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In my recent articles (listed in appendix C) I presented evidence in support of a possible major bull market which may have commenced in 2009. Here I show that another indicator, this time based on a statistical analysis of the historic data of the S&P, signals the same. But how high will the S&P go?

Nobody knows, and the best we can do is to use the historic data (which is from Shiller's S&P series) to provide us with an estimate. From the real price of the S&P with dividends re-invested (S&P-real) one finds that the best fit line from January 1871 to July 2012 fits the data rather well when both are plotted on a semi-log scale. There is no reason to believe that this long-term trend of S&P-real will not continue into the future. S&P-real and the best fit line together with its prediction band is shown in figure 1. (See appendix A for the equations.)

One observes that whenever S&P-real "bounced-off" the lower extreme of the prediction band a bull market always followed. The last time this occurred was in March 2009. Since then S&P-real has only gained about 80%. Comparing this to previous post-bounce-off-gains, which ranged from 300% to 1720%, one can only assume that we are in an early stage of a bull market with further gains to come.

Another observation from this chart concerns the length of bear markets. One sees that the periods when S&P-real was flat or lower were never longer than approximately 14 years. This would lead one to conclude that the stagnation period of the stock market since the year 2000 could now be finally over.

But what gains (if any) can we expect?

Extending the best fit line and the prediction band to 2020 provides a glimpse into the future which enables us to estimate the change of S&P-real from the current level of about 740,000. In 2020, the value of S&P-real as indicated by the best fit line is about 1,430,000, while the lowest and highest values shown by the prediction band are 740,000 and 2,770,000, respectively.

Thus the historic trend forecasts a probable doubling of the S&P over the next eight years. The worst scenario would be no change, and the best outcome would be a four-fold increase of the current price.

Commentators, such as Butler|Philbrick and Hussman warned us in December 2011 that the markets then were expensive and overbought, and that one could only expect very low returns going forward over periods as long as 20 years. Figure 2 shows the current situation in more detail and also includes the levels of S&P-real as per Butler|Philbrick (B|P) forecast of 14 December, 2011 - these are the red markers connected by the dashed red line. The B|P estimates are shown in appendix B. One can see that their estimated 15-year returns were mostly lower than the actual ones that they listed in table 2. I found that the Shiller data produced somewhat different values, but they were reasonably close to what B|P provided.

From December 2011 onwards B|P forecasts a real annual return for the stock market of only 1.46% for 15 years, and 2.08% for 20 years. Also they forecast a 6.48% annual return from March 2009 to March 2024. One can see that the March 2024 level is quite possible as it is just above the lower extreme of the prediction band. But it would appear that the December 2026 and 2031 forecasts are overly pessimistic as their location relative to the lower extreme of the prediction band would only be matched by a single occasion when S&P-real was that low, which was in 1932. (See figure 3 in appendix B which shows that one can reasonably expect a 2.60% return instead of 1.46% for 15 years.)

Also if B|P were correct in their forecast, then this would mean that the level of S&P-real in the year 2027 would be equal to the year 2000 level, and that the 2032 level would not be much higher. As observed before, there was never a period when the market was flat or lower that lasted more than 14 years. Additionally, S&P-real was always significantly higher over 30 years. Thus one must assume that there will be a bull market in this period and that the 2027 and 2032 levels of S&P-real will be higher than anticipated by B|P.

If one applied B|P's anticipated 1.46% growth rate then the market will only be 24% higher by the December 2026 from where it was in December 2011. So far, to August 17, 2012, the S&P with dividends is 18.7% higher than when their article was published on December 14, 2011. This equates to an inflation adjusted gain of 17.5% in the first eight months of the 15 year period. Since the total projected return is 24%, we can logically only expect another 6.5% gain over the next 14 years and 4 months, if B|P's forecast were to be correct. What remains therefore is only a 0.40% annual growth rate for the S&P over the next 14 years. (In B|P's recent update they anticipate from the end of July-2012 only a 0.69% real annual growth rate for the S&P to July-2027. Accordingly one can only expect a total gain of 10.9% over this period. Since the market already gained 3.0% since their forecast date, the remaining gain is only 7.9% which equates to a growth rate of 0.51% over the next 15 years. Substantially the same low rate as calculated from the December-2011 projection.)

Even perma-bear Hussman presently expects a prospective 10-year annual nominal return of nearly 4.6% on stocks, which assuming an inflation rate of 2%, would be a real return of 2.6%. This is more than six times the 0.4% growth one can expect, if one were to believe B|P's forecast.

So what is going on here? Why are the "experts" so far apart? The only explanation is that we are in a bull market now, which will later be followed by a bear market that will take the S&P to the lower forecast levels, if those forecasts are indeed correct. But while the bull market is on the go we should be in the market.

Investors who are not in the market now, because they were discouraged by the low growth expectations of the S&P, as put forward by B|P and Hussman in December 2011, and who did not follow my buy signal which was published one day before B|P's article, have clearly lost out.

For example, the participants in the Hussman Strategic Growth Fund HSGFX have so far lost 13.57% from December 14, 2011 to August 17, 2012, instead of gaining 18.67% if this fund had merely matched the return of an index fund of the S&P 500. To put this into perspective, they would have been better off by 32.24%, or expressed in numbers - the fund's December 2011 assets of $5.77 billion would have increased by $1.08 billion if the fund had tracked the S&P 500 over the last eight months, and the fund's assets would, by the middle of August 2012, have amounted to about $6.8 billion instead of the current $4.9 billion – the difference being the tidy sum of about $1.9 billion which the participants in this fund now don't have, because of the fund manager's negative outlook for the stock market.

The message from the above example is obvious. One should not be discouraged by dire forecasts of long-term market returns. One has to be invested when the market goes up, and one will know soon enough when it is time to get out if one follows the signals from my investment models mentioned below. The exit signals may not occur when the market is at its highest, but historically they did occur in time to prevent major losses.

**Conclusion**

I have now presented three unrelated analyses which provide macro signals that are all forecasting the same - a new bull market.

The models are:

- a trough formation of the 50- and 200-month moving average of the S&P,
- a P/E5 move from below to above 13.40 and
- a "bounce-off" by S&P-real from the lower extreme of the prediction band.

As I have shown, the buy-and-hold strategy is expected to only provide a 0.4% average annual real return over the next 14 years, according to Butler|Philbrick, and about 2.6% if one believed Hussman. Bill Gross expects similar low real returns from stocks, although there is good reason to believe that he is wrong.

But investors can improve stock market returns if they are not wedded to a buy-and-hold investment strategy.

Even in trend-less markets there will always be up- and down-market periods, and one should therefore invest bearing this in mind. My MAC system and IBH model anticipate market direction and exploit market movements for better investment performance than what one would achieve with a buy-and-hold strategy. For example, over 15 years, with equal recurring investments made every year, the easy to implement MAC system out-performs a buy-and-hold strategy of the stock market on average by a factor of three. So although future buy-and-hold returns could be meager, they can be significantly enhanced by using the simple MAC system.

**Appendix A**

The best fit line and prediction band were calculated using statistical software from PSI-Plot. There were 1699 data points.

The equation of the best fit line is y = 10^{(ax+b)}.

y = is the dependent variable of the best fit line.

x = are the number of months from January 1871 onwards.

a = 0.0023112648

b = 2.02423522

The Pearson correlation coefficient is 0.992. This number is most appropriately applied to linear regression as an indication of how closely the two variables approximate a linear relationship to each other. A perfect fit would have a correlation coefficient of 1.000.

The equation of the upper and lower extremes of the prediction band is y = 10^{(ax+b)}

with parameters 'y', 'x', and 'a' as before, but with

b = 2.31005634 for the upper extreme line, and

b = 1.73841411 for the lower extreme line of the prediction band.

**Appendix B**

Table 1: Butler|Philbrick estimated returns for the stock market from December 2011

Table 2: Butler|Philbrick estimated 15 year real return for the stock market

Figure 3 shows the B|P model's 15-year forecast returns and actual returns which I calculated using the Shiller data. One can see that except for the December-1974 forecast, the actual returns were always greater than the forecast returns. Thus one can expect the actual 15-year return from December 2011 onwards also to be greater than the forecast return of 1.46%, which is indicated on the chart, and estimated to be 2.60%, similar to the Hussman expectation.

**Appendix C**

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*Georg Vrba is a professional engineer who has been a consulting engineer for many years. In his opinion, mathematical models provide better guidance to market direction than financial "experts." He has developed financial models for the stock market, the bond market and the yield curve, all published in Advisor Perspectives. The models are updated weekly. If you are interested to receive theses updates at no cost send email request to vrba@snet.net.*