By Scott Roark, MBA, PhD | December 20, 2019

Re-Balancing with Numbers

In a recent blog post, I discussed the importance of re-balancing and how it fits into the spending phase of retirement.  In this article, I want to look at some specific re-balancing with numbers and how it has worked out over the past 5-15 years.  The numbers I put together actually go back 17½ years, but that doesn’t sound quite as nice as 5, 10 and 15-year horizons.  Nevertheless, in the table showing the summary results, I will include the 17½ year results as well.

Key Assumptions

In any re-balancing evaluation, there are a few key assumptions needed.  One is how often a re-balance will occur.  In this case, I did it every six months – at the beginning of each year and mid-way through each year.  Another key assumption is what you are starting with and, when considering the spending phase of retirement, what your regular withdrawal is.  I assume a $1 million initial account balance, with a 4% annual drawdown, paid out twice a year.  I further assume annual inflation of 3% over the analysis.  Given that all of these are assumptions, that means all of these could be argued about and fussed over, but they provide a reasonable starting point for the discussion.


Next for the mechanics of re-balancing.  For a portfolio, you start with a target allocation (for instance 45% US stocks, 15% international stocks, 30% US bonds and 10% international bonds) and at re-balancing, you buy or sell enough of the holdings to return to the target allocation.  For instance, if we assume a starting point of January 1, 2002 and look at a re-balance six months later, one will see that the broad stock market in the US declined by about 14% and an index of international bonds increased in value by about 11.5%.  In terms of re-balancing, because the US stocks have declined and the International bonds have increased, this will mean that the allocation has moved away from the target.  In order to return to the target allocation, one would sell some International bonds and buy some US stock funds – in just the right proportions to get you back to your desired allocation.

Model Portfolios

Before I get to the numbers, one last piece of description is needed.  Over a 17½ year window, I considered five different portfolios which closely mirror five model portfolios from Morningstar.  The five portfolios are Conservative (20% equity/80% fixed income), Conservative Growth (40% equity/60% fixed income), Moderate (60% equity/40% fixed income), Moderately Aggressive (80% equity/20% fixed income) and Aggressive (95% equity/5% fixed income).  While the equity and fixed income are the two broad asset classes, we use 5-6 low cost index funds in each portfolio to get exposure to subsets of the two broad classes (e.g. international bonds and international stocks).  Based on the asset allocation, these model portfolios reflect increasing risk moving from Conservative to Aggressive and they would also reflect increased expected return.

Now to the Numbers

Over a 17 ½ year window starting in January 2002, the Conservative Portfolio held up well.  The ending value of the portfolio was about $1,040,000 and it paid out the twice-a-year drawdowns without any issues.  The lowest account balance was $962,000 and occurred in July 2002 (right after “retirement”).  With the financial crisis of 2008-2009, the portfolio held up well – going from a high point of $1,075,000 in January 2008 to a low point of $970,000 in January 2009[1].  During that short window, the portfolio paid out over $48,000 in drawdowns as well.  In all, the portfolio made payments of over $900,000 (the starting point was $40,000 per year, but that grows with inflation!) over the 17 ½ year horizon.  Finally, the standard deviation – a measure of how volatile the portfolio value was – was $46,889.  In all, it was a relatively smooth ride for the Conservative portfolio since January 2002.  In the table below, I show some key metrics for the 5, 10 and 15-year intervals as well.

Metric 5-Year Window 10-Year Window 15-Year Window
Ending Value[2] $984,000 $1,230,000 $1,097,000
Low Point $925,000 (Jan 2019) $1,064,000 (Jan 2010) $972,000 (Jan 2009)
High Point $991,000 (Jan 2015) $1,232,000 (Jul 2014) $1,160,000 (Jul 2014)
Amount Paid[3] $214,000 $462,000 $751,000
Standard Deviation $22,098 $60,531 $51,694


That is a lot of numbers to digest – and we’ve only considered the Conservative portfolio!  The big takeaways I see here are the fact that the Conservative portfolio acted like it should – it maintained a relatively stable value (relatively low standard deviation) and it largely kept up with inflation by maintaining most of the principal and paying out an inflation adjusted $40,000 per year.

In the interests of space, I am going to conclude this blog post with a look at the other extreme – the Aggressive portfolio.  It is made up of 95% equity with 5% in fixed income so we would expect it to be much more volatile over time.  With the 17 ½ year horizon, this portfolio is much more affected by the tail end of the market downturn from 2001-2002.  With a retirement modeled as happening on January 1, 2002, the Aggressive portfolio takes an immediate dive down to $800,000 by the start of the next year.  However, the market recovered and the portfolio value went inexorably up – moving to $1,550,000 by July 2007 – all the while providing money for drawdowns.  Of course, there was a rather large correction in 2008-2009 and the portfolio again took a dive – this time down to $880,000 (as measured in January 2009).  Over the last 10 years, however, this particular portfolio has enjoyed a very healthy, if bumpy, ride up and the highpoint of $1,941,000 is reached with the ending value  (as of July 2019).  Of course, with each new day it seems that there is a new record for the stock market, so this portfolio – currently – is sitting pretty.  But there was a price to be paid for all the growth – the volatility was breathtaking over the past 17 ½ years.  The standard deviation over that time in the portfolio value was $313,618.  Below is the table showing the other time horizons for the Aggressive portfolio.

Metric 5-Year Window 10-Year Window 15-Year Window
Ending Value[4] $1,155,000 $2,311,000 $1,739,000
Low Point $925,000 (Jan 2016) $1,109,000 (Jul 2010) $762,000 (Jan 2009)
High Point $1,155,000 (Jul 2019) $2,311,000 (Jul 2019) $1,739,000 (Jul 2019)
Amount Paid[5] $214,000 $462,000 $751,000
Standard Deviation $83,519 $379,450 $257,067


There are a couple of things to point out with these numbers as I conclude.  First, it is apparent that the 10-year window is the best for this portfolio – which makes a great deal of sense.  We’ve had a (largely) uninterrupted run up in equity values over the past 10 years – minor corrections notwithstanding (the standard deviation tells the tale of the bumpiness involved).  This portfolio was far more volatile than the Conservative one – as it should be.  But with that came a much higher ending value – especially when one considers longer horizons.

I’ll plan on one more blog post on this re-balancing topic and we’ll look at what happened with the Conservative Growth, Moderate and Moderately Aggressive portfolios there.

[1] The low point is as of re-balance dates – not the absolute lowest point over the life of the portfolio.
[2] The initial value is always assumed to be $1,000,000.
[3] The amount paid is based on an assumed 4% withdrawal rate (i.e. $40,000 per year) starting at the appropriate time.
[4] The initial value is always assumed to be $1,000,000.
[5] The amount paid is based on an assumed 4% withdrawal rate (i.e. $40,000 per year) starting at the appropriate time.