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.