# The Pursuit Of Mediocrity - Fallacy Of Dollar Cost Averaging And The Abuse Of Indexing

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by: Dane Bowler

Certain tools for viewing or investing in the stock market are deeply misunderstood. Even savvy investors can end up using such tools with the intent to create an optimized portfolio only to end with an impotent self-defeating construct. In this article, we will examine various fallacies of the stock market and demonstrate how they remove intelligence from the decision making process. Upon first glance, this may sound harsh, but the meaning will become clear with our first fallacy; dollar cost averaging.

As we know, the principle of dollar cost averaging states that if we invest a fixed dollar amount into a security periodically over time, it will result in a reduced weighted average cost per share. The core of this effect is that money spent when shares are more expensive will buy less shares and that spent when shares are cheaper will buy more shares. Therefore, the lower cost shares will have greater effect and pull the average cost down. All of this is true, but the fallacy lies in the perception that this method is superior to a random purchase timing. We will demonstrate that the dollar cost average is in fact identical to the arithmetic mean of all possible random purchases through a logical proof.

The graph is not necessary for the logic, but for the visual thinkers (which I am) it helps clarify. The number of shares purchased is simply the number of dollars invested divided by share price which we will denote I/P. For a dollar cost averaging purchase, one would invest perhaps 1/5 of their overall investment amount at each of 5 intervals. Therefore, the overall number of shares purchased (denoted as S) would equal 1/5 (I/P1 + I/P2 + I/P3 + I/P4 + I/P5) where Pn = price at time interval n. We have now established S or shares purchased for dollar cost averaging with total investment I.

Now to calculate the mean shares purchased with a single investment of amount I.

Well what is an arithmetic mean? It is the sum of all possible outcomes divided by the number of possible outcome. Mathematically, the arithmetic mean number of shares purchased looks like this:

S = 1/n (I/P1 + I/P2 . . . . . . . . + I/Pn)

In other words, the average number of shares purchased through a single randomly timed purchase will be mathematically equal to a perfect infinite series of dollar cost averaging purchases.

We have logically concluded that dollar cost averaging is not better on average than a single randomly timed purchase. Furthermore, the use of dollar cost averaging precludes intelligent timing of investment. Overall this technique provides no benefit and creates a net removal of the opportunity for intelligent timing.

Abuse of indexing

Before we get to the fallacies of index investing, let us go over the costs and benefits of investing in various indices.

The S&P 500 Trust ETF (NYSEARCA:SPY)

Benefits: diversification across 500 stocks, liquidity of a heavily traded issue, tracks the index.

Costs: 0.09% management fee and the foregone opportunity to make intelligent stock picks with the invested capital.

PowerShares Trust ETF (NASDAQ:QQQ)

Benefits: diversification across 100 companies, liquidity, targeted exposure to tech stocks, and tracks the index.

Costs: a hefty 0.20% management fee and the foregone opportunity to make intelligent stock picks with invested capital.

I am not making an argument that either of these is a good or bad investment, but rather that the value of each of these to a given investor is entirely dependent on the situation of that investor. The nature of the costs and benefits actually change situationally and to a high degree. To clarify this point, let us view the costs and benefits of these ETFs again, but valued by the needs of to 2 different investors.

Investor A is a highly skilled portfolio manager with a large sum of assets under management.

To him/her the benefits of these ETFs are nullified. Given the large pool of money to work with, commission costs are negligible, so development of an equally diversified portfolio through picking of individual stocks becomes plausible. A highly skilled investment professional should be able to generate above market returns, so the market tracking of the ETF is no longer a benefit, but a liability.

In addition to the weakened benefits, the costs of ETF investing are amplified for Investor A. With such a large amount of capital, the 0.09% and 0.20% fees from SPY and QQQ respectively become a material loss. To a skilled investor, the foregone opportunity to intelligently invest can be huge.

Investor B is a doctor with \$50,000 saved up that he/she wishes to grow for retirement. Investor B is generally intelligent, but new to the stock market.

To Investor B the benefits of an ETF are amplified: Diversification without an ETF becomes difficult as commissions are a sizable portion of investment and tracking of market returns is desirable. The costs are also reduced as percentage fees on \$50,000 are not excessive.

Investor A should definitely not engage in index investing, while it seems to be a viable choice for investor B.

Much of this information is intuitive, but herein lies the abuse. Many investors capable of generating above market returns in a self-chosen portfolio have money in ETFs. After deducting management fees, these usually underperform the market. The true functionality of ETFs is for a small niche of investors with very specific needs, yet ETFs have a dominant market presence.

What is worse is that many hedge fund managers are charging clients large fees only to dump their money into an ETF.

Conclusion

Do not use dollar cost averaging as it provides no benefit and precludes intelligent timing. Unless done through a dividend reinvestment program or some other sort of commission evasion, it can be extremely costly. ETFs while potentially beneficial are massively overused. Evaluate yourselves as investors and consider if indexing is really the right play.