Mathematical Illusion: Why Dollar-Cost Averaging Does Not Work

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Mathematical Illusion: Why Dollar-Cost Averaging Does Not Work
by John G. Greenhut, Ph.D.

Executive Summary In spite of the weight of evidence provided in academic literature against the strategy of dollar-cost averaging, DCA continues to be practiced by investors and recommended by financial advisors. Beyond its psychological appeal, the popularity of the approach can be said to stem from simple illustrations that show DCA resulting in greater stock holdings across a stock market cycle than is achieved by a one-time, lump-sum investment. Alternatively presented, the average cost per share purchased under DCA is demonstrated, by example, to be less than the average price of stock over its cycle. This paper challenges that illustration. It shows that variations in stock prices should not follow the mathematical pattern assumed in the examples. In fact, the price movement should follow a particular mathematical form that yields the same number of shares purchased, whether by DCA or lump-sum investing. Absent any benefit from stock price volatility in reducing average cost, the performance of DCA rests on the trend in stock prices, with DCA outperforming in downward markets and lump sum outperforming in upward markets. Since the latter case is the norm over time, customary empirical findings in the finance literature of underperformance by DCA are explained. The theory in this paper is confirmed by examining a broad sample of stocks, contrasted over the high-growth trend in the second half of the 1990s against the general market malaise over the following half-decade. In the absence of this trend, DCA and lump sum provide equivalent results. John G. Greenhut, Ph.D.