User:Leeraar/Dollar cost averaging

Dollar cost averaging (DCA) is an investing technique that is often recommended or considered for new or cautious investors, or for those who have received a windfall. DCA involves dividing an available lump sum into (equal) parts that are then invested over time. This is opposed to making a Lump Sum Investment (LSI) immediately.

Behavioral and psychological issues
Much of the justification and rationalization for DCA rests on the assumption that people are averse to short-term loss, but perhaps more tolerant of a loss that occurs after a longer term. Investment advisors say their clients are hesitant to invest. If DCA is a way to get those clients to invest, so be it.

DCA can be a very plausible argument. Since the general trend of the market is positive, people are fearful they are investing “at the top” or “at an all-time high”. If they invest a little at a time, they feel they will be shielded during a short-term decline in market prices.

Terminology and history
DCA involves retaining, and not investing, available funds. It does not mean periodic or systematic investing, which is to invest funds as and when they become available, for example, by payroll deduction.

The term DCA arises from an accident of arithmetic. If you purchase an equal amount of shares per month, you will pay the (simple arithmetic) average price over time. If, on the other hand, you invest an equal dollar amount, you will pay the harmonic mean price per share, which is always lower than the average price. This fact has no real significance, but has been used by some writers in the past to encourage systematic investing of constant dollar amounts.

Expectations for DCA
If you invest in a fixed number of shares per interval (no matter the price), the average price per share will be the simple mean. The simple mean of 4 and 6 is (4+6)/2=5.

If you invest a constant dollar amount per interval (no matter the number of shares) the average price per share will be the harmonic mean, which is always less than the simple mean. The harmonic mean of 4 and 6 is 2/(1/4+1/6)=4.8.

Suppose that DCA involves taking an available lump sum, dividing it into twelve parts, and investing each part monthly over the next year. That strategy is contrasted with LSI, investing the entire lump sum immediately. Suppose also that the not invested part of the DCA funds are held risk-free, a fairly generous assumption. DCA involves more trading, and those costs are also ignored here.

The LSI price is simply the price paid. The DCA price is the harmonic mean of the prices of the individual lots. Note that the DCA price does not depend on the trend or order of the prices, but simply on their average (harmonic mean).

With LSI, one is fully invested over the entire period. With DCA, one is, on average, 50% invested. One can then postulate that DCA will then have about half the return of LSI, and this is essentially true.

An analysis of DCA vs. LSI using historical data for the total return of an S&P500 index fund (“DCA by the numbers” [link]) shows that, indeed, DCA provides half the market return that LSI does. That return may be up or down. There is a lot of scatter in the data, but the correlation is unmistakable.


 * Lump-Sum-versus-Dollar-Cost-Average-Returns.jpg

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Risk
Intuitively, DCA would seem to reduce risk, since less money is at risk. By that token, LSI has an asset allocation of 100/0 (%equities/%cash) while DCA has an asset allocation of approximately 50/50. Constantinides, says that DCA is a “sub-optimal” way to reduce risk: A constant 50/50 AA is better.

In the thread “DCA by the numbers” the following are calculated from historical data:

Any reasonable riskless return used to calculate the Sharpe ratio, shows, by that measure, that the risk-adjusted return of DCA is inferior to that of LSI.

Related concepts
As noted above, the term Dollar-Cost Averaging is sometimes used to describe periodic automatic investing (almost universally utilized by individual investors to fund retirement accounts out of earned income).

“Reverse dollar cost averaging”  pertains to periodic automatic withdrawals made during retirement. This has also been analyzed as “Sequence of returns risk” [ref].

Value Averaging closely resembles dollar cost averaging but differs in that the investor selects a target growth rate or amount on his or her asset base or portfolio each period, and then adjusts the next period's contribution according to the relative gain or shortfall made on the original asset base.