Model portfolios

July 30, 2013

[updated on 3/10/2020.  Reference 17 identifies a useful tool, the portfolio visualizer, for designing and backtesting portfolios.]

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no fees for financial services, all dividends were automatically reinvested, and the portfolio holdings were neither withdrawn nor rebalanced.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.

17.  Vikram Chandrasekhar, 2016.  What is the best tool to backtest a portfolio online?

Asset classes

November 30, 2012

For purposes of investment, an asset is any item of economic value owned by an individual or corporation.  The fundamental assets of our economy –natural resources, skilled labor, and infrastructure– are used to produce a wide variety of goods and services 1.  Included among all goods and services are the financial assets that can be converted to cash in marketplaces where trading generates profits and losses.  An asset class is a group of financial assets that have the same legal structure and share the same market exposure 2.  Table 3 lists the asset classes of greatest interest to individual investors.

Table 3.  Asset classes for individual investors.

Asset class Global capital Risk Return Liquidity
Bonds 45 Low Low High
Equities (Stocks) 28 High High High
Real estate 6 Low High Low
Cash equivalents 4 Low Low High
Derivatives 650 High High High
Commodities High Volatile High
Gold Medium Low High
Infrastructure Medium Medium Low
Art & Collectibles Medium Medium Low

 Legend:  Asset class is an investment category that can be characterized by market region, business sector, and other useful criteria.  Global capital  is the estimated year-end total amounts of capital invested in asset classes during 2004-2008, except that derivatives were valued as the total theoretical principal value during 2010 3,4,5.  Each number represents trillions of U.S. dollars.  The Risk of an investment loss and likelihood of an investment Return are use to facilitate decisions about allocating assets to an investment portfolio.  Liquidity refers to the ease of trading financial assets.  Assets that are easily convertible to cash have high liquidity 2.


Bonds are debts that require the borrower (issuer) to pay a lender (investor) the amount borrowed (principal) plus interest over a specified time (maturity).  Interest is the relevant source of future cash flow to investors.  Bonds offer businesses and agencies an alternate source of borrowed capital in addition to bank loans in the currency market.  Central government bonds typically have the highest credit ratings in their countries.

  • Credit ratings are used to evaluate the risk of borrower default on timely payments of interest and principal.  Bond default is any missed or delayed payment, or the exchange into a new package of securities.  Riskier bonds (i.e., junk bonds) generally have higher yields that the safer investment-grade bonds.
  • Bond yield (ratio of interest/price) serves as an index of investment return.
  • Bond liquidity is variable and decreases with the length of maturity.

Classes of bonds that qualify for inclusion in a bond market index are government, securitized, corporate, high-yield, and emerging-market debt.  Interest rates on bonds tend to increase with inflation because fixed income investors require a real return 5.


Equities are shares of ownership in a company that provide rights to corporate income and capital after the settlement of all obligations to creditors.  Shareholders typically have voting rights in matters of corporate governance.  The relevant source of future cash flow is characteristically linked to corporate earnings and dividends.  The long-term return of equities –~7% in mature markets– is considered to be high and tends to provide protection against inflation.  In contrast, the short-term return on equity tends to decline during periods of high inflation 5, 6.

Private equity is a group of unlisted equities that are traded in private markets, rendering them illiquid (and opaque) by comparison to the ease of trading in public markets 5.

The global capital markets can be divided into developed markets and emerging markets 4.  In 2010, emerging markets comprised 16% of the global equity market capitalization.  Emerging market equities have characteristically higher risk and higher returns than developed markets 5.

Real estate

Real estate investments provide ownership of physical assets (i.e., commercial and residential properties) and rights to future income stream from the property & land.  The best way to view real estate is as a physical asset in which the relevant source of future cash flow is cash yield (e.g., rent).  Physical assets deteriorate unless maintained by costly capital expenditures.  The appraisal value of a property is its current and future income stream.  Various real estate assets provide a spectrum of risks and returns to investors.  Investors can enter the real estate market through private or public markets.  Private markets promote unlisted investments in property and funds.  Private real-estate investments are valued at net asset value of the underlying property.  They tend to be high cost, high return, and illiquid enterprises.  The opposite tendencies apply to real estate investments in public markets.  Public markets list shares of real estate companies and real estate investment trusts (REITs).   The investments are valued at public auction prices.  Assuming that most of the return from real estate investment is derived from stable long-term income, real estate investments are considered low-risk, high-return.  Real estate is an illiquid investment due to pricing discrepancies and transaction time 5, 6.


Derivatives are contracts between a buyer and seller that are based on the price movements of underlying assets.  In 2010, the underlying assets were distributed among interest rates (79%), currencies (8%), credit default swaps (4.6%), equities (2%), commodities (0.4%), and otherwise unallocated (6%).  The biggest demand for derivatives arose from the risk management of portfolios by financial institutions.  For example, Banks use interest rate derivatives to manage potential mismatches between assets and liabilities.

“Futures” are contracts to buy (‘long position’) or sell (‘short position’) an asset for a fixed price at a future date.  Price movements of futures mimic those of the underlying assets 5.  “Swaps” are contracts to exchange payments based on different assets.  For example, the interest rate swap requires an exchange between the cash amount for a fixed interest rate and the cash amount for a floating interest rate.  The contract is written to begin with equal fixed and floating interest rates.  The sides of the swap are called legs; the fixed leg and the floating leg.  “Options” are rights, not obligations, to buy or sell an underlying asset at a fixed price (‘strike’) up to the time of maturity.  The buyer of an option pays a premium for the right to buy or sell.  The right to buy is known as a “call” and the “long position”.  The right to sell is known as a “put” and the “short position”.   The right, not the obligation, to trade distinguishes the option contract from the future and swap contracts 5.


Commodities are materials (e.g., precious metals, base metals, foods, energy) that produce no direct income.  They have no obvious claim to an underlying cash flow but are viewed as liquid assets which provide diversification and a hedge against inflation.  The volatiles prices are driven by perceived differences between supply and demand 5.

Gold is a precious metal held by central banks and used interchangeably with money.  Gold historically provides a long-term hedge against inflation, but this may not continue.  Gold is highly liquid and used as an “insurance policy” 5.


Infrastructure is a class of physical assets (e.g., toll roads, healthcare facilities) that require the management of contracts and capital reinvestment.  They are permanent assets needed for the orderly operation of an economy.  The underlying cash flow from infrastructure is expected to be stable and sufficient to hedge against inflation.  New assets are expected to generate capital growth and established utilities are expected to generate dividend yield 5.

Art and collectibles

Physical assets such as art and wine don’t have an underlying cash flow, but may increase in value over time.  They may be expensive to store and maintain.  Investments in art are considered to be high risk (due to low returns in a down market), costly, and illiquid 5.

Investments excluded from asset classes

Hedge funds and related funds are able to use leverage to gain investment exposure to currencies and asset classes.  Currency is not considered an asset class since it is a basic property of all financial assets.  However, the forward currency market enables the capture of excess currency returns 5.

The allocation of asset classes to an investment portfolio is an important determinant of investment returns that deserves further discussion.

Copyright © 2012 Douglas R. Knight


1.           “Free exchange.  The real wealth of nations”.  The Economist, June 30, 2012.

2.           Asset class.  Dictionary of Financial Terms. Copyright © 2008, Lightbulb Press, Inc.

3.           Global Investable Capital 2004 ppt.  Frontier Asset Allocation Slides.  SunGard Online Investment Systems, Copyright 1997-2005 SunGard Expert Solutions.

4.           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. .

5.           John Nestor, Sion Cole, David Buckle, et al.  Charity Compendium 2011. A long-term perspective on charity fund investment.  UBS Wealth Management.  © UBS 2011. All rights reserved. October 2011.

6.           Buttonwood: The great divide. Why American house prices have corrected more than those in Europe.  The Economist. Apr 28th 2012, Copyright © The Economist Newspaper Limited 2012.

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