Monthly Archives: October 2013

To DCA or not to DCA: that is the question (Part 2)

In the last post I explored the math behind DCA.  I’m going to expand on that analysis and later address some of the real-world issues associated with investing lump sums of cash.

Exhibit 1 below adds bonds to the “DCA Advantage” analysis as well as 60/40 portfolio (60% stocks, 40% bonds).  The bonds in this case are represented by the Vanguard Total Bond Market Index (VBMFX) – it’s a very broad index of investment-grade U.S. bonds and unlike many other bond index funds it has been around since 1986.

After including bonds, the DCA Advantage rules hold – DCA is good in the down market and bad in an up market.  The results are what one would expect – adding bonds to the portfolio smoothes out the returns and reduces volatility.  This holds true for the DCA Advantage part of the analysis as well.  What’s most interesting to me is the revelation that DCA “eats away” about 20-25% of the cumulative return over the period in both stocks/bonds and the combined portfolio.  That’s a pretty steep price for feeling a little more comfortable.

Exhibit 1 – Portfolio DCA Advantage and Cumulative Statistics


Of course, this 14 year period is just an example and is not necessarily representative of a “typical” experience.  However, our conclusions from the previous post hold – Lump Sum should be the preferred investment method since markets (both stocks and bonds) have a strong upward bias.

While mathematically the case for Lump Sum is fairly clear, there are other factors affecting these decisions:

  • Psychological / behavioral – it’s a hard thing to commit a large sum into the market all at once.  There is certainly no shortage of headlines to keep investors nervous – Government Shutdown, Taper, Sequestration, Debt Ceiling, Syria, Obamacare to name just a few.  Most of these come and go without any lasting impact on the markets.
  • Waiting for a pullback – this is very common and can drive you crazy.  Recently, the market keeps making new highs and investors feel like it “has to” pull back.  So they wait and wait, then get frustrated and pull the trigger at the worst moment.  Or when the pullback finally comes, it’s usually on the back of some disturbing news (see above) and few people actually take advantage of the opportunity to buy into the weakness.
  • Business risk for financial advisors – it’s a hard thing to explain to a new client how your portfolio started out with a million and dropped to $800,000 in a few months due to inopportune timing.  Not many advisors will admit to this, but using dollar-cost averaging is a “safer” approach for retaining new clients.

I follow a few simple rules to remain consistent and avoid frustration:

  • If the money was invested before (401k rollover, advisor change, etc.), I put it right back in the market
  • If it’s “new” cash (business sale, inheritance, etc.), I typically come up with a DCA schedule.  This can take anywhere from 3 to 12 months to get fully invested.  The timeframe depends on:
    • Current market position – this one is subjective and tricky
    • The amount involved relative to overall portfolio
    • Frequency of the event – a one-off business sale vs. annual cash bonus

At the end of the day, you have to do what will get you invested.  If it takes using dollar-cost averaging so be it.

One final thought: if you chose do DCA, set a schedule and stick to it.  Do not get cute and try to time each little investment you make.  It’s going to drive you crazy and you won’t do any better than following a pre-defined plan.


To DCA or not to DCA: that is the question

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 1/12th ($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.

The Great Yield Hunt

The first post of this blog will explore the tendency to hunt for yield to support portfolio withdrawals.  Some investors have a strong preference for living off the income that portfolio produces and do not want to touch the principal under any circumstances.  This might have been a sound approach in the past, when the yields on “safe” investments such as CD’s and Treasuries were significantly higher and outpaced inflation.  Unfortunately, the current rates on such investments are very low.  As recently as 2005, CD rates were in the 3-4% range vs. 0.3-0.5% now.  As shown in the table below, the yield on a sample portfolio consisting of 20% CDs, 30% Treasury Notes and 50% Stocks declined from 5.8% in 1990 to 1.8% currently.


With such low rates on “core” investments, the investors are “reaching for yield” to obtain 4-5% income they require.  In the fixed income area, the popular categories include bank loans, emerging market bonds, preferred stocks and high yield (junk) bonds.  While these investments provide higher current yield than traditional investment grade bonds, they can have large declines during periods of market volatility.  This, of course, defeats the purpose of allocating part of the portfolio to “stable” investments that in theory offset more volatile equity allocations.  As the table below shows, 2008 was not kind to these “yieldy” bond areas. Moreover, these investments tend to act more like stocks than bonds over the longer periods of time.  For example, over the past five-year High Yield bonds have been much more correlated with S&P 500 than the Total US Bond Market Index (R2 is a measure of correlation or the tendency of the investments to move similarly.  You can read more about it here).  I would note, however, that the relationship has changed over the past 12 months.


Some of the equity areas seeing strong fund inflows over the last couple of years are shows in the table below.  While these investments do offer more attractive income streams, they represent relatively small parts of the total US stock market.  When large pools of capital start “chasing” these small niches (2-3% of the overall market), valuations get distorted and can lead to unexpected behavior.  In other words, prices can go up for no reason other than strong investor demand (which might eventually reverse).


Another risk for these investments is that they are much more sensitive to rising interest rates than the overall stock market.  With interest rates likely to continue climbing, investors should pay close attention.  As you can see in the chart below, since the Fed first started talking about “tapering” their bond purchases (QE), interest rates have gone up resulting in losses for these areas while the broader stock market has held up.


There is nothing wrong with having some portfolio exposure to any of the areas discussed above.  It does become dangerous when investors significantly overweight them to obtain higher yield.  It can increase overall portfolio risk and lead to some unexpected results.

I plan to look into some of those investment areas in more detail in future posts.

Hello World

My name is Denis Smirnov and I’m a financial planner at Gordian Advisors in Tucson, AZ.  I decided to start “Plan by Numbers” blog as an attempt to explore the financial planning topics that I come across in my work with clients.  The idea is to use numerical examples to simply illustrate complex concepts related to planning, investments and economics.  Some of the posts are geared towards individual investors, while others are more suitable for advisors and other financial professionals.  Please leave comments and ask questions about the posts that interest you.