Tuesday, January 30, 2007

Asset Class Reader: International Stocks

Asset Class Reader: International Stocks

The following papers analyze International and Emerging Market stocks.

International Equity Investing: Long Term Expectations and Short Term Departures: Vanguard Institutional Research

International equity: Considerations and recommendations: Vanguard Institutional Research

The Worldwide Equity Premium: A Smaller Puzzle: Dimson, Elroy, Marsh, Paul and Staunton, Mike

The Long Term Risks of Global Stock Markets: Jorion,Phillipe

Value vs. Growth: The International Evidence: Fama,Eugene and French,Kenneth R.

Factor Funds, Mean-Variance Efficiency, and the Gains From International Diversification: Eun, Cheol S., Lai, Sandy and Zhang, Zhe

Long Term Global Market Correlations: Goetzmann,William N., Li,Lingfeng and Rouwenhorst,K. Geert

Investing in Emerging Markets: Vanguard Institutional Investors

Asset Class Reader: REITS

Asset Class Reader: REITS

The following papers examine the portfolio characteristics of Equity REITS as an asset class:

Commercial Real Estate: The Role of Global Listed Real Estate Equities in a Strategic Asset Allocation: Ibbotson

The case for a strategic allocation to global real estate securities: Ted Bigman and Christina Chui

Cointegration of Real Estate Stocks and REITs with Common Stocks, Bonds and Consumer Price Inflation - An International Comparison: Westerheide, Peter

International Evidence on Real Estate as a Portfolio Diversifier: Hoesli, Martin, Lekander, Jon and Witkiewicz, Witold

The Performance and Diversification Benefits of European Public Real Estate Securities: Bond, Shaun A. and Glascock, John L.

Investing for the Long-Run in European Real Estate: Fugazza, Carolina, Guidolin, Massimo and Nicodano, Giovanna

Real Estate Investing The REIT Way: Barclays Global Investors

Commercial equity real estate: A framework for analysis :Vanguard Research & Counseling

Asset Class Reader: Inflation Indexed Bonds

Asset Class Reader: Inflation Indexed Bonds

Papers examining the investment characteristics and diversification benefits of Inflation Indexed Bonds:

Understanding And Using Inflation Bonds: Hammond, P. Brett

The Rationale and Design of Inflation-Indexed Bonds: Price, Robert

Diversification Benefits of Treasury Inflation Protected Securities: An Empirical Puzzle: Mamun, Abdullah and Visaltanachoti, Nuttawat

Asset Allocation With Inflation Protected Bonds: Kothari,S.P. and Shanken,Jay

Monday, January 29, 2007

Saturday, January 27, 2007

Tobin's Separation Theorem : The Dilution of Risk

Ever since the 1957 publication of James Tobin's seminal paper on what has become known as "The Separation Theorem" (Liquidity Preference as Behavior Towards Risk for those intrepid souls willing to sample it) , investors have had the theoretical basis for modulating portfolio risk.

In essence, the Theorem postulates that an investor can control the risk of a basket of risky investments by either borrowing at the risk free rate and leveraging the portfolio (and its risk), or alternately, lending at the risk free rate and tempering risk. Since most investors are risk averse, the clear preference of most investors is to combine the risky basket of securities with risk free bonds, and thereby lower the downside risk of the portfolio. In common parlance, we would term this the stock/bond asset allocation decision.

The risk free bond allocation is usually defined as short-term treasury securities (1 to 5 year maturities), or perhaps expanded to include short term investment grade corporate paper. It is sometimes suggested that the risk free allocation should be made up of inflation indexed treasuries. (My personal individual preference is to combine both securities for risk dilution by dividing the risk free allocation between the two.)

In his excellent paper, The Long-Term Risks of Global Stock Markets, Phillipe Jorion finds that "a globally diversified portfolio would have displayed much less downside risk than any single market." The global equity portfolio is therefore a proxy for the risk basket of securities.

We can derive a notion of the downside risk for this risky basket by reference to the superb Dimson, Marsh, and Staunton paper, The Worldwide Equity Premium: A Smaller Puzzle, a table from which is reproduced in the following pdf. file.

The table rewards careful scrutiny. It covers 106 years of market history, not only for the US market, but also including four foreign markets (UK, France, Germany, and Japan) as well as the World Market and the World Market Ex-US. The table provides real rates of return for various market episodes; highest and lowest period returns; and longest runs of negative real returns. The rewards and risks of equity investment are manifestly apparent. Although future returns and economic episodes are uncertain as to limits, the historical record does demonstrate that the world equity portfolio has surrendered as much as 50% of its real value during past down market cycles.

The following table (courtesy of William Bernstein, The Intelligent Asset Allocator) puts the Separation Theorem to practical use, showing the required bond allocation for diluting the downside risk potential of equities to tolerable levels. (The choice of maximum loss preference would, of course, depend on the risk tolerance of the individual investor). One must also caution that, as the Dimson, Marsh, and Staunton paper reminds us, hyperinflation can render even risk-free assets worthless, a reminder that uncertainty is an inescapable fact of life. An allocation to commodities might be advisable to hedge this risk.

Table 1. Downside Risk Reduction
Maximum Loss
Equity Allocation

Thursday, January 25, 2007

Asset Allocation: Rebalancing

Rebalancing an investment portfolio to one's target policy allocation is, as asset class returns vary, often necessary to maintain a portfolio's risk characteristics. The following papers examine the intricacies of rebalancing a portfolio. (For individual investors, annual rebalancing within 5% variance bands should provide sufficient risk control, and under certain investment environments a "rebalancing bonus" in absolute return.)

The first paper, from Vanguard Institutional Investors, is geared towards the institutional investor, albeit the insights are applicable to individual investors. The conclusion is especially relevent for taxable accounts.

We include a number of papers examining the rebalancing issue from William Bernstein's Efficient Frontier. One may also find the following study in the FPA Journal to be of interest:

Rebalancing for Tax-Deferred Accounts: Just Do It—Don't Worry How" by Mark W. Riepe, CFA, and Bill Swerbenski, CFA

Portfolio Rebalancing in Theory and Practice

Executive summary
A portfolio’s asset allocation determines the portfolio’s risk and return characteristics. Over time, as different asset classes produce different returns, the portfolio’s asset allocation changes. To recapture the portfolio’s original risk and return characteristics, the portfolio must be rebalanced to its original asset allocation. This paper identifies the factors that influence a rebalancing strategy. We present a conceptual framework for developing rebalancing strategies that can accommodate changes in the financial market environment and in asset class characteristics, as well as account for an institution’s unique risk tolerance and time horizon. Our findings indicate that:

• Determining an effective rebalancing strategy is a function of the portfolio’s assets: their expected returns, their volatility, and the correlation of their returns. For example, a high correlation among the returns of a portfolio’s assets means that they tend to move together, which will tend to reduce the need for rebalancing. In addition, the investment time horizon affects the rebalancing strategy. A portfolio with a short time horizon is less likely to need rebalancing because there is less time for the portfolio to drift from the target asset allocation. In addition, such a portfolio is less likely to recover the trading costs of rebalancing. The effect of a rebalancing strategy on a portfolio depends on return patterns over time. If security prices approximately follow a random-walk pattern, then rebalancing more frequently or within tighter bands reduces a portfolio’s downside risk (absolute as well as relative to the target asset allocation). In a trending or mean-reverting market, the impact of rebalancing may be somewhat different when viewed on an absolute or relative-to-target basis.

• Additional factors to consider when implementing a rebalancing strategy include preference and costs, such as time spent, redemption fees, or trading costs. Each cost incurred will reduce the return of the portfolio. The nature and magnitude of trading costs affect the choice of rebalancing strategies.

• Due to differing risk tolerances, two institutions with identical asset allocations may prefer different rebalancing strategies.


To ensure that a portfolio’s risk and return characteristics remain consistent over time, a portfolio must be rebalanced. The appropriate rebalancing strategy depends on a number of factors such as the market environment and asset-class characteristics. Rebalancing achieves the goal of risk control relative to the target asset allocation in all market environments. Although market return patterns may create opportunities for tactical rebalancing, this active strategy is challenging. Based on reasonable expectations about return patterns, average returns, risk, and correlations, we conclude that for most broadly diversified stock and bond fund portfolios, annual or semiannual monitoring, with rebalancing at 5% thresholds, produces an acceptable balance between risk control and cost minimization. To the extent possible, this rebalancing strategy should be carried out by appropriately redirecting interest income, dividends, new contributions, and withdrawals.


Efficient Frontier Articles

The Rebalancing Bonus: Theory and Practice September, 1996

When Doesn’t It Pay to Rebalance? January, 1997

Rebalancing: Practical Issues July, 1997

Case Studies in Rebalancing Winter, 2000

Rebalancing Individual National Markets Spring 2000

Wednesday, January 24, 2007

The 1/N Solution

Individual investors rarely employ sophisticated asset allocation methodologies, such as mean variance optimization, monte-carlo simulation, or probabalistic scenario analysis in formulating and implementing investment policy. Instead, they often employ "naive" strategies, such as equally dividing the pallete of asset classes. Such "Couch potato" or "cowards" portfolios are designated "1/N Heuristic" portfolios by academia. Examples of 1/N Heuristic Portfolios, from simple to complex would take the following forms (assuming an equal 50/50 equity/fixed income division):

Two Asset Class 1/N Heuristic Portfolio

Vanguard Total Stock Market Index 50%
Vanguard Total Bond Market Index 50%

Four Asset Class 1/N Heuristic Portfolio

Vanguard Total Stock Market Index 16.7%
Vanguard Total International Index 16.7%
Vanguard REIT Index 16.7%
Vanguard Total Bond Market Index 50%

Six Asset Class 1/N Heuristic Portfolio

Vanguard Total Stock Market Index 10.0%
Vanguard Small Value Index 10.0%
Vanguard REIT Index 10.0%
Vanguard Total International Index 10.0%
Vanguard Total Bond Market Index 25.0%
Vanguard Inflation Protected Bond 25.0%

How do such naive asset allocation models stand up to academic analysis? Surprisingly well, as the following studies indicate.

The 1/n Pension Investment Puzzle

Heath Windcliff and Phelim P. Boyle

This paper examines the so-called 1/n investment puzzle that has been observed in defined contribution plans whereby some participants divide their contributions equally among the available asset classes. It has been argued that this is a very naive strategy since it contradicts the fundamental tenets of modern portfolio theory. We use simple arguments to show that this behavior is perhaps less naive than it at first appears. It is well known that the optimal portfolio weights in a mean-variance setting are extremely sensitive to estimation errors, especially those in the expected returns. We show that when we account for estimation error, the 1/n rule has some advantages in terms of robustness; we demonstrate this with numerical experiments. This rule can provide a risk-averse investor with protection against very bad outcomes.

The 1/N Heuristic in 401(k) Plans

Huberman, Gur and Jiang, Wei, "The 1/N Heuristic in 401(k) Plans" (March 15, 2004). EFA 2004 Maastricht Meetings Paper No. 2036

Records of more than half a million participants in more than six hundred 401(k) pension plans indicate that participants tend to use a small number of funds: The number of participants using a given number of funds peaks at three funds and declines with the number of funds for more than three funds. Participants tend to allocate their contributions evenly across the funds they use, with the tendency weakening with the number of funds used. The median number of funds used is between three and four, and is not sensitive to the number of funds offered by the plans, which ranges from 4 to 59. A participant's propensity to allocate contributions to equity funds is hardly sensitive to the fraction of equity funds among those offered by his plan. The paper also comments on limitations on inference available from experiments and from aggregate-level data analysis.

Naive Diversification Strategies in Defined Contribution Saving Plans

Shlomo Benartzi and Richard Thaler

There is a worldwide trend toward defined contribution saving plans and growing interest in privatized Social Security plans. In both environments, individuals are given some responsibility to make their own asset-allocation decisions, raising concerns about how well they do at this task. This paper investigates one aspect of the task, namely diversification. We show that some investors follow the “1/n strategy”: they divide their contributions evenly across the funds offered in the plan Consistent with this naive notion of diversification, we find that the proportion invested in stocks depends strongly on the proportion of stock funds in the plan.

How Inefficient are Simple Asset-Allocation Strategies?

DeMiguel, Victor, Garlappi, Lorenzo and Uppal , Raman, "How Inefficient are Simple Asset-Allocation Strategies?" (February 2005).

In this paper, we wish to evaluate the performance of simple asset-allocation strategies such as allocating 1/N to each of the N assets available. To do this, we compare the out-of-sample performance of such simple allocation rules to about ten models of optimal asset-allocation (including both static and dynamic models) for ten data sets. We find that the simple asset allocation rule of 1/N is not very inefficient. In fact, it performs quite well out-of-sample: it typically has a higher Sharpe ratio, a higher certainty equivalent value, and a lower turnover than the policies from the optimal asset allocation. The intuition for the good performance of the 1/N policy is that the loss from naive rather than optimal diversification is smaller than the loss arising from having to optimize using moments that have been estimated with error. Simulations show that the performance of policies from optimizing models relative to the 1/N rule improves with the length of the estimation window (which reduces estimation error) and also with N (which increases the gains from optimal diversification). But, even with an estimation window of 50 years, the difference in the performance of the 1/N policy and the policies from models of optimal asset allocation is not statistically significant.

Tuesday, January 23, 2007

2006 Year End Portfolio Rebalancing

My portfolio rebalancings at 2006 year end simply returned my portfolio to policy weights. My rebalancing included:
  • Allocating my annual transfer of SIMPLE IRA accumulations over to my Traditional IRA and placing the proceeds into Inflation Indexed Bonds;
  • Allocating my 2007 Roth contribution into Short Term Bonds;
  • Rebalancing my Variable Annuity REIT Index holdings into Variable Annuity Short Term Bonds;
  • Rebalancing from my taxable account short term reserves into Total Stock Market Index and Tax-Managed International Fund allocations.

Asset Allocation and Asset Location

The following papers examine the optimal division of asset classes between taxable and tax preferenced accounts. A fine tool for determining asset location can be found at Easy Allocator.

Maximizing Long-Term Wealth Accumulation:It’s Not Just About "What" Investments To Make,But Also "Where" To Make Them

Robert M. Dammon, Carnegie Mellon University
James Poterba, Massachusetts Institute of Technology
Chester S. Spatt, Carnegie Mellon University
Harold H. Zhang, University of Texas at Dallas

Individuals who are saving for retirement are likely to know that the level of savings and the asset allocation of their savings are two very important factors affecting wealth accumulation. Another factor called asset location — which refers to the placement of certain types of assets in tax-deferred accounts and other types of assets in taxable accounts — is far less understood
The winners of the 2004 TIAA-CREF Paul A. Samuelson Award tackled this issue head-on, and concluded that equities are far better suited for taxable accounts than for tax-deferred accounts, and that bonds are far better suited for tax-deferred accounts than for taxable accounts. The reason for this preference is the different tax treatment of equity investments compared to fixed-income investments. Other research findings include:
  • Choosing the right asset location for a pair of asset classes is more important when the tax rate differential between the two types of assets is greater and when the rate of return on the relevant assets is high.
  • The relative proportions of taxable and tax-deferred wealth are an important factor in determining one’s optimal asset allocation. According to the Samuelson award-winning authors, other factors being equal, an investor’s optimal equity allocation will be higher when a larger proportion of his/her total wealth is held in taxable accounts, and that his/her optimal bond allocation will be higher if the bulk of his/her wealth is held in tax-deferred accounts.
  • The ideal situation occurs when the desired asset allocation is reached by investing the entire tax deferred account in bonds and the entire taxable account in equities. More often, the proportions of financial assets don’t match up neatly with the desired asset allocations, and so adjustments may be needed. The authors state that for maximum tax efficiency, individuals should not hold mixed portfolios of equities and bonds in both their taxable and tax-deferred accounts.

Tax Efficient Saving and Investing

By William Reichenstein, Ph.D.,
TIAA-CREF Institute Fellow, Baylor University
February 2006


A central component of investment advice in recent decades both for individual and institutional investors has focused on asset allocation, and rightly so since it plays a critical role in determining returns. For individual investors, tax management also plays a significant role in maximizing wealth but it typically does not receive the attention it deserves. This Trends and Issues examines four types of tax considerations that can reap benefits to investors:

Choice of Savings Vehicle. To the degree possible, individuals should take maximum advantage of tax-favored savings vehicles, including tax-deferred accounts such as 401(k)s, 403(b)s and traditional IRAs, as well as after-tax accounts such as Roth IRAs, Roth 401(k)s, and Roth 403(b)s. All of these accounts essentially allow for tax-exempt growth on their after-tax values.
After-Tax Asset Allocation. As noted, most individuals are aware of the importance of asset allocation but they calculate it as though assets in tax-deferred accounts are worth the same amount as those in taxable accounts. As a result, they overstate the allocation to the dominant asset class held in tax-deferred accounts. When calculating their asset allocation, they should convert all assets to after-tax values and then calculate their asset allocation using these after-tax values. For example, assets in tax-deferred accounts should be converted to after-tax funds by multiplying the pretax value by 1 minus the expected tax rate during retirement. Sometimes assets in taxable accounts also need to be converted to after-tax values, but the adjustments generally are not as large.
Tax-Efficient Investing (Including the Role of the Stock Management Style). Examples of tax-efficient investing in one’s taxable account include: a) tax-loss harvesting, in which capital losses are realized in order to offset capital gains or ordinary income; and, 2) passive, index-type investing where unrealized gains are allowed to accumulate, thus providing tax deferral and even exemption if assets ultimately receive a step-up in basis or are donated to charity.
Asset Location. This concept refers to appropriate location of equities and fixed income. In general, fixed income should be held in retirement accounts such as 403(b)s and Roth IRAs and equities, especially passively-managed stocks, should be held in taxable accounts. The reason for this preference is that, when held in taxable accounts, equities are generally taxed more favorably than fixed income. Equities in taxable accounts can benefit from lower capital gains tax rates, and taxation on gains can be deferred as long as the investor continues to hold the equities. Taxation on gains can even be avoided altogether if the owner holds the equities until death, at which time they receive a step-up in basis. In addition, capital losses can offset capital gains and reduce income.

Non-qualified Annuities in After Tax Optimizations

William Reichenstein, Baylor University

This study first explains why individuals should calculate an after-tax asset allocation. This asset allocation distinguishes between pretax funds in say a 401(k) and the generally after-tax funds in a taxable account. Separately, it performs mean-variance optimizations for individual investors. It concludes that, in general, almost all investors should locate bonds in Roth IRAs and qualified retirement accounts (e.g., 401(k)) and stocks, especially passively held stocks, in taxable accounts. At lower levels of risk tolerance, investors should substitute bonds held in non-qualified annuities for stocks held in taxable accounts. At higher levels of risk tolerance, they should substitute stocks for bonds held in Roth IRAs and qualified retirement accounts. The analysis suggests that the people who should be most interested in holding stocks in annuities are those who trade too frequently to qualify for preferential capital gain tax rates. Finally, this study may be the first to demonstrate that an individual investor bears more risk when an asset is held in an annuity instead of taxable account, and it considers the implications of this conclusion for optimal asset-allocation and asset-location decisions.

Asset Allocation and Insurance Hedging

The question of how to hedge risks to human capital (early in life) and indeterminate life expectancy (later in life) by broadening the asset allocation paradigm to included insurance hedging with life insurance and immediate annuities are examined in the following two papers:

Human Capital, Asset Allocation, and Life Insurance

P. Chen, R. Ibbotson, M. Milevsky and K. Zhu
Version: February 25, 2005

Human capital should be taken into account when building portfolios for individual investors. One unique risk for an investor’s human capital is mortality risk, the loss of human capital in the unfortunate event of premature death. Life insurance hedges against mortality risk. Human capital affects both the optimal asset allocation and the optimal life insurance demand. However, asset allocation and life insurance decisions have consistently been analyzed separately in theory and practice. We develop a unified human capital based framework to help individual investors make both decisions. We investigate the impact of the size of human capital, its volatility, and its correlation with other assets; bequest preference; and subjective survival probability through five case studies. Our analysis validates some intuitive rules of thumb and provides additional results.

Merging Asset Allocation and Longevity Insurance: An Optimal Perspective on Payout Annuities

by Peng Chen, Ph.D., and Moshe A.Milevsky, Ph.D.

Although several recent papers in the Journal of Financial Planning have discussed the mechanics and importance of lifetime, or payout annuities, the industry currently lacks a coherent and formal model of how much wealth should be allocated within and between these products.This paper revisits the importance of longevity insurance—while discussing the concerns with a strategy consisting purely of fixed payout annuities—and then addresses the proper asset allocation between conventional financial assets and payout annuity products. Our focus is on maximizing a suitably defined objective function in an intuitive,comprehensible and practical manner. In addition to the usual risk and return preferences of investors, our modeling framework requires inputs on the relative strength of retirees’bequest motives, their subjective versus objective health status, and their pre-existing longevity insurance (aka pensions).To illustrate the model,we provide some brief case studies.

Beyond Markowitz: A Comprehensive Wealth Allocation Framework for Individual Investors

Beyond Markowitz: A Comprehensive Wealth Allocation Framework for Individual Investors

Chhabra, Ashvin B., "Beyond Markowitz: A Comprehensive Wealth Allocation Framework for Individual Investors" . The Journal of Wealth Managment, Vol. 7, No. 4, pp 8-34, Spring 2005

In sharp contrast to the recommendations of Modern Portfolio Theory (MPT), a vast majority of investors are not well diversified. This neglect of diversification is seen across all wealth segments, including the affluent. This paper attempts to provide a solution to this “diversification paradox,” by expanding the Markowitz Framework of diversifying market risk to also include the concepts of Personal Risk and Aspirational Goals.

The Wealth Allocation Framework enables individual investors to construct appropriate portfolios using all their assets, such as their home, mortgage, market investments and human capital. The investor may choose to accept a slightly lower “average rate of return” in exchange for downside protection and upside potential. The resulting portfolios are designed to meet individual investors' needs and preferences, as well as to protect individuals from Personal, Market and Aspirational risk factors.

The Wealth Allocation Framework attempts to bring together MPT with aspects of Behavioral Finance through a single pragmatic Framework. A major conclusion of this work is that, for the individual investor, Risk Allocation should precede Asset Allocation.