Tuesday, February 6, 2007

Portfolio Diversification – 401K

Before kicking off, let me state that I am not a qualified investment advisor. The summaries provided in this blog should not be construed as official investment advice but simply as my thoughts. You should see a qualified “fee-only” investment advisor if you need direct advice about your individual financial situation for retirement.

This being said…..

Portfolio Diversification – 401K Overview

Most companies in the U.S. offer 401K plans to their employees. Nearly all of these plans are administered by large mutual fund plans such as Fidelity Investments. Generally the employee’s 401K plan offers a few basic mutual funds that cover several sectors and investment styles.

What is the most important thing an employee should keep in mind when selecting funds for their 401K? ---- Diversification. For long term success, it is critical that an employee properly diversify within the context of the mutual funds offered in the plan. The selection of funds must keep in mind the risk tolerance and age of the participant, but also focus on to reducing the portfolio risk while maximizing returns.

A diversified portfolio does not concentrate on merely one or two investment categories. Instead it includes an array of funds covering all the basic sectors, some of these sector returns will excel while the returns of other investments lag. Each year the particular funds that shine may rotate in the plan; a mutual fund that provides the strongest returns this year may be the laggard the following year. A properly diversified selection of funds will ensure lower volatility in your overall retirement returns.

Modern Portfolio Theory - MPT

Modern Portfolio Theory “defines investments in terms of their their expected long-term return rate and their expected short-term volatility. The volatility is equated with "risk", measuring how much worse than average an investment's bad years are likely to be. The goal is to identify your acceptable level of risk tolerance, and then to find a portfolio with the maximum expected return for that level of risk.”

MPT focuses on the standard deviation of returns over time of particular investments. The portfolio theory defines a statistical portfolio including multiple minimally correlated components to focus on providing the most efficient overall returns for the risk taken. Utilizing concepts such as covariance, a portfolio is defined using a combination of low risk and high risk investments which over time should smooth out fluctuations in value while achieving superior returns.

One good article on Modern Portfolio Theory can be found at:

The commentary below is going to provide an overview of how to design a diversified 401K investment plan using standard corporately-offered mutual funds within the guidelines of modern portfolio theory.

Corporate 401K Plans

Most 401K plans offer a core set of funds that allow the employee to implement basic investment diversification but not broad diversification. Usually the primary fund offerings with proper allocation should meet the needs of many employees for retirement. Any 401K investment should be diversified in mutual funds across six basic sectors:
- Large Cap – U.S. stocks with market capitalization above $10B
- Mid Cap – U.S. stocks with market capitalization between $2B and $10B
- Small Cap - U.S. stocks with market capitalization below $2B
- Foreign Stocks – stocks in markets outside the U.S.
- Bonds – Corporate bonds generally issued by U.S firms
- Cash – Money Market account

An employee at a company offering a 401K plan from Fidelity is likely to have a small set of standard investment options similar to the list of funds outlined below:

BGI Extended Market Index – matches Wilshire 4500 Completion Index
Fidelity Growth & Income Portfolio (FGRIX) – actively-managed large growth fund
Fidelity International Discovery Fund (FIGRX) – actively-managed foreign large blend fund
Fidelity OTC Portfolio (FOCPX) – actively-managed large growth fund
Fidelity Overseas Fund (FOXFX) - actively-managed foreign large blend fund
Harbor International Instl CL (HAINX) - actively-managed foreign large value fund
MSI LGCP Rel Val A (MSIVX) – actively managed large value fund
Spartan U.S. Equity Index Fund (FUSVX) – matches S&P 500 Index
US Equity Market Index – matches Wilshire 5000 Total Market Index
Wells Fargo Small Cap Value CL Z (SSMVX) – actively-managed small growth fund
Fidelity Magellan (FMAGX) – actively-managed large growth fund

Blended Fund Investments:
Fidelity Freedom 2000 Fund (FFFBX) – actively managed blend fund
Fidelity Freedom 2010 Fund (FFFCX) – actively managed blend fund
Fidelity Freedom 2020 Fund (FFFDX) – actively managed blend fund
Fidelity Freedom 2030 Fund (FFFEX) – actively managed blend fund
Fidelity Freedom 2040 Fund (FFFFX) – actively managed blend fund
Fidelity Freedom Income (FFFAX) – actively managed income fund
Fidelity Puritan Fund (FPURX) – actively managed blend fund

Fidelity Investment Grade Bond Fund (FBNDX) – actively-managed bond fund
BGI U.S. Debt Index Fund – matches Lehman Brothers Aggregate Bond Index

Money Market:
Fidelity Institutional Money Market (FMPXX) – money market fund

The Curse of Size and Some Hard Truths

Before taking a closer look at 401K portfolio diversification, there are some hard truths about the funds offered in most retirement plans. Index funds for large and mid cap stocks tend to outperform actively-managed funds. Most actively-managed large and mid cap funds offered in 401K plans tend to have a large amount of assets and are institutional performance “has-beens” that do not offer much upside. The most common funds placed by institutions into corporate 401K plans are the largest in asset size and generally ranked in the bottom of performance. In the case of Fidelity, there have been multiple articles over the past years demonstrating this. It is always preferable to invest in mutual funds with a moderate asset size; funds with huge amounts of assets have difficulty in remaining flexible enough to deliver strong returns. Remember size does matter when it comes to the assets of mutual funds, and smaller is generally better.

Fidelity Magellan is a prime illustration of the curse of size and a victim of its own earlier success. Mutual funds that contain a colossal amount of assets find it difficult to effectively maneuver in the market to deliver returns. For example, when the fund wants to invest 2% of its assets in a particular stock, the amount of money represented by the 45 billion Magellan is enormous. Even a mere 2% of the fund is represents a monetary amount greater then the openly available shares of many stocks listed on U.S. exchanges. This means that there is only a limited list of stocks that Fidelity Magellan can effectively purchase; most are very large capitalized stocks that offer only limited growth potential.

The other issue that a fund the size of Magellan must contend with is that every significant purchase or sale of stock moves the market. When the fund wants to purchase a stock, it usually takes several weeks of work to acquire the shares, and its own purchases drive up the price of the targeted stock. In effect the fund sabotages its own efforts causing it to miss the targeted entry price. Similarly the large sales tend to drive the price lower imploding returns on the exit. This “slippage” is a significant competitive disadvantage for sizeable funds when getting in or out of an equity position.

Avoid actively-managed funds in your 401K plan that have a huge amount of assets.

Actively-Managed Funds vs. Index Funds

Normally 85% of mid and large cap mutual funds under-perform their associated indexes in any given year. Generally the funds with a large amount of assets offered by most institutional 401K plans are extremely likely to under-perform. This means that most investors are better off looking for an index fund with low expenses in these particular market sectors. Is there any sector where actively managed funds are more likely to outperform their associated index funds? Actively-managed small cap and foreign market mutual funds have a greater chance of beating their associated indexes; some surveys demonstrate that nearly 40 to 50% of these funds outperform the indexes in most years. Similarly many actively-managed bond funds out-perform the standard bond indexes.

What does this means to the average 401K investor; they should look for low-expense index funds in their 401K plan that cover the mid and large cap sectors. However they should consider actively managed funds for the small cap, foreign stock, and bond sectors, especially if the fund expense ratios appear to be reasonable.

Selecting the Funds

So how do we pare down the list of funds in this example to a group that can be used to demonstrate diversification?

First remove all the “Fidelity Freedom” funds from consideration. These funds are targeted at people who want to select a retirement year and simply “set & forget”. Furthermore, these types of funds also tend to have increased fees due to the fact that they are really a mutual fund of other sub-tending funds. Due to the higher fees and “auto-diversification” features these funds will not be used in this analysis.

The next funds to pare out are the actively managed large and mid-cap funds; this drops Fidelity Growth and Income, Fidelity Magellan, Fidelity OTC, and MSI LGCP Rel Val A. This leaves Spartan U.S. Equity Index Fund (FUSVX) as the obvious large cap selection.

In this case, there is an obvious weakness in the lack of an actively managed mid-cap fund offering or standard index mid-cap offering included in the funds offered in the plan. The weighting of the components included in the BGI Extended Market Index fund make it lean towards representing middle capitalized equities better then the smaller capitalized stocks included in the index. The BGI Extended Market Index fund will be selected to represent mid-caps in this example. The T. ROWE PRICE EXTENDED EQUITY M using symbol PEXMX closely matches the returns of this index, and will be used as a proxy for performance analysis because it has a five year history. All the mutual index funds that match the Wilshire 4500 Completion Index are considered mid-cap blend funds in the Morningstar database.

Remember, it is wise to look for actively managed small stock and foreign stock funds within a 401K plan. If the offered funds in these sectors appear to have strong performance over time with reasonable fees; then they should be considered for inclusion in your 401K portfolio. The obvious small cap choice is Wells Fargo Small Cap Value CL Z (SSMVX). There are three foreign stock funds are offered in this Fidelity plan; Fidelity International Discovery Fund (FIGRX) will be used in this example, but any of the funds could be considered.

In the same way the Fidelity Investment Grade Bond Fund (FBNDX) will represent bonds over using the BGI U.S. Debt Index Fund. Actively-managed bond funds tend to outperform the bond indexes. Knowledgeable bond fund managers can use several active interest rate and bond swapping methods to boost yields; bond index funds are stuck with their structured holdings.

The Final List

The following list of funds will be used in our 401K basic diversification example:
Large Cap: Spartan U.S. Equity Index Fund (FUSVX)
Mid Cap: BGI Extended Market Index (proxied by symbol PEXMX)
Small Cap: Wells Fargo Small Cap Value CL Z (SSMVX)
Foreign Stock: Fidelity International Discovery Fund (FIGRX)
Bond: Fidelity Investment Grade Bond Fund (FBNDX)
Cash: Fidelity Institutional Money Market (FMPXX)

Type of Investors – Risk Tolerance

Investors need to take into account their risk tolerance when designing their retirement portfolio. My definitions of investor profiles are provided below:

Conservative – Very much dislikes loose money in any given year, willing to accept a lower rate of return for less volatility and risk in their portfolio
Moderate – Willing to accept a 10-15% draw-down in a given year. Expects the long term returns to mirror or slightly exceed the overall market.
Aggressive – Willing to take a 20-30% draw-down without flinching. Hopes their long term returns will exceed the overall market.

Many times an investor will be more tolerant of risk when they are young and find it less acceptable as they approach retirement. This means that their risk profile will go from Aggressive to Conservative over a long period of time. A 401K investor first must determine how much risk they can stomach before proceeding to design a portfolio.

The standard allocation of the portfolio will also vary based on the person’s age. One general rule of thumb for retirement accounts is that:

The % allocation in stocks = 110 minus (your age)
For example if you are 30 years old then 110 – 30 = 80% of your 401K portfolio should be in stocks.

This formula provides an approximation of the stock vs. non-stock investments for investors of a specific age group. The allocation of the stock sectors is driven by both risk tolerance and age.

401K Portfolios by Age and Risk Tolerance

Before proceeding to the outlined 401K portfolios below, please understand that several assumptions are made in regards to these portfolios:

1) The individual will be retiring at age 65 and start withdrawing the money then. Retiring earlier or later then this requires a shift in age-based investment strategy.
2) The money in the 401K plan is not needed for any purpose prior to retirement.
3) The individual is not borrowing against the 401K plan. This creates all sorts of complexities in planning.

Crunching the numbers for the selected funds provide the following portfolio allocation results for investors in different age groups who have varying risk appetites. The results are based on the concepts of Modern Portfolio Theory.

Please note that this is not official investment advice, but simply an exercise to demonstrate how the allocations in a 401K plan will vary for investors of different ages and risk acceptance levels.

401K Portfolio for Ages 20-30


401K Portfolio for Ages 30-40


401K Portfolio for Ages 40-50

401K Portfolio for Ages 50-60


Where did these magic numbers come from?

The first immediate question from most people is where did all the magic percentages come from for all the proposed portfolios above? These numbers come from running a set of spreadsheets that calculate standard deviation for each mutual fund, followed by covariance, efficient frontier, and other calculations such as Monte-Carlo calculations. Constraints are used to create a portfolio that is appropriate for each particular age group. The moderate portfolio is the middle case; the conservative portfolio looks at safety in the worst “risk-of-ruin” case, while the aggressive portfolio focuses on maximum returns while allowing significant draw downs.

The next question should be “why are all the numbers so nice and round?” Well it is because the results are rounded to the closest 5% mark normally. So 13.84% is rounded to 15% rather then being left as a difficult to remember number. Will this rounding impact your returns over the long term? Yes, but not by much when taking in account the dollar cost averaging used in 401K investing and other factors relating to the mathematics of retirement investing. In other words, you are just slightly off the best theoretical results in terms of yield vs. volatility. Also based on performance results and the time period selected; that number may be 15.1% rather then 13.84% when the calculations are run six months from now. The reality is that the results, within the constraints allowed, converge approximately on the percentage allocation.

Some people will note that the utilization of MPT tends to skew the selected investments towards more volatile small caps and foreign stock funds that have greater risks while many times offering greater returns. This is expected, but leads to results where some investment advisors for middle-age employees may urge them to tilt towards large caps in their stock fund selections in the belief that this will provide greater safety. Modern Portfolio Theory does not actually back up this type of advice, the math leads towards placing greater amounts of money in non-correlated sector investments to provide greater overall returns with less risk. If anything 401K plan participants may want to possibly consider placing greater percentages into non-large cap stock funds as they get older then the tables present.

Also keep in mind that the results are automatically constrained by practical limits in some cases. For example, as an extreme case it is possible for an un-restrained calculation to show that the best investment alternative for a 60 year old was to place 80% of their money in foreign stocks while performing an efficient frontier calculation. Well the results would have to be constrained by the fact that anyone of that age should have approximately 40-50% of their money in bonds. Including this type of boundary constraint leads to more reasonable results.

A good site, from retired math professor Peter Ponzo from the University of Waterloo, for spreadsheets that allow for the number crunching is:

The site contains a wealth of information on the number crunching side of investing.
Some spreadsheets of interest will be:
Standard Deviation
http://www.gummy-stuff.org/download-stocks.htm (calculate SD for multiple stocks or funds).
Efficient Frontier
Monte-Carlo Survival Rate

There are a number of limitations and errata to this 401K model that will be explored in more detail in later posts. These include but are not limited to:
1) The cash is viewed as a risk less asset, and the allocation is based on traditional retirement advice.
2) It really would be better to break down age in 5 year increments, after all a 50 year old that is 15 years from retirement has very different needs then a 60 year old who is within 5 years of the mark.
3) Different fund selection can lead to different results.
4) Does not take in account increasing salary over time (greater 401K investments over time). Assumes a constant amount every year. The allocations are a static snapshot.
5) Does not take into account variations in company match.
6) Inflation or changing risk less interest rates not taken into account.
7) Some calculations tend to minimize return risk against the S&P 500, in other words the results are correlated against the “market” which is generally represented by the S&P 500 index as a benchmark. This will explain the tendency to lean towards large cap index funds as the person approaches age 60.
8) No consideration given to standard blend funds such as Fidelity Puritan in the fund selection process.
9) and quite a bit of other stuff.

Are the percentages provided in the tables above perfect for all situations? No, however they should serve as a starting point and guideline for people considering how to allocate their 401K investments. The key take-away point is that investors MUST diversify across all the sectors and not place all of their money in merely one or two funds.

Once again, if you need professional investment help for 401K planning then I urge you to see qualified “fee-only” financial advisor. See the following site for more information:

NAPFA, the National Association of Personal Financial Advisors, is the nation’s leading organization dedicated to the advancement of Fee-Only comprehensive financial planning.

As a disclosure let me state that I do invest my 401K money in some funds not included in this example. Therefore my personal 401K portfolio does not exactly match any of the portfolios provided above. However all the funds used in the example above are part of my 401K fund selections.


Why do investors need to re-balance? After a while a 401K investors percentages allocated to each investment will be out of proportion as some funds increase in value quicker then others. This means that the investor will have to re-balance their investments to the target percentages to get back to being in equilibrium.

Some people may ask “is re-balancing sort of like backing your return losers and punishing the funds that excelled”? Well not exactly because the fund that excelled last year may be the dog this coming year. Leading sectors tend to rotate every year. Studies have also shown that adding assets to a portfolio component during a period when they underperformed actually results in higher returns and lower risk over time. This is especially true for 401K plans which automatically implement dollar cost averaging, an excellent form of time diversification.

How often should a 401K investor re-balance? Investors should review their 401K performance each quarter but only need to rebalance about once per year. I normally re-balance in January each year. Some studies have shown that the optimal re-balancing period is 17 months; of course there is the usual academic debate over this selection of timeframe.

Extremely Aggressive Investors and that guy who failed to Diversify

Some 401K plans offer options to invest money in stocks and funds outside the basic fund plan. Many very aggressive investors use this as an opportunity to implement swing trading in their 401K account. Many of these individuals have some success; however most do not beat the market in the long term. 80% or more lose retirement savings doing this. Nearly all would be better off investing with a long term perspective. If you want to trade stocks, I would urge you to open a brokerage account outside of your 401K for this activity; focus your retirement accounts strictly on long term investing.

If you are going to utilize the option to purchase investments outside your core 401K plan then you need to be doing it for the right reason --- broader diversification for your long term investments. For example with Fidelity, the brokerage-link option will allow you access to REIT, commodity, and high-yield funds. If you are a knowledgeable investor then it makes sense to put a small allocation of your retirement savings into these types of offerings.

Another possible reason to select funds outside your core plan is to fill in a missing sector gap or selection of a fund with a lower expense ratio. This should be done with a long term picture in mind; chasing returns by rotating in and out of funds is not advisable.

Also keep in mind the importance of diversification. The individual in the next cube bragging this year about their 34% return who placed all their 401K money in foreign stocks, is the same person that will be crying next year that they lost 50% of the money in their 401K. The cause of their emotional rollercoaster is the failure to properly diversify and seek risk adjusted returns over the long run. Retirement investing is won by the turtle, not the rabbits.

Today’s Heresy

This discussion did not touch on value vs. growth vs. blend funds in context of creating a basic 401K portfolio, I may be so bold to state that within the framework of selecting rudimentary funds to provide simple diversity – the fund style (growth, value, and blend) does not matter. There may be some people who view this as heresy; however my perspective is that in an environment in which many of the fund selections are indexes or actively-managed funds that attempt to beat basic indexes then it is not worth time to obsess over value vs. growth. Most 401K investors would do best to ignore these fund style concerns when creating a basic portfolio of mutual funds included in their core plan. If multiple options must be selected from within a particular sector then the employee would do best to select a “blend” type of fund, or balance between growth and value selections.


The merits of the selected funds from the overall list in this example can be debated. However the focus of this summary is the proper creation of a diversified 401K portfolio that will increase long term returns while minimizing risk. The concepts remain the same no matter which company you work for and what particular funds you select -- it is critical to diversify your 401K selections across all the basic sectors.

A future posting will take a closer look at the returns of some of the proposed 401K portfolios, taking a look at the mechanics of standard deviation and risk.

Others may quibble over the benefits of indexing versus active-managed funds. There are a number of opinions in this area. Generally I have found that it is difficult for actively managed U.S. large caps funds to beat the S&P500 index; especially since the funds offered in most 401K plans that have a huge amount of assets. Historically most mid-cap funds do not beat their associated indexes either. There are a few standout mid-cap funds; if your 401K plan is fortunate enough to include one of these actively-managed mid-cap funds with a history of beating the index then you may want to consider the fund as an alternative to mid-cap indexing.

The focus of this summary is to define the important benefits of fund diversification within your 401K plan characterized in the context of modern portfolio theory. While the mathematical theory may be complex, the conceptual outcome is not. The results demonstrate that a 401K investor should focus on proper diversification across basic sectors offered in their core funds to achieve the best long term results with their retirement savings. The portfolio ratios may change due to age or risk tolerance, but the prerequisite to win in the long term remains the same – Diversification is critical to funding your retirement success.

Some further links on portfolio diversification:



GregB said...

I appreciate the feedback left by some of the readers. I hope you enjoyed the 401K post!

Some quick feedback to the comments:

1) A five year period was used to calculate the mean and SD. Took a look at calculating on a daily, weekly, and monthly timeframe from the results perspective. It would be preferable to use a greater number of years for these calculations but you are constrained by the available historical information for some funds. I plan a follow-up post that discusses the mechanics of the results and points to some observations about changes that occur if different parameters/assumptions are used.

2) The definition of "market return" for the example was the S&P 500 index. There are several factors that drive this as the "representative of the market". This also drives the tendency to bend "risk-of-ruin" and other calculations towards selecting funds that more closely correlate to the S&P 500 for shorter time frames (one of the errata) as you get closer to retirement.

3) The article focused on basic diversification. Personally my retirement investments are broadly diversified including REIT, commodities, high yield, and other funds. In this example I wanted to demonstrate the importance of basic diversification and how to achieve it. There are a number of people who place all of their 401K money into a single fund or two, and are not properly diversified. I wanted to demonstrate in this post (and the follow-up) the critical need to diversify, even at a basic level rather then a broad-based level.