A common financial planning question is whether one should invest a large cash “windfall” as a lump sum or spread it out over some time period. This applies to a variety of situations such as inheritance, life insurance proceeds, bonuses, sale of a business or real estate property, etc.

There are many considerations affecting such a decision: math, psychology, risk tolerance, market outlook and so forth. In this post I will focus on one question – are you mathematically better off investing as a lump Sum or dollar-cost averaging (DCA). As is true with the vast majority of financial planning topics, the answer is: ** “it depends”**.

Here are the rules for our little experiment:

- Invest $100,000 into SPDR S&P 500 (SPY)
- Lump Sum – invest the entire $100k on January 1
- DCA – invest 1/12
^{th}($8,333) every first of the month

- Reinvest all dividends and fund distributions

**Exhibit 1** shows the calculation for 2012 as an example. Both methods start January 1 with $100k. The monthly balances change as the cash is invested and the market ebbs and flows.

At the end of the year we have a balance of $105,341 using the DCA and $115,988 under the lump sum method. Let’s introduce a concept I’ll call ** “DCA Advantage”** – that is the percentage difference of the ending balance between the two methods. It can be calculated as follows:

(DCA End Balance / Lump Sum End Balance) – 1 **=** ($105,341 / $115,988) – 1 **=** -9.2%

Thus, in 2012, following the DCA method would have left you with 9.2% lower ending balance (by $10,647). If we expand on this example and calculate the annual “DCA Advantage” since 2000, a pattern begins to emerge:

**Exhibit 2 – Annual S&P 500 Returns and DCA Advantage**

Based on this sample, we can draw some conclusions:

- Market performance during the year dictates which investing strategy is more effective
- If the market goes down, DCA works better
- If it goes up, Lump Sum is the preferred method
- The higher the magnitude of the market move, the larger the difference between two methods

Another observation is that the sequence of monthly returns matters quite a bit. For example, 2010 and 2012 had very similar annual returns for the index, but the DCA Advantage metrics were quite different (-1.5% vs -9.2%). In 2010, first six months of the year saw a negative return with a big rally in the back half of the year. 2012 was more uniform in the monthly return distribution (**Exhibit 3**).

**Exhibit 3
**

Another way to look at the return sequence and how it impacts DCA Advantage is presented in **Exhibit 4.** The bars represent monthly percentage return, blue line is the month-end balance under DCA and orange line is the balance for Lump Sum method (both start the year at $100k). You can see that the Lump Sum orange line gets ahead nicely in the beginning of 2012 and the difference remains significant throughout the year.

**Exhibit 4 – Graphical comparison of 2010 and 2012
**

Based on this mathematical analysis, in positive years investors are better off putting their money to work as a lump sum. Of course, we never know ahead of time whether the S&P 500 will go up or down in any given year. However, the market has a strong upward bias and has gone up about 80% of the years (**Exhibit 5**). Thus, Lump Sum should always be the preferred investment method.

**Exhibit 5 – Positive & Negative S&P 500 Returns since 1970**

This analysis doesn’t take into account the psychological aspects of investing a large sum of money. In the next post I will explore that side of the argument as well as analyze the long-term impact of dollar-cost averaging on your portfolio.