# Dollar-Cost Averaging Theory

### Key Terms

Dollar-Cost Averaging: Strategy of buying a fixed dollar amount for an investment on a consistent schedule, regardless of price. The strategy is meant to reduce the potential risk of market volatility.

Equity: A stock or any other security representing ownership.

### The Constant Dollar Plan or Dollar-Cost Averaging

Let’s make the assumption you, as an investor, are 100% sure what equity you would like to purchase. We’ll call it Stock A. Now you have two options.

1) A lump sum investment. Simply buying as much of the equity you can at once. You plan to invest \$10,000 and do so with one large trade.
2) Buying the equity in portions over a set time-frame. An example would be deciding to buy \$1,000 worth of Stock A each month, for ten consecutive months.

In scenario two, you invest the same dollar value (total investment being \$10,000) but spread the trades out over ten months. Over the ten month time span, Stock A’s price will likely change in value. Regardless of price fluctuations a \$1,000 worth will be bought each month.

Let’s say Stock A posts higher earnings than expected, therefore increases in value during month three. But by month five, the stock crashes due to unforeseen circumstances. During month three you will have bought less shares and during month five you will buy many more shares.

Given this scenario let’s compare lump sum investing and dollar-cost averaging. For simplicity, Stock A only pays a single dividend a year and is not distributed during the time frame being examined.

#### Lump Sum

Fluctuating Market Investment Amount Share Price Shares Purchased
Month 1 \$10,000 \$50 200
Month 10 \$0 \$35 0
Total \$10,000 Average = \$50 a share 200 shares

#### Dollar-Cost Averaging

Volatile Market Investment Amount Share Price Shares Purchased
Month 1 \$1000 \$50 20
Month 2 \$1000 \$50 20
Month 3 \$1000 \$75 20
Month 4 \$1000 \$75 13.3
Month 5 \$1000 \$25 40
Month 6 \$1000 \$25 40
Month 7 \$1000 \$25 40
Month 8 \$1000 \$30 33.3
Month 9 \$1000 \$30 33.3
Month 10 \$1000 \$35 28.5
Total \$10,000 Average = \$42 a share Over 288 shares

While this example is quite extreme it is meant to demonstrate how market fluctuations can benefit those implementing dollar-cost averaging. By the end of the ten month period, the investor who choose a lump sum strategy would own 200 shares of Stock A worth \$35, for a total of \$7,000. The investor who elected for the dollar-cost averaging strategy now owns 288 shares at \$35, worth \$10,080. He or she bought shares at an average of \$42.

Even through a drastic price change, dollar-cost averaging allowed the investor to profit on his original investment by purchasing more shares when the price dropped.

### Conclusions

Dollar-cost averaging eliminates emotion and a need for market timing from investing. It lessens the risk of investing a large amount in a single holding at the wrong time (I can’t imagine what is was like for young investors just starting in 07-08′). Side note, if you contribute to a 401(k) plan bi-weekly or monthly you are already unknowingly using dollar-cost averaging principles.

The math behind dollar-cost averaging is straightforward. More shares are purchased when prices are low, and fewer shares are bought when prices are high. While I first saw merit in this theory while reading the classic The Intelligent Investor: The Definitive Book on Value Investing written by one of the greatest investors of all time, Benjamin Graham, critics of dollar-cost averaging are plentiful.

A white paper study published by Vanguard concluded over 2/3 of lump sum investing outperformed dollar-cost averaging in the U.S., U.K. and Australia over a time span of 1 to 30 years.

Personally I have historically chosen lump sum investing. Mainly because I was buying during a consistent bull market. As I write this in late July of 2015, the majority of core financial instruments indicate U.S. stocks are overpriced. Moving forward I may consider a constant dollar plan. With dollar-cost averaging in a bull market you lose because you miss out on potential profits but in a bear market you lose less than if you invested in a lump sum. Overall I would recommend this strategy for novice investors beginning their investing journey or for long-term investors wary of a bull market transitioning back to a bear market.