Topic 8. Selection and Decision. CMT II. 2016.

TOPIC 8. SELECTION AND DECISION.

Exam Exam CMT Level II Exam Topics, Learning Objectives and Question Weightings Weights Questions Topic 8. Selection and Decision. 10% 15 Uncorrelated assets. . Determine appropriate asset selections based on correlation data. Relative strength. . Determine appropriate asset selections based on relative strength. Forecasting techniques (pattern and trend recognition). . Determine appropriate asset selections based on trend and pattern forecasts.

Chapter 4 Intermarket Analysis Markos Katsanos, Intermarket Trading Strategies (Hoboken, New Jersey: John Wiley & Sons, 2008), Chapter 3 Determining Intermarket Relations (*) Using Intermarket Correlations for Portfolio Diversification Chapter 5 Correlation Markos Katsanos, Intermarket Trading Strategies (Hoboken, New Jersey: John Wiley & Sons, 2008), Chapter 2 All sections included Chapter 14 A Stock Market Model Added in 2016 Ned Davis, Being Right or Making Money (Hoboken, New Jersey: John Wiley & Sons, 2014), Chapter 3 All sections included Chapter 15 A Simple Model for Bonds Added in 2016 Ned Davis, Being Right or Making Money (Hoboken, New Jersey: John Wiley & Sons, 2014), Chapter 4 All sections included Chapter 40 Relative Strength Strategies for Investing Mebane Faber, Relative Strength Strategies for Investing, Cambria Investment Management. All sections included

(*) This section is included in Topic 6 Confirmation.

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8.1. Using Intermarket Correlations for Portfolio Diversification (Katsanos).

Investors and portfolio managers all over the world know the huge benefits of diversification. For example, U.S. stock portfolio managers usually include international equities, bonds and cash in their portfolios. However, globalization has reduced the benefit of international equities because all equities tend to move in the same direction (positive correlation). On the other side, commodities and currencies (foreign exchange) are less used to diversify because of the false impression that these securities are excessively risky. This is an erroneous perception and most commodities are excellent candidates to diversify a stock portfolio. For example, in bear equity markets, commodities act as a hedge, and commodities are usually considered as an important inflation hedger. Just as the standard deviation is a standard in terms of financial risk, the correlation coefficient is an essential tool for investment management. The correlation coefficient is used to determine whether two investments or asset classes move together or in opposite direction. A portfolio is effectively diversified if it is composed of assets that are not correlated (low or negative correlation coefficient), that is, assets that do not move in the same direction. High positive correlation is negative in terms of portfolio diversification, and low or negative correlation increases the benefits of diversification and reduces downside volatility (standard deviation). However, as we reduce the risk of our portfolio, our portfolio return will also suffer. The key concept here is trying to maximize the risk to return ratio of our portfolio. Markos Katsanos introduces an example to illustrate the benefits of diversification: the equity line of a portfolio consisting of 70% equities (S&P 500 index) and 30% oil futures is more stable than the equity lines of both securities individually. In a second and more comprehensive example, Markos Katsanos creates some portfolios using as inputs the annual returns of a great variety of securities (stock market indices, fixed income, commodities, cash and currencies). Table 8-1 illustrates the annual returns from 1997 to 2006, as well as the mean and standard deviation (σ) of these financial time series. The last three rows are represented in bold letters. refers to the arithmetic mean of these returns. refers to the standard deviation (volatility), and is the risk-adjusted return. According to this statistical measure, cash is the best security followed by bonds and the GBP (Great Britain Pounds), although all these three securities have lower annual returns than stock market indices or commodities.

Annual Returns from 1997 to 2006 (10 years) Year S&P 500 FTSE Hang Seng Bonds GBP Gold Crude Oil Cash 1997 33.36% 23.98% -17.30% 9.65% 2.31% -21.8% -31.90% 5.25% 1998 28.58% 17.02% -2.15% 8.69% 6.47% -0.26% -31.70% 5.06% 1999 21.04% 17.22% 71.51% -0.82% 2.37% 0.00% 112.40% 4.74% 2000 -9.10% -15.60% -8.96% 11.63% -1.85% -5.55% 4.69% 5.95% 2001 -11.90% -17.60% -22.0% 8.44% 1.39% 2.48% -26.00% 4.09% 2002 -22.1% -8.79% -15.1% 10.26% 13.56% 24.80% 57.30% 1.70% 2003 28.68% 27.60% 38.55% 4.10% 14.35% 19.09% 4.23% 1.07% 2004 10.88% 18.43% 16.30% 4.34% 12.25% 5.58% 33.61% 1.24% 2005 4.91% 9.70% 7.82% 2.43% -5.78% 18.00% 40.48% 3.00% 2006 15.79% 27.77% 37.35% 4.33% 18.85% 23.17% 0.02% 4.76% 10.01% 9,97% 10,60% 6,31% 6,39% 6,55% 16,31% 3,69% σ 19.14% 17,52% 30,36% 4,00% 8,02% 14,74% 45,66% 1,80%

0.52 0,57 0,35 1,58 0,80 0,44 0,36 2,05

Source: Markos Katsanos. Table 8-1

Table 8-2 shows the Pearson’s correlation coefficient of these securities using monthly returns from 1997 to 2006. According to this table, U.S. equities (S&P-500) are highly correlated with international equities (FTSE and Hang Seng) due to the globalization factor. However, the correlation with fixed income,

Alexey De La Loma ©FINANCER TRAINING Pag. 251/476 CFA, CMT, CAIA, FRM, EFA, CFTe Topic 8. Selection and Decision. CMT II. 2016. commodities, and currencies is negative, which is excellent in terms of diversification. The lowest correlation corresponds to GBP and FTSE with a negative 0.30 correlation coefficient.

10-year correlation matrix of monthly percentage returns

S&P Hang Crude FTSE Bonds GBP Gold 500 Seng Oil

S&P 1.00 0.81 0.57 -0.06 -0.09 -0.04 -0.03 500

FTSE 0.81 1.00 0.57 -0.02 -0.30 -0.06 0.03

Hang 0.57 0.57 1.00 0.05 0.00 0.11 0.18 Seng

Bonds -0.06 -0.02 0.05 1.00 0.10 0.08 0.11

GBP -0.09 -0.30 0.00 0.10 1.00 0.36 0.00

Gold -0.04 -0.06 0.11 0.08 0.36 1.00 0.18

Crude -0.03 -0.19 0.18 0.11 0.18 0.18 1.00 Oil

Source: Markos Katsanos. Table 8-2

Finally, in Table 8-3 Markos Katsanos illustrates the performance of four simulated passive portfolios in order to show the positive effects of diversification from the perspective of a U.S. equity investor. Portfolio A only contains US stocks and this is our reference point. Portfolio B contains a typical asset allocation mix with a 70% invested in equities, 10% in cash, and 20% in fixed income securities. By including uncorrelated assets (bonds and cash) with the US equities, we reduce both risk and return, but the reduction is risk is bigger than the return’s reduction and this is reflected in the increase of the risk-adjusted return (0.66). Then, portfolio C maintains the allocation in bonds and cash and introduces international equities (FTSE, Hang Seng) into the asset allocation. The results are very modest with a slight increment in the risk-adjusted return (0.70). Finally, portfolio D excludes international equities and Cash, includes commodities (Crude Oil and Gold) and increases the fixed income’s allocation. In this case, the inclusion of commodities plays a key role reducing relevantly our portfolio risk. The results are impressive with a risk-adjusted return of 1.28.

Portfolio Minimum Risk Maximum Return Portfolio A Portfolio B Portfolio C Portfolio D Allocation Portfolio Portfolio S&P 500 100% 70% 50% 40% 10% 60% Cash 10% 10% FTSE 10% Hang Seng 10% 10% Bonds 20% 20% 40% GBP 55% Gold 10% Crude Oil 10% 15% 30% 10.01% 8.64% 8.69% 8.81% 8.92% 11.96% σ 19.14% 13.1% 12.5% 6.86% 6.38% 18.70%

0.52 0.66 0.70 1.28 1.40 0.64

Source: Markos Katsanos. Table 8-3

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Markos Katsanos uses the Excel’s Solver tool to create two final portfolios, the first is a minimum risk portfolio, and the second a maximum return portfolio. Of course, the future performance rarely measures up fully to past results, and finding the maximum return and minimum risk portfolios using past data and the Solver tool cannot be used to create a portfolio. Rates of return are often less predictable, and correlation coefficients can also change over time.

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8.2. Correlation (Katsanos).

8.2.1. Relationships between variables (Pearson’s correlation coefficient). If you consider more than one variable in our analysis, the measure of dispersion that is commonly used is the covariance. Therefore, we could say that covariance is the two-variable version of the variance (standard deviation). If you have two variables (A and B), the covariance between both variables is:

( 8.1)

In our example, A and B could be stock market time series with a number of returns equal to “n”. However, covariance suffers the same drawback as variance. Remember that variance is not used because its units of measurement are not meaningful, and we solve that problem by taking the square root (standard deviation). The same limitation occurs with covariance, its units of measurement are useless, and we solve this drawback by taking the ratio of the covariance to the product of the standard deviations of both variables. This is called the correlation coefficient, and it can be represented by the following equation:

( 8.2)

The correlation coefficient generates a number that is between -1 and +1. If the number generated is -1, we say that both variables are perfectly negatively correlated, while if the number generated is +1, we say that both variables are perfectly positively correlated. If the coefficient correlation is close to 0, it means that no discernible relationship between the two variables is present. Note that the correlation coefficient only measures linear relationships between variables. Another relevant measure between variables is the regression analysis. If we take the time series of our two securities (A and B) and plot them in both coordinate axis, we could establish a line that tries to connect all dots. We refer to this as the regression line or the best-fit line. From a mathematical point of view, the regression line is based on the least-squares method, and what we are trying to do with this approach is to minimize the sum of the squares and plot a line. The coefficient of determination is a number between 0 and 1, and it is a way to measure the goodness-of-fit, in other words, how much of the variability of the dependent variable can be explained by the independent variable. For instance, if the coefficient of determination is 0.85, our model is explaining 85% of the variability of one of the time series over the other. If the regression is conducted with only two variables, there are some similarities between the correlation coefficient and the regression line, because the coefficient of determination is just the square root of the correlation coefficient. In a two-variable regression model (simple regression):

( 8.3)

Take into account that the coefficient of determination in multiple regression models (more than one independent variable) cannot be calculated as the simple square of the Pearson’s correlation coefficient. This is only valid with simple linear regression models.

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In the following examples we can see the different values of r and their significance in a regression analysis of two price series:

. r > 0. If r is positive, we have a positive linear correlation. The data points are above and below a straight line going upward to the right. In Figure 8-1, r = 0.514.

Figure 8-1 . r < 0. If r is negative, we have a negative linear correlation. The data points are above and below a straight line going downward to the right. In Figure 8-2, r = - 0.634. This means that when one variable goes up, the other goes down.

Figure 8-2 . r = 0. If the correlation coefficient is zero or near zero, we have no linear correlation at all. In Figure 8-3, r = 0.03.

Figure 8-3 . r = +1. If r is equal to +1, a perfect positive correlation exists. The data points are along a straight line going upward to the right. In Figure 8-4, r = 0.98.

Figure 8-4 . r = –1. If r is equal to –1, a perfect negative correlation exists. The data points are along a straight line going downward to the right. In Figure 8-5, r = – 0.98.

Figure 8-5

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Markos Katsanos introduces in Table 8-4 an interpretation of the Pearson’s correlation coefficient using both raw price data and percent changes. The interpretation for negative values is exactly the same.

Correlation Coefficient Raw Prices Percentage Changes in absolute value 0.9 to 1.0 Extremely Strong Extremely Strong 0.8 to 0.9 Very Strong Very Strong 0.7 to 0.8 Strong Very Strong 0.6 to 0.7 Moderately Strong Strong 0.5 to 0.6 Moderate Moderately Strong 0.4 to 0.5 Meaningful Moderate 0.3 to 0.4 Low Meaningful 0.2 to 0.3 Very Low Low 0.1 to 0.2 Very slight Very Low 0.0 to 0.1 Non-existent Non-existent

Source: Markos Katsanos. Table 8-4

. The correlation coefficient and diversification. The correlation coefficient is often used to demonstrate one of the most fundamental concepts of portfolio theory: the reduction in risk found through combining assets that are not perfectly positively correlated. Figure 8-6 represents the returns and standard deviation of assets A and B, and the three possible scenarios that we can find in terms of the correlation coefficient.

ρ = -1 B

Expected Expected Return

-1 < ρ < 1

ρ = 1

A

Standard deviation

Source: Own Elaboration. Figure 8-6

1. Perfect positive correlation. If the Pearson correlation coefficient is 1, we face the least diversification potential. The line is straight, meaning that there are no benefits to diversification.

2. Perfect negative correlation. If the Pearson correlation coefficient is -1, we face the greatest risk reduction. The two straight lines connecting points A and B move directly to the vertical axis, the point at which the standard deviation is zero.

3. Correlation between -1 and +1. If the Pearson correlation coefficient is not in one of its extreme values, it represents the most realistic representation. This is the more common scenario. The key point to the represented curve is that when imperfectly correlated assets are combined into a portfolio, a portion of the portfolio’s risk is diversified away. The risk that can be removed through diversification is called diversifiable, nonsystematic, unique, or idiosyncratic risk.

In the case of asset returns, true future correlations can only be estimated. Past estimated correlation coefficients not only are subject to estimation error but also are typically estimates of a moving target,

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since true correlations should often be expected to change through time as fundamental economic relationships change. Further, correlation coefficients tend to increase (offer less diversification across investments and asset classes) in times of market stress, just when an investor needs diversification the most.

8.2.2. Modern Portfolio Theory (additional reading). We all know that diversification is necessary to reduce the risk of securities portfolios. We all know that diversification is based on “Don’t put all your eggs in one basket! However, from an academic standpoint, MPT began in 1952 with the work of the Nobel Prize winner Harry Markowitz. The Modern Portfolio Theory attempts to quantify the relationship between risk and return. Instead of analyzing just individual securities within a portfolio, the idea is to infer the statistical relationships between the members of the portfolio, and their relationships to the market. These are some of the key results of MPT:

. The mean return of a portfolio is a simple weighted average of the mean returns of the individual stocks. . The standard deviation (of returns) of a portfolio is a quadratic function. . The standard deviation of a portfolio is almost always less than a simple weighted average of the individual stock standard deviations. . Even with weak positive correlation, there are significant benefits to diversification. . If an investor is only concerned with the mean return and standard deviation of portfolio, it is possible to eliminate many portfolios from consideration. . For large portfolios, the variance of each stock contributes to the overall portfolio variance. However, the covariance of each stock’s returns with the returns of all the other stocks is quite important.

Consider a portfolio composed by two assets (A and B). The return and standard deviation of the portfolio will be as follow:

( 8.4)

( 8.5) where,

RP = Portfolio Return

σP = Portfolio Standard Deviation

wA = Weight of Asset A

wB = Weight of Asset B

ρAB = Correlation on between A and B

According to the modern portfolio theory (MPT), the expected return on any stock is given by the following equation, which we will call the CAPM equation:

( 8.6) where,

This means that β is the product of the correlation coefficient between the stock and the market as a whole times the standard deviation of the stock relative to that of the market. So, if the stock’s correlation with the market is 0.4 and its standard deviation is three times that of the market, then its β is 1.2. What is the β for the

Alexey De La Loma ©FINANCER TRAINING Pag. 257/476 CFA, CMT, CAIA, FRM, EFA, CFTe Topic 8. Selection and Decision. CMT II. 2016. market as a whole? In practice, the S&P500 is often used to represent the market portfolio. A stock with a β greater than 1 is an above-average risk stock. If the stock’s β is less than 1, its risk is below average.

8.2.3. The Spearman Rank Correlation Coefficient. The Pearson correlation coefficient is not the only measure of correlation. There are some especially useful measures of correlation in alternative investments that are based on the rank size of the variables rather than the absolute size of the variables. The returns within a sample for each asset are ranked from highest to lowest. The numerical ranks are then inserted into formulas that generate a correlation coefficient that usually range between -1 and +1. The Spearman Rank Correlation Coefficient is a popular example, and it is considered as the best-known non-parametric correlation coefficient, named after Charles Spearman. Unlike Pearson’s correlation coefficient, it does not require the normality assumption but, like Pearson’s correlation, linearity is still an assumption. Therefore, when two variables appear to be normally distributed is better to use Pearson’s correlation coefficient, otherwise use Spearman’s correlation. In Table 8-5 we can see an example with two assets and three periods. The first step is to replace the actual returns with the rank of each asset’s return. The ranks are computed by first separately ranking the returns of each asset from highest (rank 1) to lowest (rank 3), but keeping the returns arrayed to their time periods.

Time period Return of Asset #1 Return of Asset #2 Rank of Asset #1 Rank of Asset #2 Difference in Ranks (di) 1 61% 12% 1 1 0 2 -5% 6% 3 2 1 3 0% 4% 2 3 -1

Source: Anson, Chambers, Black and Kazemi (2012). Table 8-5

This table demonstrates the computation of di, the difference in the two ranks associated with time period i. The Spearman rank correlation coefficient can be computed employing the following equation. After this equation we show the results achieved taking the data of our example.

( 8.7)

Rank correlations are sometimes preferred because of the way rank correlation handles the effects of outliers, and this is the main advantage of the Spearman correlation (it is not sensitive to outliers). For example, the enormous return of asset 1 in the previous example is an outlier, which will have a disproportionate effect on a correlation statistic. Extremely high or low values of one or both of the variables in a particular sample can cause the computed Pearson coefficient to be very near +1 or -1, since deviations are squared as part of the computation. By using ranks, the effects of outliers are lessened.

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8.2.4. Assumptions (linearity and normality). . Linearity. One of the main assumptions of both the Pearson’s and the Spearman’s correlation measures is that the relationship between variables has to be linear. When there is another kind of relationship between both variables (e.g. curvilinear, logarithmic, etc.), this statistical measures can be misleading. In Figure 8-7 we can see different price approximation to compare them with the linear approximation (regression line). Fortunately, the correlation coefficient is not greatly affected by minor deviations from linearity. The way to detect deviations from linearity is to look at a scatterplot of both variables. Examples of scatterplots are illustrated in: Figure 8-1, Figure 8-2, Figure 8-3, Figure 8-4, and Figure 8-5.

Price Curvilinear Price Exponential

Linear

Log

Time

Source: Perry Kaufman. Figure 8-7

. Normality. Another crucial assumption derived from the Pearson’s correlation coefficient is that variables must distribute as a normal or Gaussian distribution. In the case of most financial series this assumption is not justified, and a nonparametric measure such as the Spearman rank correlation coefficient might be more appropriate. We can detect normality using statistical inference or a visual inspection of the price and frequency distribution.

. Price and frequency distributions. The measurement of distribution is very important because it tells you generally what to expect. The following measurements of distribution allow you to put a probability, or confidence level, on the chance of an event occurring. In all of the statistical analysis that follows, we will use a limited number of prices or – in some cases – individual trading profits and losses that will be called the sample. We want to measure the characteristics of our sample. All of these measures will show that the smaller samples are less reliable. The frequency distribution can give a good picture of the characteristics on the data. Theoretically, we expect prices to spend more time at low price levels and only brief periods at high prices. That pattern is shown in a discrete format in Figure 8-8 (a) and in a continuous format in Figure 8-8 (b). To calculate a frequency distribution, we find the highest and lowest prices to be charted, and divide the difference by the number of bins we want to create, in Figure 8-8 (a) we have created 15 bins. Once sorted all the data, we count the number of elements that fall into each bin and the result is a histogram, as the one presented in Figure 8-8 (a).

Median

Mode

Frequency Frequency Mean (a) (b)

Lower Prices Higher Lower Prices Higher Source: Perry Kaufman Figure 8-8

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. Median and Mode. In a normally distributed price series, the mode, the mean and median all occur at the same value; however, as the data becomes skewed, these values will move farther apart. The general relationship, as shown in Figure 8-8 (b), is:

Mean > Median > Mode ( 8.8)

A normal distribution is commonly called a bell curve, and values fall equally on both sides of the mean. For much of the work done with price and performance data, the distributions tend to be skewed to the right (higher prices or higher trading profits), as shown in Figure 8-8 (b). If you were to chart a distribution of trading profits and losses based on a trend system with a fixed stop-loss, you would get profits that could range from zero to very large values, while the losses would be theoretically limited to the size of the stop-loss. There are no normal distributions in a trading environment. As an example of two frequency distributions (histograms), in Figure 8-9, we can see a Net Profit Histogram with 5000 items derived from a Monte Carlo Simulation of a trading system. This histogram has been created using 63 bins.

Source: Excel Figure 8-9

8.2.5. Outliers. Outliers can also be a significant problem for the Pearson’s correlation coefficient. It is worthwhile noting that regression analysis is conducted through a mathematical model that minimizes the square of the distances of data points from the line (ordinary least squares) and this creates a problem when outliers appear. Outliers have a great impact on the slope of the regression line and, consequently, on the value of the correlation coefficient. This is more of a problem when working with financial series with small samples (less than a year). A way to solve this drawback is using the Spearman rank correlation coefficient. In order to see the significant impact of outliers in the correlation coefficient, we proceed to calculate an example in which the regression line (characteristic line) and the correlation coefficient will be calculated taking actual prices. We are using 120 monthly returns (2005 to 2014) for two security time series (Walt Disney and the S&P-500 index. We take S&P 500 as the independent variable and the time series of Walt

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Disney as the dependent variable. We are not showing the calculations, but interpreting the results. As we can see in Figure 8-10, the coefficient of determination is 61.21%. The coefficient of determination (R2) is a number that indicates how well data fit a statistical model – sometimes simply a line or a curve. The correlation coefficient of this model (not illustrated in the figure) is 0.782. If we multiply by 10 the return of Walt Disney at point A (9.39% ; 20.59%), point A becomes a huge outlier (9.39% ; 200.59%), and the new regression line changes its slope (Figure 8-11). The correlation coefficient drops down terribly from 0.782 to 0.415.

A

Source: Excel Figure 8-10

A

Source: Excel Figure 8-11

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8.2.6. Homoscedasticity. The Pearson’s correlation coefficient is based on the following assumption: the variance must be the same at any point along the linear relationship. Otherwise this statistical measure will give us a misleading result. In statistics, a sequence or a vector of random variables is homoscedastic if all random variables in the sequence or vector have the same finite variance. Serious violations in homoscedasticity result in underemphasizing the Pearson coefficient. Heteroscedasticity does not invalidate the analysis and can be usually rectified by transforming the price data to yields or logarithms. Figure 8-12 illustrates the difference between homoscedasticity and heteroscedasticity from a graphical point of view.

Source: BinaryOptions.com Figure 8-12

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8.3. Introduction to Relative Strength (Charles Kirkpatrick).

According to Charles Kirkpatrick, in 2007, almost 8000 stocks traded in the U.S. stock market. This is a massive number for any analyst to cope with. Imagine a technical analysts searching for chart patterns at frequent intervals in such a huge number of charts. Technicians need a way to filter the whole database, and an efficient way to do so is through relative strength (RS). RS is a straightforward concept. It is usually based on a ratio (ratio method) between two securities, two sectors, a security and its index, etc. Once the RS is calculated it is plotted using a line chart and it is compared with the absolute strength chart. For instance, we plot the chart of a security and below the chart of a relative strength ratio of the same stock divided by its reference index or benchmark. The interpretation of this line is quite simple; an increasing line means the security (numerator) is outperforming the index (denominator), while a decreasing line means the security is underperforming the index. According to Charles Kirkpatrick “It is a reliable concept that has been demonstrated academically to have value and the presumption behind the concept of relative strength is that strength will continue.” It is important to show the difference between the RSI (Relative Strength Index) and the RS (Relative Strength). RSI is an indicator that measures absolute strength (not Relative Strength), so it is quite a confusing name. The next four bullets illustrate the concept of RS (Relative Strength):

. RS is a very useful concept if we are interested in understanding an intermarket relationship (e.g., dollar versus T-Bond) or to compare two securities in order to determine which one is stronger. . In commodities we usually use the word spread to refer to RS. A spread involves the ratio between one commodity to another, such as corn to hogs, or tries to illustrate the relationship between a distant contract and a nearby one. . A currency is really a relative relationship. There are no such things as the “US Dollar”, or the “Euro”. . The most popular and relevant way to use RS ratios is through a stock and its reference index. For instance, taking the ratio of IBM to the DJIA, or the ratio of Banco Santander to the IBEX-35.

Relative Strength (RS) is usually interpreted in comparison with another asset. However, it can also be used in the same way as absolute prices are. For instance, we can draw trendlines, supports, resistances, and we can detect price patterns, and apply indicators and oscillator to a RS line. According to Charles Kirkpatrick, RS lines show more random noise than absolute price lines, so technicians usually prefer weekly or monthly timeframes to analyze this kind of charts.

. Positive and negative RS divergences. RS can be used to detect divergences as we did with technical oscillators. As illustrated in Figure 8-13, when the RS line fails to confirm new highs being set by the price itself, a negative divergence occurs and this has a bearish bias. This implies the stock is underperforming the stock market index. The confirmation comes when prices break the bullish trendline. The opposite set of circumstance holds true with a positive divergence. When both the price and the RS are rising, they are said to be “in gear”.

Stock price Stock price

RS

RS

RS and negative divergence RS and positive divergence Source: Martin Pring Figure 8-13

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. Moving Average Crossovers. Sometimes it is a good idea to run a moving average through the price and using the crossovers as legitimate signals of change in trend. This is also possible with the RS line, but because the RS line tends to be much more volatile, this technique often proves unprofitable and Martin Pring recommends using a crossover of two averages applied to the RS line.

. Trendline violations. Martin Pring considers that a better alternative to the MAs approach is to construct trendlines in the RS line and when that is violated to look around for a legitimate trend-reversal signal in the price itself to act as confirmation.

. Price Patterns. Price patterns, as Head and Shoulders and triangles, can also be employed to analyze trends in RS, the same way we use them in absolute charts.

. RS and Momentum. Since classic trend-determining techniques can be applied to RS lines, it is a small step to expand the analysis to embrace momentum indicators derived from RS lines. While it is certainly practical to apply oscillators to short-term momentum of RS lines, by far the best use of momentum in relative work, according to Martin Pring, is to use oscillators based on long-term spans that have been carefully smoothed. RS lines are far more cyclical in the patterns than absolute price. This makes the use of smoothed long- term oscillators far more accurate. Remember that absolute prices can be subject to strong linear trends, which means that even the best-designed smoothed long-term momentum indicator will offer premature buy and sell signals.

. Spreads. RS is widely used in the futures markets under the heading “spread trading” in which market participants try to take advantage of market distortions. Spreads are often calculated by subtracting the numerator from the denominator rather than dividing, however the ratio is preferred. Pring considers that over a short period of time (e.g. 6 months) subtraction or ratio makes no great difference. Spread relationships arise because of six principal factors:

. Product relationships such as soybeans versus soybean oil or meal. . Usage such as hogs, cattle, or broilers to corn. . Substitutes such as wheat versus corn, or cattle versus hogs. . Geographic factors such as copper in London versus copper in New York. . Carrying cost such as when a specific delivery month is out of line with the rest. . Quality Spreads such as T-Bills versus Eurodollars or S&P versus Value Line.

Some of these relative relationships, such as London versus New York cooper, really represent arbitrage activity and are not suitable for the individual investor or trader. On the other hand, the so-called TED Spread, which measures the relationship between (high-quality) T-bills versus (low-quality) Eurodollars, is a popular trading vehicle.

Although we have introduced the ratio method to explain the concept of RS, there are four methods to measure relative strength, as stated by Charles Kirkpatrick in his book Technical Analysis:

. Percentage Change Method. As an example, we could take the six-month price changes of a broad set of issues (e.g. stocks), and then rank them according to these rates of changes. This is the preferred method for Charles Kirkpatrick, because some academic papers have found that the higher decile stocks continued to be strong for the next three to ten months and all performed similarly both in the in-sample and the subsequent out-of-sample tests.

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. Alpha Method. The Modern Portfolio Theory (MPT) determines a model based on alphas and betas. This model is based on a regression between stock market prices as the dependent variable and a stock market index (e.g. S&P-500) as the independent variable. Usually, weekly data is used in a percentage change format. Linear regression models are often fitted using the least squares approach. A line is drawn through these plots on a best-fit basis, and the slope of this line is known as the beta, while the intercept with the vertical axis is known as the alpha. Therefore, over a specific period of time, each stock is defined by an alpha and a beta. For instance, if after applying this model over a weekly timeframe, we get a beta of 1.2 and an alpha of 2.44, this means that our stock will move up and down a 60% more than the stock market index (e.g. S&P-500) on a weekly basis, and also that our stock has been outperforming the S&P by 2.44% on average over the time of the series. Beta is considered as a measure of volatility and sensitivity of our stock relative to the stock market index. Therefore, stocks with higher betas are considered riskier than stocks with lower betas. From an academic standpoint, risk is measured by volatility (e.g. standard deviation, beta, etc). According to the MPT, markets are basically efficient so alphas tend to zero or close to zero, because no systematic gain can be produced in an efficient market. However, in actual markets, alpha does not remain at the zero level and has thus become a measure of how much better or worse the stock is performing relative to the S&P. This model is used to show relative strength by taking the alphas of a set of stocks, and raking them according to this measure. Stocks with higher (lower) alphas are considered as the strongest (weakest) stocks.

. Trend Slope Method. This method is easier than the previous one, and it is based on ranking the stocks based on the slope of the price curve in percentage terms over a specified period through a linear regression formula for each stock. Therefore, it is based on betas instead of alphas, so it is simpler than the alpha method.

. Levy Method. The last of the four methods, explained by Charles Kirkpatrick, to measure relative strength was developed by Robert Levy in 1965. This method is based on a ratio between the current prices of each stock to its 131-day moving average. Once all these calculation are made, we must rank these ratios to determine our relative strength classification. According to Robert Levy, this calculation must be based on the last six months, because any shorter period tends to be full of whipsaws, while any longer period tends to be too close to when the performance begins to regress back to the mean. Robert Levy also found that when the overall stock market headed downward into a lengthy bear market, relative strength continued to be reliable but gradually lost its ability to pick winning stocks.

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8.4. Relative Strength Strategies for Investing (Mebane).

This chapter is based on a white paper, Relative Strength Strategies for Investing, written by Faber Mebane, a portfolio manager for Cambria Investment Management, in April 2010. The goal of this white paper is to show simple quantitative methods based on relative strength that improve risk-adjusted returns for investing in US equity or in global asset class portfolios. Faber Mebane tested a relative strength (RS) quantitative model on the French-Fama US equity sector data back to the 1920s. The conclusion is that RS portfolios outperformed a buy and hold strategy by a 70% in the whole backtested period, and more important than that, returns are persistent across time. Trend following and relative strength are considered as momentum based strategies, and momentum has been one of the most widely discussed and researched investment strategies. Academics refer to this kind of strategies as “market anomalies.”

. Equity sectors used to backtest the RS strategy. The backtesting of this strategy is based on 9 industry portfolios with monthly returns from July 1929 to December 2009, including over eight decades of US equity sector returns:

US Equity Sector Components Consumer Non-Durables Food, Tobacco, Textiles, Apparel, Leather, Toys Consumer Durables Cars, TV’s, Furniture, Household Appliances Manufacturing Machinery, Trucks, Planes, Chemicals, Office Furniture, Paper, Commercial Printing Energy Oil, Gas, Coal Extraction and products Technology Computers, Software, Electronic equipment Shops Wholesale, Retail, Some Services such as Laundries and Repair Shops Health Healthcare, Medical Equipment, Drugs Utilities Other Mines, Construction, Transportation, Hotels, Entertainment, Finance, etc

Source: Own Elaboration. Table 8-6

. RS Ranking. Each month these sectors are ranked on trailing total return including dividends. Faber Mebane uses varying periods of measurement ranging from 1 to 12 months (1, 3, 6, 9, and 12), as well as a combination of multiple months. For example, if relative strength is being tested at the one (three) interval on the 31st of July 2015, all the sectors are simply sorted by the July (by their three month May- June-July) total returns including dividends.

. Buying and selling RS strategy rules. This is a long-only strategy with different options. For Top 1 strategy, the system is 100% invested in the top ranked sector. For Top 2 strategy, the system is 50% invested in each of the top two sectors, while for Top 3 strategy, the system is 33% invested in each of the top three sectors. Since this system is based on a simple ranking of sector, sell rules are based on a monthly rebalance where new top sectors replace the old top sectors. Buying and selling rules are based on the following three principles:

1) All entry and exit prices are introduced at the closing price of the day in which the signal is triggered. The system is only updated once a month on the last day of the month. Price fluctuations during the rest of the month are ignored. 2) All data series include dividends that are updated monthly. 3) No commissions, slippage or taxes are included.

. Results of the relative strength method. According to this white paper written by Faber Mebane, the relative strength method is a winning strategy on all the measurement periods from one to twelve months, as well as a combination of the 1, 3, 6, 9, and 12 month time periods. Additionally, the RS method outperforms a buy and hold strategy 70% of all years, achieving a rough estimate of 300-600 basis points of outperformance per year, so results are excellent.

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. Solutions to the drawbacks of the relative strength method. The more relevant disadvantage of this quantitative model is that the portfolio is long-only and fully invested, thus leaving the portfolio exposed to the risks of the particular asset beta, specifically, US equity beta. This drawback is reflected in the results in terms of volatility and maximum drawdowns. In order to reduce both figures, Faber Mebane introduces two changes in this strategy: (1) hedging and (2) adding non-correlated asset classes.

 Hedging. Hedging can be implemented moving to cash or hedging with short positions, and it can also be implemented on a sector basis or on portfolio wide asset class basis. Additionally, the hedging can be static or dynamic. In a static hedge, the portfolio managers always hedge a predetermined percentage of the portfolio, or even the entire portfolio if the strategy is market neutral. The main disadvantage of a static hedge is that portfolios are hedged when the market is appreciating. On the other side, in dynamic hedge, the portfolio managers looks for hedging the portfolio when conditions are more favorable to market declines, and an example of this kind of hedge is using a moving average. This is how Faber Mebane improves the original relative strength system: the portfolio moves entirely to 100% cash (T-Bills) when the S&P 500 is below its 10-month SMA. The results are quite encouraging because both volatility and drawdowns are relevantly reduced. For example, the original 70-80% drawdown is now at a more reasonable level of 40-50%. However, it is still a high drawdown.

 Addition of non-correlated asset classes. As this is a long-only strategy focused on just US equity, another possible solution is to add non-correlated global asset classes to the portfolio in order to diversify the portfolio reducing both volatility and drawdowns. In this case, Faber Mebane introduces the following five asset classes:

. S&P 500 Index. This is a capitalization-weighted index of 500 stocks that is designed to mirror the performance of the United States economy.

. MSCI EAFE Index (Europe, Australasia, Far East). This is a free float-adjusted market capitalization index that is designed to measure the equity market performance of developed markets, excluding the US and Canada. As of June 2007 the MSCI EAFE Index consisted of the following 21 developed market country indices: Australia, Austria, Belgium, Denmark, Finland, France, Germany, Greece, Hong Kong, Ireland, Italy, Japan, the Netherlands, New Zealand, Norway, Portugal, Singapore, Spain, Sweden, Switzerland, and the United Kingdom.

. U.S. Government 10-Year Bonds.

. Goldman Sachs Commodity Index (GSCI). This index represents a diversified basket of commodity futures that is unlevered and long only. Total return series is provided by Goldman Sachs.

. National Association of Real Estate Investment Trusts (NAREIT). This is an index that reflects the performance of publicly traded REITs. Total return series is provided by the NAREIT.

This second option reduces both volatility and drawdown of the portfolios. However, the better solution comes from a combination of both solutions: rotation among global asset classes but only investing in the asset class if it is trading above its 10-month SMA (otherwise that portion is invested in T-Bills). The results are slightly improved Sharpe ratios and similar absolute returns.

. Conclusion. The purpose of this paper was to demonstrate a simple-to-follow method for utilizing relative strength in investing in US equities and global asset classes. The results showed robust performance across measurement periods as well as over the past eight decades. While absolute returns were improved, volatility and drawdown remained high. Various methods were examined that could be used as solutions to a long only rotation system including hedging and adding non-correlated asset classes.

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8.5. A complex stock market model and a simple bond market model.

In this chapter we are reviewing one of the NDR’s mayor models for stocks, the Fab Five. The Fab Five was the nickname for the 1991 University of Michigan men's basketball team recruiting class that is considered by many to be the greatest class ever recruited. It is an environmental system with four components: tape, sentiment, monetary and combo. The tape component is given double weight, it accounts for two-fifths of this timing model.

. Tape component (40%). . Sentiment component (20%). . Monetary component (20%). . Combo component (20%).

An environmental model is based on keeping risk at low levels without sacrificing too much on the long side. It takes into account what the Fed is doing, what the so-called smart money is doing, how speculators are feeling, what interest rates and inflation is doing, and, above all else, what the primary trend is.

8.5.1. Tape component (40% of the Fab Five).

The tape component is made up of seven individual indicators, and as with all of the components, each individual indicator is assigned with a -1, 0, or +1, and the result is formed by simple addition, and it is a model designed to work in four separate time frames. Since there are seven indicators in the tape component, the range should be [-7 ; 7]. However, as one of the indicators (thrust) cannot go negative, the real range is [-6 ; 7]. The brackets for the model are set at -1.5 and 3.5, and the final contribution to the overall Fab Five is -2 or +2 because it is a double-weighted component.

1) Golden cross with 50-day and 200-day moving averages. The first is a trend-following indicator based on the bullish crossing of a 50-day moving average over a 200-day moving average. This kind of buy signal is sometimes called a golden cross (the bearish signal is sometimes called a death cross). When the fast moving average (50) is above (below) the slow moving average (200), this indicator is positive (negative). According to the NDR backtesting, since 1929, the 50-day moving average has been above the 200-day moving average nearly two-thirds of the time and during that period, the S&P-500 has returned a 9.1% annually. On the contrary, when the 50-day moving average has been below the 200-day moving average, the market has returned a -1.1% on an annual basis.

2) Stochastic. The second is a popular trend-sensitive (mean-reverting) indicator called stochastic. This model employs an 85-day stochastic, smoothed with a 5-day moving average and with brackets at levels 11 and 65. The signals are generated according to the traditional way, called by NDR as a reverse bracket. A buy order is generated when the smoothed result crosses below 11, and then crosses above this same level. On the contrary, a selling signal is triggered when the smoothed result crosses above 65, and crosses below this level. Selling signals are used to buy T-bills instead of shorting the market. Take note that this indicator can be +1, 0, or -1.

3) Volume breadth. The third is a breadth indicator based on the evaluation of volume supply and demand. If a stock advances on the day, all the volume trade on that day is considered as advancing volume or demand, while the volume of declining stocks is considered as declining volume or supply. Additionally, if a stock remains flat, volume is discarded. Then, supply and demand volume is added and that is considered as 100%. According to the NDR backtesting, when demand has been above supply, as it has been the case in 79% of the time, the S&P-500 has advanced at 11.8% on an annual basis. On the contrary, when demand is below supply, the market return is a poor -1.2%. Evidently, when demand is above supply, this indicator produces a value of +1, while a -1 value is derived when demand is below supply.

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4) Breadth thrust. The fourth is an advance/decline ratio taking a 10-day sum of advancing stocks, divided by a 10-day of declining stocks over a relevant number of common stocks. In this model an uptrend is triggered when the A/D ratio exceeds 1.9 and this bullish mode remains active the following 80 market days. According to this rule we have two options when a new breadth thrust occurs. We could either reset the count on every new signal in the 80-day window or ignore every new signal. After some backtesting, the model applies the second methodology. The contribution of this indicator to the Fab Five tape component is either +1 or 0. It can never be negative.

5) High-low logic indicator. The fifth is a breadth indicator developed by Norman Fosback. This indicator was designed to determine how bullish the market is, according to the following rule: when new 52-week highs overwhelm new 52- week lows, or when new 52-week lows overwhelm new 52-week highs the market is in an uptrend. The rest of time the market is not bullish. The high-low logic is calculated by taking the ratio of either new 52-week highs or new 52-week lows, whichever is less, to the total number of issues and then smoothing this ratio with a 10-week exponential moving average.

6) Diffusion indicator. The sixth is another breadth indicator known as a diffusion indicator. It takes the number of stocks over an extensive database that trade above their 50-day moving average. According to NDR backtesting, if 71% or more of global markets are above their 50-day moving averages, the U.S. market returns an astonishing 20.2% annually. On the contrary, if only 41% of global markets are above their 50-day moving average, the market returns just a -2.3%. This indicator contributes to the tape component with -1, 0, or +1.

7) Big Mo (Momentum). The seventh and last indicator is named Big Mo by Ned Davis, and it refers to a diffusion index representing the percentage of bullish individual trend and momentum indicators taken from 96 subindustry indices elaborated by NDR. The trend indicators are based on the direction of a subindustry’s moving average, while the momentum indicators are based on the ROC of the subindustry’s price index. The ratio of momentum to trend indicators is around 2:1. The weight of this indicator in the tape component is quite tricky. When Big Mo is rising and above 56 a +1 is assigned; when it is rising and below 56, a 0 is assigned; when it is falling and above 79, a +1 is assigned; when it is falling and between the brackets, its value is 0; while falling and below 56 implies we assign a -1 value.

8.5.2. The sentiment component (20% of the Fab Five).

The sentiment component is made up of the following six indicators (plus one more P/E ratio), delivering each indicator a score of -1, 0, or +1. One of the indicators, known as the daily sentiment has double weight, so the final range is [-8 ; +8]. The brackets of this component are set symmetrically at [-1.5 ; 1.5]. As a general rule, sentiment indicators are useful when they rich extreme values. For instance, when investors are extremely bullish and there is no one left to buy, this is an indication of a potential market top. On the contrary, when are extremely bearish and they have sold virtually all they can sell, this is an indication of a potential market bottom. Evidently, the trick is determining when a bullish or a bearish extreme has been reached.

1) Percentage of bullish advisors over bullish + bearish advisors by Investors Intelligence. Investors Advisors is a company that has been reporting advisors’ sentiment for over 40 years, following more than 100 independent market newsletters, and classifying each of them as bullish, bearish, or on the fence. In NDR they are interested in the percentage of bullish advisors over the sum of bullish and bearish advisors. It is a long-term indicator because it is reported weekly and the ratio is smoothed over 10 weeks. An excessive optimism is a bearish signal, while excessive pessimism is bullish. As we mentioned before, the trick is finding the right brackets to trigger timing signals. In NDR they use a reverse-bracket method. A sell signal derived from excessive optimism is triggered when the indicator crosses above the upper bracket, and then crossed down the same bracket. A buy

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signal derived from excessive pessimism is triggered using two methods, the first one is when the indicator crosses below the lower bracket, and then it crosses above again, and the second method is exactly the same but instead of the lower bracket, it is based on the middle bracket. Evidently, the lower bracket represents a more bearish situation than the middle bracket, but backtesting is in favor of both ways.

2) P/E ratio indicator. The second indicator is a simple P/E ratio using the median earnings yield of the stocks in the NDR Multi-Cap Equity Series. The median statistic is used to avoid the influence of questionable earnings reports (outliers). A P/E ratio works like a sentiment indicator, a value above the upper bracket shows excessive optimism, and a value below the lower bracket is indicative of excessive pessimism. A value between both brackets is neutral deriving a value of 0 for the sentiment component.

3) Relative measure of earnings to interest rates. The third indicator could also be included in list containing valuation or monetary indicators. In this indicator NDR employs an interest-rate component based on a composite calculated as the average yield of 91-day T-bills, 10-year Treasury notes, and Moody’s Baa corporate bonds. Then, a 60-week moving standard deviation with ± 1.3 standard deviations is applied to determine extreme valuations. The contribution to the Fab Five sentiment component is +1 if the indicator is above the upper bracket, 0 in between brackets, and -1 below the lower bracket.

4) Arms Index, TRIN or MKDS. The fourth indicator is usually associated with breadth instead of sentiment, because it compares upside and downside stocks. It is calculated by dividing the ratio of advancing issues to declining issues by the ratio of advancing volume to declining volume. TRIN’s normal 10-day moving average is determined by adding up individual day readings and dividing the result by 10. The Open 10 TRIN, on the other side, is determined through the 10-day totals of each TRIN component (advancing stocks, declining stocks, upside volume, and downside volume) instead of using individual daily computations. Once these component totals are determined for 10 days, they are inserted in the usual TRIN formula. The Open 30 TRIN is calculated using 30 days rather than 10 days. High values of both TRINs indicate an oversold market that is ready for an upswing.

( 8.9 )

5) VLMAP (Value Line Median Appreciation Potential). The fifth indicator is a Value Line indicator known as VLMAP. It is an indicator based on its analysts’ three-to-five-year P/E projections for their universe. The VLMAP is calculated by multiplying each stock’s current earnings by its future P/E projection as determined by Value Line analysts. NDR uses this indicator through a moving standard-deviation reverse bracket solution. The standard deviation is nine months and the brackets are asymmetric at [-1.0 ; +0.6]. The contribution to the Fab Five sentiment component is +1 when the six-week smoothing of the VLMAP drops below the upper bracket and -1 when it moves from below to above the lower bracket.

6) Daily trading composite indicator. This indicator has double weight, and it is a composite indicator made up of 27 individual indicators from six areas. Each of the 27 indicators uses moving average standard deviation brackets. When an indicator needs to be corrected for volatility, instead of regular brackets, we can use moving standard deviation brackets, which automatically adjust to changing conditions, creating a new normal as indicators move strongly up or down. The composite itself is basically an inverted diffusion index: inverted so that high numbers are excessively optimistic and therefore bearish, while low numbers are pessimistic and therefore bullish.

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. Advisory Service Sentiment. These are polls from the National Association of Active Investment Managers, Investors Intelligence, the American Association of Individual Investors, etc.

. Asset flows. Commitment of traders (COT) report and mutual-fund flows.

. Overbought/Oversold Indicators Volume related indicators and A/D lines.

. Valuation/Sentiment Indicators. They look at earnings relative to interest rates.

. Volatility. These are based on the VIX (Volatility Index from CBOE) and SKEW (index that tries to show the volatility of an extreme market event, such as a market crash).

. Put/Call ratios. Put/Call ratios from CBOE (Chicago Board Options Exchange).

8.5.3. The monetary component (20% of the Fab Five).

The monetary component has a final range of [-8 ; +8], and the brackets of this component are set asymmetrically at [-1.5 ; 2.5]. Therefore, it is easier to get a sell than it is to get a buy.

1) Rate of change of interest rates. The first indicator is based on a 26-week percent change of Moody’s corporate Baa yields. A high level of interest rates is negative for the stock market and vice versa. NDR applies the following contribution to the monetary component: +1 if this indicator is below -3%, 0 between -3% and 6%, and -1 if it is above 6%.

2) M2 money supply minus industrial production and PPI commodities. The second indicator illustrates the relationship between monetary and economic environments, using the M2 money supply, a measure of the money available for spending, and subtracting from this monetary measure the industrial production and the commodity price component of the producer price index (PPI). When the value of this indicator is above the upper bracket, the contribution is +1 because there is money available for spending and some of this liquidity flows into stocks. When the value is between the two brackets, the contribution is 0, and finally, when this indicator is below the lower bracket, the contribution is -1.

3) S&P-500 versus 10-year yield deviation-from-trend. The third indicator is an interest-rate indicator for the stock market using the benchmark 10-year Treasury note’s yield. This indicator is based on a moving average of the differential and a regression line representing the interest rate trend and the difference between the prediction and the actual result representing the deviation. The contribution to the Fab Five monetary component is -1 above the upper bracket, 0 in between, and +1 below the lower bracket.

4) Reuters Continuous Commodity Index (CCI). The fourth indicator applies the Reuters CCI as a proxy for inflation. Inflation pressures measured by this index have a negative effect on the stock market, and vice versa.

5) Interest-rate sensitive stocks. NDR uses the AMEX Securities Broker/Dealer Index, which tracks interest-rate sensitive financial stocks as a proxy for interest rates, because this kind of stocks behave poorly when interest rates are rising and vice versa. Additionally, financial stocks tend to lead the markets. NDR uses this index smoothing it over 10 days, and employing moving standard deviation brackets to predict where the market thinks interest- rate risk is headed.

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6) Free reserves measured by the Fed. This indicator is based on the simple concept that liquidity or lack of liquidity helps to move markets. Most banks must keep a certain percentage of their deposits with the Federal Reserve (required reserves). When banks have a total reserves amount that exceeds the required reserves, this shows a high level of liquidity (expansionary policy), and vice versa. NDR uses data from the Fed Board and normalize it through the spread between the 3-week moving average and the 52-week moving average. The idea of this spread is to show deviations from the longer term trend. When the fast moving average crosses above the slow moving average, the monetary policy is becoming expansionary, and vice versa.

7) Extreme values in the growth of M1 (money supply). Although an increase in M1 is positive for the stock market and vice versa, when the growth rate reaches an extreme value, this can be seen a as bearish signal, and vice versa. These extreme values are determined by moving average deviation brackets in NDR.

8.5.4. The Fab Five combo component (20% of the Fab Five).

The last component is called combo because it is a combination of six stock-market models, each of them made of a variety of indicators. The idea of this variety of indicators is looking for a consensus to make better investment decisions. As there are six indicators, the range of this component is [-6 ; +6], and the brackets are set at [-1.5 ; 2.5].

1) Don’t fight the tape. In NDR they know this indicator as “Don’t fight the tape”. It is a simple long-term indicator based on a monthly timeframe, and it is made up of two parts, a tape indicator and a monetary indicator. The monetary indicator is based on the crosses of the 90-day commercial paper yield against its 10-month moving average. Upside crosses are seen as negative for the stock markets, while downside crosses are positive. The tape indicator is a 12-month moving average cross of the S&P 500 Total Return Index against its moving average. An upside cross is positive for the stock market, while a downside cross is negative.

2) A mix of trend-sensitive, monetary and sentiment indicators. The second indicator is a mixture of 8 indicators.

3) The environmental risk index. The third indicator is a mixture of four external components, including monetary, economic, sentiment, and valuation with a total of 71 indicators.

4) Trend-sensitive indicators. The fourth indicator is made up of eight trend-sensitive indicators and it is presented as a diffusion index. This indicator adds a bit more diversity to the Combo component.

5) Thematic mix of indicators. The fifth indicator is a mixture of economic, interest rates, sentiment, and valuation indicators.

6) Adaptive trading model. The sixth indicator is a model (ATM) made up of three components. The first component is designed to distinguish between a trending and a mean-reverting market. The second component is a trending model that applies if the first component considers the market is trending, while the third component is a mean-reverting model that starts to apply if the first component shows the market is mean-reverting.

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8.5.5. A simple bond market model.

In this chapter we are reviewing one simple model designed for bonds and explained in Being right or making money, written by Ned Davis. In this review, we are not getting in too much detail as we did in the stock market model. It is a model based on four indicators [-4 ; +4] with the simple objective of staying in gear with the tape and in gear with the Fed. This model embraces the KISS (keep it simple stupid) rule, and the foundations of this model were provided by Marty Zweig.

1) The short-term slope of the Dow Jones 20 Bond Average. Buy when the index rises from a bottom by 0.6 percent and sell when the index falls from a peak by 0.6 percent.

2) The longer the term slope of the Dow Jones 20 Bond Average. Buy when the index rises from a bottom by 1.8 percent and sell when it falls from a peak by 1.8 percent.

3) Changes in the discount rate. Buy when the discount rate (rate at which banks borrow from the Fed) drops by a least one half of a percentage point and sell when the discount rate rises by at least a half point.

4) The yield curve based on the difference between the yields on AAA corporate bonds and 90-day commercial paper. Buy when the spread crosses above 0.6 of a percentage point and sell when the spread falls below -0.2. Go neutral between -0.2 and 0.6.

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