Friday, January 1, 2016

Asset Allocation and the Implementation of the Four Percent Rule

Asset Allocation and the Implementation of the Four Percent Rule

The most commonly used version of the four percent rule sets initial disbursement at four percent of the assets of a 401(k) plan and links future disbursements to inflation.   The rule is a useful rule of thumb used by many financial advisors to guide disbursement decisions from 401(k) plans during retirement.

Whether or not the rule is sustainable depends on a number of issues.   This post deals with one narrow issue impacting the performance of the four percent rule, the mix of assets in the 401(k) plan.  The post examines one narrow choice of assets and one time period.

Situation:   A person retiring in January 2003 has $300,000 in assets.  She will take a monthly disbursement of $1,000 (0.04/12 x $300,000.)

She is considering two different investment strategies.   The first strategy involves placing all $300,000 in one fund VTSMX, which covers the entire U.S. stock market.

The second strategy consists of placing $150,000 in a large-cap fund VFIAX and $150,000 in a mid-cap fund VXF.

Disbursements from the two-fund strategy are assumed to be proportional to fund balances at the time the disbursement is made.

There are two sources of differences in financial outcomes between the two strategies.   First, the return-risk profiles of the two portfolios differ.   Second, the two-fund strategy creates a situation where the retiree will reduce asset sales from a fund that is temporarily doing poorly.


·      What were the return/risk outcomes of the funds over the 2003 to 2015 time period?
·      Can the two-fund strategy provide a more stable financial outcome and more wealth in the long term than the one-fund strategy?
·      What is the lowest level of wealth for the two investment strategies over the 2003 to 2015 time period?
·      What is the terminal level of wealth from the two investment strategies?

Description of fund risk and return:

There are differences in the three funds being considered by this retiree.

·      VTSMX provides exposure to the entire U.S. stock market.  Its top 10 holding are around 15% of the fund’s value.

·      VFIAX invests in the 500 largest U.S. companies.  Its top 10 holding are around 19% of the fund’s value.

·      VXF seeks to track an index composed of small and mid-size companies.   Its top 10 holding are less than 5% of the fund’s value.

Below are the statistics on the financial performance of the three funds over the 2003 to 2015 time period.  

Financial Statistics for Three Funds
# of Months
Mean Return
STD of Return
Minimum Monthly Return
Maximum Monthly Return

Sample covers 155 monthly returns from February 2003 to December 2015.


·      VXF (the small-cap and mid-cap fund) had higher returns and higher variability of returns than either the overall stock market fund or the large-cap fund.
·      The return/risk profile for the overall stock market fund and the S&P 500 fund are really quite similar.  VTSMX has slightly higher returns.  VFIAX has a slightly lower level of risk.   (This is as expected.)  Basically, it appears as though the S&P 500 firms dominate VTSMX so there is little difference between the two funds.

Discussion of potential advantages of the two-fund strategy:

Total disbursements are $1,000 regardless of whether the retiree chooses one fund or two funds.   There is however a major difference between a one-fund strategy and a two-fund strategy.

The person who invests all money in one fund must disburse all funds from the single fund each month regardless of market conditions.  The shares sold each period from the one-fund strategy are

Share sold VTSMX = $1,000/Price of VTSMX

The person who chooses to invest in two funds can choose to increase disbursements from a fund that is doing well and decrease disbursements from a fund that is doing poorly. 

The two-fund example presented here assumes disbursements are proportional to asset balances.

Shares sold VFIAX= (Value VFIAX/Value Both Funds)  X $1,000 / Price VFIAX

Shares Sold VXF = (Value VXF/Value Both Funds) X $1,000/ Price VXF

When VFIAX increases relative to VXF disbursements from VFIAX increase.  When VXF is high relative to VFIAX disbursements from VXF increase.

The proportional disbursement rule is quite passive.   I could come up with a more aggressive disbursement policy. This question is on my to-do list.

Wealth outcomes for the one-fund and two-fund strategies:

Payout and the wealth trajectory from the two strategies are calculated in a spreadsheet.

Financial Results From Two
Investment Strategies
One-Fund Strategy
Two-Fund Strategy
Minimum Account
Maximum Account


The two-fund strategy dominated the one-fund strategy in terms of both return and risk for this particular time period.

·      The minimum account balance (which occurs in early 2009 during the financial crisis) is around $17,000 higher for the two-fund strategy than for the one fund strategy.

·      The difference in the max balance of the two funds an event that occurred in early 2015 was around $115,000.

·      The gap between the two-fund and one-fund strategies has fallen in 2015 because of the recent decrease in the price of the mid-cap and small-cap fund.   The difference in wealth from the two strategies is now around $90,000.

A prescient investor or astute wealth advisor would have taken money off the VXF table early in 2015.  Hindsight is always 20/20.

One final thought:  Part of the savings from the two-fund strategy is from the higher disbursements from the VXF fund.  

·      The proportionate disbursement strategy led to $68,000 in disbursements from VFIAX.

·      A $150,000 investment in FVIAX in isolation under the four percent rule would have led to a disbursement of $77,500.

In this period superior returns from VXF reduced disbursements from VFIAX.

The analysis in this post is not a recommendation of a 50/50 VXF VFIAX allocation.   Such an asset mix is

Concluding thoughts: 

The analysis in this post is not a recommendation of a 50/50 VXF VFIAX allocation.   Such an asset mix is fairly risky.     Investors need to but some money in other asset classes and have some liquidity.

The four percent rule gives decent results so far for the person who retired in January 2003.  The outcome for an investor who follows the four percent rule and uses either of these asset mixes would not have been nearly so pretty for a person who retired at the start of the financial crisis in 2007.

Wall Street’s solution to obtaining a secure pension is for people to save more.  Unfortunately, saving more will not help if you retire at the wrong time and adopt the wrong investment strategy.

More posts on how to manage your retirement fund will follow.

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