Timing Model
The Timing
Model is a proprietary computerbased mathematical/statistical model that
issues buy and sell signals as it detects changes in the direction of stock
market trends based on a set of predictive indicators.
Right off
let’s say that economics and finance, as social sciences, are not pure sciences
and so the models are more likely to be imperfect, even disastrously wrong,
than in pure science. This page
describes a backtested model, a timing system, that has outperformed buynhold
(greater return, less risk) in real
time since 1990.
Note also that each new year brings a revised model that incorporates the previous year’s data. Then the revised model is used “live” or real time during the entire new year. Why do this? The stock market is evolutionary as it changes and adapts… and so must the model.
The
accompanying table and charts summarize the backtested performance of the
timing model over selected time periods, with comparisons to inflation, money
market based on Treasury Bills, and buy and hold for the S&P 500 index…
starting with $1000. The S&P 500
index is used because of its importance: it’s the most followed, most used as a
benchmark, has a long history, most used to compensate fund managers,
and covers most of the marketcap of the
The timing strategies determines what to do when a sell or buy signal is issued by the model. The standard timing strategy is fully in stocks (based on the S&P 500 Index) during a buy signal and completely out in a money market (based on Treasury Bills) during a sell signal. The aggressive timing strategy ups the ante with a multiplied (greater by half) investment during a buy signal and a gain during a sell signal equivalent to a market decline (or a loss equal to a market gain). Specifics are described at the bottom of the table.
Timing Model Version: 2018 
Starting
Amount $1000 




1970s 
$2,038 
7.4% 
9.7 


TBills (Money Market) 
1,834 
6.2% 
11.4 
0.0% 

Buy & Hold 
1,750 
5.8% 
12.4 
7.2% 
26.6% 
Model Using Standard Strategy 
4,020 
14.9% 
5.0 
1.6% 
1.9% 
Model Using Aggressive Strategy 
6,931 
21.4% 
3.6 
1.5% 
5.8% 
1980s 
$1,644 
5.1% 
13.9 


TBills (Money Market) 
2,335 
8.9% 
8.2 
0.0% 

Buy & Hold 
5,004 
17.5% 
4.3 
2.4% 
5.0% 
Model Using Standard Strategy 
10,844 
26.9% 
2.9 
0.0% 
None 
Model Using Aggressive Strategy 
24,127 
37.5% 
2.2 
0.4% 
None 
1990s 
$1,332 
2.9% 
24.2 


TBills (Money Market) 
1,609 
4.9% 
14.6 
0.0% 

Buy & Hold 
5,309 
18.2% 
4.2 
1.4% 
3.2% 
Model Using Standard Strategy 
7,540 
22.4% 
3.4 
0.3% 
None 
Model Using Aggressive Strategy 
17,295 
33.0% 
2.4 
0.7% 
2.7 
2000s 
$1,283 
2.5% 
27.8 


TBills (Money Market) 
1,307 
2.7% 
25.9 
0.0% 

Buy & Hold 
908 
1.0% 

9.3% 
37.0% 
Model Using Standard Strategy 
2,744 
10.6% 
6.9 
1.4% 
3.0% 
Model Using Aggressive Strategy 
7,076 
21.6% 
3.5 
0.4% 
None 
2010s 
$1,141 
1.7% 
42.0 


TBills (Money Market) 
1,017 
0.2% 
326.9 
0.0% 

Buy &
Hold 
2,831 
13.9% 
5.3 
0.0% 
None 
Model Using Standard Strategy 
2,520 
12.2% 
6.0 
0.1% 
0.9% 
Model Using Aggressive Strategy 
2,638 
12.9% 
5.7 
1.1% 
6.7% 
19702016 
$6,536 
4.0% 
17.7 


TBills (Money Market) 
9,158 
4.7% 
15.0 
0.0% 

Buy & Hold 
119,464 
10.5% 
7.0 
4.2% 
37.0% 
Model Using Standard Strategy 
2,272,683 
17.5% 
4.3 
0.7% 
3.0% 
Model Using Aggressive Strategy 
53,998,329 
25.5% 
3.1 
0.8% 
6.7% 
Buy & Hold is buying and holding the S&P 500 Index
through thick and thin, including reinvested dividends. Model Using Standard Strategy is
100% in the S&P 500 during buy signals,
including reinvested dividends, and 100% in TBills during sell
signals. Model
Using Aggressive Strategy is 150% long the S&P 500
(dividends not received) during buy signals and
100% short the S&P 500 (dividends not paid) during sell signals.
See here for alternative
aggressive strategies. Returns for the model are based on nextday trades at the
close. Per Year Return is the annualized return that would
give the ending amount over the given time horizon, including any reinvested
dividends, but not including expenses or taxes. Each account started with
$1,000 and was updated (compounded) on a weekly basis. Years to Double is the number of
years it would take to double the value of the account given the per year
return for the relevant time span. Morningstar
Risk
is average under performance relative to the threemonth TBill's annual
return, a la Morningstar. Max Annual Drawdown is
the maximum loss sustained for the entire year (the biggest decline based on
annual returns). 
Buying and holding stocks from 1970 forward would have returned an annualized 10.5%, including nine losing years with losses up to 37%. The standard timing strategy returned an average 17.5%, while the aggressive timing strategy further upped the return to 25.5%. Putting $1,000 into stocks in 1970 and letting it ride would have accumulated about $119 thousand by the end of last year. The equivalent money market indexed on T Bills would have been about $9 thousand. The same starting amount based on the timing system would have grown to about $2.2 million using the standard strategy and $54 million using the aggressive strategy. The average performance of the standard timing strategy doubles a portfolio in 4.3 years. To account for real return we can subtract the inflation rate. For example, over the entire time frame from 1970 on, the annualized real return for buy and hold is about 6.5% (10.5 less 4.0%). Note that the artificially low interest rates by the Fed resulted in Tbills either just beating inflation (in the 2000s) or not keeping up with inflation (2010s). The real return for buy and hold over the 2000s is 3.5%, worse than the 1% shown.
The 37% buyandhold worst drawdown loss over the test period far exceeded the 3% and 7% losses for the standard and aggressive strategies. And note that the 2000s “lost decade” shows a 1% yearly loss for the S&P 500, but annualized gains of about +11% and +22% for our timing strategies.
The
aggressive timing strategy gained an impressive +26% during the debilitating bearmarket in 197374, while
the standard timing strategy lost 5%
and buynholders liquidated about 42% of an S&P 500 portfolio. During the bear market of 20002002, buy
& hold portfolios shrank 46%, while the standard portfolio shaved 1% and the aggressive portfolio surged +38%.
The bear market of 20072009 axed 55% from the S&P 500,
while the standard
strategy lost 10% and the aggressive
strategy gained +45%.
The timing
model has its warts as well. It missed the severe corrections in 2010 (16% over 11 weeks) and 2011 (18%
over 17 weeks). The standard strategy had four losing years (1.9, 3.0, 2.3, and 0.9%);
the aggressive strategy also had four losing years (5.8, 2.7, 1.7, and 6.7%). By
comparison, buy and holders lost money in nine years, with losses ranging from 3 to 37%. Over 48
years, the standard strategy underperformed buy & hold in 8 years,
breaking even in 20, and winning 20. The
aggressive strategy beat buy and hold in 75% of the years.
Still, the timing model's strategies yielded superior results over the once popular, although theoretical and discredited, buynhold strategy. And it accomplished this with much less risk of underperforming the money market alternative during weak stock market years. In particular, note the results for the risky and tough investment period spanned by the 1970s. During that turbulent decade, buyandhold returned less than money markets. Worse yet, inflation sprinted to an annualized rate of 7.4%, giving a real (inflationadjusted) negative return for both money markets and stocks! And, the results are even worse for buy & holders during the 2000s decade.
Risk is often expressed and calculated as volatility in returns. From my perspective, however, it's not simply a measure of volatility; it's a measure of downside volatility. In one version, as implemented by Morningstar Mutual Funds, a portfolio exhibits risk if it under performs the money market alternative. For example, in 1990 the buyandhold S&P 500 strategy lost 3.2%, whereas TBills returned +7.5%. The risk for that year is the 10.7 percentage points by which the S&P 500 under performed TBills. The risk for a year is zero whenever a portfolio's return exceeds the TBill rate. A risk calculation in the table is the sum of risk results for each year divided by the number of years. By this definition of risk, a money market's risk based on TBills is zero. Note that the standard strategy's Morningstar risk is about onesixth that of the considerably riskier buyandhold S&P 500 strategy (0.7 v 4.2%).
The accompanying Return vs (Morningstar) Risk chart shows the standard portfolio above (higher return) and to the left (lower risk) than the buy & hold portfolio. A good timing model “can have its cake and eat it too.” It can achieve higher return with lower risk than the widelypromoted buyandhold strategy. Note, however, that the aggressive strategy yields higher return than the standard strategy, but at the expense of greater risk. This result is consistent with financial research (and conventional wisdom) that higher return incurs higher risk. Yet, the aggressive strategy sustains just onefifth the risk of buying and holding (0.8 v 4.2%). A good timing model can turn conventional wisdom on its head.
Maximum drawdown is another risk
criterion. For buy and holders this risk amounted to a devastating 37%
annual loss (in 2008), compared to about 3%
(2002) for the standard portfolio, and 7%
(2015) for the aggressive portfolio. Standard
deviation (Sigma) is another
measure of statistical risk that’s widely used in theoretical financial models,
although it treats upside and downside variations from the average or mean
equally, an undesirable trait for capital preservation. Sortino Sigma accounts strictly for downside deviations, a more
appealing metric of risk. As expected,
the model’s strategies have lower Sortino Sigmas, as seen in the accompanying
table.
Two popular
methods of accounting for riskadjusted
returns are the Sharpe Ratio and
Sortino Ratio, the former named after Nobel Laureate William
Sharpe. These calculate the excess returns (returns less riskfree returns
based on 90day Tbills, our money market benchmark) and divide by their respective
Sigma and Sortino Sigma. In other words,
each ratio measures excess return per unit of standard deviation. It’s useful in comparing the performances of
different portfolios during the same time period.
The model’s strategies clearly outperform buynhold on a riskadjusted basis as well. Note that the standard strategy has higher riskadjusted returns than the more volatile aggressive strategy, meaning that the latter didn’t generate enough additional return to compensate for the additional volatility. During the strongly cyclical decades of the 1970s and 2000s, the standard strategy exhibits much less risk than buying and holding, by any measure.
Yet another take on risk is value at risk (VAR), which in our case addresses the question "How much do we stand to lose from one week to another?" The accompanying table yields some interesting answers, including responses to the dual question "How much can we gain in a week?"
From a VAR viewpoint, the red cells tell a potentially harrowing story for riskaverse investors. Buy & holders suffered losses in 43% of the weeks, just above the 41% for the aggressive timing strategy; the standard timing strategy reduces this risk to 30%. The worst weekly drawdown was about 18% for buying & holding; again, the standard strategy shows lower risk at about 9%, while the aggressive strategy posts 13%. The maximum drawdown for buy & holders was sustained during the extremely turbulent 2008; the model's maximum loss was in September, 1974 during the 19731974 bear market. Out of 2505 weeks, the standard strategy lost more than 7.5% in just two weeks. Buy & holders incurred 10 such losses, but the aggressive strategy showed 20 severe weekly losses exceeding seven and onehalf percent.
The aggressive
strategy does compensate the risk takers, with some spectacular weekly returns.
The +21% maximum return in the table is not
a misprint; it was achieved in the first week in October, 1974, as the S&P
500 vaulted from the bottom of the bear market during a buying panic, marking
the end of that bear market, and a point in time that many analysts cite as the
beginning of the great secular (longterm) bull market that ended in
2000. At that time the aggressive strategy was 150% long.. Its next best weekly performance was +18% in the second week of October, 2008, a short
position during a week that featured an 18%
selling panic in the waning weeks of that bear market.
Regarding volatility, as seen near the bottom of the table, the model's standard portfolio strategy shows a lower standard deviation than buying and holding, as expected. The aggressive strategy shows the highest variability, although this measure is influenced by returns both below and above the average return.
The standard
and aggressive strategies have the highest Sharpe
ratios, about 2 1/2 times that of buy and hold. From a weekly standpoint, the standard and
aggressive strategies have about the same Sharpe ratio. The standard portfolio has a lower return
than the aggressive portfolio, but its much lower standard
deviation compensates when risk is taken into consideration. On an annual basis standard beats aggressive,
as shown in the earlier table.
Alpha and Beta are
still other metrics for performance
and risk, as seen within the table at right. Alpha
is a measure of a portfolio’s excess return relative to the risk assumed by
buying and holding an index, in this case the S&P 500. The positive alpha for the standard strategy
indicates that this strategy adds value to its investments in the S&P
500. Numerically, the strategy would
return an average +9.2% in a year when the S&P 500 broke even. A negative value here would indicate downside
risk. Beta can be thought of as the volatility of a portfolio (up and
down, not just down) relative to the index.
Beta for the standard strategy says that its annual up/down return
movements are on average just about 62% of the annual return changes for the
S&P 500. Lower volatility would be
expected, given that this strategy resides in TBills 23% of the time. As seen,
both strategies yield excess return and lower volatility than buying and
holding. See here for how
these metrics are calculated. As
reported in this table, returns are riskadjusted by subtracting the riskfree
return for each year. Also, the “fit” of
the regression line is much more significant for the standard strategy
(Rsquare 0.56), but less so for the aggressive strategy (Rsquare 0.16),
meaning that the estimates in the table are more reliable (significant as seen
by p) for the standard strategy than for the aggressive strategy. The aggressive strategy’s low correlation
with the S&P 500 also says that this strategy offers diversification (and
lower volatility) when part of a portfolio that also includes the S&P500.
The stock market can be hazardous to our shortterm wealth, with severe price shocks to the downside. The standard timing strategy has historically reduced this form of risk, but it does take a steady hand at the helm during these shortterm squalls.
The timing model calculates a score in the range 0 to 100. A score of 50 is dead neutral, roughly stating that the odds of a currently up trending market are the same as a currently down trending market. A score of 80, for example, says that the likelihood of a primary uptrend is 80%, or four to one odds; a score of 10 indicates only a 10% probability (odds of 1 to 9) of a primary uptrend. A primary uptrend is defined as an increase of 8% or more in the S&P 500 Index over at least eight weeks, based on endofweek closings (usually Fridays). Similarly, a primary downtrend is defined as a decrease of 8% or more in the index over at least eight weeks, based on closings at the end of a week. Basically, we want to be in stocks during primary uptrends and in cash during primary downtrends. The table at left shows common stats for the lengths of primary trends. Note that up trends filled 73% of the total weeks and are longer than primary downtrends.
So, for
example, based on closings at week’s end:
If we're currently in a primary uptrend and then the market starts falling, the
trend will change to downtrend if a closing price exceeds an 8% decline
from the uptrend's weekending peak after at least 8 weeks, else the trend
remains an uptrend. Conversely, if now
in a primary downtrend
and the market subsequently rises 8% or more from the downtrend's weekending
low, then the trend changes to an uptrend, providing that at least 8 weeks have
passed. To reduce volatility, these changes have to occur over a period of
time, eight weeks or more, as a means to reduce the illmodeling effects of
countertrend spikes. The model views an
uptrend as a series of 1s and a downtrend as a series of 0s. It then predicts (as a probability between 0
and 100) whether the end of a current week is in an uptrend.
Buy and sell trades
(signals) are triggered by comparing the model's score to rigorously tested buy
and sell bands. A score at or above the buy band
(currently 61) is positive or bullish
for stocks; a score at or below the sell band
(currently 44) is bearish or negative. If
we're in a sell phase (the last signal was a sell trade), the score must hit or
pop above the buy band 61 for the model
to issue a buy trade; otherwise, it remains a sell. Likewise, if we're in a buy
phase, the score must hit or sink below the sell band 44 to issue a sell trade; else the model stays on
its buy signal. We can interpret scores within the band as hold current
position.
So, from the
standpoint of primary trends, if currently on a sell and the score rises to 61 or
above, the model decides the primary trend has changed to up. Likewise, if currently on a buy and the score
drops to 44
or below, then the model decides we have a new primary downtrend. That's why in
the downloadable data files you see a series of 1s and 0s. Based on rigorous
testing the boundaries 44/61 for the current model determine the model's
view if the primary trend has changed.
And does it in a way that maximizes the value of the portfolio over the
test period since 1970.
The accompanying
chart and tables show 51 switch signals (trades) over 48 years, averaging about
one per year. An average 51 weeks passed between trades. Buy trades ranged from 1 to 407 weeks,
averaging 71 weeks, where onehalf were above 32 weeks in length; sell trades
lasted anywhere from 2 to 78 weeks, averaging 22 weeks, with onehalf the sells
lasting over 18 weeks. Of the 51 trades, there was 1 oneweek switchback (a short sell), 3 switched
back after two weeks (2 of these short buys), and 1 lasted three weeks. Twelve
trades (24%) were less than 8 weeks. The
model spent 77% of the time in stocks.
This
model issues fewer trades than preceding models, although an average of 1.1
trades per year can be misleading. The
model switches more frequently during turbulent periods. There were 5 signals in less than a year
during November 2007 to May 2008, the
start of the financial
crash that included twin bear markets.
That last sell mostly stepped aside from a market that collapsed 50% into March, 2009 (see 49%
Max Avoidance in table below). During
many switches it’s tempting to ignore one or more trades, behavior that can
dent returns given the asymmetry of results in the table below. Note that the model easily beat buy and hold
during the difficult 1970s (table at the top of the page): annualized 6% for buy and hold, 15%
standard timing, 21%
aggressive timing. During the 20072009
debacle buy and hold crashed 55%, the standard
timing strategy lost 5%, and the aggressive
timing strategy surged 45%.
This model’s historical record shows that 19% of the sell trades (5 of 26) resulted in missed gains (regrets) averaging +3.1%, ranging from +0.1 to +6%. (See table left.) The 81% successful sells avoided losses of 11.5% on average, ranging from 0.7 to 49.4%. On average, a sell trade avoided a loss of 8.7%. These asymmetric results suggest that it’s wiser to follow sell trades than not. Buy trades were successful 68% (17 of 25) of the time with gains ranging from about 1 to +266%, averaging +50%. The 32% unsuccessful buys incurred losses of up to 4.5%, averaging 2.3%. Overall, buy trades gained an average +33.4%. We can think of regret sell losses and losing buy losses as insurance premiums for avoiding severe losses during serious market declines.
The model is made up of components called indicators or predictors. I revise the model each year in January, as
data for the preceding year are incorporated into the model’s structure. During
this process, new and revised hypothesized indicators are researched and
vetted, as I seek improvements in the model’s performance. Think of this as
developing a product with a number of ingredients, the particular mix and
strength of these ingredients affecting the efficacy of the product, say, a
drug or a food. Each new ingredient in combination with existing ingredients is
laboriously tested, as in a chemical or biological lab. Is the new ingredient
(indicator) effective as it interacts with others in the mix? Can I change the
nature of that particular ingredient to create a better product? Each indicator is a mathematical/statistical
manipulation or transformation of one or more data points. So, for example, if chili powder is one of the
ingredients (indicator) in chili (the model), what constitutes chili powder
includes its own set of fundamental ingredients (data points).
The initial selection of an indicator is rooted in the scientific method: formulate a
hypothesis, design the experiment, test the hypothesis, draw a conclusion. For example, a socalled null hypothesis might be “Yield spread (Tbill minus Dividend
Yield) is unrelated to primary
trends.” The experiment is the structure of the model used and the inclusion of
this indicator in the model. Its test is
running the revised model to identify primary trends. The conclusion would be to further consider
this indicator if it’s statistically
significant, meaning that the hypothesis is rejected. In other words, yield spread is related to primary trends. The
monetary performance of the revised model is then evaluated. If it improves return, then the new indicator
is incorporated in the model. The
current model does include yield spread as an important indicator: As yield
spread increases the model’s score decreases (a negative correlation).
The current
model included tests of indicators that were carefully constructed (derived or
transformed) from a set of data points, based on financial and technical
hypotheses. (No miniskirt or Super Bowl indicators here.) Of these, 14 indicators using 28 data points
passed experimental muster over the test period from 1970 to date. These
distilled indicators feed the model’s score calculation. Note from the
chart above that the model is an oscillator
that generates probabilities as it fluctuates (oscillates) between 0 and 100
(probabilities of 0100% or 0 to 1), depending on the influence of its indicators. Moreover, within the range of about 20 to 80 the model is particularly sensitive to its indicators. Conversely, scores near the upper or lower
end change reluctantly.
A buy trade is issued when the score is 61 (probability 0.61)
or above; a sell trade is given when the score
is 44 (probability 0.44)
or below. Scores between 44 and 61 say hold
the current position, whether on a buy or sell.
So, if currently following a buy signal and a sell signal is issued (the
score changes to 44 or below), the standard
portfolio switches to a money market, and stays there while the score is under 61. If the
model is currently on a sell signal, then the standard portfolio stays out of
the market while the score is under 61, but
buys the market should the score hit 61 or
above.
We can group
indicators into four categories for descriptive purposes. Technical
indicators reflect levels, changes, and other measures of stock market
price activity, the end results of the battles between the forces of supply and
demand. Momentum, trends, and volatility
in stock market indexes, internal (underthesurface) indicators relating to market breadth
calculated in various ways based on up and down volume action, relationships
between new highs and lows, and measures of advancing issues versus declining
issues are all examples of technical indicators. The model’s technical indicators
include its own versions of the popular Bollinger
bands, TRIN,
death cross,
and golden cross
indicators. Monetary indicators include levels, changes, and differences
in various interest rates, as in their effects on yield curves;
certain actions by the Federal Reserve that implement changes in monetary
policy; and money supply measures that influence economic activity, such as the
widely reported M2. Sentiment indicators gauge emotion in the market.
Many of these indicators take advantage of the "herd
mentality" by giving signals that run contrary to extremes in
sentiment. For example, high levels of cash in mutual funds not only may
mean that cash is available to fuel an up move in the stock market but also that
stock fund managers are bearish on the market. As another example,
extremely bullish sentiment among financial newsletter writers or retail
investors often means that the market is about to reverse course to the
downside (if everyone is already bullish, who's left to buy?). The model
includes the widelyfollowed AAII Investor
Sentiment Survey and other metrics to account for this factor. Fundamental indicators describe economic
and valuation activities. These include measures of inflation, growth, GDP, and
other factors related to the overall economy; they also embrace relationships
among stock prices, corporate earnings, and dividends, such as price/earnings
ratios and dividend yields. Research
indicates that large stock market losses are more likely when valuation levels
are high, not low. This result shows up
in the model’s choice of fundamental indicators. The literature usually includes monetary
indicators under fundamental. Here we
break it out as a separate category that’s uniquely important and widely
studied and reported.
Valuation
calculations such as trailing or forward p/e and Schiller p/e are not reliable
"timing" indicators in and of themselves, but they are useful in
predicting forward returns and within the context of other indicators in the
model that are longterm oriented. Extreme high levels are more a function of
either overlyoptimistic sentiment or recessionary earnings; extreme low levels
overlypessimistic sentiment. These can remain at extreme levels for long time
periods, while the market continues its longerterm up or down trend. The model
includes two valuation metrics.
Several
indicators include two categories: monetary/sentiment, tech/monetary,
monetary/fundamental, and tech/sentiment.
For example, the VIX
used in the model reflects sentiment (fear) but is a technical calculation for
30day implied volatility in statistical finance. When this metric is elevated, fear is high
and impulsive selling episodes are more likely, especially during bear
markets. During the twin bears in
20002002 min/max/ave VIX daily closings were
16/45/25; 16/81/33 for the twin bears in 20072009. When fear is lower (VIX below average 20 down
to minimum 9) the market more easily shrugs off bad news and “climbs the wall
of worry.” Another example: The model's hybrid monetary/fundamental indicator
considers two counteracting effects. Fundamentals such as price/earnings and
dividend yields are negative influences when prices rise and/or dividends and
earnings decrease. But, low interest rates cushion their effect and ultralow
rates totally negate their negative influence on the model.
Fundamental
and monetary indicators can be thought of as measures over longer term
horizons, as attempts to divine secular trends and cycles such as recessions,
bear and bull markets. Technical and
sentiment indicators are more useful as intermediate term measures, more
associated with 1020% corrections.
As mentioned
elsewhere, the model is adaptive, in that it incorporates the previous year’s
data. The revised model is then used live in the current year. The change from year to year is far from
dramatic, as the model is reasonably stable. Its indicators for this year
remained at 14, while improving overall statistical significance and
performance. Two technical indicators were replaced by two other more effective
technical indicators; one fundamental indicator was revised by using year over
year changes in inflation rather than monthly changes, thereby reducing the
model’s volatility.
No one
indicator dominates the model. Many
analysts focus on one or two indicators regarding market direction, a decidedly
narrow view that ignores other competing influences. For example, many pundits, the media,
analysts, and investors often view interest rate increases as a stockmarket negative.
It’s more complicated than that. The extent of this influence depends on many
factors. Which rates changed, by how
much, and how fast the sequence of changes? At what point are we in the
interest rate cycle? Where are we in the
business or profit cycle? Is market
momentum strong? What appears under the
hidden technical surface? Is the market
overvalued, undervalued, or fairvalued?
How much is emotion influencing the market? What external political or
global events currently have the market’s attention? The model tracks four
interest rates (Fed funds rate, TBill, commercial paper, and Prime rate) with
complicated effects that are too detailed for here, as they cross all four of
the model’s indicator categories: technical, monetary, fundamental, and even
sentiment. On balance the result can be
negative, positive, or a wash.
Think of the
model more as a diagnostic rather than predictive tool. It does not predict the
future but does assess the risk of portfolio losses as the probability that the
week just passed is part of a primary uptrend.
In other words, it estimates the probability of outcomes that affect a
portfolio. A diagnostic framework, then, helps to identify a potential problem
(such as a likely but uncertain market decline) without having to precisely
predict when it will occur. It opens the
investment mindset to preparation (such as more diversification or changes to
allocations) rather than to prediction.
In
sum, the
model stirs 14 indicators into the pot, making its decisions based on the
interactions that determine this brew’s composite flavor.
The selected
model for the new year and its buy/sell triggers maximize total return by
applying the standard strategy from 1970 to the end of the recently completed
year.
More readings? Technical analysis
For the technically inclined…
Over
the years, I’ve tested buy/sell triggers and hundreds of indicators over
countless trials that affect the model’s performance. Performance in this case
is the standard strategy’s total return, based on the ending value of a
portfolio that begins in 1970 and ends the year just completed, providing the
model itself and all indictors are statistically significant. After too many
trials to count, I select the model (mix of indicators) and sell/buy triggers
that optimize (maximize) the portfolio’s total return, providing the resulting
model is reasonably stable with respect to a limited number of trades and
robust regarding small changes in its parameters (numeric constants used in the
model). Moreover, each candidate indicator for inclusion in the model must be statistically
significant at p<0.05. The current
model has all p<0.02 and most zero to three digits.
The accompanying chart
plots the model’s function, a binary logistic
regression. The term “binary”
refers to the use of 0 or 1 to respectively describe a primary downtrend and
uptrend. This is the target variable used by the logistic regression to
approximate the pattern of zeroes and ones over time. The xaxis (horizontal
axis) is the function’s calculated result based on specific values for its
indicators in a particular week; the yaxis (vertical axis) is a (logistic)
transformation from the xaxis that gives an equivalent probability, that is, the likelihood that we’re in a primary uptrend, or the probability that
the particular week is associated with a “1.”
Note that the function approaches the yaxis asymptotically, meaning
that it gets closer and closer to its extremes (0 or 1) but never gets there,
regardless of how far out we go. Note
also that the model is steep within its midrange probabilities (roughly 0.2 to
0.8), suggesting that it is sensitive to bigger changes in the middle than at
extremes.
The
visual setup of the data shows a table (matrix) whose rows represent weeks and
columns represent indicators and the target variable (0s and 1s). Minitab
is used for the analysis. In Minitab the
binary response (target) variable is specified and regressed against the 14
predictors (indicators). Using the function f’(x) = β_{0} + β_{1}
x_{ 1} + … + β_{14}
x_{ 14} , the software generates two columns of maximum likelihood
estimates for the β parameters and probabilities using an
iterativereweighted least squares algorithm. As an example, consider the
calculated score 82.5 for January 14, 2018, as seen in the bottom frontpage
table at this web site. Plugging the 14 values for that week (to name three,
10.16 for VIX, 1.427 for M2 Velocity, and 0.36 for yield spread given by TBill minus dividend yield) into f’(x) gives 1.55 to two
decimals (6 decimals are actually used). This is the value along the horizontal
axis in the chart at right. The
probability is mapped to the yaxis using the natural log transformation
(logistic function) e^{1.55}/(e^{1.55 }+1)
giving 0.825, a score of 82.5.
A
threedimensional surface (not shown) was generated in Excel with axes buy,
sell, and total return. The surface for
the selected final model has a fairly smooth, flat top of total returns for the
“optimal” range of buy/sell triggers. The buy/sell trigger combination that’s
selected for the final model corresponds to a point on the surface
wellembedded within the flat top, to minimize the instability associated with
steep dropoffs. In other words, the final buy/sell triggers are not
necessarily those that correspond to the maximum total return, although they
might; rather they correspond to a total return more or less in the middle of a
flat area of the highest total returns, thereby better ensuring the stability
of the triggers.
Here’s
a question I’ve been asked: “Your model has 4 indicator categories. Do you mind
sharing the approximate weight of each category?” This is a great
question that inexplicably never occurred to me, let alone the
answer. Unfortunately, this simple question requires a notsosimple
answer regarding the "weight" of each category (technical, monetary,
sentiment, fundamental). The model is nonlinear and includes continuous as
well as binary variables, with logarithms further complicating the answer. The answer would be easy if the model were
linear with scores attached to each indicator within a category and then adding
up the points for category weights. But... maybe this would help. Of the 14 predictors, 7 are pure technical, 2
pure monetary, 0 pure sentiment, 1 pure fundamental, 1 tech/monetary, 1
monetary/fundamental, 1 monetary/sentiment, and 1 tech/sentiment. Including overlapped categories (double
counting), we have 9 tech, 5 monetary, 2 sentiment,
and 2 fundamental. Mixed categories cloud the picture, although we can safely
say that technical indicators dominate when looking at overall presence,
followed by monetary, and finally tied sentiment and fundamental. If we
consider ranking based on statistical significance for each predictor, we have
tech at #1,4,8, 1011,1314; monetary at #3,7; fundamental at #12,
tech/monetary at #6; monetary/fundamental at #2; monetary/sentiment at #9; and
tech/sentiment at #5. So, based on average ranking, we can say that monetary
leads the pack, while fundamental, sentiment, and tech are bunched up at the
rear. Technical and sentiment indicators focus more on short to intermediate
time horizons, whereas monetary and fundamental indicators are more concerned
with intermediate to long time spans.
The model’s smoothing coefficients for relevant indicators emphasize
intermediate to longterm averages. In
the final analysis, it's the composite score that matters relative to the
buy/sell bands.
I’ve also been asked if so many
indicators (14 for the current model) represent a mathematical overfit to the data. The answer would be no, given that the binary
logistic regression used here and the great number of weeks would require about
66 indicators to represent an overfit, based on the Rule
of 10. Fourteen are used here. Did
the model’s development include outofsample
trials? No, not directly, but the yearlonglookahead application of the model
over 28 live years shows successful outofsample tests. Does testing so many combinations of
indicators and buy/sell triggers introduce
datasnooping or
datamining bias? The approach does have elements of this type of bias,
although this is mitigated by choosing indicators based on financial
hypotheses, by their statistical significance, by not using bulk methods, and
by the applied and successful use of the model with outofsample data each new
year. Also, the embedded selection of
the final buy/sell triggers within a flat top of total returns reduces, but
does not eliminate, data snooping and overfitting, while increasing stability.
Another technical issue that’s often
presented in the media relates to sigma multiples (number of standard
deviations that a value is from its average, often called a zscore) in the context of overbought or
oversold market conditions, when an actual SPX series is well above (or below)
the given smoothed series (trend line). For example, some analysts raise alarms
when the SPX is 2 or more sigmas (standard deviations) above a smoothed trend
and is therefore poised for a reversion to the mean (back to the trend
line). While often true, depending on
the time frame and how the metrics are calculated, a reversion to the mean will
happen eventually in one of these ways: a pullback to the mean, a time
correction that allows the mean to catch up, or a combination of the two. The
model uses a longer term (400 weeks) moving sigma and trend (both
exponentiallysmoothed) that currently (at the end of 2017) show the SPX with a
zscore of 1.7, below overbought thresholds of 2.0 (5% tail based on the
model’s historical data), 2.2 (2.5%), and 2.4 (1%). While no one indicator consistently signals
trouble, this indicator did breach the overbought 2.0 threshold two weeks
before the terrifying October 19, 1987 market crash and ensuing 34% bear
market. But did not reach an oversold
threshold before the 20002002 and 20072009 twin bears. It did hit an oversold
2.0 at the bear market low in March, 2009.
In the final analysis, the model and its
triggers are validated by realtime use and performance (return and risk) since
1990. See Reality Check and TimerTrac.
Note:
See download page for pdf files and
Excel workbook that include tested time series of the S&P 500, timing model
scores, buy/sell bands, switch signals, TBills, and dividend yields from 1970
forward.
Financial modeling is not like modeling in
classical physical sciences. It's not precisely measurable and predictable.
It's more like sociology, influenced by emotions, irrationalities, gullibility,
the flow of hormones, noisiness, fear, greed, envy... you name it. They
simplify reality yet provide useful insights of economic phenomena. Still,
don’t confuse the map [model] for the territory [reality].
Fabled
Quants: Renaissance Technologies
In its
simplest form, a buy signal suggests that the portfolio should emphasize
stocks; a sell signal shifts the emphasis to cash. What proportions should be stocks or cash
would depend on the investor’s age, net worth, propensity for risk, and other
personal attributes.
Note that the
timing model addresses only the stock portion of a portfolio. An investment strategy based on the standard
strategy is simple to implement. Telephone or online switches are made between money
market funds and stock mutual funds or exchange
traded funds (ETFs) whenever
market conditions favor one or the other based on switch signals. An ETF
mimics the behavior of an index and trades like a stock within a brokerage
account. Thus, an investor who wishes to
closely follow the standard strategy would position the portfolio’s stock
portion in a money market fund during a sell signal and in an S&P 500 ETF
such as SPY
or VOO or an index
mutual fund such as Vanguard 500 Index (VFINX) during a buy
signal. The counterpart to the aggressive strategy is to be in a fund such as Rydex Nova (RYNVX)
during buy signals and Rydex
Inverse S&P 500 (RYURX) or an ETF such as SH during
sell signals.
NOTE: Important advantages of ETFs over mutual funds are no
restrictions on number of trades and the ability to trade at any time of the
day. A disadvantage: Dividends are issued, but not reinvested; instead they
flow to the core cash account. Dividends
and their reinvestment significantly add to performance over long time periods,
making up about 50% of S&P 500 total return since 1926 (its lifespan) and
about 30% since 1970 (model’s lifespan).
Those of you
who wish to mimic the behavior of the aggressive portfolio should keep in mind
that this strategy requires a high tolerance for volatility... and nerve. At a
buy signal, this portfolio switches all funds into a 150% long position basis the
S&P 500 Index. This would be equivalent to a mutual fund or ETF with beta 1.5 (multiplier 1.5x), or one
that generates 50% greater daily gains (on the upside) and 50% greater daily
losses (on the downside) than the S&P 500 Index. At a sell signal, all money
is 100% short the S&P 500 (multiplier
1x or beta 1.0). Thus, if the
S&P 500 were to lose 10%, this position would gain 10%. Conversely, a 10%
gain in the Index translates into a 10% loss for the portfolio. In theory the aggressive strategy should work
very well; in practice, less than perfect timing, daily updates over time, the multiplier, and volatility can reduce performance over what we would expect (see
this CAUTION).
I wouldn't bet the bank on these leveraged and volatile investment
strategies... and I would restrict funds to only a modest portion of my overall
portfolio.
The FAQs page
expands portfolio diversification and alternative standard and aggressive
investments. To generalize, a buy
signal suggests that the stock portion of an actual portfolio should be
invested in its favorite stock mutual funds and ETFs, based on that portfolio’s
target allocation for stocks, say, 50 to 90%, depending on individual
preferences. Diversified stock
investments would likely include a menu of large to medium to small stocks,
stocks based on growth and value, and stocks outside the
Abiding by the timing model's signals does require patience and discipline. False switchbacks aside, the timing system has an intermediate to longterm perspective, months to years, rather than days to weeks. The less we trade the better off we are with respect to the payment of expenses and taxes. Moreover, we have to control emotions when following a switch signal. Often, the model gives a buy signal at a time of high investor anxiety, as in November 1987, October 1990, September 1998, May 2003, and February 2009. And it can give a sell signal when times look okay, as it did in early October 1987 and October 2000.
A stock market index exhibits cyclicality and randomness, the former over months to years, the latter over days to weeks. There is too much randomness within short time frames to model with any accuracy; long term offers more stable outcomes (probabilities), but misses out on too many cyclical opportunities. The model takes the middle ground to judge probabilities for its trades. The timing model is tuned to cyclicality, as it anticipates changes of 8% or more in the S&P 500 Index over a minimum eightweek period, based on the closing value at the end of a week. It leaves the smaller, riskier, choppier, random waves for the traders to try to fathom. Declines of about 5% are common and scary, but extremely difficult to anticipate with any accuracy. I treat these with equanimity (usually!) when they happen, letting the model tell me when to consider a switch.
Market timing
is controversial and not suitable for everyone. "Buying and holding"
was the mantra based on the spectacular returns during the 1980s and 1990s…
until the serious bears in 20002002 and 20072009. Few souls can hold through
thick and thin, or commit new money when times are scary. Asset allocation
strategies are more conservative, giving up gain for lower risk, although those
who rebalance portfolios are practicing a form of market timing. And how about
buying good stocks and sticking with them? How do we pick the good stocks? Do
we really hang on? Academic studies and research in behavioral finance suggest
that individuals buy high and sell low their individual stocks and mutual
funds; yes, even during the 19742000 super bull market. Longterm good stock
picking surely rewards the pickers and their followers. Witness Peter Lynch,
George Soros, and Warren Buffett. But few of us have neither the time, the
emotional makeup, nor the talent for successful stock picking... and how do we
pick the good pickers? And will we ride it down with them during prolonged and
severe market
downturns? Few bulls come out the back end of a serious bear market.
Remember that
investment strategies have a dual objective: Preserve capital during bad times
and build wealth during good times. The avoidance of major losses during steep
declines is far more important than capturing all gains during uptrends.
Drawdowns leading to permanent losses drain wealth and victimize emotions,
factors that require models to seriously consider risk.
We can think
of investors as having three risk profiles: riskaverse investors who only
build modest capital; riskseeking investors who alltoooften blow up;
risksmart investors who take calculated risks on selective and timed
investments based on probable outcomes. The model addresses the latter
investor.
This work is
as much art as science, with a good smack of luck. Any trading system is
imperfect in practice. I accept the bad along with the good, as long as the
good outweighs the bad. This underscores a key advantage of working with a good
system: It offers an investment plan and promotes discipline, while stabilizing
emotions and curtailing actions that constantly play to fear and greed. I can't
guarantee future results based on past performance, but I haven't found a
better way for myself.
Don't
gamble; take all your savings and buy some good stock and hold it till it goes
up, then sell it. If it don't go up, don't buy it.
Will Rogers
The
performances described are theoretical in the sense that the model's
makeup is tested and revised annually to “optimize” return based on historical
data. In other words, the model that’s used is developed by backtesting the data
since 1970 (socalled insample training). For the new year, the model is real
time or "live" (is applied to outofsample data) when it’s used for
real. We can’t expect, on average, that a live model will outperform its
backtested parent. And that’s indeed the case, as measured by a metric called shrinkage, the difference between a
backtested model’s average return and its degraded average return when used
live. Shrinkage since 1990 is about 5% per
year, as seem in Reality Check,
starting with the model’s earliest implementation in fullyear 1990.
In theory, there is no difference between
theory and practice. In practice, there is.
Last revised 15 Jan 2018
Distribution
Copyright © 2018 Richard Mojena. All rights reserved. All materials contained
on this site are protected by
Disclaimer
Specific and personalized investment advice is not intended by this
communication. Its contents are for the public record as a free public service.
Information is based on the analysis of past data and assessments by the
models. Future performance may not reflect past performance. Profitable trades
are not guaranteed. No system or methodology ensures stock market profits. No
guarantee is made regarding the reliability or accuracy of data. In other
words, use this stuff at your own risk!
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