Thursday, April 7, 2011
Wednesday, April 6, 2011
S&P 500 Intraday Bias
I have conceived of an intraday indicator, based on market internals, sector relative strength and part judgment (like interpreting news reactions), to estimate what I call an intraday bias. During any given period of normal trading hours, market direction(S&P 500) may have a positive, negative, or neutral bias. The bias can also change intraday, from neutral to positive or negative and vice-versa.
The advantages of this type of indicator is that it is not based on market prices; such trend following indicators are more wont to give delayed signals. The bias' best signals are when positive during a market dip (safer buy) or negative during a market rise (safer sell). Last, the signal does not tell you when or at what price to buy, sell or hold; it only suggests whether the environment is favorable to any of those trades. I originally devised this to aid me in day trading the S&P 500 e-mini futures.
The indicator usually requires 30 min of intraday data to give a clear signal. Hence, I plan to post the bias near 10 AM, and will post again if the signal changes.
Since judgment is involved, I have not kept a historical record on its accuracy. It is also time consuming.
The advantages of this type of indicator is that it is not based on market prices; such trend following indicators are more wont to give delayed signals. The bias' best signals are when positive during a market dip (safer buy) or negative during a market rise (safer sell). Last, the signal does not tell you when or at what price to buy, sell or hold; it only suggests whether the environment is favorable to any of those trades. I originally devised this to aid me in day trading the S&P 500 e-mini futures.
The indicator usually requires 30 min of intraday data to give a clear signal. Hence, I plan to post the bias near 10 AM, and will post again if the signal changes.
Since judgment is involved, I have not kept a historical record on its accuracy. It is also time consuming.
Monday, April 4, 2011
S&P 500 2011 Projection
The S&P 400 Mid Cap index deserves attention, perhaps more than the other indexes. It has broken through the 2007 high and successfully tested it on a pull back. If there were a strong enough bearish force in the market, the 2007 highs would not have been surpassed! The Nadsaq 100 (NDX) and the equal weighted Nasdaq 100--which neutralizes the positive bias Apple has on the index--have also breached the 2007 highs.
The first two charts below (weekly bars) show the Mid Caps and NDX; included in each are channels and a Fibonacci ratio. The Fib line connects the March 2009 low to the April 2010 peak. A possible target is where the 1.618 level and the upper trendlines meet, which projects about 15% more upside on each index. The temporal target on the channels is 3Q-4Q 2011.
The third chart is of the S&P 500 with the same Fibonacci analysis. Amazingly, the 1.618 level between the two points specified is 1560, essentially the 2007 high.
What conclusions do I draw from the studies above? Well, out of the many different scenarios one can conjure up, I would consider 15% upside for the balance of the year to stand out as one worth contemplating. I will observe market developments in the coming weeks and months to determine the degree to which the market is or is not fitting into this and other projections.
The first two charts below (weekly bars) show the Mid Caps and NDX; included in each are channels and a Fibonacci ratio. The Fib line connects the March 2009 low to the April 2010 peak. A possible target is where the 1.618 level and the upper trendlines meet, which projects about 15% more upside on each index. The temporal target on the channels is 3Q-4Q 2011.
The third chart is of the S&P 500 with the same Fibonacci analysis. Amazingly, the 1.618 level between the two points specified is 1560, essentially the 2007 high.
What conclusions do I draw from the studies above? Well, out of the many different scenarios one can conjure up, I would consider 15% upside for the balance of the year to stand out as one worth contemplating. I will observe market developments in the coming weeks and months to determine the degree to which the market is or is not fitting into this and other projections.
Sunday, April 3, 2011
Revising the Reward-Risk Ratio
This article was first published in the April edition of the Market Technicians Association's newsletter.
Reward-Risk is a term for the ratio of the potential profit to the potential loss of a trade. In using such analysis, the entry price and the prices at which profits or losses will be taken are predetermined. Measuring the units of reward per risk in advance aids in deciding whether to enter a position. However, since the outcome of a trade is uncertain, this widely known and used measurement must be revised in order to account for the probability of the trade’s success or failure, which can be done through expected value.
In expected value, a set of future values, or payouts, are adjusted to reflect the probability that each will materialize. For a stock, given a $10 entry with a profit target of $16 and a stop-loss at $8, the reward-risk is $6 to $2, a 3:1 relationship; these are the set of future values. Additionally, say the probability of prices reaching the target before the stop-loss is 40%. The odds of being stopped out are thus 60% [=1-0.4].To obtain the expected value, one multiplies the chances of a profit by the potential profit, .4*$6 = $2.4, and the chances of loss by the potential loss, .6*$2 = $1.2. Thus, the expected reward-risk (ERR) is $2.4 to $1.2, or 2:1. The expected value is the gain minus the loss, or $1.2 [=$2.4-$1.2]. The unadjusted ratio of $6:$2, or 3:1 will from here on be referred to as the simple reward-risk (SRR). Note how in this example, the SRR is 3:1 but the ERR is 2:1. With a probability of success of .25, instead of .4, the expected reward is $1.5 [=.25*$6], the expected risk is $1.5 [=.75*$2], and the expected value is 0, or breakeven. Calculating an ERR of 1:1 reveals the odds needed to break even on a trade.
To use a non-market and non-monetary example, say a football player makes two-thirds, or roughly 67%, of his field goals. A field goal is worth 3 points if obtained, or 0 points if missed. For this player, his expected value is 2 points [=.67*3 + .33*0]. If in the last play of the game, his team is down by 3 points and he is up to kick a field goal, a strictly rational gambler will bet against the team. If the team is down by 1 point, the gambler will bet for the team. Although non-intuitive, a better description of reality is that this player scores 2 points per field goal rather than 3 points per field goal. Our gambler, by the way, will stay in business.
An SRR accounts for one observation, whereas an ERR accounts for all possible observations. Over the long term, the values of the ERR will materialize, similar to how the football player only scores 2 points per field goal. And like the gambler, a rational trader will base his decisions on ERR profiles that have a positive expected value. A positive expected value, however small, will result in long term success, and vice-versa.
Let us return to the example of the $10 stock with the SRR of 3:1. Given the present market conditions, the trader has assessed that either $16 or $8 will be reached first; whichever target is reached first will close the trade. If the analysis ends there, the trader unwittingly assumes that there is a 50/50 chance of a profit (of $6) or a loss (of $2). The expected return is thus $3 [=.50*$6] and the expected risk is $1 [=.50* $2]. Observe that the $3 profit to $1 loss remains a 3:1 relationship; the SRR equals the ERR. Any and every reward-risk setup that does not define probabilities assumes a 50/50 chance that its respective targets will be met. Therefore, the classical concept of reward-risk does—and has always— incorporated expected value, but as a passive assumption! Determining an expected reward-risk based on trade specific probabilities is not a supplement to the simple reward-risk construction, but rather, a revision of it.
The passive assumption of a 50/50 chance for a profit or loss has exerted a silent influence on the subject of reward-risk. Literature in Technical Analysis often prescribes a minimum reward-risk of 3:1 for one to remain profitable over time. As discussed above, “over time” is when expected values pave over individual observations. If a risk-reward lower than 3:1 is considered to ultimately result in a trader’s ruin, one can extract the assumed probabilities. The breakeven odds for an SRR of 3:1 are 25/75. Therefore, one assumes that successful traders are profitable slightly over 25% of the time, because anything less than 3:1 will result in a negative expected value. Interestingly, this success rate matches the figure of 30%, which is the percentage of time that the market is estimated to be trending.
A positive expected return can result from various reward-risk proportions and their respective probabilities of success and failure. For example, assume an SRR of 1:2.5, that is, for every potential profit of 1, there is a potential loss of 2.5. With a probability of success of .8, the ERR is 0.8:0.5, or 1.6:1, and the expected value is .30. Over the long term, this reward-risk profile makes .30 per trade—not per every winning trade, but per trade. That’s success. Now, examine a trade with a large profit potential and a “tight” stop-loss, a temptation particular to futures traders. Even with an SRR of 7:1, a 90% chance of being stopped out yields an ERR of 0.7/0.9, or .77:1, and a negative expected value, -.40. Trading only these 7:1 setups ensures a quick bankruptcy. As you can see, even if the SRR is less than 1, any trade with a positive expected value—adjusting for commissions and other frictions—should be undertaken. In this light, the prescription of trading only 3:1 or higher setups is crude, and most likely a result of an implicitly assumed success rate of around 25-30%, which may be related to the fact that markets trend 30% of the time.
Estimating the Probability
Trading is inherently probabilistic. The preceding arguments strongly suggest that if one is to use a reward-risk ratio in assessing trades, an expected value must be calculated and serve as a deciding factor.—Well, that’s the easy part. The real challenge to this model is in determining an accurate measure for the probability that will be used to arrive at expected values. Due to the complex nature of trading in the financial markets, probabilities can only be estimated, not determined. In the examples throughout this article, the probabilities used were assumed to be accurate for the sake of illustration. This section sketches four methods that can be used to estimate the probability of success for a given trade. Note that only one value needs to be calculated, because 1 minus the probability of success equals the probability of failure.
Historical Success Rate
For an individual trader with a consistent style, his historical success rate can be used as a proxy for the probably of success. For example, if he finds that 55% of his trades are winners, .55 and .45 will be the probability of success and of failure, respectively. With these probabilities, an SRR of .82:1 yields an ERR of 1:1, or breakeven.
You will see later on in this article, the probability of success can be inversely related with the reward to risk ratio. As higher price targets are attempted, there are fewer successes and vice-versa. The trader can balance the success rate and reward-risk proportion to see what combination yields the highest expected value. In the example above, the SRR must be greater than .82:1 for profitability. Based on the inverse relationship established above, to maintain a 55% success rate the reward may not extend too far beyond .82:1. Note, however, that if these measures of probability are consistent and accurate all one needs is a positive expected value for a trade to be worthwhile; in this example, even an SRR as “low” as 1.05:1 will have an expected value of 0.1275 per trade.
The historical success rate approach has the following advantages and disadvantages:
Advantages
• Based on empirical data
• Quick and simple to calculate
• Requires no estimates
• A long enough track record has some reliability
Disadvantages
• Past performance is not indicative of future results; the conditions that have allowed that style obtain a given success rate may change
• Not a scientifically rigorous approach
Technical Analysis Statistics
Technical traders use various methods to determine buy and sell signals. These include trendlines, support and resistance, continuation and reversal patterns, indicators, and many more. The statistical success rates of these methods of technical analysis can be used for calculating probabilities.
In Charles Kirkpatrick and Julie Dahlquist’s Technical Analysis, the authors summarize the results from Thomas Bulkowski’s Trading Classic Chart Patterns. In his book, Bulkowski documented the success rate of various technical continuation and reversal patterns from a sample of 700 stocks during a span of ten years. I will use his figures for illustrative purposes.
For a rectangle pattern, also known as a trading range, if there is a viable upward breakout, established after the fact in Bulkowski’s research, 80% of the time there will be a gain of 10%. (Technical Analysis, p. 315) That yields an expected reward of 8%. A stop-loss at -4% [.2*-4% = -8%] is thus the breakeven point. A stop-loss of less than 4% below the entry price is necessary to obtain a positive expected value. Continuing with this example, 75% of rectangle breakouts are false signals, making the ex ante success rate 20% [=.8*(1-.75)]. The expected reward is not 8%, but 2%. A stop-loss at 2.5% yields an expected value of 0. The breakeven SRR is thus 5:1, a 10% gain to a 2.5% loss. Pretty grim. These numbers also assume that the odds already discount the possibility of being stopped-out prior to the 10% gain.
Using technical analysis statistics to determine probabilities has the following advantages and disadvantages:
Advantages
• If technical analysis is used to determine the reward and risk targets, this method is the most consistent with the analysis
• Expected values are simple to calculate
• Requires no estimates
Disadvantages
• The body of research on the success rate of technical patterns and indicators is limited, an enormous hindrance to this approach
• Based on historical data
• Both the success rates of valid signals and the likely percentage gain prior to a reversal of the signal must be known to properly calculate the probability
Volatility of Returns
All else equal, of two price targets in opposing directions, the target closer to the entry price has greater odds of being reached first. To a trader, a stop-loss being reached prior to an upside target is not an inconsequential occurrence. The standard deviation of returns, specified for the expected holding period, aids in assessing the chances of being stopped out of a trade due to the proximity of the profit and loss targets to the entry price.
Assume a trade with an expected four month holding period. The security in question has a historical four month mean return of 1% and a standard deviation (σ) of 3%. The entry price is $10, profits will be taken at $10.70, and a stop-loss is placed at $9.80. Once these reward-risk targets are set, one can determine the distance, in standard deviations, of each from the entry price. In this example, the upside target is 7%, 2σ from the mean of 1% and the stop-loss is at 2%,-1σ from the mean. On a normal distribution, +2σ or higher is reached 2.4% of the time and -1σ or lower is reached 16% of the time. The balance for which neither target is achieved is 81.6%. The image below depicts these zones; red is for the loss target, green is for the profit target, and blue is neither.
Two assumptions needed to simplify the example is that the trader will not readjust the stop-loss or the price target and that after the four month holding period, the trade will be exited at the middle of the blue target range if neither target has been met. Since there are three probabilities involved, there must be a third step in calculating expected value.
Expected reward: .024*7% = .168%
Expected risk: .16*-2% = -.32%
Expected exit if neither target achieved (middle of blue range): .816*2.5% = 2.04%; since the result is positive, must be added to expected reward
Expected reward-risk: 2.208% to .32% = 6.9:1
Expected value = .168% + -.32% + 2.4% = 1.89% profit
The simple reward-risk of 7% to 2%, or 3.5:1, is not a meaningful number
Let’s examine the reverse setup, in which the profit target is 1σ, 4%, and the stop loss is 2σ, -5%:
Expected reward: .16*4% = .64%
Expected risk: .024*-5% = -.12%
Expected exit if neither target achieved (middle of blue range): .816*-0.5% = -.408%; since the result is negative, must be added to expected risk
Expected reward-risk: .64% to .528% = 1.2:1
Expected value: .64% + -.12% + -.408% = .132% profit
The simple reward-risk of 4% to 5%, or .8:1, is not a meaningful number
As you can see, the proximity of profit and loss targets to an entry price, and the resulting probability of which target will be reached first, shapes the reward-risk profile. Also, where the trade is closed if neither target is reached will significantly impact the expected value. If the exit price was assumed to be at breakeven, instead of at the middle of the blue range, the first and second trades would have an expected value of -.152% and .52%, respectively.
Note that such an analysis is direction neutral; it simply relies on volatility to characterize the potential profitability of a trade. Someone seeking only to identify statistical setups may find this direction neutral quality appealing; however, a discretionary trader usually buys with the bias that prices will rise.
The volatility of returns approach has the following advantages and disadvantages*:
Advantages
• Accounts for the randomness of market direction
• Sets more realistic expectations of whether a profit or loss target will be achieved
• Scientifically sound way to extract probabilities
Disadvantages
• Does not incorporate the tools of technical analysis, e.g., trend lines, patterns, indicators
• Statistics are imperfect predictors
• Assumes a normal distribution of returns
*Direction neural is either an advantage or a disadvantage, depending on the trading style
Multi-Factor Model
Another approach is to use a multi-factor model to the determine probabilities. Such a model calculates the statistical relationship of various independent variables, called “factors,” to the dependant variable, resulting in the following equation:
P = α + c1F1 + c2F2 + c3F3 + ……+ cnFn + e
where:
P = dependant variable (in this case, probability of success)
α = intercept term (the of value P if all factors equal zero)
c = factor coefficient
F = factor
e = error term (due to imperfect statistical relationships)
A trader could determine that the following five factors are sufficient to explain a trade’s probability of success: technical strength, fundamental strength, the entry price’s distance, measured in standard deviations, from the profit target, the entry price’s current distance, measured in the inverse of the standard deviation, from the stop-loss, and the trader’s historical success rate. The coefficient is the degree to which each factor influences the dependant variable, holding all other factors equal. The table below lists the five factors, their coefficients, and the factors’ values for a particular trade. (All listed values are simply illustrative.)
*This value indicates that the stop loss is negative 2 standard deviations from the entry price [1/σ = 1/-2 = -.5]. There is an inverse relationship between the price’s distance from the stop-loss and the probability of success.
From the values on the third column of the table, note that the stock is in a strong technical position, a neutral fundamental position, and the trader is profitable 60% of the time. Let us assume the trade in question is from the example used in this article’s section on volatility: the trader aims for a 4% return (1σ) with a 5% risk (-2σ). Let us also assume that the intercept and error term equal zero. Using the factor model and the values from the table, the probability of success is as follows:
P = 0 + 1.2(7) + 1(5) + -1.5(1) + 2.2(-.5) + .8(60) = .588
The probability of success for this trade is 58.8%. With a 4% return and a 5% stop loss, the ERR is 2.35%/2.06%, or 1.14:1, with an expected value of 0.292.
The multi-factor model approach has the following advantages and disadvantages:
Advantages
• Various inputs can be used, including inputs from the above stated methods
• Model acknowledges that more than one factor influences probabilities
• Scientifically valid
Disadvantages
• Extremely complex to construct correctly
• Some inputs may require estimates
• Requires a large supply of data
• Model must be properly specified, that is, it must properly account for the factors that influence the dependant variable
Revising the simple reward-risk measure to account for expected value results in a much richer analysis. It may also prove to be more accurate in determining a trader’s long term profitability. As such, research on how to best estimate the probability of success or the probability of failure for a trade with a defined reward and risk would be valuable.
To quickly touch upon two complications not addressed in this article: first, the ERR discussed here was for the onset of a trade; once the trade is executed, the ERR profile will change as a function of price action, changing probabilities, and trader decisions, such as raising a stop-loss. Second, conditional probabilities may be needed to calculate viable expected values.
To summarize the major points of this article:
• Trading is probabilistic by nature
• Expected value should be incorporated into reward-risk analysis
• To determine the expected reward-risk (ERR), first multiply the reward by probability of success and the loss by the probability of loss; the ratio of these two is the ERR
• The expected reward minus the expected risk is the expected value of the trade
• An ERR of 1:1 is a breakeven setup, with an expected value of zero
• The simple reward-risk ratio (SRR) is actually an ERR that passively assumes that the probability of success is .50
• A positive expected return can result from various reward-risk proportions and their respective probabilities of success and failure
• The classical prescription of a 3:1 SRR may have been implicitly based on the fact that the percentage of winning trades was slightly higher than 25%
• The crux of calculating an expected reward-risk ratio is in estimating a viable probability of success or of failure
• I have introduced four possible methods for estimating the probability to be used in calculating the ERR. These are, the trader’s historical success rate, statistics on methods of technical analysis, volatility of returns, and a multifactor model
• Research on methods of obtaining the probability of trade success in the context of reward-risk would greatly contribute to this type of analysis
Reward-Risk is a term for the ratio of the potential profit to the potential loss of a trade. In using such analysis, the entry price and the prices at which profits or losses will be taken are predetermined. Measuring the units of reward per risk in advance aids in deciding whether to enter a position. However, since the outcome of a trade is uncertain, this widely known and used measurement must be revised in order to account for the probability of the trade’s success or failure, which can be done through expected value.
In expected value, a set of future values, or payouts, are adjusted to reflect the probability that each will materialize. For a stock, given a $10 entry with a profit target of $16 and a stop-loss at $8, the reward-risk is $6 to $2, a 3:1 relationship; these are the set of future values. Additionally, say the probability of prices reaching the target before the stop-loss is 40%. The odds of being stopped out are thus 60% [=1-0.4].To obtain the expected value, one multiplies the chances of a profit by the potential profit, .4*$6 = $2.4, and the chances of loss by the potential loss, .6*$2 = $1.2. Thus, the expected reward-risk (ERR) is $2.4 to $1.2, or 2:1. The expected value is the gain minus the loss, or $1.2 [=$2.4-$1.2]. The unadjusted ratio of $6:$2, or 3:1 will from here on be referred to as the simple reward-risk (SRR). Note how in this example, the SRR is 3:1 but the ERR is 2:1. With a probability of success of .25, instead of .4, the expected reward is $1.5 [=.25*$6], the expected risk is $1.5 [=.75*$2], and the expected value is 0, or breakeven. Calculating an ERR of 1:1 reveals the odds needed to break even on a trade.
To use a non-market and non-monetary example, say a football player makes two-thirds, or roughly 67%, of his field goals. A field goal is worth 3 points if obtained, or 0 points if missed. For this player, his expected value is 2 points [=.67*3 + .33*0]. If in the last play of the game, his team is down by 3 points and he is up to kick a field goal, a strictly rational gambler will bet against the team. If the team is down by 1 point, the gambler will bet for the team. Although non-intuitive, a better description of reality is that this player scores 2 points per field goal rather than 3 points per field goal. Our gambler, by the way, will stay in business.
An SRR accounts for one observation, whereas an ERR accounts for all possible observations. Over the long term, the values of the ERR will materialize, similar to how the football player only scores 2 points per field goal. And like the gambler, a rational trader will base his decisions on ERR profiles that have a positive expected value. A positive expected value, however small, will result in long term success, and vice-versa.
Let us return to the example of the $10 stock with the SRR of 3:1. Given the present market conditions, the trader has assessed that either $16 or $8 will be reached first; whichever target is reached first will close the trade. If the analysis ends there, the trader unwittingly assumes that there is a 50/50 chance of a profit (of $6) or a loss (of $2). The expected return is thus $3 [=.50*$6] and the expected risk is $1 [=.50* $2]. Observe that the $3 profit to $1 loss remains a 3:1 relationship; the SRR equals the ERR. Any and every reward-risk setup that does not define probabilities assumes a 50/50 chance that its respective targets will be met. Therefore, the classical concept of reward-risk does—and has always— incorporated expected value, but as a passive assumption! Determining an expected reward-risk based on trade specific probabilities is not a supplement to the simple reward-risk construction, but rather, a revision of it.
The passive assumption of a 50/50 chance for a profit or loss has exerted a silent influence on the subject of reward-risk. Literature in Technical Analysis often prescribes a minimum reward-risk of 3:1 for one to remain profitable over time. As discussed above, “over time” is when expected values pave over individual observations. If a risk-reward lower than 3:1 is considered to ultimately result in a trader’s ruin, one can extract the assumed probabilities. The breakeven odds for an SRR of 3:1 are 25/75. Therefore, one assumes that successful traders are profitable slightly over 25% of the time, because anything less than 3:1 will result in a negative expected value. Interestingly, this success rate matches the figure of 30%, which is the percentage of time that the market is estimated to be trending.
A positive expected return can result from various reward-risk proportions and their respective probabilities of success and failure. For example, assume an SRR of 1:2.5, that is, for every potential profit of 1, there is a potential loss of 2.5. With a probability of success of .8, the ERR is 0.8:0.5, or 1.6:1, and the expected value is .30. Over the long term, this reward-risk profile makes .30 per trade—not per every winning trade, but per trade. That’s success. Now, examine a trade with a large profit potential and a “tight” stop-loss, a temptation particular to futures traders. Even with an SRR of 7:1, a 90% chance of being stopped out yields an ERR of 0.7/0.9, or .77:1, and a negative expected value, -.40. Trading only these 7:1 setups ensures a quick bankruptcy. As you can see, even if the SRR is less than 1, any trade with a positive expected value—adjusting for commissions and other frictions—should be undertaken. In this light, the prescription of trading only 3:1 or higher setups is crude, and most likely a result of an implicitly assumed success rate of around 25-30%, which may be related to the fact that markets trend 30% of the time.
Estimating the Probability
Trading is inherently probabilistic. The preceding arguments strongly suggest that if one is to use a reward-risk ratio in assessing trades, an expected value must be calculated and serve as a deciding factor.—Well, that’s the easy part. The real challenge to this model is in determining an accurate measure for the probability that will be used to arrive at expected values. Due to the complex nature of trading in the financial markets, probabilities can only be estimated, not determined. In the examples throughout this article, the probabilities used were assumed to be accurate for the sake of illustration. This section sketches four methods that can be used to estimate the probability of success for a given trade. Note that only one value needs to be calculated, because 1 minus the probability of success equals the probability of failure.
Historical Success Rate
For an individual trader with a consistent style, his historical success rate can be used as a proxy for the probably of success. For example, if he finds that 55% of his trades are winners, .55 and .45 will be the probability of success and of failure, respectively. With these probabilities, an SRR of .82:1 yields an ERR of 1:1, or breakeven.
You will see later on in this article, the probability of success can be inversely related with the reward to risk ratio. As higher price targets are attempted, there are fewer successes and vice-versa. The trader can balance the success rate and reward-risk proportion to see what combination yields the highest expected value. In the example above, the SRR must be greater than .82:1 for profitability. Based on the inverse relationship established above, to maintain a 55% success rate the reward may not extend too far beyond .82:1. Note, however, that if these measures of probability are consistent and accurate all one needs is a positive expected value for a trade to be worthwhile; in this example, even an SRR as “low” as 1.05:1 will have an expected value of 0.1275 per trade.
The historical success rate approach has the following advantages and disadvantages:
Advantages
• Based on empirical data
• Quick and simple to calculate
• Requires no estimates
• A long enough track record has some reliability
Disadvantages
• Past performance is not indicative of future results; the conditions that have allowed that style obtain a given success rate may change
• Not a scientifically rigorous approach
Technical Analysis Statistics
Technical traders use various methods to determine buy and sell signals. These include trendlines, support and resistance, continuation and reversal patterns, indicators, and many more. The statistical success rates of these methods of technical analysis can be used for calculating probabilities.
In Charles Kirkpatrick and Julie Dahlquist’s Technical Analysis, the authors summarize the results from Thomas Bulkowski’s Trading Classic Chart Patterns. In his book, Bulkowski documented the success rate of various technical continuation and reversal patterns from a sample of 700 stocks during a span of ten years. I will use his figures for illustrative purposes.
For a rectangle pattern, also known as a trading range, if there is a viable upward breakout, established after the fact in Bulkowski’s research, 80% of the time there will be a gain of 10%. (Technical Analysis, p. 315) That yields an expected reward of 8%. A stop-loss at -4% [.2*-4% = -8%] is thus the breakeven point. A stop-loss of less than 4% below the entry price is necessary to obtain a positive expected value. Continuing with this example, 75% of rectangle breakouts are false signals, making the ex ante success rate 20% [=.8*(1-.75)]. The expected reward is not 8%, but 2%. A stop-loss at 2.5% yields an expected value of 0. The breakeven SRR is thus 5:1, a 10% gain to a 2.5% loss. Pretty grim. These numbers also assume that the odds already discount the possibility of being stopped-out prior to the 10% gain.
Using technical analysis statistics to determine probabilities has the following advantages and disadvantages:
Advantages
• If technical analysis is used to determine the reward and risk targets, this method is the most consistent with the analysis
• Expected values are simple to calculate
• Requires no estimates
Disadvantages
• The body of research on the success rate of technical patterns and indicators is limited, an enormous hindrance to this approach
• Based on historical data
• Both the success rates of valid signals and the likely percentage gain prior to a reversal of the signal must be known to properly calculate the probability
Volatility of Returns
All else equal, of two price targets in opposing directions, the target closer to the entry price has greater odds of being reached first. To a trader, a stop-loss being reached prior to an upside target is not an inconsequential occurrence. The standard deviation of returns, specified for the expected holding period, aids in assessing the chances of being stopped out of a trade due to the proximity of the profit and loss targets to the entry price.
Assume a trade with an expected four month holding period. The security in question has a historical four month mean return of 1% and a standard deviation (σ) of 3%. The entry price is $10, profits will be taken at $10.70, and a stop-loss is placed at $9.80. Once these reward-risk targets are set, one can determine the distance, in standard deviations, of each from the entry price. In this example, the upside target is 7%, 2σ from the mean of 1% and the stop-loss is at 2%,-1σ from the mean. On a normal distribution, +2σ or higher is reached 2.4% of the time and -1σ or lower is reached 16% of the time. The balance for which neither target is achieved is 81.6%. The image below depicts these zones; red is for the loss target, green is for the profit target, and blue is neither.
Two assumptions needed to simplify the example is that the trader will not readjust the stop-loss or the price target and that after the four month holding period, the trade will be exited at the middle of the blue target range if neither target has been met. Since there are three probabilities involved, there must be a third step in calculating expected value.
Expected reward: .024*7% = .168%
Expected risk: .16*-2% = -.32%
Expected exit if neither target achieved (middle of blue range): .816*2.5% = 2.04%; since the result is positive, must be added to expected reward
Expected reward-risk: 2.208% to .32% = 6.9:1
Expected value = .168% + -.32% + 2.4% = 1.89% profit
The simple reward-risk of 7% to 2%, or 3.5:1, is not a meaningful number
Let’s examine the reverse setup, in which the profit target is 1σ, 4%, and the stop loss is 2σ, -5%:
Expected reward: .16*4% = .64%
Expected risk: .024*-5% = -.12%
Expected exit if neither target achieved (middle of blue range): .816*-0.5% = -.408%; since the result is negative, must be added to expected risk
Expected reward-risk: .64% to .528% = 1.2:1
Expected value: .64% + -.12% + -.408% = .132% profit
The simple reward-risk of 4% to 5%, or .8:1, is not a meaningful number
As you can see, the proximity of profit and loss targets to an entry price, and the resulting probability of which target will be reached first, shapes the reward-risk profile. Also, where the trade is closed if neither target is reached will significantly impact the expected value. If the exit price was assumed to be at breakeven, instead of at the middle of the blue range, the first and second trades would have an expected value of -.152% and .52%, respectively.
Note that such an analysis is direction neutral; it simply relies on volatility to characterize the potential profitability of a trade. Someone seeking only to identify statistical setups may find this direction neutral quality appealing; however, a discretionary trader usually buys with the bias that prices will rise.
The volatility of returns approach has the following advantages and disadvantages*:
Advantages
• Accounts for the randomness of market direction
• Sets more realistic expectations of whether a profit or loss target will be achieved
• Scientifically sound way to extract probabilities
Disadvantages
• Does not incorporate the tools of technical analysis, e.g., trend lines, patterns, indicators
• Statistics are imperfect predictors
• Assumes a normal distribution of returns
*Direction neural is either an advantage or a disadvantage, depending on the trading style
Multi-Factor Model
Another approach is to use a multi-factor model to the determine probabilities. Such a model calculates the statistical relationship of various independent variables, called “factors,” to the dependant variable, resulting in the following equation:
P = α + c1F1 + c2F2 + c3F3 + ……+ cnFn + e
where:
P = dependant variable (in this case, probability of success)
α = intercept term (the of value P if all factors equal zero)
c = factor coefficient
F = factor
e = error term (due to imperfect statistical relationships)
A trader could determine that the following five factors are sufficient to explain a trade’s probability of success: technical strength, fundamental strength, the entry price’s distance, measured in standard deviations, from the profit target, the entry price’s current distance, measured in the inverse of the standard deviation, from the stop-loss, and the trader’s historical success rate. The coefficient is the degree to which each factor influences the dependant variable, holding all other factors equal. The table below lists the five factors, their coefficients, and the factors’ values for a particular trade. (All listed values are simply illustrative.)
*This value indicates that the stop loss is negative 2 standard deviations from the entry price [1/σ = 1/-2 = -.5]. There is an inverse relationship between the price’s distance from the stop-loss and the probability of success.
From the values on the third column of the table, note that the stock is in a strong technical position, a neutral fundamental position, and the trader is profitable 60% of the time. Let us assume the trade in question is from the example used in this article’s section on volatility: the trader aims for a 4% return (1σ) with a 5% risk (-2σ). Let us also assume that the intercept and error term equal zero. Using the factor model and the values from the table, the probability of success is as follows:
P = 0 + 1.2(7) + 1(5) + -1.5(1) + 2.2(-.5) + .8(60) = .588
The probability of success for this trade is 58.8%. With a 4% return and a 5% stop loss, the ERR is 2.35%/2.06%, or 1.14:1, with an expected value of 0.292.
The multi-factor model approach has the following advantages and disadvantages:
Advantages
• Various inputs can be used, including inputs from the above stated methods
• Model acknowledges that more than one factor influences probabilities
• Scientifically valid
Disadvantages
• Extremely complex to construct correctly
• Some inputs may require estimates
• Requires a large supply of data
• Model must be properly specified, that is, it must properly account for the factors that influence the dependant variable
Revising the simple reward-risk measure to account for expected value results in a much richer analysis. It may also prove to be more accurate in determining a trader’s long term profitability. As such, research on how to best estimate the probability of success or the probability of failure for a trade with a defined reward and risk would be valuable.
To quickly touch upon two complications not addressed in this article: first, the ERR discussed here was for the onset of a trade; once the trade is executed, the ERR profile will change as a function of price action, changing probabilities, and trader decisions, such as raising a stop-loss. Second, conditional probabilities may be needed to calculate viable expected values.
To summarize the major points of this article:
• Trading is probabilistic by nature
• Expected value should be incorporated into reward-risk analysis
• To determine the expected reward-risk (ERR), first multiply the reward by probability of success and the loss by the probability of loss; the ratio of these two is the ERR
• The expected reward minus the expected risk is the expected value of the trade
• An ERR of 1:1 is a breakeven setup, with an expected value of zero
• The simple reward-risk ratio (SRR) is actually an ERR that passively assumes that the probability of success is .50
• A positive expected return can result from various reward-risk proportions and their respective probabilities of success and failure
• The classical prescription of a 3:1 SRR may have been implicitly based on the fact that the percentage of winning trades was slightly higher than 25%
• The crux of calculating an expected reward-risk ratio is in estimating a viable probability of success or of failure
• I have introduced four possible methods for estimating the probability to be used in calculating the ERR. These are, the trader’s historical success rate, statistics on methods of technical analysis, volatility of returns, and a multifactor model
• Research on methods of obtaining the probability of trade success in the context of reward-risk would greatly contribute to this type of analysis
PE Multiples, Part 1: Calculating the PE
Any participant in the financial markets can benefit from an awareness of the price-to-earnings ratio, commonly referred to as the PE ratio or multiple. Even passive viewers of CNBC will hear this term frequently. PE is the first financial concept my father introduced to me. I plan to provide a thorough understanding of this ratio through a series of posts. Trust me, there is a lot one must write in order to fully explore this concept. Also, beyond explaining what it is, I will also add some of my own insights, particularly, how it is both a fundamental and a partially technical figure.
To derive the PE of a stock, simply look up its price and its earnings and divide the two. (Yahoo Finance provided all of the data used in this post.) On Friday, April 1st Exxon Mobil, ticker XOM, closed at 84.72. Its previously reported earnings per share (EPS) was $6.22. Its PE is thus 13.62 [=84.72/6.22]. An investor may want derive this multiple based on the company’s future earnings, which are expected to be $8.37 per share, yielding a PE of 10.12. So, 13.62 and 10.12 are the trailing PE and the forward PE, respectively.
The earnings used in the calculations above was the net income, which is affected by balance sheet asset depreciation, stock compensations, interest paid on debt, taxes and other factors. One may consider those factors not as relevant to the long term profitability of a company, so instead of using net income to calculate the PE, one can use what’s known as operating income. Operating income, which does not take into account the factors mentioned above, is the earnings net of various expenses, like research and development, production costs, marketing and sales, all of which are essential elements of the company’s operations. Exxon’s most recent operating income was 8.42. Its trailing PE based on operating income is 10.05.
To summarize, the PE is the ratio of a stocks price to some measure of its earnings. This measure can be current earnings, future earnings, or operating earnings. Each of those three provides a slightly different perspective on the company so it is worthwhile to inspect all of them when researching a stock. Since the trailing PE is based on historical data, it is a factual measure that requires no estimates. A forward PE, on the other hand, requires an estimate of future earnings, which can be inaccurate. However, the forward PE is more important because markets price stocks based on forward earnings and future expectations in general. Lastly, using operating income instead of net income may better represent the company's fundamentals.
This is a good place to stop this first post. To those for whom this post is elementary, I promise more advanced concepts are to come.
The next topic will be the significance of the PE ratio.
To derive the PE of a stock, simply look up its price and its earnings and divide the two. (Yahoo Finance provided all of the data used in this post.) On Friday, April 1st Exxon Mobil, ticker XOM, closed at 84.72. Its previously reported earnings per share (EPS) was $6.22. Its PE is thus 13.62 [=84.72/6.22]. An investor may want derive this multiple based on the company’s future earnings, which are expected to be $8.37 per share, yielding a PE of 10.12. So, 13.62 and 10.12 are the trailing PE and the forward PE, respectively.
The earnings used in the calculations above was the net income, which is affected by balance sheet asset depreciation, stock compensations, interest paid on debt, taxes and other factors. One may consider those factors not as relevant to the long term profitability of a company, so instead of using net income to calculate the PE, one can use what’s known as operating income. Operating income, which does not take into account the factors mentioned above, is the earnings net of various expenses, like research and development, production costs, marketing and sales, all of which are essential elements of the company’s operations. Exxon’s most recent operating income was 8.42. Its trailing PE based on operating income is 10.05.
To summarize, the PE is the ratio of a stocks price to some measure of its earnings. This measure can be current earnings, future earnings, or operating earnings. Each of those three provides a slightly different perspective on the company so it is worthwhile to inspect all of them when researching a stock. Since the trailing PE is based on historical data, it is a factual measure that requires no estimates. A forward PE, on the other hand, requires an estimate of future earnings, which can be inaccurate. However, the forward PE is more important because markets price stocks based on forward earnings and future expectations in general. Lastly, using operating income instead of net income may better represent the company's fundamentals.
This is a good place to stop this first post. To those for whom this post is elementary, I promise more advanced concepts are to come.
The next topic will be the significance of the PE ratio.
Saturday, April 2, 2011
Taking Requests
Once this site picks up some speed, I will be offering readers the ability to requests topics they would like an educational post on. The purpose would be to explain investment or trading concepts in clear and simple language. Here are examples of acceptable requests, for different levels of experience:
Beginner: What's the meaning of PE ratio?
Novice: How can I incorporate PE ratios into my investing?
Novice: What does RSI mean?
Novice: Why is copper used as an economic and trading indicator?
Advanced: What indicators can be used to confirm intraday Ts?
These are not acceptable requests:
Where do you think Xerox will be trading next week?
What's your opinion on copper?
My goal is for this feature to be entertaining and useful to as many readers as possible.
Beginner: What's the meaning of PE ratio?
Novice: How can I incorporate PE ratios into my investing?
Novice: What does RSI mean?
Novice: Why is copper used as an economic and trading indicator?
Advanced: What indicators can be used to confirm intraday Ts?
These are not acceptable requests:
Where do you think Xerox will be trading next week?
What's your opinion on copper?
My goal is for this feature to be entertaining and useful to as many readers as possible.
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