the US and LDN.
• Includes energy (at least 33% of the index), industrial metals (13%), precious metals, grains (13%), tropicals, agricultural and livestock.
• The CRB Index formula includes commodity contracts that lie within six months of the current date. 

1. Two systems: system X (the emotional part of the brain) and system C (logical and deductive in the way it handles information). 
    
2. The X-system deals with information in an 'associative way' and can therefore handle vast amounts of data simultaneously. Because system C is logical, it can only follow one step at a time and is therefore slower.
    
3. We tend to use system X more often because it pre-screens information before we are consciously aware of it (making it the default option). Also, system C is slow and deliberate. Finally, from an evolutionary angle, we needed emotions far before we needed logic.

1. (i) We are hard-wired to (focus on) the short-term; (ii) We appear to be hard-wired to herd; 
    
2. Self-control over these impulses is very hard and a limited resource.
    
3. Since we have understood that 'real' pain and 'social' pain are felt in the same parts of the brain, using 'contrarian' strategies can leave investors feeling the same amount of pain as actual physical pain since they are the equivalent of seeking social pain.

1. Under emotional distress, people shift towards high-risk high-pay-off options even if they are objectively poor choices.
    
2. When self-esteem is threatened, people become upset and lose their capacity to regulate themselves. This leads them to rush to prove something great, overriding their normal rational way of dealing with life. 
    
3. Self-regulation is required for many forms of self-interest behaviour. However, self-regulation is a limited resource. Decisions therefore become increasingly costly or foolish as we become tired and depleted.

1. H*E*SD*I(S)*: (i) Heuristic (Simplification); (ii) Emotion; (iii) Self-Deception; (iv) Interaction (Social)
2. The illusion of knowledge is the tendency for people to believe that the accuracy of their forecasts increases with more information. 
3. The remedy to the 'illusion of knowledge' is to recognise that it is not necessarily the amount of information that is important. Instead, it is what you do with it that matters. 

• Biases can be traced back to four categories: self-deception (limits to learning), heuristic simplification (information processing errors), emotion/affect, social
   
• 'Self Deception' includes overoptimism, overconfidence, self-attribution bias, confirmation bias, etc.
   
• 'HS' includes representativeness, framing, anchoring, loss aversion (prospect theory), etc.
   
• 'Emotion' includes 'mood,' self-control, regret theory.
   
• 'Social' includes imitation, contagion, herding, cascades.

1. Don't overweight Personal Experience; 
2. Focus on Facts, not stories; 
3. Look for information that Disagrees with you; 
4. Examine Mistakes to improve (rather than blaming losses on bad luck); 
5. Accept that Biases apply to everyone!
6. Recognise that more information doesn't equal better information - focus on quality Info;
7. Sell Losers and ride winnners; 

1. Illusion of Knowledge: The tendency for people to believe that the accuracy of their forecasts increases with more information. Results in 'overoptimism' and 'overcofidence.' Paul Slovic's study of experienced bookmakers with the list of variables (accuracy did not improve with number of variables, but confidence in their forecasts did).  
2. Big is Not Important: Investors tend to place great weight on low strength issues (e.g. high historical earnings growth), resulting in overreactions, and low weight on high strength issues (e.g. dividend cuts).
3. Confirmation Bias: Looking for information that agrees with us rather than info that doesn't.
4. Self-attribution Bias: Attributing good outcomes to skill and bad outcomes to bad luck. 
5. Hindsight Bias: When people are sure they knew (after the fact) that something was going to happen (e.g. dotcom bubble). 
6. Anchoring: Using irrelevant information to guide decision-making under uncertainty. Study: rigged wheel of fortune and (numerical) general knowledge questions. 
7. Representativeness: Judging events by how they appear rather than by how likely they are (e.g. good companies make good investments). 
8. Recency Effect: People are more likely to recall vivid, well-publicized or recent information (investors' experience will be a major determinant of their perception of reality). 
9. Framing: We do not see through the way in which information is presented to us (e.g. 'would you prefer a plan that saved 200 people out of 600 for sure or one in which all 600 people have a 1/3 prob. of surviving and a 2/3 prob. of everyone dying?').
10. Status Quo Bias: Inaction inertia, linked to the 'endowment effect' (i.e. placing a higher value on something once you own it). 

1. Empathy Gap: difference between stated behaviour and actual behaviour. We are very poor at forecasting both our future feelings and actions, and end up underestimating the influence of emotional situations on our choices, actions and preferences.
2. Impact Bias: people overestimate the influence of emotional situations on the intensity and duration of their feelings (e.g. end of a romantic relationship); 
3. Empathy gaps are likely to be more of a problem. 

1. A study of day-traders showed that subjects whose emotional reaction to monetary gains and losses was intense on both the positive and negative side exhibited significantly worse trading performance. 
    
2. A group of men were asked how aroused they were by certain acts when they were not in a particularly high state of arousal. Their answers changed (i.e. they felt more aroused) when they were in a greater state of general arousal; 
    
3. Having a simple but non-negotiable precommitment style trading rules.

1. Self-attribution bias: we attribute success to skill and failure to bad luck;
2. Hindsight bias: we convince ourselves that we could have predicted certain outcomes ex-ante;
3. Illusion of control: we believe we can influence things that are beyond our control;
4. Feedback distortion: we reach conclusions that we want to find (i.e. distort feedback/information so that it fits our views and abilities);
5. Keep a written log of decisions and the rationale behind those decisions.

1. Forecasts: Placing forecasts at the heart of the investment process (pride, overconfidence, anchoring); 
2. Info (Overload): Seeking to accumulate vast amounts of information rather than focus on a few key data points (illusion of knowledge); 
3. (Meeting) Management: Overinsistence on meeting regularly with company management; 
4. Timing (Extremes): Trying to time tops and bottoms (hubris); 
5. (Short Time) Horizons: Due to pressure of quarterly performance reviews;
6. Committee: Decision-taking as a result of group interaction;
7. Stories: Acceptance of stories.

1. Using value strategies based on trailing earnings; 
2. Momentum strategies based on past prices.

1. Closet-indexing: Asset managers, being rewarded using a fixed percentage of AUMs, wish to avoid losing assets. The easiest way to avoid underperformance is to track the benchmark as closely as possible. 
2. Drop in average holding period: Contraction of the ultimate investors' time horizons has driven/coincided with a collapse in time horizon of institutional fund managers (avg. holding period has dropped from 7-8 years in the 1950s to just 11 months). This implies stock investing is increasingly driven by speculation rather than long-term value philosophies.
3. Corporate managers forego long-term valuable investment projects: A 2005 Harvard study found that nearly half of the CFOs interviewed would be willing to sacrifice a long-term valuable project if it meant missing earnings by $0.20

• EBDM involves collecting evidence, creating a story to explain the evidence, then using the story (rather than the original evidence) to make a decision;
• 78% of jurors found a suspect guilty when the defense presented them with evidence and the prosecution presented stories. When the formats were reversed, only 31% of the jurors found the suspect guilty!
• Economies with the highest GDP growth delivered lower returns than those with the lowest GDP growth. This was because investors end up overpaying for the hope of growth.

• Sector-relative factors allow us to get around many problems associated with accounting regimes and capital structures; 
• Constructing portfolios based on absolute measures reduces sector diversification. A sector-relative approach might allow for a more diversified portfolio without dimishing the exposure to any given factor 
• Back-testing suggests that value and size work best on a sector-adjusted basis, while price momentum does not.

1. Displacement: an exogenous shock that creates profit opportunities in some sectors whilst shutting them down in others. 
2. Credit Creation: Accomodative monetary policy, which spurs private sector credit creation (e.g. margin buying).
3. Euphoria: When speculation for price increase is on the rise (manifested mostly as 'momentum' trading).
4. Financial Distress: When insiders cash out (critical stage) and when speculators become increasingly concerned about the risk of a rush for liquidity.
5. Revulsion: When people no longer want to participate in the market. 

• Displacement: Generally an exogenous shock that triggers the creation of profit opportunities in some sectors while shutting down profit availability in other sectors;
• Essentially, a boom is engendered;
• As long as the opportunities created are greater than those that get shut down, investment and production will pick up to exploit these new opportunities;
• Euphoria: Speculation for price increase is added to investment for production and sales
• This is momentum trading or the "greater fool theory" of investment;

1. Ratio of inexperienced to experienced traders is high; 
2. Greater uncertainty over fundamental value;
3. 'Lottery characteristics' of the security are high (i.e. small chance of a big pay-off); 
4. Buying on margin is possible; 
5. Short-selling is difficult.

R*I*F*I

1. Rational/near-rational;
2. Intrinsic; 
3. Fads; 
4. Information. 

The specific behavioural foundations of various bubble types influence the market dynamics of the 'de-bubbling' process.

• Near rational: Myopia; illusion of control; illusion of knowledge; overconfidence.
• Intrinsic: Representativeness; overoptimism.
• Fads: 'Groupthink'; representativeness; framing
• Information: Lack of aggregation

• Whereas 'rational' bubbles depend on exogenous factors to encourage their formation, 'intrinsic' bubbles grow as the fundamentals improve. 
• Intrinsic bubbles tend to be characterised by overreactions to news about fundamentals. 
• This kind of bubble is characterised by investors extrapolating previously high growth rates into the future.
• The commodities market of 2004, where demand for raw materials inputs by China created rapid acceleration in terms of speculation.

• Fundamental value is the value based on all the information available to all traders. If prices fail to reveal all the information ('information aggregation failure'), then prices deviate from fundamental value, and an informational bubble can form;
• It occurs because it is impossible to have an informationally efficient market because information is costly; 
• Information aggregation failure (also) occurs (when) investors place too much emphasis on past price history in an attempt to use public information ('information cascades');
• These 'information cascades' are inherently fragile because they develop on the basis of very little information (i.e. they are based on the behaviour of others rather than actual information). 

• Smith found that trading behaviour changed following the development and crash of one bubble and that the characteristics of each bubble changed accordingly.
• The first bubble resembled a 'fad' and the second a 'near rational' bubble).

• Representativeness bias involves 'judging things as they appear' rather than how statistically likely they are (e.g. companies with 'good track records' are 'obviously great companies' and will 'always be great companies'); 
• Long-term growth expectations that result from this type of thinking are ratcheted higher and higher whilst comprehension of risk falls further (e.g. dotcom bubble);
• 'Intrinsic' and 'fad' bubbles are influenced by representativeness bias  

1. 'Relatively short-lived rebounds' after the initial correction phase following the 'bursting' of a bubble (similar to Wave B in a EW corrective sequence).
2. They seem to be driven by 'conservatism bias,' which is an unwillingness to let go of previous beliefs. They are exacerbated by the fact that it takes time for investors to let go of such beliefs. Also, when such transitions do occur, they do so very slowly.
3. Vernon Smith's 'laboratory recreation' of bubble environments demonstrated that inexperienced traders will engage in bubble-inducing behaviour at least twice before they begin to keep prices more in-line with fundamental valuations.

• Dow Theory posits that markets have three  components: primary trends, secondary reactions, and daily fluctuations
• A 'bubble echo' would be described in the context of Dow Theory as a 'cyclical bull market rally' ('secondary reaction') within a 'secular bear market' ('primary trend')

• Objective (3-box mainly): Bullish (bearish) support (resistance) lines are drawn at 45 degrees diagonally through the corners of the square below (above) an important low (high), connecting higher lows (lower highs). Once a bullish support line is broken (confirmed by a double-bottom sell signal), a new 45 degree downtrend line is drawn;
   
• Subjective (1-box mainly): Require a reaction point after a trend has started.

1. (i) Count the number of boxes in the vertical column; (ii) Obtain the 'extension' = multiply number of boxes by the reversal size and natural log (ln) of the box size (e.g. ln(1.01) for a 1% box size); (iii) Take the ln of the anchor point; (iv) Calculate the exponential (e^) of the sum of (ii) and (iii). 
2. Log scale counts tend to overstate both the downside and upside targets (i.e. extensions are compounded by 1% per box). 
3. Example answer = approx. 1,291

• Scaling is irrelevant for RS - what is important is the trend. PF shows and defines trend better than any other chart. For example, 45 degree trend lines on 3-box PF charts define the main up and down trends objectively. 
• PF charts of RS are analysed exactly the same way as PF charts of price. In general, log scale RS charts using a 1% box size are the most effective. 1-box reversal charts are also effective.

• The 'Bullish %' measures the percentage of shares comprising an index or a market with charts showing bullish P&F patterns. 
• They can only be constructed from 3-box reversal charts because double-top buy signals are a 3-box signal (not a 1-box signal).
• It can be plotted as a line and interpreted as an oscillator (i.e. if the bullish % surpasses 70%, it is considered overbought).
• A break about 70% is not a sell signal because strong uptrends can stay overbought for many months, if not years. 
• The 50% line is the real indicator of trend change (e.g. a break above 50% indicates a strong probability of a change to a bull trend).
• It is better to draw a 2.5% band on either side of the 50% level and using those levels as signals.

• Bear market: within a range of 20-30 at the low end up to an upper resistance zone of 55 to 65
• Bull market: within range marked by a support zone of 40 to 50 toward an upper resistance zone of 80 to 90
• When the market's trend is about to reverse, so too will the oscillator ranges. As such, the stock will initially bounce off support at the upper boundary for the bear market (55 to 65) before finding support at the support zone of the bull market (40 to 50). This move will likely repeat once more before the oscillator rallies to the resistance range reserved for a bull market

A*C*E

1. Alternation: If wave 2 is sharp, wave 4 will be sideways (if 2 is sideways, 4 will be sharp);
2. Equality: Two of the (non-extended) motive waves will tend towards equality in time and magnitude. When wave 3 is the longest wave, waves 5 and 1 will be equal. Otherwise, a 0.618 multiple is the next likely relationship; 
3. Channeling: A parallel trend channel typically marks the upper and lower boundaries of an impulse wave. Draw one as early as possible to determining wave targets.

• Corrective waves are less clearly identifiable because moves against the trend of one larger degree tend to occur with a 'seeming struggle.' 
• Motive waves, by contrast, always flow with comparative ease in the direction of the one larger trend. 

1. About half of Wave 1s are part of the basing process, and therefore tend to be heavily corrected by Wave 2; 
2. Lots of short selling (crowd "convinced" trend remains down); 
3. Technically more constructive than past bear market rallies (breadth and volume increase, accumulation beginning); 
4. Unless they rise (somewhat strongly) from a large base (i.e. the other 50%), the first wave will be ugly

1. Erodes much of the Wave 1 advance; 
2. Crowd convinced that the "bear is back" ('one last chance to sell'). Market psychology/sentiment will very often be worse at the bottom of Wave 2 than Wave 1. 
3. Often ends on low volume

1. Strong and broad - trend is unmistakable; 
2. Increasingly favourable fundamentals, investor confidence returns; 
3. Tend to generate the most significant volume and price movements. 'Third wave of the third wave' will be the most volatile point of strength in any wave sequences; 
4. Continuation gaps and break-outs on significant volume are likely/possible; 
5. Holds the most valuable keys to the price action's 'personality'

1. Predictable in depth and form due to the guideline of alternation (i.e. using Wave 2 as a reference); 
2. Most often a sideways move (due perhaps to the sharp nature of Wave 2 and/or the strength of Wave 3), building the base for Wave 5; 
3. Initial deterioration sets the scene for non-confirmations of new highs in Wave 5

1. Less dynamic than third waves in terms of breadth; 
2. Usually display a slower maximum speed of price change as well;
3. Look for lesser volume as a rule in fifth wave as opposed to the third (for waves of less than Primary Degree);
4. Optimism runs extremely high despite a narrowing of breadth;
   * Will have price targets based on Waves 3 & 4

1. Investment world is generally convinced that this reaction is just a pullback pursuant to the next leg of an advance
2. First really technically damaging cracks in individual stock patterns start to appear
3. Wave A sets the tone for Wave B to follow
4. Five-wave A indicates a zigzag for wave B. A three-wave A indicates a flat or triangle.

1. B waves are 'phonies' (bull traps, dumb institutional complacency, etc.);
2. Involve a focus on a narrow list of stocks;
3. Tend to be 'unconfirmed' (Dow Theory) and otherwise technically weak. However, B waves of a Primary Degree (or greater) can display heavier volume than that which accompanied the preceding bull market

1. Declining C waves are usually devastating in their destruction. There is virtually no place to hide but cash; 
2. Fear takes over the illusions from Waves A and B.

• Volume can help verify wave counts and project extensions;
• A low point in volume often coincides with a turning point in the market;
• In advancing 5th waves of less than Primary degree, volume tends to be less than the 3rd wave;
• If volume is increasing in the 5th wave, then we most likely have a 5th wave extension;
• Volume often spikes briefly at the throw-over point of a parallel trend channel line;
• Other secondary methods can be used in the context of negative divergences, confirmations, etc.

• Zigzag: the length of wave C is usually equal to that of wave A, although it is not uncommonly 1.618 or 0.618 times the length of wave A. 
• Regular Flat: waves A, B and C are approximately equal.
• Expanded Flat: wave C is often 1.618 times the length of wave A. Wave B is sometimes 1.236 or 1.382 times the length of wave A.
• Triangle: at least two of the alternate waves are typically related to each other by 0.618 (e.g. wave C = 0.618a, wave d = 0.618b, etc.). 

• A penetration of the fifth wave's upper trendline
• If volume is heavy as the fifth wave approaches its upper trendline, it indicates the possibility of a throw-over
• A throw-over is occasionally telegraphed by a preceding "throw-under" either by wave 4 or by wave two of 5
• It is confirmed by an immediate reversal back below the upper trend line

ED:

• Special type of motive wave that occurs primarily in wave 5 or wave C at times when the preceding move has gone "too far too fast". 
• Unlike impulse waves, Wave 4 of an ED almost always enters into the price territory of Wave 1. 
• They take a 'wedge shape' within two converging lines producing an overall count of 3-3-3-3-3 and diminishing volume.
• Rising diagonals are bearish and usually followed by a sharp decline (at least) back to the level where it began. Falling diagonals are bullish.

LD:

• Occurs in wave 1 position of impulses and in the wave A position of zigzags. 
• Trace out a 5-3-5-3-5 pattern. 
• The five-wave subdivisions of the actionary wave communicate a "continuation" message as opposed to a "termination" implication of the three-wave subdivisions in the actionary waves of the ED.
• Main key: decided slowing of price change in the fifth wave relative to the third.

• Situation in which the fifth wave does not move beyond the end of the third;
   
• Can be verified by noting that the presumed fifth wave contains the necessary five subwaves;
   
• Often occurs following a particularly strong third wave.

• The occurence of combination corrections often appear to be the flat correction's way of extending sideways action.
• A combination is composed of simpler types of corrections, including zigzags, flats and triangles.
• The simple corrective pattern components are labeled W, Y and Z.
• Reactionary waves are labeled X. They can take the shape of any correctivce pattern, but are most commonly zigzags.
• Triangles tend to occur at the end of of the pattern.

1. Grand Supercycle
2. Supercycle
3. Cycle
4. Primary
5. Intermediate
6. Minor

1. Reconstruct the channel by connecting waves two and four and placing the parallel in line with the peak of wave 3 (that is if W1 and W3 are 'normal');
2. A parallel to the baseline that touches the top of W1 is typically useful

• Wave 4 of an impulse wave typically ends when it is within the price range of subwave 4 of Wave 3;
• Wave 4 of a diagonal always ends in the price territory of wave 1;
• Wave B of a Zigzag typically retraces between 38% to 79% of Wave A;
• Wave B of a Flat always retraces at least 90% of Wave A, and typically retraces between 100% and 138% of Wave A;

• When a zigzag or flat appears too small to be the entire wave with respect to the preceding wave, a combination is likely;
• For example, if the 'a' wave of the correction does not break the Wave 2 to Wave 4 channel from the preceding motive wave, it typically suggests that we will have a complex correction (no matter how deeply wave 'c' retraces the previous wave);
• The slope of Wave 2 should be less steep than Wave 1. If Wave 2 is steeper, it is a sign that the correction is not over yet and that we wil have a complex correction;

• To determine the primary or major movement of the market.
• Once a trend has been established, it is assumed to hold until a reversal is proved. 
• It is concerned with the direction of the trend rather than the duration or size of the move.
• It should be used as a 'barometer of general business trends' (rather than as a forecasting device for the stock market).

1. The averages discount everything (using daily closing prices)
2. The market has three movements (primary movements, secondary reactions and minor movements)
3. Lines indicate accumulation or distribution ('movement'). Lines are 2-3 week long price movements.
4. Price/volume relationships provide background.
5. Price action determines the trend (e.g. higher highs positively reinforce uptrends).
6. The averages must confirm (i.e. DJIA and DJTA).

• Many of its signals have proved to be late, often 20 to 25% after a peak or trough in the averages has occurred. 
• Altering the % of their equity exposure if dividend yield on the DJIA is too high or low. Practitioners consider a dividend yield of 3% or less on the DJIA as sign the market is at least near a top. A yield of 6% or more suggests a bottom.

• Bull markets begin with "accumulation" by far-sighted investors whilst financial reports are at their worst, grow on a "big move" that attracts broader attention, and end on "excess" or euphoria as the 'public' enters the market and all the financial news is good. 
• Primary down trends begin with "distribution" in the latter stages of the preceding Bull Market. Volume is still high but tends to diminish on rallies. The second phase is the "big move" phase of 'panic' as sellers become more urgent. The third and final phase ends in "despair" and is characterised by liquidation as all possible bad news is priced in.

• A sideways movement in one or both of the averages, which lasts for two or three weeks, or sometimes for as many months, in the course of which prices fluctuate within a range of approximately 5% or less (NB: can be wider than 5% as long as the boundaries are well-defined).
• The formation of a Line signifies that pressure of buying and selling is more or less in balance. 
• The longer the Line (in duration) and the narrower its price range, the greater the significance of the ultimate break-out.
• They may develop at important tops or bottoms, signalling periods of distribution or of accumulation, but arise more frequently as interludes of rest or consolidation in the progress of establishing major trends.

• DT pays no attention to any extreme highs or lows, which may be registered during a day. 
• It only takes into account the closing figures.

1. A ND system avoids emotion, which is advantageous because traders often lose money due to emotional decisions.
2. A ND system also reduces other trading pitfalls: overtrading, premature action, no action, and constant decision-making.
3. Trading with a properly designed mechanical system also prevents large losses and risk of ruin, which most traders have never quantified or understood (risk control can actually be one of the most important advantages of a mechanical system).
4. Trading with a ND system also provides certainty, develops confidence and produces less stress.

1. The more a system is optimised, or curve-fitted, the less reliable it will be in the future.
2. ND systems often make profits in clumps - the wait for the drawdown to be recovered poses an emotional problem for the user, potentially resulting in a loss of confidene just as the system is about to kick in.
3. Even good systems require periodic updates, creating a source of confusion for the designer: is it time to update an underperforming system or is the performance about to kick in?

1. Trend Following: The most profitable (market) background is a trending one because the moves are larger and generate fewer transaction costs. TF systems have been the most productive even though they do not seek to buy at the lows and sell at the highs, but they suffer in trading range markets. TF systems are the most reliable of all system types, especially (Bollinger Band) break-out systems followed by moving-average cross over systems.
2. Pattern Recognition: Partially discretionary in nature because the recognition of patterns requires some interpretation during trade entry. 
3. Countertrend: Based on the buy-low-sell-high philosophy within a trading range. Requires a certain amount of volatility between the peaks and valleys of ranges. Generally discretionary in nature. 
4. Exogenous Signals: Rely on signals from outside the market being traded (e.g. gold prices for the bond market).

• The large percentage of consecutive small losses that produce significant draw-downs.
• To lessen the sequence of losses, we can use a countertrend system or initiate only small positions on a signal until the trend is well-established. Another strategy is to run another trend-following system in parallel that has a longer or shorter period.

1. Is the data used to test the system the same data you will use in actual trading? Data should always be the same as what will be used when the system is running in real time.
2. Does the test data include periods in which the (asset's) price increased, decreased and moved sideways?
3. Did the period generate enough trades (at least 30) to test the quality of the signals produced?
4. Were any out-of-sample tests run?

• Fact or characteristic about the population that we would like to know. 
• It is unknown or unknowable because the entire population cannot be observed. 
• In the case of a TA rule, the population parameter is the rule’s expected performance over the immediate practical future. 
• We assume that it is equal to 0 (i.e. the tested rule has no predictive power).

• The SS sheds light on the population parameter.
• The SI is the inductive leap from the observed value of a sample statistic to the value of the population parameter (known vs. unknown). 
• If the positive performance (SS) is consistently too high to be reasonably attributed to sampling variability, the reasonable SI is that the rule possesses genuine predictive power and a positive expected return - hence, we can say that the sample statistic is 'relevant' if the positive performance is too high to be attributed to sampling variability.

• A relative frequency distribution built from an infinite number of observations and intervals of zero width.
• A PDF is the result of increasing the numbers of observations within a relative frequency distribution. 
• As we tend towards an infinite number of observations, the width of each price change interval becomes gradually thinner such that the histogram turns into a sine wave ('hump').
• Thus, a PDF is a relative frequency distribution composed of an infinite number of observations whose intervals are infinitely narrow. 

• Both are concerned with the unknown value of a
  population parameter. 
   
• A hypothesis test tells us if an effect is present or not.
   
• An estimate tells us about the size of an effect.

• Point Estimate: “The rule’s return is 10%”; 
• Interval Estimate: “There is a 95% probability that this return falls within the range of 5% and 15%”.
• The latter is more informative because the point estimate conveys no sense of the uncertainty in the estimate due to sampling error. 
• The confidence interval solves this problem by combining the information of the point estimate with the information about the estimator's sampling distribution.

• Type I: When a low p-value leads us to reject H0 when it is in fact true. 
• Type II: When the p-value is not low enough for us to reject H0, but H0 is in fact false. 
• Type I is more serious since we are actually exposing the capital to risk to a rule that in reality does not have predictive power.

• Both the bootstrapping and monte carlo methods randomly resample (reuse) the original sample of observations to produce new computer-generated samples. 
• They differ in that (1) each method tests different versions of the null hypothesis, and therefore require different data; (2) they use different random sampling methods – one with replacement (bootstrapping) the other without (MC).

• DM bias is defined as the expected difference between the observed performance of a rule (in testing) that wins the DM competition and its true expected performance. 
• Many rules are tested using algorithms and the rule with the best observed performance is selected.
• There is no guarantee that the selected rule will have similar performance in the future, nor indeed will it be continue to be the best rule

1. Number of rules back-tested: rules back tested en route to discover the highest performing rule. The larger the number of rules, the larger the DM bias; 
2. Number of observations used to compute the performance statistic: the larger the number of observations, the smaller the DM bias; 
3. Correlation among rule returns: degree to which performance histories of the tested rules are correlated (i.e. more highly correlated rules shrinks the effective number of rules being tested). The less correlated they are, the larger the data-mining bias; 
4. Presence (and magnitude) of positive outliers: if there is a very large return on a particular day. When outliers are present, DM tends to be larger (unless their effects are diluted by a large number of observations); 
5. Variation of expected returns among rules: if all rules have similar merit in terms of predictive power (thus low variation), there will be a high degree DM.

1. Out-of-sample testing: excluding one or more subsets of the historical data from the data-mining sample, then using this period to test the best rule discovered in the mined data; 
2. Data-mining correction factors: Deflates the observed performance of the rule that did the best; 
3. Randomization of methods: Uses methods like bootstrapping and Monte Carlo to allow significance testing of several rules without having to hold data aside.

1. X-variable: this is the slope of regression (e.g. the beta of a stock); 
2. t-stat: Statistical significance (best if the X-variable's t stat > 2); 
3. p-value: Likelihood result was achieved by chance (best if the X variable's p-value < 0.05); 
4. R-squared: how much of the variation in the dependent variable's data (returns) is explained by the independent variable's data (returns); 
5. f-statistic significance: should be equal to the X-variable's p-value if we are just regressing one variable

• Stationary time series are generally stable, with a degree of structure. A problem in which the statistical characteristics change over time is said to be non-stationary (e.g. not replacing beads in the jar of grey and white beads each time we take a sample);
• Stock prices are usually nonstationary (because they trend up and down) but returns are often stationary;
• We test for stationarity using a unit root test, with the hypothesis that the series has a unit root (i.e. it is not stationary); 
• If the series does not have a unit root, we reject the hypothesis and conclude that the series is indeed stationary.