Mojena Market Timing
Frequently Asked Questions

I've heard timing systems sound great, but performance figures are based on theoretical models that are tuned to historical data.  In reality, they switch too often.  And they have to be right twice: getting out of the market and getting back in.  And they don't beat buy and hold.  Right?

Yes, many timing systems are guilty on all counts. Historical data are used because it gives us a means to discover patterns and relationships that affect investment performance. The trick is to generalize as much as possible, so that future patterns are recognized when similar to past patterns and adaptable when not. The work reported in the Hulbert Financial Digest, the popular chronicler of market timers, shows that the top-performing timing services just about match a buy and hold strategy, but at much lower risk (less downside volatility).

Buying and holding is okay in theory but dangerous in practice. In reality, few investors are capable of buying and holding. Emotions get in the way of needed analysis and discipline. Panic selling and comfortable buying usually lead to selling low and buying high. Moreover, I'm not so sure that authentic buy-and-holders exist. Those who decry timing are perhaps "closet" timers themselves. Examples include raising cash by money managers, rebalancing portfolios among asset classes, and buying and selling individual stocks, whether based on fundamentals, technicals, rumors, tips, emotion, or whims. 

A buy-and-hold strategy can under-perform for long periods of time. For example, the stock market lost out to both inflation and money markets over the ten years spanned by the 1970s and again in the 2000s “lost decade,” yet the timing model's backtested standard portfolio more than doubled the market's performance. It can also decimate portfolios by the end of a severe bear market, particularly if funds need to be withdrawn shortly thereafter. The 20% declines in 1990 and 1998 and the 34% crash in 1987 were followed by reasonably fast recoveries of capital for those who stayed invested. But the 48% grind in 1973-1974 delayed new highs for seven years, as did the 49% 2000-2002 bear market. The nearly three-year pounding starting with the crash in 1929 devastated Dow-based portfolios by some 90%; it then took 25 years for the Dow to regain its former high!  The 2007-2008 bear market took the S&P 500 down by 52%. The bear in 2009 marked a low 57% under the all-time peak in 2007.  The Index rescaled that peak 5 ½ years later.  Note that buy-n-hold assumes that investor never sell through panic or fear, not once, never seriously consider that the return of capital can take precedence over the return on capital.

The déjà vu markets are more subtle and frustrating when misfortunate points in time are picked. The Dow hit a high of 995 in 1966 and finally crossed 1000 six years later, with intervening roller-coaster rides of down 22%, up 48%, down 36%, up 73%, and then... the 48% debacle of 1973-74. Once again the Dow sank below 1000... for another six years into 1980. It then seesawed above and below 1000 for a couple more years, bottoming at 777 in August, 1982, and not piercing above 1000 for good until late that year.  (See chart.) Imagine living as a buy-and-hold investor through that grueling 16-year odyssey! How many did?  Eventually conviction is broken during serious and prolonged declines… and it’s sell, Sell, SELL… all too often near the bottom.

The usual investor behavior that’s well documented in the literature is to chase (buy) stocks late in bull-market cycles and shed (sell) stocks late in bear-market cycles.  Moreover, the typical investor carries high cash balances, degrading performance during the roughly 70% of the time the stock market is in an uptrend.  And keep in mind that a -50% portfolio axing takes a subsequent +100% gain to break even; a -25% trim requires +33%.  It takes time to recover such losses. Time is a real loss that can’t be recovered.  A good timing system avoids major downturns (preserves capital and time), so we don’t have to spend time afterwards recovering capital to break even.

Various studies of S&P 500 losses show the following results based on different perspectives:

·        5% losses three times a year, 10% losses once a year, 15% losses once every two years, 20% losses once every three to four years. 

·        More than 5% losses about half the time, more than 10% about one-third the time, and more than 20% about one-quarter the time.

·        Probability of a 5% or more decline in any 12-month period about 50%, 10% or more about 30%, 15% or more about 20%, 20% or more about 10%.

The model’s focus is on the 10% plus losses.  We ignore the noisy, mostly random 5% or so fluctuations as far too difficult to anticipate.  Moreover, note that the last set of probabilities are unconditional, that is, not conditional on the market’s state of “health.” The timing model would bend these probabilities in a favorable direction, as its probability score is conditional on the state of the market. In other words, low scores, primary downtrends, and sell signals are associated with more risk and greater likelihoods of declines.

The buy-n-hold mantra (usually accompanied by buy-n-hope) popularized during the remarkable super-bull markets of the 1980s and 1990s was shattered by the “lost” 2000 decade and its triple bear markets.  Holding through severe down cycles postpones dreams at best, shatters them at worst. And how about the ulcers? Yet, long term, the stock market is the only game in town that leads to financial wellbeing (see Did you know that...? below).

The conduct of the market over long periods is cyclical, revealing sustained uptrends lasting months to years, followed by persistent, but shorter, downtrends.  The 1966-82 market was a shining example of cyclical behavior, a timer's dream market. The period 1982-1990 also offered persistent cycles, surrounding an increasing secular (long-term) trend, unlike the flat trend of the earlier period. The 1990s market was unusually acyclical, with a steep uptrend.  Cyclical behavior was back during the 2000-2009 decade. Markets mirror our human affairs, the push and pull of conflicted greed (envy too) and fear.  And they are seriously complex, especially in reaction to often irrational and emotionally fragile investors.  Prices are influenced by fundamentals, yes, but clearly determined as well by our human foibles, negating the belief that efficient markets set the “right” price.

Market prices show cyclicality and randomness. The shorter the time frame, the more influential the random effect; conversely, the longer the time frame the more dominant the cyclicality.  That's why the model is mid-term to long-term oriented and describes its primary trends to reduce randomness, by the chosen percentage fluctuation (more than 8%) and number of weeks (at least 8) that define primary trends (within these cycles). The timing model's objective then is to detect changes in these cyclically-influenced primary trends as they happen.  It's not a model that tries to forecast the future level of the S&P weeks or months ahead, a considerably difficult exercise that's been largely unsuccessful in the literature with which I'm familiar.  Rather, it's a model that tries to identify cyclical inflection points, the tops and bottoms of primary cycles (named primary trends in my work), the points at which the primary trend changes direction. To be successful, a model does not have to be right twice, out at tops and in at bottoms, as critics maintain; it "just" needs to sell higher than its buy points and buy lower than its sell points, ideally with few trades.

Have you heard this one from the critics?  If a timing system misses the best x weeks (or days, months) over some investment horizon, its performance drops to about half that of buying and holding, assuming its performance is the same as buying and holding over the remaining weeks.  Yes, true.  But this view is decidedly one-sided and self-serving; they fail to mention what happens if the timing model avoids the worst x weeks, which after all, is a capital preservation objective of all timing systems.   Looking at the 1970-2017 period, investment performance drops by 40% should a timing system miss the 30 best weeks, while remaining invested the rest of the time. Let's be self-serving ourselves.  If a timing system avoids the 30 worst weeks and remains invested the rest of the time, its performance beats buy and hold by 45%.  Ok, let's be fair.   Suppose the timing system misses the 30 best weeks but avoids the 30 worst weeks, while remaining invested the rest of the time.  Now, the timing system beats buy and hold by 5%.  In the final analysis, these exercises are simplistic and futile, because (1) best and worst weeks are more likely to occur within respective cyclical up and down trends, not randomly, and (2) cycle-aware timing models are designed to detect these trends, not best or worst weeks per se

Backtested Per Year Returns Basis S&P 500, with Reinvested Dividends (Last row is Total Return)


Buy and Hold

Standard Timing

Aggressive Timing

















2000 peak - 2017




As the accompanying table illustrates, both timing and the timing period are everything.  The standard strategy based on this year’s tested timing model just beat buy and hold over the placid (acyclical) 1988-97 period.  The edge for timing was more decisive over 1978-87, a period that included a down 27% bear market over 21 months during 1980-82 and a 34% bear market that lasted four months in 1987.  The model trounced buy and hold during 1973-82, a span that housed the devastating 1973-74 bear that sliced portfolios nearly in half.  The 2000s “lost decade” included three severe bear markets, once again giving the timing model a serious capital-preservation and return advantage.  Through the end of last year buy-n-hold returned just 5.8% from the bull market peak in 2000. Just 5.8% total return over 17+ years. The timing strategies well outperformed during this time.  Timing models feed on cycles for sustenance.

The timing model has been live since the middle of 1989, slightly besting buy-n- hold through last year based on total return, but with much less risk, and with far higher risk-adjusted return. The 1990s ushered in an era of historically low downside volatility, except for the brief near-bear markets in 1990 and 1998. And we have not had a bear market since the last one ended in 2009. It's nearly impossible for a timing model, indeed for anyone as the records show, to beat buy-n-hold in markets that exhibit very little cyclical behavior and no punishing downturns.  The live model's advantage clearly became apparent during the 2000-2002, 2007-2009 bear markets and the lost decade 2000-2009. 

The model is built around probabilities; it assesses probabilities. It's far from exact, but pretty good regarding high vs low probabilities, which is why we have the gap between buy/sell bands, to account for inaccurate probability estimates.

Keep in mind that we can expect losses from time to time, although the model has stepped aside from serious losses in its live performance.  The model’s actual historical record shows a reduction in downside volatility, as would diversification, especially across asset classes such as bonds, utilities, REITs, and precious metals.

And, to be honest, the live implementation (using out-of-sample data) of a model rarely performs better than its backtested results (using in-sample data).  Since 1990, the annually-revised live models under-performed the current theoretical model by about 5 percentage points per year (10% v 15%), a metric called shrinkage. The question is: Does its use improve my investment performance... and soothe my nerves? For me the answer is yes, on both counts. 

 I am more concerned about the return of my money than the return on my money.

Mark Twain

A politician [strategist, technician, quant] needs the ability to foretell what is going to happen tomorrow, next week, next month, and next year. And to have the ability afterwards to explain why it didn't happen.

Winston S. Churchill


On Capital Preservation

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. 

Experiments in behavioral economics show that the pain of loss is twice as great as the joy of gain, a result consistent with the psychological value of preserving rather than losing capital.

So, we want to avoid as much pain as possible (loss), but also experience joy (gain).

As the Wall Street adage says: Cut your losses short and let your gains run.


On time

If you’re young, time is on your side, given the magic of compounding; otherwise, time is not on your side.

Remember that a 50% loss of capital needs a 100% gain back to break even and usually requires years of lost time in doing so.

Capital preservation is important; lost time might be even more important.

We can rebuild capital if we have the time, but we can’t recover time.

Near and during retirement capital preservation dominates time. Big losses must be protected, time is short.

Disciplined investment strategies address both capital preservation and time.



Investment truths?

 Do nothing, stand still, be patient, or stay the course (at your own risk).

Time in the market beats timing the market (see preceding box).

Don't time the market (unless you follow a proven timing system).

Cash is trash (except during bear markets).

Cash is king (except during bull markets).

Practice dollar cost averaging with new purchases and you will be fine (ok, but meanwhile you might lose half your current capital).

Stocks outperform in the long run, stick to your plan (Buy & hold and don't sell?  We’re all dead in the long run anyway).



Just what is a bull or bear market?  And what’s the difference between cyclical markets and secular markets?

Based on the commonly-cited 20% change to define cyclical bull and bear markets, the S&P 500 printed 16 cyclical bear markets and 15 cyclical bull markets (technically, we’re now in the 16th bull market) since 1929.  The average bear lost 38% over 17 months, with half losing more than 34% in 17 months; the average bull gained 144% over 45 months; half the gains exceeded 101% over 44 months.  The 45-month average length of a bull cycle is also the average time between bear markets, almost 4 years.  It’s not a zero-sum game; it does pay to be in the market most (about 70%) of the time.


The bull-market high in March, 2000 was followed by an 18-month 37% cyclical bear.  This low was technically followed by a lightening cyclical bull market that gained 21% over four months, ending in January, 2002.  Another cyclical bear followed into October, 2002, ending a 9-month 34% cyclical bear decline, very close to the averages.  The next cyclical bull market ran five years into October, 2007, yielding a 101% gain.  A 13-month bear market followed, axing 52% from the index by November, 2008.  This was followed by the shortest bull market on record, a 24% surge over two months. Consistent with recent volatility, the succeeding bear market shaved 28% over a record-short two months.  We’re in a 16th bull market as of this writing, confirmed by a greater than 20% gain since March, 2009.


Secular markets are not clearly defined, but do span multiple cyclical bull and bear markets.  A secular bear market is characterized by lower cycle highs and lower cycle lows (a downwardly sloping M, the opposite of a secular bull’s upwardly sloping W).  Secular bear markets show lower returns than average; secular bulls higher returns than average. Flat secular markets show more or less zero cumulative returns, as cyclical bears and bulls cancel each other out. The five-year secular bear that ended in 1942 dropped 60%; the somewhat flat eight-year secular bear that ended in 1974 shaved about 34%.  The great secular bull that started in 1974 ended in March, 2000, a record 26 years with a stunning gain of 2353%, more than doubling the previous record gain from 1942 to 1966. From an alternative vantage point, the secular trend from 1966 to 1982 was essentially flat, with a 9% gain. A secular bull measured from 1982 to 2000 posted a gain of 1389%. The secular trend from 2000 to 2007 is flat, characterized by both new cyclical highs and lows (Ms and Ws); the view from 2000 to 2009 is that of a sharp downward (bearish) secular trend with an overall loss of 57%.  The secular trend from 2000 through 2017 rises at an increasing rate, by about 62 points per year.  This flattens further if the annualized return of 5.4% over these 18 years is adjusted for 2.1% inflation, giving a real return of 3.3%. This secular trend could continue as the economy (individuals, private and public sectors) unwinds debt from the debt super-cycle of the past 20 years or so… and if elevated valuations such as price/earnings come down from rising profits.  Moreover, the secular trend might very well turn downward if economic freedom in the US continues its decline (11th for the linked report).  Or… it’s possible that the 2009 bottom marked the end of that secular bear and we’re now in the 9th year of a new secular bull that could get extended life from business-friendly policies in Washington.  We will know only in hindsight.  Long, somewhat flat secular markets with many bull and bear cycles are tailor-made for good timing systems.


Price to Earnings ratios (P/Es) often define the beginning and end of a secular market.  The average P/E for the S&P 500 is about 16.  At the bottom of a secular bear (beginning of a secular bull) the P/E is below 10.  Many secular bulls end (secular bears begin) with a P/E in the mid-20s.  The 1966-82 flat secular started with a P/E of 24 and ended with 7.  A major bull secular followed into 2000. The secular top in 2000 was characterized by a blowout P/E of 44 (what were we thinking?); at the 2009 bottom the P/E stood at 15, suggesting that the current flattish secular trend may have more to go.


It's part art and part technicals that define secular trends, with far from universal agreement on the number, length, and returns that describe them.  According to this article, five secular bulls from 1877 through 2009 lasted an average 16 years with average gain 415%; five secular bulls averaged 10 years and 65% loss.  The jury is still out on the secular trend since the 2009 low.


While we prefer secular uptrends for better and more reliable market performance, returns are also available during secular flat to down trends, as the index cycles above and below the secular trend.  The model has done a reasonable job of riding a good portion of the upward waves (cyclical bulls) and not sticking long with the downward waves (cyclical bears).  See its live performance in Reality Check.  In particular, compare performances in the 2000s summary table during the 2000-2009 secular bear market.


By the way… impressive countertrend rallies during bear markets are far more common than we might believe, even dramatic, with frequent 50% or so retracements of the gap between low and high The twin-bears over 2000-2002 (-48%) had 6 weekly gains greater than +4%, the biggest at +7%; the shorter twin bears spanning 2007-2009 (-56%) marked 5 rallies over +4% in one week, the best clocking in at over +10%.

Cyclical bear markets and recessions are often linked by pundits in the media, many saying that we’re not having a bear because a recession is not in the cards, while others say a recession is coming and so a cyclical bear market is certain.  Take a careful look at this chart.  This shows that we’ve had 9 cyclical bears and 10 recessions since 1950, with the closely allied twin cyclical bears in 2000-02 and 2007-09 in the table above joined as one (they had very short bull markets in between).  Of these, 4 bears started before and ended within recessions (1956-57, 1968-70, 1973-74, 1980-82), 4 recessions were free of bears (1953-54, 1960-61, 1980, 1990-91), 3 bears did not experience recessions (1961-62, 1966, 1987), 1 twin bear entirely included a recession (2000-02), and 1 twin bear coincided with a recession (2007-09).  Of the 9 cyclical bears, 6 were associated with recessions, 3 were not.  In all 6 associated cases (2/3 overall), the start of a bear market presaged a recession. 

Recessions and cyclical bears are related, but one is neither a sufficient nor necessary condition for the other.  In particular, an upcoming recession does not necessarily mean an upcoming cyclical bear market.  Moreover, a cyclical bear market does not require a recession.  But, the most severe cyclical bears (1973-74, twins 2000-02, twins 2007-2009) have overlapped with recessions. And the start of a cyclical bear signals a 67% likelihood that a recession is imminent, although this probability is based on a very small sample.  Note that cyclical bear markets are easily identified by the 20% rule, but recessions are confirmed well after the fact.

Having said this, the model does not directly concern itself with bull or bear markets per se; rather it strives to detect the beginning of primary up or down trends of 8% or more over at least eight weeks.  These primary trends do operate within the context of cyclical bull and bear markets.  Primary uptrends often last months during cyclical bear markets as countertrend rallies; 14% of primary uptrends are present within cyclical bears, 86% within cyclical bulls. Surprisingly, 60% of primary downtrends occur within cyclical bull markets, the minority 40% within cyclical bears.  While it’s possible to exploit a primary uptrend within a bear market, or a primary downtrend within a bull market, experience with the model shows that it’s difficult to do so.  And that such counter-signals are likely to be short-lived.  During cyclical bears and steeply downward secular trends, intermediate to long-term strategies should pretty much remain in capital preservation (money market) modes.  Eventually, patience will be rewarded with a new bull market and the dry powder to exploit it.  Hanging on to your money for future deployment (capital  preservation) is, after all, the main benefit of a good timing system.

Sentiment Cycle

Here is one version of a sentiment cycle that starts at the bottom of a bear market:

                                                                                                                                                 Despair (all or most out)

                                                                                                                                                 Disbelief (that a new bull market has started, frozen in the headlights)

                                                                                                                                                 Acceptance (cautious buying)

                                                                                                                                                 Euphoria (all or most in)

                                                                                                                                                 Disbelief (that a new bear market has started, frozen in the headlights)

                                                                                                                                                 Acceptance (cautious selling)

                                                                                                                                                 Despair (here we go again).

Long disbelief/acceptance stages promote long trading ranges (sometimes many years, as in SPX 1966-1982) that are often followed by big moves (sometimes many years, SPX 1982-2000) when the market breaks either up or down.

 History doesn't repeat itself, but it does rhyme.

Mark Twain


Bull markets are born in pessimism, grow on scepticism, mature on optimism and die on euphoria..
Sir John Templeton


The bull market story is always most compelling on the highs. The bear market story is always most compelling on the lows.

The Tenth Man


I'm unhappy with switching 100% into stocks at a buy signal, or into a money market at a sell signal. Does it have to be all or nothing?

No. By a 100% switch we mean the stock portion of a portfolio.  And as stated elsewhere, this all-or-nothing trade is used as a means to compare performance to buy-n-hold. To generalize, a portfolio would raise cash during a sell signal and add stock positions during a buy signal.  Your stock allocation should be a percentage that you can sleep with and would be dependent on factors such as age, net worth, propensity for risk, and other personal attributes.   

If you want to be up to 60% invested in stocks, move 60% or less of your overall portfolio into stock funds at a buy signal. If you always want to have at least 25% in stocks, keep that amount in stock funds during a sell signal. Or progressively shift funds following a switch signal. For example, you could move some proportion into stocks just after a buy signal. Then wait for a market pullback of, say, 3-5% and move another portion into stocks. Given a sell signal, another partial standard strategy execution might be to “lighten up” on stocks, shifting part of the stock portfolio to a money market fund, while waiting for either the next buy signal or continued market weakness or a rally to “take additional stocks off the table.”  Alternatively, you could phase in a sell switch, as in moving into cash over a period of weeks. 

Pullbacks present opportunities to add to stock positions, consistent with risk profile and while the model is on a buy signal.  Conversely, rallies are opportunities to reduce stock positions, again consistent with risk profile and while the model is on a sell signal. Or, regardless of the signal, rallies and pullbacks might tell us to sit tight if comfortable with risk exposure while we wait for the model’s continuing assessments.

Slow, cautious exit and entry strategies during signal changes make sense during high market turbulence and a series of short switch signals, as was the case in 2015.  Also see about diversification, next FAQ.

You favor domestic stock ETFs and mutual funds.  What about diversification?  How about bonds, gold, commodities, foreign equities, and individual stocks?

From Investopedia:  An exchange-traded fund or ETF is a security that tracks an index, a commodity or a basket of assets like an index fund, but trades like a stock on an exchange. ETFs experience price changes throughout the day as they are bought and sold.  By owning an ETF, you get the diversification of an index fund as well as the ability to sell short, buy on margin and purchase as little as one share. Another advantage is that the expense ratios for most ETFs are lower than those of the average mutual fund. When buying and selling ETFs, you have to pay the same commission to your broker that you'd pay on any regular order.  

A closed end fund or CEF is a publicly traded investment company that raises a fixed amount of capital through an initial public offering (IPO). The fund is then structured, listed and traded like a stock on a stock exchange.  Unlike regular stocks, a closed-end stock fund represents an interest in a specialized portfolio of securities that is actively managed by an investment advisor and which typically concentrates on a specific industry, geographic market, or sector. The stock prices of a closed-end fund fluctuate per market forces (supply and demand) as well as the changing values of the securities in the fund's holdings.  Many CEFs, by the way, are bond funds. A popular stock-based CEF these days is CUBA, which I have traded from time to time.

NOTE: Important advantages of ETFs and CEFs 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). Also, when you trade ETFs and CEFs pay attention to the difference between the market price per share of the ETF or CEF and its net asset value (NAV), the value per share of the underlying securities (plus cash) represented by the ETF or CEF.  Ideally, we would want to buy at a discount to NAV (a negative value expressed as a percent difference between price and NAV). Finally, pay attention to the expense ratio. Many ETFs that track major indexes have low expense ratios (about 0.1% or less), unlike those that mimic more unusual strategies. 

To follow the standard strategy for a portfolio's stock investments suggests the use of an indexed mutual fund or ETF that tracks the S&P 500. Mutual fund families such as Fidelity and Vanguard include menus of index funds. A low-cost alternative to individual stocks and mutual funds is to trade ETFs, such as Spiders (S&P 500 Depositary Receipts, symbol SPY) through your broker, a derivative that mimics the S&P 500 and "looks, sounds, and acts" like a stock.  If you want low fees, tax efficiency, and diversification among many categories then indexing on a broad index such as the S&P 500 or Wilshire 5000 is the way to go. Keep in mind, however, that our performance figures include dividends and their reinvestment, which over time account for a significant portion of total returns.  It’s worth remembering that ETFs issue dividends to the core cash account, but do not reinvest these dividends.

And remember that the timing model addresses only the equity portion of a portfolio, which generally should not be the entire portfolio.  It’s a good idea to diversify portfolios with other asset classes such as bonds, precious metals, commodities, international securities, and real estate. 

Diversification is a method of managing risk, besides that offered by the model, by owning asset classes that have different risk profiles, meaning that correlations across asset classes are less than correlations of investments within the same asset class. Think of higher correlation as higher synchronicity, whereby cross-asset prices tend to move in the same direction. Note that the timing model addresses only the equity portion of a portfolio, which generally should not be the entire portfolio.  My portfolio is modestly diversified by including ETFs with traditionally-lower correlations with the S&P 500, such as bonds, maybe gold, and sometimes index-based commodities.

Diversification also includes investment styles (value vs blend vs growth) and company sizes (large cap vs mid cap vs small cap). The S&P 500, for example, would be classified as a large-cap blend Index by Morningstar. The model’s buy and sell trades are focused on the S&P 500, which is correlated with many stock indexes, although imperfectly due to differences in investment styles and company sizes.  This means that investing in a menu of stock mutual funds and ETFs that reflect styles and sizes different from the S&P 500 would be appropriate during a buy signal, as it would add another (weaker) layer of diversification, yet keep movement in a direction consistent with the buy signal. I also invest in several stock ETFs that are highly but imperfectly correlated with the S&P 500, the model’s focus, which adds style diversification. 

The so-called diversification quilt is an effective visual that illustrates diversification strategies and the dynamics over years regarding returns.  

Note, however, that diversification among stock classes and countries may help little during a crash or bear market, given today's interconnected global world and the resulting high correlations among stock indexes. During these times, a good timing system helps.  For example, in 2008, a painful bear-market year, the S&P 500 plunged -37%, including dividends; the live model’s standard strategy mitigated the loss to -13%, while the aggressive strategy eked out a gain of +3%. Here’s how some of my favorite stock ETFs fared in 2008, confirming that, at least in these examples, stock/country diversification mostly made matters worse: SPY -38% (benchmark); QQQ -42%; IWM -35%; IWR -42%; IWS -40%; VEU -45%; VWO -55%. Including bonds as an asset class would have helped: TLT +28% (wow, as the Fed seriously eased interest rates and liquidity); LQD -3%; BND +2%.  As for gold and utilities: GLD +5%; XLU +5%.

If you wish to allocate 40% to assets other than stocks, then move up to 60% of your portfolio between stocks and money market funds at switch signals.  The ETF database is a good source for alternative ETFs, as is Morningstar.

By the way, "domestic" funds and ETFs usually hold a fair percentage of offshore stocks. Also, large domestic companies are multinational, and many other companies profit from overseas economies, so there's actually a substantial international exposure within most domestic stock ETFs and mutual funds.  Moreover, as of early 2018, the S&P 500 includes asset classes like real estate (2%), health care (14%), utilities (3%), energy (6%), technology (21%), financial services (17%), and Europe/Asia (1%).

It's also okay to use individual stocks, but keep in mind that their price behavior can differ substantially from the market's behavior. At a sell signal, you should consider either dumping or reducing exposure to individual stocks, unless you have reason to believe that they will swim upstream, or the tax consequences are too much for you to "bear". Consider buying your favorite individual stocks at a buy signal, because an up trending market is often favorable for most stocks.

We can think of diversification across asset classes as strategic diversification and changes in asset classes based on timing as tactical asset allocation.  Here is a good explanation of these strategies. 

Jeff Bezos, of Amazon fame, once allegedly said, “We are stubborn on the vision. We are flexible on the details.” The model's signals reflect both the strategic (vision) and tactical (details) investment views.  Should we or should we not be exposed to the stock market. The micro or operational or tactical speaks to the implementation of the strategic decision: what percent exposure, what diversified asset allocation, and what specific investments that reflect the tradeoff between return and risk.


Care with the intra-day timing of ETF investments during volatile market action. The flash crash on August 24, 2015 included some startling early-trading deviations between the prices of ETFs and the net asset values of their respective underlying securities.  Some examples… QQQ was down 17% yet the underlying index was off 10% at the same time; the S&P 500 was down 5% but its proxy SPY fell 8%. And these are very large, liquid ETFs. The less liquid the worse the difference of price from NAV, although some big ones were also hit pretty bad, such as Guggenheim S&P 500 Equal Weight ETF (RSP) off 43% from its previous close, but down “just” 4% by the end of the day.  SPLV, the S&P 500 “low volatility” ETF, dropped as much as 48% from the close of the previous day.  Many ETFs were down 30-50% while their underlying indexes were off around 10-15%. Bid-ask spreads early during that day were much wider than later in the day, especially near the open.  Best not trade at the open under such volatile circumstances, although a quick-witted investor might buy a favorite at a big discount to the underlying NAV during a selloff… or sell at a big premium during a buying panic.  Or just wait until ETFs adjust to their underlying indexes as trading continues... don't use sell stop or market orders during such unstable action.  If you must trade use “limit orders” stipulating the highest price at which you would buy (or the lowest at which you would sell).

A rising tide lifts “all” boats.

A retreating tide “drops” all boats.


I would like to be more aggressive with some investments at buy and sell signals. What strategies are available? And what do you do during buy and sell signals?

At a sell signal, aggressive portfolios might consider the purchase of mutual funds or exchange traded funds (ETFs) that anticipate down markets (short the markets).  So-called inverse mutual funds include ProFunds Bear (BRPIX) and Rydex Inverse S&P 500 (RYURX).  These mutual funds are designed as an inverse to the S&P 500, with a beta  of -1 (multiplier -1x where x is daily return).  For example, if the S&P 500 declines 5% in one day, they should theoretically advance 5%.  Other alternatives include ETFs that short an index: DOG for the Dow30, SH for the S&P 500, and PSQ for the Nasdaq 100.  Ultra funds are still more aggressive alternatives.  These include either a mutual fund such as ProFunds UltraBear (URPIX), which shorts the S&P 500 200% (-2x), or one of several -2x ETFs: DXD for the Dow30, SDS for the S&P500, and QID for the Nasdaq 100.  Super aggressive portfolios might look into -3x funds and ETFs, such as SPXU for the S&P 500. We can also directly short the S&P 500 through Spiders (SPY), the Dow Industrials via Diamonds (DIA), or the Nasdaq 100 Index using Nasdaq-100 Shares (QQQ).  These ETFs act like index funds but trade like shares and are bought and sold in stock brokerage accounts.  The most aggressive alternative for very sophisticated investors is buying index put options for the Dow Jones Industrials (^DJX), S&P 500 (^GSPC), S&P 100 (^OEX), Major Market (^XMI), Nasdaq 100 (^NDX), or Russell 2000 (^RUT).

At a buy signal, ETFs that mimic our main indices include the previously mentioned DIA, SPY, and QQQ. For example, Rydex Nova (RYNVX) has a beta of 1.5, meaning that its expected daily return is 50% better than the S&P 500 return in an up market (multiplier 1.5x).  The dark side of this flip is an expected 50% greater loss in a down market!  Ultra funds offer more aggressive alternatives.  ProFunds UltraBull (ULPIX) has a multiplier of 2x.  Ultra ETFs leveraged 200% (2x) include DDM for the Dow30, SSO for the S&P500, and QLD for the Nasdaq 100.  So-called 3x long funds and ETFs are also available, such as UPRO for the S&P 500.  Buying Spiders, Diamonds, or Nasdaq-100 Shares on margin are other aggressive buy strategies.  Even more aggressive alternatives for sophisticated investors include index call options.

These risky strategies can turbo-charge returns, but should be exercised only by sophisticated investors with high risk tolerances and cast-iron stomachs. They can do serious damage to portfolios should the market go against the model’s signal and trade. Keep commitments to these leveraged instruments, if at all, to a small portion of a portfolio, the actual percentage depending on tolerance for risk and confidence in the model’s signals.  See CAUTION following the table.

The accompanying table summarizes the simplest implementations of the model's standard and aggressive strategies using commonly-traded mutual funds and ETFs.

Easy Portfolio Implementations




Sample Investments



100% long S&P 500 (1x)



Any S&P 500 index mutual fund, such as Fidelity's Spartan 500 Index (FUSEX) or Vanguard 500 Index (VFINX).

SPY ( "spiders") or VOO or IVV shares.    Note that dividends may not be reinvested for these ETFs.

In general, add to stock holdings.



Ultra Aggressive

150% long S&P 500 (1.5x)


200% long S&P 500 (2x)



300% long S&P 500 (3x)

Rydex Nova mutual fund (RYNVX).


ProFunds UltraBull (ULPIX)

Rydex S&P 500 2x Strategy H (RYTNX)

SSO shares.

UPRO shares



100% T-Bills

Any money market mutual fund that emphasizes Treasuries. 

In general, reduce stock holdings.






Ultra Aggressive

100% short S&P 500 (-1x)





200% short S&P 500 (-2x)




300% short S&P 500 (-3x)

Mutual fund such as Rydex Inverse S&P 500 (RYURX) or ProFunds Bear (BRPIX).

SH shares.


ProFunds UltraBear (URPIX).

SDS shares.

SPXU shares

Ultra aggressive strategies leverage either 200% or 300% long during a buy signal (instead of the 150% long used in these pages) and 200% or 300% short during a sell signal (instead of 100% short as used here).  ETFs make it easy to implement these ultra strategies, as in the preceding table. The following tables show performance results for alternative strategies, first for the back-tested model and next for the live models that would be used in practice (ignoring expenses for proper comparisons to buy-n-hold).

For example, buying SSO (2x) during buy signals and SDS (-2x) during sell signals, then according to Ultra Aggressive C in the first table, starting with $1,000 in 1970, would (in theory based on backtesting) end with $3.7 billion this past year, versus about $54 million for our stated 1.5x/-1x aggressive strategy and about $2 million for the standard strategy.  Yeah, you read that right… that’s billion.  This would pump the annualized return to 37% (versus 25% and 17%).  Ultra Aggressive D blew up the spreadsheet. ;-) 

Results are more realistic in the live table, where the start is 1990 vs 1970. Note that ultra strategies that use -1x Sell in the live table perform better than those using -2x Sell, suggesting that when actually (live) using the model we’re better off keeping sells at -1x inverse, rather than leveraging up to -2x… and pumping buy leverage up to 3x.

Ok, this ain’t gonna happen in the top table. Don’t even think about it. Let’s not let greed get the best of us as we rush to convert our portfolio to an ultra strategy.  In practice, expense ratios, trading fees, and especially decay from holding daily ultra leveraged instruments for long time periods in very up and down volatile environments can seriously reduce expected performance.  On the other hand, low volatility can give better than expected results, should the dominant direction of the volatility favor the model’s position (long or short).

Keep in mind that so far in practice the aggressive strategy (second table) underperforms the standard strategy, and with more risk to boot.  The live implementation of a backtested system will normally underperform the optimized backtested version, a reality called shrinkage. See actual results in Reality Check.  But then Ultras A and B did outperform in the live trials seen in the second table.  So, if you would rather implement an ultra strategy based on the model, think ultras A & B, but don’t bet the bank.  Allocate a small percentage (maybe 5 to 10%) of the overall portfolio to any ultra aggressive strategy.


 A disadvantage of aggressive (leveraged, ultra) long and short mutual funds and ETFs is volatility decay or beta slippage, the negative performance effect of daily up/down volatility and leverage over periods greater than a day, as these funds are designed to replicate the multiplied return for the underlying index on a daily basis. Here is a simple arithmetic example of decay, taken from an article in A Wealth of Common Sense:

If you invest $100 into the 3x leveraged ETF and the index is up 5% the ETF would be up 15% and go to $115. If the index then loses 5% the next day your 15% loss would drop the market value to $97.75.

An investment in the simple index would be worth $99.75 in this scenario ($100 to $105 to $99.75) meaning your loss of -2.25% in the 3X leverage is much higher than the index loss of -0.25%.

Unlike their unleveraged (1x) counterparts or the use of margin for aggressive strategies, a 150% (beta 1.5 or multiplier 1.5x) long fund or ETF will not likely give a 15% return if the underlying index gains 10% over an extended measurement period, and may even show a loss, depending on multiplier, volatility, and time horizon. For example, the year-long buy signal in 2009 resulted in a gain of about 23% for the S&P 500 index (27% with reinvested dividends), but just 30% for Rydex Nova (31% not counting the expense ratio), not the approximately 35% that would be expected by a simple 50% increase over the index.  These results are reasonably close because the index in 2009 showed mostly daily gains rather than daily losses.  Note that the live aggressive portfolio in Reality Check returned 34% in 2009, closer to the 35% we would expect.  This is because the model updates weekly, not daily, therefore reducing the volatility component in the calculation.

The greater the multiplier (most ultra ETFs use 2x or 3x for long funds and -2x or -3x for inverse funds), the longer the time period, and the greater the up and down daily volatility during the signal’s period, the greater the potential for loss decay, a result shown mathematically based on compounding formulas. When volatility is very low an ultra fund can return more than expected, sometimes spectacularly so, if either daily gains dominate and the multiplier is positive or daily losses prevail and the multiplier is negative.  See also this and this and  these tables on pages 85 (for SH) and 120 (SDS) within the Prospectus for ProShares Funds. 

Again: These instruments and strategies are risky and should constitute a small percentage of a portfolio, if at all.


As for myself...

I’m often asked what I do during buy and sell signals.  To generalize, I let the model identify primary trends and trade in that direction: high cash/low stocks and small shorts during sells and low cash/high stocks during buys.

At a buy signal I’m up to 70% in equity ETFs.  SPY or VOO is my core investment, both of which track the model’s own benchmark, the S&P 500.  This allocation is up to half of my stock investments.  Next in importance are QQQ and IBB, to cover technology and biotechnology long-term themes.  I might fill the rest of the stock portfolio with optional and various combinations of IWM (small-cap), VBR (small-cap value), IWR (mid-cap), IWS (mid-cap value), VEU (all-world x-US), SCZ (international small caps), and VWO (emerging markets, to acknowledge about half of world GDP).  The remaining 30% or more includes a money market, and especially if interest rates are falling, maybe one or two bond funds such as TLT (long Treasuries), LQD (corporate investment grade), JNK (corporate high yield), PIMCO’s total return BOND, and Vanguard’s total bond BND, the latter two as good globally diversified bond ETFs.  Straddling these might be XLU (utilities), which can behave either like a stock fund or a bond fund (based on dividends and the direction of interest rates) or both.  In fact, the behavior of utilities is included in a monetary composite within the model.  I also consider a small position (5 to 10%) in GLD, if its chart looks good and geopolitics warrant.  I also might include a commodity index, such as DBC or DBA.  And I might allocate a small portion to a REIT, such as VNQ, depending on my read on the economy, interest rates, and housing.  I also might allocate 5% to SSO (2x buy) or UPRO (3x buy) during a 5% or more pullback, if I have high confidence that the buy signal will stick, with stop losses, and a short-term time horizon (days to weeks).

Here is one way to keep it diversified and simpler during a buy signal: Buy VOO (25%), VTI (25%), VXUS (20%), BND (15%), maybe GLD (5%), maybe DBC or DBA (5%), and a money market. Vanguard’s VTI is a total U.S. stock market ETF that covers nearly 4 thousand stocks across styles and capitalizations; Vanguard’s VXUS blankets the international stock space (ex-U.S.) with nearly 6000 securities in developed and emerging markets. See also the Ivy portfolio. And take a look at ARK for some innovative but volatile ETFs that I dabble in with small positions.  And for you risk seekers out there looking at the cryptocurrency space: I also trade GBTC with limit orders and a very small position of about 1%.

At a sell signal I sell most if not all stock ETFs, proceeds stashed in a money market fund, maybe a portion in an enhanced short-maturity fund such as MINT or GSY, and maybe up to a 10% position in SH, an S&P 500 inverse.  Moreover, I might keep some bond funds and/or utilities, depending on my reads on the direction of interest rates and flights to safety (the risk-off trade).  And if we have turbulent geopolitics or the specter of inflation, I might buy TIP (inflation-protected US Treasuries) and keep or buy GLD as well.  That’s about it. 

Please keep in mind that I don’t give individualized investment advice.  I’m willing to tell you more or less what I generally do, as here, but not what you should do. 


I'm not sure how to interpret the terms "Annualized Return," "Years to Double," and "Morningstar Risk" in the performance comparisons?

The label "Annualized Return" is the annual compound rate that would give the ending amounts over the given time horizon. For example, a return of 40% in the first year and a loss of 10% in the second year is equivalent to an annualized return of about 12.2%. If we were to apply the 12.2% rate over each of two years, we would end up with the same amount of money as if we had applied 40% one year and -10% the other year. Note that the annualized rate is not a simple average!  In the literature, this is sometimes abbreviated AR (Annual Return), CAR (Compound Annual Return), CAGR (Compound Annual Growth Rate), and ATR (Annualized Total Return).  See this for its mathematical calculation.

The term "Years to Double" is the number of years it would take to double an investment for the given annualized return. It's an alternative measure of performance that's easy to relate to: "Now let's see, if I park my money in a money market with returns equivalent to T-Bills and the average performance over the 1990s is repeated, my investment should double in about 15 years. Umm..."

These pages emphasize risk as quantifiable losses or downside volatility by different measures: Morningstar risk, max drawdowns, and Sortino standard deviation.  There are other forms of risk, such as the risk of lower returns than needed for life style or retirement; of running out of capital in retirement; of not keeping up with inflation; sequence of returns risk, meaning precipitous portfolio capital declines resulting in forever lost shares during early retirement, bear markets, and significant withdrawals. But in real time, in our day to day investment existence, the most visible risk is the risk of loss, which is historically measurable by the mentioned metrics.  To be invested means to assume risk.

“Risk” is the cost we pay for seeking reward (return), should capital be injured.  Risk is an attempt to quantify a rather illusory and subjective concept. We can think of risk as the loss of capital. A popular calculation is the percent drawdown of a portfolio by day, week, month, quarter, or year.  Another is the Sortino Standard Deviation, described below and elsewhere within this site.  A third is explained next.

The label "Morningstar Risk" in these pages says that risk is incurred if the portfolio can't beat the return on cash, where T-Bills serve as the proxy for cash or money markets; it's the average deviation between a position's return and the corresponding year's T-Bill return for those returns that under performed T-Bill returns. For example, suppose that over a two-year period T-Bills return 4% and 5%. Over the same two years, investment A gains 20% and loses 10%, while investment B shows returns of 10% and 50%. The average risk for A is 7.5% (the sum of 0 in the 1st year and 15% in the 2nd year divided by 2 years) and the average risk for B is 0% (it outperformed the cash alternative in each year). Investment A is showing risk because it under performed the "riskless" cash alternative in one of those years, whereas investment B did not exhibit this type of risk over those two years. Interestingly, the traditional quantitative measure of risk (standard deviation of returns) would show that B is more "risky" than A (it's more volatile). I'll take upside volatility anytime. It's downside volatility that I want to avoid. By the way, this measure of risk is conceptually the same as that used by Morningstar in their calculation of a fund’s risk, which eventually leads to their method of calculating a fund’s star rating within its category.

Return is often adjusted to account for risk as well.  In these pages the risk-adjusted return is simply the annualized return divided by a risk calculation.  For example, a 12% annualized return with Morningstar risk 4% would show a 3% risk-adjusted return.

Two often-cited metrics that combine return and risk are the Sharpe Ratio and Sortino Ratio.  The Sharpe Ratio is excess return (return less risk-free return given by T-bill return) divided by standard deviation.  So, for an S&P 500 annualized return of 9%, T-Bill of 3%, and standard deviation of returns of 12%, the Sharpe Ratio would be 0.50 or (9-3)/12.  A shortcoming of the Sharpe Ratio from a timing standpoint is that the standard deviation includes both upside and downside volatility.  To eliminate the upside component (which is welcome in timing) we would use the Sortino Standard Deviation, a standard deviation of losses and thus an alternate metric for risk.  The Sortino Ratio then is calculated as in the Sharpe Ratio, but by substituting the alternate standard deviation.  Thus, in our preceding example, given a Sortino Standard Deviation of 2%, the Sortino Ratio would be 3.00 or (9-3)/2. 

All three of these risk-adjusted-return metrics are used in these pages to compare buy-n-hold, standard timing, and aggressive timing.

A key objective of this timing system is to generate returns that match or exceed those of its S&P 500 benchmark index, but with lower risk, that is, lower downside volatility as calculated, which would also give higher risk-adjusted returns.

How does the model account for external events such as political, terrorist, or military crises?  Or for the occurrence of rare, unanticipated events?

Models do not include these so-called exogenous (external) events. While the model is not directly influenced by unique military, political, terrorist, and natural or man-made disasters, it does have its finger on the pulse of the market-patient based on its diagnostic readings, which do react indirectly to current events through its technical and sentiment indicators.  The model does not assess the cause that explains the market’s behavior; rather it focuses on the market’s symptoms.  Using a medical analogy, it analyzes the patient’s behavior or symptoms based on measurable diagnostics.  The model looks for neither a cure nor root cause; it looks for a course of action (buy or sell) that responds to the symptoms (its diagnostic indicators).  The model thus assesses how the “patient” reacts to these events, much like a real patient’s vital signs are measurable by instrumentation.  When vital signs (scores) are strong, the patient is healthy and can better sustain shocks to the system (harmful external events such as the destructive Japanese tsunami in 2011).  When the model is weak, negative external events can tip it into a sell signal, if not already on a sell signal, as it was at the beginning of the 2008 financial crisis. Other than short time periods, it would seem that sentiment trumps external events.

Nor can financial models anticipate future Black Swan events, very rare or extremely improbable, surprising and immensely consequential occurrences that nevertheless do happen in the historical record.  Statistically speaking, these rare consequences illustrate extreme tail risk, often erroneously based on the assumption and sketch of a normal probability distribution (bell curve) with skinny tails describing extremely low probabilities for events very far away from the center (5 to 10 sigma or more for the statistically savvy out there), in either direction.  These events, which can lead to either positive or negative consequences, are not capturable in advance by financial models, although it is possible to model Black Swans after the fact, in hindsight, once they’re better understood. A positive Black Swan was the invention of the internet, with huge (mostly) positive consequences that are ongoing.  Another is electronic miniaturization.  Interestingly, both of these examples are the result of military and aerospace research. 

Historically, negative events include the Black Monday stock market crash in 1987, the burst dot-com bubble in 2000, the attack on September 11, 2001, and the financial crisis in late 2008.  Negative future examples?  We could have a series of cascading and interlinked detrimental and wholly unexpected global economic events that engulf the world in a depression that might make the 1930s seem like happy times. Or, in response to American and Israeli covert or even overt military actions, Iran could possibly shut down the Strait of Hormuz, a chokepoint through which ships about 20% of the world’s daily oil, an overnight crippling blow to world economies. Or North Korea could shoot a missile at Hawaii or California, causing havoc in financial markets. Or ISIS might successfully execute a serious terrorist attack on a major city, such as a dirty bomb.  Or we could have another “flash crash” as in May, 2010, at which time the Dow dropped nearly 1200 points (11%) from its intraday high, although recovering to a loss of “just” 3% for the day.  That particular Black Swan was caused by the malfunction of a high-frequency-trading program, but a repeat or worse could be precipitated by either a software attack or a major, believable spoof.  A cyberterror attack that severely disrupts power grids or critical financial infrastructure would be another Black Swan, very negative for most of us, probably positive for companies that deal in cyber security.  The same goes for a massive electromagnetic pulse (EMP). 

Note that positive Black Swans usually develop over long periods of time; the negative variety typically happens in compressed time.  Moreover, future Black Swans can be classified as narrated (known unknowns as their possibilities are discussed in the media) or totally unknown (unknown unknowns or those we haven’t even thought of).  The Black Swan examples cited here are narrated, which we can better prepare for in our investment choices.  See The Black Swan by Nassim Taleb for a compelling and entertaining read on the Black Swan Theory.

Unfortunately, the use of a normal curve in finance, with its known probabilities and mathematical amenability within models, underestimates the probabilities of rare events.  In other words, most actual probability curves have fat (heavy) tails that show greater probabilities for rare events than those estimated by the skinny-tailed normal distribution.  Thus, “rare” events such as stock market crashes are not quite so rare as believed.  For example, the tails of oil crises appear to be “fatter” than  previously believed; so is the likelihood of a Chinese market crash.  We assume fatter tails in these examples because they are narrated Black Swans.  Moreover, the perfectly informed, unemotional, and normal-curve-based mathematical world envisioned by Efficient Market and Random Walk Theories (which negate the possibility of market timing) are clearly inconsistent with market behavior and tail risk.  The newer theory of endogenous (internal) risk first described in research papers at Stanford University and engagingly explained in Woody Brock’s book American Gridlock addresses the endogenous factors in financial systems (and models) that give rise to rare events, including the uncertainty of which models correctly price assets, the role of leverage, the use of hedging strategies, and the existence of mistakes.  More generally, the book uses rigorous deductive logic to address economic crises and gridlocked political issues such as distributive justice, government deficits, and the health-care dilemma.

The probabilities of future Black Swans are not predictable by definition, but we can seek to protect against their negative consequences and exploit their positive effects.  A robust market timing model reduces, but far from eliminates, the likelihood that we would be caught in a very negative event (by being out of a vulnerable market) and increases the likelihood that we will be in the market when it’s receptive to very positive events.  The live model, for example, took some losses following the dot-com fiasco and its 2000-2002 effects on markets, but which were mitigated compared to actual market losses; ditto the 2008 crisis (see Reality Check).  The real-time model in 2016 got caught on the wrong side of the Trump-Bump trade following the Presidential election; the backtested model that’s used live this year rode the wave up.

Extreme tail events in finance are uncommon, but far from rare… to fear them so that we remain perpetually uninvested would be unwise… and surely a prescription for chronic financial underperformance. Think not investing since the Black-Swan crashes in 1929 and 1987.  The backtested model, by the way, captures the 1987 event, given hindsight and the historical data to work with.  And, keep in mind, that the model does not predict the future behavior of the stock market; rather, it seeks to detect whether or not the just-completed week affirms or rejects a primary trend, based on its particular historical data going back to 1970.  Still, a healthy dose of skepticism is warranted by hedging our bets based on the model, should we have negative and sudden Black Swans, as these would not be in the model’s DNA: by not being fully invested during buy signals, by diversifying across asset classes, and by taking some positions that might benefit from negative consequences.  And even then there are no guarantees of even partial inoculation.

Those who do not remember the past are condemned to repeat it.

George Santayana

The third-rate mind is only happy when it is thinking with the majority. The second-rate mind is only happy when it is thinking with the minority. The first-rate mind is only happy when it is thinking.

A.A. Milne


I’ve read that it’s best to sell in May and go away until November.  Really?

Not really.  It’s true that historically the period from May through October has a lower return and is more volatile than the season from November through April.  But you would be giving up return and capital by only staying in the market during the favorable season.  Take a look at these results for the time frame 1990-2016, which include reinvested dividends when invested and T-Bill returns when not.  Working with weekly data we would sell at the end of the last week of April and buy at the end of the last week of October. 

 The table left tells us that, over the entire 27 years, the seasonal strategy underperforms buy and hold (B&H) by a 0.9% annualized return (9.4% v 8.4%), which amounts to a deficit of $236,491.  So, it’s best to simply buy-n-hold over the given seasonal strategy.  The live standard model outperforms buy-n-hold by 0.6 percentage point annualized, which amounts to a greater portfolio ending value by $193,116.  Note that these results are real time (live) for the model, as in the Reality Check menu link, not backtested.

Looking at return specifics within each season in the table right, we see that the average seasonal return during the “Sell Season” May-Oct is 2.8% for B&H (market return) v 1.4% for Sell May (T-Bill return), a regret average of 1.4% per season.  Again, the model outperforms both at 3.9% by avoiding some declines during this season, while staying invested otherwise.  During the Nov-Apr “Buy Season,” B&H is equivalent to Buy Nov, as expected.  Here the model underperforms as it misses some gains during uptrending periods.

The seasonal strategy does reduce risk from a drawdown perspective.  It shows no losses during the May-Oct seasonal (since the strategy is not invested), while B&H took a 9.1% average loss and a worse drawdown of 29.9%.  So, the tradeoff in choosing to implement the seasonal strategy is lower annualized return (9.4% v 8.4%)  as a  price for lower drawdown risk (9.1% v 0% average loss May-Oct and 29.9% v 9.3% worse seasonal drawdown).  As expected, the average loss and worse drawdown is less for the Model than for B&H. 

So, we can say that the seasonal strategy does reduce risk some, but at the expense of a return deficit.  One strategy is to reduce stock exposure during the May-Oct season, thereby reducing the likelihood of a major selloff (29.9%), while giving up some gains.  Or, work with a good timing model and maybe have your cake (higher return) and eat it too (lower risk).


What motivated you to develop the model?  Why is your service free? Do you plan to charge in the future?

New York Times


Bedlam on Wall St.

It was October 19, 1987.  Black Monday.  A Black Swan for sure. A nearly 23% dizzying plunge, in one day. Think about that: nearly one-quarter of capital evaporates!  One quarter. In one day. Poof.  I panicked along with most everyone. The evaporation of retirement dreams, the loss of financial freedom?  That crash in 1987, those days of terror, made for some soul searching. My 1971 PhD was in quantitative analysis and finance. The financial buzz since the 1950s included terms such as Modern Portfolio Theory (MPT), Capital Asset Pricing Model (CAPM), the efficient frontier, portfolio insurance, markets as random walks, the folly of timing the market. “Folly” was a kind word. It was more like “stupidity,” and worse. Subsequently (in 1990) the Nobel Prize in Economics was awarded to three Americans for their pioneering work in the theory of financial economics, including Harry Markowitz for his development of MPT and William F. Sharpe, of CAPM and Sharpe ratio fame.

Never mind. Within a week of the crash I started thinking about and subsequently developing a model rooted in financial hypotheses and constructed with the building blocks of mathematical statistics and forecasting. Invention is born out of necessity, alarm in this case. After more trial and error than I would want to recount, or even remember, I had the first really good working model by mid-1989, with full-year implementation in 1990. Each year since then the model has been tested, revised, and improved. A new model each year. (All models have issued sell signals one week before the ‘87 crash.) The current model is optimized (or tries) to max the value of the standard portfolio, based on historical data since 1970; the actual (live) performance of each model since 1990 (for its respective year) is seen in Reality Check. See this for a veteran’s account of Black Monday.  And check out this video.

I would not have retired in 2007 if not for the model’s guidance since 1990.

There is no registration, newsletter, or email updates for this free service.  What you see at this website is what you get:  Complete current and year-by-year tested (from 1970) and actual (from 1990) results with no spin and no bias regarding selected performance dates.  A for-fee service is not available.

It started as a free service in 1995 more because of time constraints and other commitments than anything. My university faculty job was full time, the market timing modeling work was part of my research function, and the free site was part of my service function. It did serve to establish a public record, it's been consistent with the original (free) spirit of the Internet among researchers, and it's been fun. I plan to continue this service as a free giveback for the foreseeable future.

There is only one kind of shock worse than the totally unexpected: the expected for which one has refused to prepare.

Mary Renault

Did you know that... ?

Since 1926, a money market investment based on T-Bills would have earned about 3.3% per year, barely edging out inflation at 2.9%. Long-term cash investments are like bad dreams where you run in place. They're the slow boat to poverty. Long government bonds have done ok, at about 5.7% annually. But the S&P 500, with reinvested dividends, clocked in at 10.1%, a wealth building real (inflation-aware) difference. In plain dollars, Rip-van-Winkling one thousand bucks into T-bills in 1926 would give about $21 thousand for today's wakeup present. Pretty shabby, especially considering that it takes about $14 thousand today to buy the equivalent of $1 thousand then. Bonds did better, upping the wealth to $158 thousand.  But stocks looked good in the Roaring 20s. If Rip had placed the money in stocks, the wakeup fund would have grown to an eye-popping $7.2 million. Rip's dreams came to pass... but do we have that much time? And do we remain oblivious to market volatility... as Rip surely did and buy and holders must?

Compound interest is man’s greatest invention.

Albert Einstein (allegedly)

In the long run we are all dead.

John Maynard Keynes

Last revised 21 Jan 2018

Copyright © 2018 Richard Mojena. All rights reserved. All materials contained on this site are protected by United States copyright law and may not be reproduced, distributed, transmitted, displayed, published or broadcast without the prior written permission of Richard Mojena at You may not alter or remove any graphics, copyright or other notice from copies of the content.  You may download or print one machine readable copy and one print copy per page from this site for your personal, noncommercial use only.

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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