What to Do when Traditional Diversification Strategies Fail – Revisited

Reduced costs of trading commissions are a welcome new benefit of using ETFs as portfolio building blocks, but the cost of the bid-ask spread can be significant if low-volume ETFs are mixed into a diversified portfolio.

[powerpress: http://gsbm-med.pepperdine.edu/gbr/audio/fall2010/dilellio-diversification.mp3]

Online investments going down

The market events of 2008 stressed the ability of diversification to protect against loss due to rapidly changing correlation amongst assets. But, as demonstrated in the initial article, “What to Do When Traditional Diversification Strategies Fail,” there is still a simple, repeatable approach based on utilizing previous year correlation coefficients to construct a diversified portfolio that reduces loss of principle.[1] The significant market gains of 2009 further challenge the benefits of diversification. So, the question now is: Does this approach to diversification also provide opportunity for significant positive gains? To answer this question, we revisit the simple diversification strategy featured in the previous article, which exploits correlation to reduce risk, to see if opportunities for gains exist.

Furthermore, a recent competition between brokers has been driving down commissions for online trades. In addition to lower commissions, some brokers have selected a subset of ETFs from a single provider, such as iShares’ affiliation with Fidelity, and waived all commissions when trading these financial products within their online platform. These reduced costs are important and may have a direct influence on the optimal reallocation frequency. So, a new question now is: With the reduction or elimination of trade commissions, is a more active strategy optimal? This article also examines this practical issue, and quantifies the overall benefits from $0 ETF commissions currently in the marketplace.

Hypothesis Revisited

This study revisits many of the hypotheses established in the previous study. The correlation coefficient threshold is validated from an updated illustration containing four asset classes: U.S. Large Caps, U.S. Small Caps, International, and Bonds. As seen in Table 1, correlations observed over 2008 suggest the same allocations against U.S. Large Caps (SPDR S&P 500 fund, symbol: SPY) and Bonds (iShares Aggregate Bond Fund, symbol: AGG) as suggested from correlations observed over 2007.[1] But, because of the continuing trend of lower commission costs, consideration must also be given to volume in the process of identifying uncorrelated assets. Volume is known to be inversely related to costs from bid-ask spreads and is empirically modeled in the following section. So, to provide a preference to higher volume funds that minimize the resulting bid-ask spread, the correlation matrix rows are generated in order of decreasing volume before eliminating highly correlated investment options. The result to the right of the arrow illustrates the result, applying this process to a four-asset class example.


Table 1- DiLellio

Table 1: Correlation Coefficients from Daily Returns Adjusted for Dividends in 2008, sorted by Average Daily Volume.


Table 2 shows the associated 2009 performance, based on holding both the four-asset portfolio as well as the suggested two asset portfolio based on the 80 percent correlation threshold. The diversification effect observed in 2008 reduced the 2009 portfolio gain from 21 percent to 14.3 percent. Reviewing the 2008 portfolio returns (illustrated in the previous article), we observe a loss of 27 percent and 15 percent, respectively, where the smaller loss occurrs when we apply the correlation threshold to portfolio construction. Thus, the two-year cumulative return from this simple illustration is -12 percent when no correlation threshold is applied, versus -3 percent when it is applied.


Table 2- DiLellio

Table 2: 2009 Performance of Naïve Allocation with and without use of 2008 Correlation Coefficients.


This updated simple illustration continues to suggest a benefit of multi-asset diversification or wide diversification, consistent with other research.[2][11] While these studies use longer history market indices, we show a more pragmatic view in the following sections, since the ETFs examined are easily traded by individuals, investment advisors, hedge funds, and institutional investors. Furthermore, ETF transaction costs can be accurately modeled, as shown in the next section. Unfortunately, ETFs are still fairly new investment products, so they do not offer the long histories available for many asset allocation studies employing equity, bond, and commodity-based indices used in the aforementioned studies.

Analysis Assumptions and Methodology

Continuing with the nine asset classes identified in the previous article, including the 136 unique ETFs available since January 2004, we have added an analysis of new zero-commission ETFs now being offered by Schwab, Fidelity, and Vanguard. Six of the asset classes are equity-based and consist of large cap domestic, large cap foreign, emerging markets, midcap domestic, small cap domestic, and domestic sectors. The three non-equity classes include commodities, bonds, and real estate. A summary of the nine asset classes represented by these ETFs appears in Table 3, where sector and large cap domestic assets have the largest representation, while bonds and real estate assets have the smallest.


Table 3 - DiLellio

Table 3: Asset Classes represented by 136 Exchange Traded Funds available since January 2004 (values are rounded to the nearest percent).


Based on the updated simple illustration from above, we continue to define uncorrelated assets using a correlation matrix generated by volume. We then eliminate lower volume assets that are more than 80 percent correlated with higher volume assets. All correlation coefficients were calculated based upon 12 months of daily historical returns developed from adjusted closing prices that included dividends and splits. For consistency, volume was also estimated using a 12-month average daily volume. This methodology follows the same rationale established in the initial paper.

Revisiting the existing assumption regarding switching costs, we have updated our methodology to address the practice of investment managers seeking “most liquid” ETFs.[4] To further improve the fidelity of the back-testing, we have also incorporated a nonlinear regression model for a bid-ask spread that grows rapidly with low volume. The model parameters are based on empirical data provided by Pankaj Agrrawal and John M. Clark in their 2009 article, “Determinants of ETF Liquidity in the Secondary Market: A Five-Factor Ranking Algorithm.”[3] This data is represented in Figure 1. The value of R2 = 94 percent obtained from the power-law model suggests that a significant amount of the variation has been explained between the bid-ask spread and the trailing volume, providing high confidence in the model’s ability to accurately reflect bid-ask costs based on volume.


Figure 1 - DiLellio

Figure 1: Bid-Ask Spread, in Basis Points (BP) versus Average Volume, with Power Law Regression model and Goodness of Fit Measure.


The model in Figure 1 is applied against hypothetical trades using month-end adjusted closing price and volume. Returns were calculated based on a naïve allocation approach that evenly spreads assets across uncorrelated ETFs. The purpose is to examine the data’s sensitivity to annual, biannual, and quarterly rebalances. To reflect the latest updates in commissions from discount brokerages such as Vanguard, trade commission are reduced from $10 to $5 per trade against a portfolio starting with $100,000 in a tax-free account.[7]

Empirical Results

Figure 2 appears to have a very similar downward trend, but contains a full five years of history. Once again, the increased correlation amongst assets classes increases over time, yielding fewer uncorrelated funds. Also note that including volume as part of the process to determine uncorrelated funds has had a marginal effect on the total number of uncorrelated funds, but the downward trend from 2005-2009 remains.


Figure 2 - DiLellio

Figure 2: Number of ETFs that are less than 80 percent correlated over previous year with higher volume ETFs (2005 – 2009).


Tables 4, 5, and 6 list the portfolio allocations against each of the nine asset classes for the annual, biannual, and quarterly rebalancing periods. In each case, the allocations begin in 2005 with a majority of holdings in large foreign equities, emerging markets, and domestic sectors. By 2009, large domestic equity increases significantly, while large foreign equities and emerging market allocations shrink drastically, as highlighted in orange. Highlighted in yellow, bond funds continue to grow to become 43 percent of the allocation, one of the largest percentages seen over the five-year study. Lastly, domestic sectors remain a significant percentage of the allocation throughout the five-year study, suggesting a cyclical pattern between the range of approximately 25 percent and 45 percent. In summary, these results indicate that the naïve allocation strategy appears to be achieving wide diversification, based on the portfolio containing between five and eight asset classes throughout the five-year testing period.[2] Furthermore, the strategy appears to have a dynamic component that, in times such as early 2009, approaches the classic allocation of 50/50 bond-equity allocation.


Table 4 - DiLellio

Table 4: Annual Portfolio Allocation Percentages with Naïve Allocation Approach and 80-Percent Correlation Threshold



Table 5 - DiLellio

Table 5: Biannual Portfolio Allocation Percentages with Naïve Allocation Approach and 80-Percent Correlation Threshold.



Table 6 - DiLellio

Table 6: Quarterly Portfolio Allocation Percentages with Naïve Allocation Approach and 80-Percent Correlation Threshold.


Table 7 summarizes the net returns based on the three reallocation intervals and includes the effect of modified and new positions incurring a bid-ask spread cost and the flat-rate $5 commission cost. Once again, the annual reallocation period appears optimal. Also, the commission costs do not appear to be driving the lower performance. When set to $0, returns increase by 0.6 percent, 1 percent, and 1.9 percent over the five-year period for annual, bi-annual, and quarterly reallocations, respectively. But, this increase is not sufficient to offset the larger gross returns provided by the annual reallocation frequency.


Table 7 - DiLellio

Table 7: Net Returns with Naïve Allocation



Table 8 - DiLellio

Table 8: Sharpe Ratio with Naïve Allocation


Alternatively, Table 8 shows the risk adjusted returns using data from Ibbotson & Associates’ one-month T-bill for the risk-free rate and William F. Sharpe’s methodology based on excess return and standard deviations.[5] Once again, annual reallocation provides the greatest risk-adjusted returns.

The cost impact on the portfolio due to the bid-ask spread is somewhat more complex than the flat-rate commission discussed above. While the the aim was to select higher volume uncorrelated funds, it is likely that a few of the uncorrelated funds had significantly lower volume. To examine the relative effect of the portfolio’s bid-ask spread against number of positions in the allocation, a scatter plot appears in Figure 3 from the quarterly allocation data. Interestingly, the lowest bid-ask spread cost incurred for a given allocation is achieved when 20 to 30 uncorrelated funds are identified. Alternatively, when only a dozen or so funds are available, the resulting bid-ask spread becomes significant. The larger bid-ask spread is also seen for portfolios with more than 40 uncorrelated funds, but to a lesser degree. The larger portfolio bid-ask spread is the result of a few low-volume ETFs needed to provide portfolio diversification, which were not available from higher volume alternatives. And because of the rapid growth of the bid-ask spread for low volume, a small fraction of the allocation towards low-volume ETFs can increase the portfolio bid-ask spread substantially.


Figure 3 - DiLellio

Figure 3: Portfolio Bid-ask spread (basis points) vs. number of uncorrelated funds is nonlinear.


Observations and Current Market Offerings

Revisiting the simple methodology previously established, we see that using correlation coefficients continues to provide a practical approach to obtaining the benefits of diversification. Reduced costs of trading commissions are a welcome new benefit of using ETFs as portfolio building blocks, but the cost of the bid-ask spread can be significant if low-volume ETFs are mixed into a diversified portfolio. Furthermore, based on a correlation threshold, the methodology applied here can include these low-volume ETFs in portfolios with smaller and larger numbers of uncorrelated funds.

These are important observations because, as of May 2010, Fidelity, Vanguard, and Schwab all offer $0 commissions on trades. These brokerage firms appear to be using this offer along with lower expense ratios, better exposure to asset classes, and lower tracking error as a discriminator.[8][9] But, expense ratios and bid-ask spreads are important costs to consider, particularly for lower volume $0 commission ETFs.[10] Table 9 summarizes the median cost for the 6 ETFs from Schwab, 26 from Fidelity, and 46 from Vanguard that are currently offered with $0 commissions when traded online. The costs are based on buying and selling the median ETF over a one-year holding period, and the bid-ask spread is based on the model in Figure 1 using average volume from February to April 2010.

Table 9 suggests that annual transaction costs associated with buying and selling $0 commission ETFs can quickly exceed 100 basis points, or 1 percent, when traded quarterly. While such evidence still may not deter day-trading of ETFs, one broker has announced limitations on trading their $0 commission ETFs. Vanguard incorporates a limit of 25 buys/sells of its $0 commission ETFs per year.[6] This announcement is clearly associated with Vanguard’s founder, John Bogle, and his belief in keeping costs low for long-term investments. Investors would be wise to consider this fundamental philosophy.


Table 9 - DiLellio

Table 9: Annual Median Transaction Cost of Reallocation using $0 Commission ETFs


DISCLAIMER: The exchange trade products analyzed in this article were chosen from those publicly available. They do not represent the author’s recommendations and were only used to support observations. Investment advice is neither implied, nor suggested.


[1] DiLellio, James, “What to Do When Traditional Diversification Strategies Fail,” The Graziadio Business Report, 12, no. 4 (2009).

[2] Mulvey, John M., Cenk Ural and Zhoujuan Zhang. “Improving Performance for Long-Term Investors: Wide Diversification, Leverage, and Overlay Strategies,” Quantitative Finance, 7.2 (2007): 175-187.

[3] Agrrawal, Pankaj and John M. Clark, “Determinants of ETF Liquidity in the Secondary Market: A Five-Factor Ranking Algorithm,” Institutional Investor Journals. Fall: 59-66.

[4] Hight, Gregory N., “Diversification Effect: Isolating the Effect of Correlationon Portfolio Risk,” Journal of Financial Planning, October (2010).

[5] Sharpe, William F. “The Sharpe Ratio,” Journal of Portfolio Management, Fall (1994): 49-59.

[6] Wiener, Dan, “Free Trading Vanguard’s Shotguns,” Forbes.com, May 4, 2010.

[7] Maxey, Daisy, “Vanguard Joins Cuts of ETF-Trading Fees,” The Wall Street Journal, May 5, 2010.

[8] Spence, John, “BlackRock, Vanguard Battle for ETF Assets – Being First Mover isn’t So Advantageous,” The Wall Street Journal, April 27, 2010.

[9] Kapadia, Reshma, “Identical Twins? Nope.” WSJ.com, April 5, 2010.

[10] Randall, David K., “Why Bargain Trades Are No Bargain“, Forbes, March 15, 2010.

[11] Gibson, Roger C., “The Rewards of Multiple-Asset-Class Investing,” Journal of Financial Planning, July (2004):58-71.

[14] Vanguard.com, Vanguard ETFs® https://personal.vanguard.com/us/funds/etf.



[i]Expense ratios and volumes were obtained from Brokerage Web sites in April 2010, including Fidelity.com, Vanguard.com, ishares.com, as well as finance.yahoo.com, SeekingAlpha.com, and are subject to change.

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Presidential Elections and Stock Market Cycles

For the past several decades, individuals in all walks of life have observed the cyclical nature of the stock market. Pundits have attempted to correlate these cycles with everything from referencing the position of the moon and stars to using highly sophisticated econometric models. This article, however, attempts to address the timely relationship between politics and stock market behavior.

During the first half of the twentieth century, economic theory was limited primarily to the micro study of supply and demand theory. Minimal concern was given to the macro economic environment. However, after World War II, the work of John Maynard Keynes, an English economist, began to dominate Western economic thinking with a broad macro view of economics. First presented in 1936 by Keynes, this approach was the beginning of macro economic theory. It called for governments to prescribe specific macro economic policies in an effort to ameliorate business cycles. By the late 1950s, Keynesian theory was widely accepted in academic circles and was being taught at most major U.S. universities.[1] The federal government began to embrace Keynesian economics by the early 1960s, and from that time forward, Washington has played an active role in influencing the direction of the economy.

It’s the Economy, Stupid

It wasn’t long before politicians recognized the relationship between voter approval and the state of the economy. The Federal Reserve has responsibility for monetary policy such as interest rates and alterations in the money supply, and the executive branch has limited ability to influence that part of the economy. However, the executive branch of government can influence fiscal policy—changes in taxation and spending patterns. Administrations have often yielded to the temptation to exercise fiscal policy in a manner designed to pump up the economy just prior to a presidential election and thus garner voter approval for the incumbent party. These pre-election actions and campaign promises often have created some euphoria among voters and investors alike.

On the other hand, post-election periods seem to have suffered from an opposite effect that has resulted in less investor optimism. In The Stock Trader’s Almanac, 2004, Yale Hirsch notes that based on his studies, “Presidential elections every four years have a profound impact on the economy and the stock market. Wars, recessions and bear markets tend to start or occur in the first half of the term and bull markets, in the latter half.”[2]

Because of the consistency and predictability of administrative actions and campaign rhetoric and their anticipated influences on the economy, investors have come to assume better times for business conditions, corporate bottom lines, and stock prices in the period prior to a presidential election and a less robust period following those periods. Thus, a four-year stock market cycle seems to have become a part of the investment landscape since the mid-twentieth century. From April, 1942 to October, 2002, 15 stock market cycles have occurred, each averaging approximately four years’ duration.

Major market cycles usually have abrupt “V”-shaped bottoms with declines in excess of 10 percent. The following stock market recoveries are often created (as suggested earlier) by strong economic stimulus invoked by government officials in an effort to counter potentially unpopular economic recessions. Strong doses of fiscal and/or monetary policy stimuli unfortunately often result in creating inflation, which then must be addressed, thereby perpetuating the business and stock market cycles. Given the foregoing scenario, it is not at all surprising to find that the stock market often has made major bottoms about two years before presidential elections and has risen through the end of election years.

To illustrate this pattern, consider the historical performance of the commonly used Standard & Poor’s 500 Index (S&P 500). This Index consists of 500 top U.S. companies, and it is used by Wall Street as a benchmark for tracking the overall stock market. Table 1 below shows the historical stock market cycles from 1942 – 2002.

Table 1
Historical Stock Market Cycles for the S&P 500 Index
(1942 – 2002)

Dates of Peaks & Troughs Peaks/ Troughs S & P Price Length of Bull Market (years) Bull Market Rise (%) Length of Bear Market (years) Bear Market Decline (%) Full Cycle in Years
4/42 Trough 7.47
5/46 Peak 19.25 4.08 158%
10/46 Trough 14.12 .36 -27% 4.45
6/48 Peak 17.06 1.68 20%
6/49 Trough 13.55 .99 -21 2.68
1/53 Peak 26.66 3.56 97%
9/53 Trough 22.71 .69 -15% 4.25
8/56 Peak 49.74 2.88 119%
10/57 Trough 38.98 1.22 -22% 4.10
12/61 Peak 72.64 4.14 86%
6/62 Trough 52.32 .54 -28% 4.68
2/66 Peak 94.06 3.62 80%
10/66 Trough 73.20 .66 -22% 4.28
11/68 Peak 108.37 2.15 48%
5/70 Trough 69.29 1.49 -36% 3.63
1/73 Peak 120.24 2.63 74%
10/74 Trough 62.28 1.72 -48% 4.36
9/76 Peak 107.83 1.97 73%
3/78 Trough 86.90 1.45 -19% 3.42
11/80 Peak 140.52 2.73 62%
8/82 Trough 102.42 1.70 -27% 4.44
8/87 Peak 336.77 5.03 229%
12/87 Trough 223.93 .28 -34% 5.31
7/90 Peak 368.95 2.61 65%
10/90 Trough 295.46 .24 -20% 2.85
2/94 Peak 482.00 3.31
4/94 Trough 438.92 .17 -9 3.48
7/98 Peak 1186.74 4.25 170%
8/98 Trough 957.28 .08 -19% 4.30
3/00 Peak 1527.45 1.58 60%
10/02 Trough 776.75 2.5 -26% 4.02
Averages 3.08 yrs 93% 0.94 yrs -26.4% 4.02

As we can see from Table 1, full cycles occur approximately every four years. During this period, bull markets averaged about three years, while bear markets averaged less than a year. A more detailed investigation that includes presidential election cycles for the period from 1941 through 2000 reveals some interesting findings. Stock market lows have occurred surprisingly close to mid-year congressional elections, or approximately two years before presidential elections. (See Table 2.)

Table 2
Presidential Elections and Market Troughs

Presidential Term Month and Year
of Market Bottom
Year During
Presidential Term
When Market Bottomed
1942 – 1944 4/42 2nd Year
1945 – 1948 10/46 2nd Year
1949 – 1952 6/49 1st Year
1953 — 1956 9/53 1st Year
1957 – 1960 10/57 1st Year
1961 – 1964 6/62 2nd Year
1965 – 1968 10/66 2nd Year
1969 – 1972 5/70 2nd Year
1973 – 1976 10/74 2nd Year
1977 – 1980 3/78 2nd Year
1981 – 1984 8/82 2nd Year
1985 – 1988 12/87 3rd Year
1989 – 1992 10/90 2nd Year
1993 – 1996 4/94 2nd Year
1997 – 2000 8/98 2nd Year
2001 – 2004 10/02 2nd Year
Average = 1.87 years into presidential term

Table 2 clearly shows a clustering of bear market lows around the congressional election period, or about two years into the presidential term. As can be seen, three of the 16 bear market lows occurred in year one of the presidential term, 12 in year two, one in year three, and none in year four (the election year).

Potential Investment Strategies Based on the Political Cycle

Price data for the S&P 500 Index was compiled and averaged on a weekly basis over the period from 1942 to 2003. Analyses of these data suggest that a potentially lucrative investment strategy would have included buying on October 1 of the second year of the presidential election term and selling out on December 31 of year four. This simple strategy would have sidestepped practically all down markets for the last 60 years. For the most part, bear markets have historically occurred during the first or second years of presidential terms. (A bear market is defined here as the S & P 500 Index’s decline approximately 15 percent or more over a period of one to three years, while a bull market is an environment of consistently rising prices.) As shown in the above table, no bear markets of this magnitude have occurred during an election year for the time covered.

It is also apparent that markets are subject to change from time to time because of unforeseen macro events. As a result, some cycles have been shorter and some longer than the norm. For example, 1946 to 1949 was a shorter cycle, while 1982 to 1987 and 1994 to 1998 were longer than average cycles. One cannot point to any one factor that has directly caused bull market runs of the last two decades to be longer in duration than those during previous decades. To speculate on the above is beyond the scope of this paper, although fundamental economic conditions and the role of the Federal Reserve are factors.

The Test

Based on discussions above and the notion that the S&P 500 Index seems to bottom approximately two years into presidential terms (Table 2), we can construct a hypothetical test for two investors that calculates the dollar return for two simple alternative investment strategies. In neither case is allowance given for possible dividends or interest earned. In addition, commissions and taxes are ignored for the purpose of simplicity. Prior to the 1952 presidential election, the U.S. government generally did not attempt to influence the economy in any significant way, so the period before 1952 (except for the World War II period) is not useful for testing this strategy. Therefore, the test begins with the 1952 election period.

Imagine that the first investor had consistently purchased the S&P 500 Index 27 months before presidential elections and had sold near election time on December 31 of the election year. Because a 27-month period seems to provide better returns than other studied periods before the election, a 27-month period was selected for this test. This strategy kept Investor 1 out of the market from January 1 of the inaugural year through September 30 of the second year during the test period. On the other hand, imagine further that Investor 2 bought the S&P 500 on the first trading day of the inaugural year of each presidential election during the test period and liquidated the portfolio on September 30 of the second year of the presidential term. Would either or both of these simple procedures have consistently made money for the investors? Table 3 below reveals the results on both a percentage change basis and dollar return.

Table 3
Percentage and Dollar Returns of Two Investment Strategies
(Dollars Amounts are Cumulative)
Starting Value for Investors 1 and 2 = $1,000

Presidential Election Dates Percent Change from Oct 1 of 2nd yr of Presidential term through Dec. 31 of election yr. (Investor 1 strategy) Percent Change from Jan. 1 of inaugural yr through Sept. 30 of second yr of presidential term (Investor 2 strategy) Investor 1 dollar results (beginning with $1,000) Investor 2 dollar results (beginning with $1,000)
1952 +35% +22% $1,350 $1,220
1956 +45% +8% $1,956 $1,318
1960 +16% -2% $2,271 $1,291
1964 +52% -9% $3,451 $1,175
1968 +39% -19% $4,798 $952
1972 +40% -47% $6,717 $505
1976 +70% -4% $11,418 $483
1980 +32% -12% $15,072 $425
1984 +37% +40% $20,649 $595
1988 +19% +11% $24,571 $660
1992 +38% +7% $33,909 $707
1996 +60% +42% $54,254 $1,004
2000 +34% -36% $72,701 $643

The findings in Table 3 are extremely interesting. The first investor put up money 13 times and did not lose money in any period. Gains ranged from a high of 70 percent prior to the 1976 election to a low of 16 percent before the 1960 election. Investor 1 saw the original investment of $1,000 grow to $72,701. This is a percentage gain of 7,170 percent. Investor 2 was not so fortunate. This individual also anted up 13 times, but lost six times. The largest loss of -36 percent was seen after the presidential election of 2000. Investor 2 saw the original $1,000 shrink to only $643, or a loss of -36 percent, in nearly five decades. That percentage is based on nominal dollars and does not include the impact of inflation.

Graphing the percentage gain and loss makes the difference quite obvious.

However, when you look at a graph of the cumulative dollar difference between the two strategies, the difference is even more dramatic!

Final Thoughts

It is not the intent of this paper to forecast the stock market. Even where patterns exist, there is enough variability that it is risky to try to anticipate specific turns in the market. Yet we have identified a potentially profitable four-year stock market cycle that has worked well over the better part of the last century. Investing for the 27 months before a U.S. presidential election certainly seems to be more profitable than investing during the 21 months after the elections.

However, just when you think that you have figured it all out, you find another pattern that can suggest different possibilities. For instance, another analysis shows a highly intriguing re-occurrence in the stock market index. During the entire twentieth century, every mid-decade year that ended in a “5” (1905, 1915, 1925, etc.) was profitable! This is not to say that all of these years had uninterrupted ascending trends, but by year’s end there had been impressive gains. Whether that pattern was a fluke or will continue in the 21st century is anyone’s guess. And, 2005 is also an inaugural year.

However, trying to figure out such patterns can certainly make life interesting.


[1] John Maynard Keynes, General Theory of Employment, Interest and Money, 1936. Republished by Harcourt, Inc. (1964).
A further discussion of Keynesian economics can be found in most college level textbooks on economics. There are also websites devoted to his work, e.g., http://cepa.newschool.edu/het/essays/keynes/keynescont.htm or http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Keynes.html

[2] Yale Hirsch and Jeffrey Hirsch, The Stock Trader’s Almanac 2004, Hoboken, NJ: John Wiley and Sons, (2004): 127.

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