Model portfolios

[updated on 8/6/2013]

Buy-and-hold investments are especially susceptible to market forces that inflate (upside risk) and deflate (downside risk) the value of a portfolio.  Two ways of managing the downside risk are to diversify and rebalance the portfolio holdings1,2,3.  Diversification involves selecting two or more holdings that react differently to market conditions.  They are rebalanced by replacing losses from one holding with gains from another according to an allocation plan that divides the holdings into fixed portions.  There’s no guarantee that a rebalanced portfolio outperforms the buy-and-hold portfolio.  High correlations, trading fees, and small investments are potential barriers to successful rebalancing strategies.  The purpose of this article is to design successful rebalancing strategies for diversified model portfolios that outperform the U.S. stock market at an acceptable downside risk.

Model portfolios

Expected returns.  Previous articles described the process of designing and testing buy-and-hold portfolios that track the performance of financial markets.  A computer-assisted program4 is used to design the portfolios and assess portfolio rebalancing strategies.  Selections from 9 different sectors of financial markets may be used to build model portfolios Endnote for comparison to the benchmark return from 1 market sector.  The sector for U.S. large-capitalization stocks provides a benchmark for the U.S. stock market.  Among several models5 that outperform this benchmark, one 4-sector model allocated 25% of its investment fund to each of four financial markets: i) emerging markets stocks; ii) U.S. investment-grade bonds; iii) U.S. equity REITs; and, iv) global precious metals6.  A 2-sector model allocated 60% of its investment fund to U.S. large-capitalization stocks and 40% to U.S. investment grade bonds [same or similar 2-sector models are described by Bernstein7 and Bogle8].  By all measures, the 4-sector model outperformed the 2-sector model and benchmark return (table 1).

Table 1.  Expected returns from buy-and-hold models, 1997-2011.


Legend:  Each model portfolio was initially funded with $10,000.  There were no fees for financial services, all dividends were automatically reinvested, and the portfolio holdings were neither withdrawn nor rebalanced.  Final market value was computed from the allocation plan’s weighted market returns.  Portfolio CAGR 9 is the compound annual growth rate, a convenient number for measuring the growth of portfolio value; higher CAGR infers greater returns.  Sharpe ratio10 is the portfolio’s annual rate of return in excess of the U.S. Treasury note’s return rate and adjusted for market volatility; higher ratio infers greater returns.

Correlations.  A simple correlation analysis of market returns provides correlation coefficients that help assess the diversification of portfolio holdings.  All correlation coefficients are constrained to the numerical range of -1.0 to +1.0.  If the coefficient is close to +1.0, both holdings are highly correlated and non-diversified.  Their market returns are expected to move in the same direction and maximize the downside risk of a portfolio.   If the coefficient is close to -1.0, both holding are also highly correlated, but strongly diversified.  Their market returns are expected to move in opposite directions and minimize the downside risk11.  If the coefficient is close to 0, both holdings are uncorrelated and diversified.  Their market returns are unrelated and tend to buffer the downside risk.  Most correlation coefficients in table 2 are closer to 0 than +1.0, which implies that several market sectors are sufficiently diversified to buffer the downside risk of the model portfolios.

Table 2.  Correlation coefficients


Rebalancing the models

The 4-sector and 2-sector models were initially balanced according to different allocation plans.  Market forces inevitably drove the portfolios to an unbalanced condition when some holdings began to gain or lose more returns than other holdings, causing the sector weighting factors to drift from the original plan12.  The returns from both unbalanced portfolios are listed in table 1.

Is it better to rebalance the portfolios or leave them unbalanced?  The tricky part is deciding when to rebalance them.  Should it be done according to a schedule or upon the signal of an allocation-error1,4?   Table 3 shows that different rebalancing plans (first 2 rows) earned higher returns (last 3 rows) compared to the unbalanced returns in table 1.  Notice that the increments in Sharpe ratio (table 3 versus table 1) that resulted from rebalancing the 4-sector and 2-sector models show an increase in portfolio returns relative to market fluctuation of the underlying holdings.

Table 3.  Expected returns from rebalanced models, 1997-2011.


Legend: The portfolio conditions are the same as described in the legend of Table 1 with exception that the 4-sector and 2-sector portfolios were rebalanced according to the best rebalancing strategy determined by algorithm4.

Barriers to successful rebalancing

Expense ratio penalty.  Although model portfolios are neither taxed nor charged fees, the potential impact of financial-services fees can be assessed by the computer program4.  Index fund managers typically charge an annual expense ratio below 1% of the fund’s assets, which has the effect of reducing the fund’s net asset value and its expected return.  For example, the high-end expense ratio of 1% charged every year after an initial $10,000 investment would lower the 4-sector buy-and-hold model CAGR from 8.7% to 7.6%.  The expense ratio penalty is paid by authorized participants in the primary financial market, not by ordinary investors in the secondary stock market 13.

Trading fee penalty.  Brokerage commissions penalize a rebalancing plan by reducing the expected return.  Chart 1 illustrates the penalty of paying $10 trading fees to rebalance the 4-sector model.  Irrespective of the rebalancing plan, the penalty in lost earnings (Y axis) depends on the total cost of trading (X axis).

Chart 1.  Trading-fee penalty.


Legend:  The total cost of trading (X axis) is the total number of trades multiplied by $10.  The number of trades is unique to each rebalancing strategy in the computer program4.  The lost earnings (Y axis) are the reduction in cumulative value of the rebalanced portfolio due to trading costs.

Initial investment penalty.  The net effect of financial fees depends on the size of the initial investment14.  Suppose the model portfolio were funded in increments of $5,000 starting with $1,000.  Table 4 illustrates the reduction of expected return (measured by CAGR) from rebalanced portfolios when financial services fees are charged to various amounts of invested principal.  There’s no practical advantage of rebalancing a model portfolio when the invested principal is somewhere below $5,000.

Table 4.  Impact of the initial investment on rebalanced model returns.


Legend: The data are CAGRs from rebalanced portfolios that differ according to amount of invested principal (column headings).  The rebalance plan is identified in table 3.  The financial services fees are an annual expense ratio of 1% and $10 trading fees.  A narrow range of buy-and-hold CAGRs (red font) represents the exclusion of a rebalance plan from all investments.

Downside risk

Downside risk, as measured by the semi-deviation of annual returns15, infers the expected loss after the portfolio’s annual return drops below average.  In this case, the annual returns are market returns exclusive of financial-services fees.  Table 5 shows that the downside risks of the 4-sector and 2-sector models are below the benchmark, meaning that the diversified models have lower risks of loss than the benchmark model.  The rebalanced models have nearly the same downside risk as the buy-and-hold models.

Table 5.  Downside risk of model portfolios, 1997-2011.


Legend: The data in table 5 are only an approximation of downside risk due to uncertainty that the annual returns fit a normal distribution of returns.  Lower downside risks are better outcomes.


The purpose of this article was to design successful rebalancing strategies for diversified model portfolios that outperform the U.S. stock market at an acceptable downside risk.  The 4-sector and 2-sector model portfolios had higher expected returns and lower downside risks than the benchmark for the U.S. stock market.  The 4-sector model has the advantage of being more diversified than the 2-sector model.  Furthermore, the 4-sector rebalanced model outperforms its buy-and-hold model when the rebalancing strategy is aimed at correcting an allocation error signal.  The only practical barrier to successfully rebalancing the 4-sector model is the amount of money needed to make an initial investment.   A minimum of $5,000 ensures that the costs of rebalancing don’t reduce the expected return below that of the buy-and-hold portfolio.  It remains to determine if a portfolio of index ETFs can duplicate the performance of the diversified 4-sector model.

In perspective, several decades of historical returns are necessary in order for business cycles to establish a portfolio’s expected return and downside risk.  The 15-year test period of the 4-sector model is considered insufficient time7.  At best, the 4-sector model’s expected return is an interim value based on 2 business cycles that include the 2001 Dotcom bust and 2008 Financial crisis.  The future remains uncertain, especially for that of the emerging markets stocks which comprise 25% of the 4-sector model portfolio.  The emerging markets economies have considerable growth potential despite uncertain market conditions16.  The next 15 years will place the expected return of the 4-sector model on firmer ground.


The model portfolio contains hypothetical investments in two or more sectors of financial markets that earn an expected return.

Copyright © 2013 Douglas R. Knight


1.  Beginners’ Guide to Asset Allocation, Diversification, and Rebalancing, Modified: 08/28/2009. U.S. Securities and Exchange Commission.

2.  Asset Allocation Part 1: What It Is and Why You Need It, by JIM FINK on MAY 6, 2010 in STOCKS TO WATCH , Copyright © 2012 Investing Daily, A Division of Capitol Information Group, Inc..

3.  Jason Van Bergen, 6 Asset Allocation Strategies That Work. ©2013, Investopedia US, A Division of ValueClick, Inc., October 16, 2009.

4.  #SmallTradesPortfolioDESIGNER, Small Trades Journal.

5.   Designing a buy-and-hold portfolio,  Small Trades Journal.

6.   The World Bank: The World Bank authorizes the use of this material subject to the terms and conditions on its website.

7.   William Bernstein.  The Four Pillars of Investing: Lessons for Building a Winning Portfolio, McGraw-Hill, 2002.

8.   John C. Bogle, The Little Book of Common Sense Investing.  John Wiley & Sons, Inc. Hoboken, 2007.

9.   Performance measured by CAGR, Small Trades Journal.

10.  Sharpe ratio (‘historic’). Small Trades Journal.

11.  Asset Allocation Part 2: Constructing an Efficient Portfolio, by JIM FINK on MAY 13, 2010 in STOCKS TO WATCH, Copyright © 2012 Investing Daily, A Division of Capitol Information Group, Inc.

12.  Rebalancing an investment portfolio, Small Trades Journal.

13.  ETF structure,  Small Trades Journal.

14.  Beware of trading fees, Small Trades Journal.

15.  Investopedia dictionary. Semideviation. © 2013, Investopedia US, ValueClick, Inc.

16.  Briefing| Emerging economies. When Giants Slow Down.  The Economist,  7/27/2013.

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