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This page contains a single entry by lsaret published on December 20, 2008 5:23 AM.

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Using a Portfolio's Required Return to Develop an Appropriate Risk Level

Edward A. Moses, Ph.D., J. Clay Singleton, Ph.D., Stewart A. Marshall III, Esq.

Authors' Note:
Modern Portfolio Theory has become a customary tool used by investment professionals and, as such, constitutes an industry standard that investment decision makers cannot ignore.  This academic theory has become the bedrock of investment practice.  We have elected to publish three articles in consecutive editions of Wealth Strategies Journal to provide its readership with an understanding of Modern Portfolio Theory and the application of this theory to pertinent issues surrounding the administration and formulation of portfolios.  Sequential publication eliminates the need to redevelop Modern Portfolio Theory and other concepts in each article.  Wealth Strategies Journal readers will have the option of reviewing earlier articles to clarify any points of interest in subsequent articles.
This first article in this series, "Developing and Defining a Well Managed Portfolio - A Primer on Modern Portfolio Theory", provided a foundation for understanding the underpinnings of Modern Portfolio Theory.  The current article describes the usefulness to an investment decision maker of developing an investment policy statement and how the statement can be used to develop a portfolio's appropriate risk level.  The final article in this series is "Determining the Appropriate Withdrawal Rate for a Portfolio: The Crossover Rate."

I.    Introduction

In the first article in this series, we broadly classified an investment decision maker (IDM) as anyone undertaking responsibilities associated with providing investment advice or implementation.  We defined IDMs to include, among others, fiduciaries, trustees, investment advisers, family office directors, portfolio managers, and individuals managing personal assets.  We also identified one of the most important tasks undertaken by the IDM to be portfolio design: assembling and maintaining a portfolio of assets with a risk tolerance suitable for the purposes, terms, distribution requirements, and other conditions of the portfolio.  An appropriately designed investment policy statement (IPS) can be an invaluable guide for the IDM in portfolio design.  Section II of this article will provide the rationale for developing an IPS and discuss in some detail three important elements that should be included in the IPS.

A very difficult issue facing an IDM is the assessment of an appropriate risk level for a portfolio.  Section III presents an approach to determining a portfolio's risk tolerance using the IPS's stated required rate of return based on the portfolio's return/spending level needs.  This approach employs a simulation to demonstrate the probabilities of expected outcomes and demonstrates the impact of different risk level assumptions. 

Section IV summarizes how the IPS can function as a management plan for the portfolio.  Included are the reason why an IDM may not accept the Efficient Portfolio produced by Modern Portfolio Theory, the IPS's usefulness in reconciling the portfolio's desired rate of return with an appropriate risk level, and finally, why the portfolio's strategic asset allocation decision is made after the portfolio's target rate of return and risk level have been established. 

 II.    The Investment Policy Statement

A.  The Rationale for an Investment Policy Statement.  One of the most important first steps undertaken by an IDM in portfolio design is the crafting of a well-considered investment policy statement (IPS).  The IPS serves as an effective guide in making decisions related to the management of a portfolio.

An IPS can be likened to the strategic plan of a business.  This plan, based on the business' Mission Statement, sets out the objectives of the company and the steps or processes necessary to achieve these objectives.  This blueprint guides operational decisions that manage the business.  The plan does not change, particularly in the short run, unless the facts and assumptions upon which the plan was formulated change significantly.  The IPS serves the same function as the business' strategic plan, providing a guide for the consistent implementation of an investment strategy and preventing emotional reactions to events in the market place.  This is not to say the IPS, like a strategic plan, never changes.  It should be reviewed periodically and modified if the facts and assumptions warrant a change.

Finally, it should be stressed that "one plan does not fit all."  Each portfolio, like each business, has a unique set of circumstances that warrant the development of an IPS tailored specifically to the goals and objectives of the portfolio.  To blindly adopt a published "model plan" or even a slight modification to a model plan in developing an IPS for a portfolio defeats the purpose of an IPS.  The IPS must be individualized for each portfolio to reflect its unique characteristics. 

B.  The Contents of an Investment Policy Statement.  Numerous articles and books have been written about the development and maintenance of an IPS.   Many of them are excellent guides for determining the contents of the IPS.  As indicated above, every portfolio has its unique characteristics and the IPS for the portfolio should be developed with these unique features in mind.  Given the wealth of articles and texts available as a guide for developing an IPS, we will not elaborate here on the overall content of a well-constructed IPS.  However, there are three components of an IPS that deserve elaboration and insight.  Additionally, the order in which these specific components are developed is crucial.  The three components listed below are arranged in the order in which decisions should be made.

1.  Selection of Asset Classes to be Potentially Included in the Portfolio.  Perhaps one of the IDM's most important investment related decisions is determining the appropriate asset classes to be considered for inclusion in the portfolio.  If the choices selected are too few, the probability of achieving a well-diversified portfolio is extremely low.  As illustrated in the first article in this series, the selection of asset classes to be considered for the portfolio creates the appropriate set used in the analysis.

Quite often after asset classes are identified, the IDM determines a strategic asset allocation among these asset classes without the benefit of an Efficient Frontier analysis and establishes the allowable deviations from that allocation.  This approach is problematical because it can limit the Efficient Frontier and force the IDM's portfolio choices into too narrow a range of expected returns and risk levels. 

Assume the IDM selects domestic large and small cap plus foreign equity, T-Bills, government and corporate fixed income, and real estate as the appropriate set of asset classes.  Some IDMs might allocate the portfolio among these asset classes using rules of thumb.  A typical result, along with allowable lower and upper deviations, is shown in Figure 1. 

Figure 1
Initial Allocation and Allowable Deviations

Lower Limit    Allocation    Upper Limit
Small Stocks    12%         15%           18%
Foreign Stocks    9           12               15
Large Stocks      30          35               40
Real Estate         8           10                12
Corp. Bonds       10          13                16
Govt. Bonds        8           10                12
T-Bills                  3            5                  7

While this portfolio might seem reasonable, the Efficient Frontier analysis in Figure 2 shows this portfolio is severely constrained.

In Figure 2 the allowable deviations were imposed as constraints (e.g. the 15% allocation to small stocks was limited to between 12% and 18%), and two Efficient Frontiers were generated - one without these constraints (labeled Unconstrained) and one with (labeled Constrained).  The Constrained Efficient Frontier is very short reflecting the limited opportunities available to the IDM with respect to the portfolio's expected return and risk.

Figure 2
Constrained and Unconstrained Efficient Frontiers

 The better approach is to establish target allocations that are consistent with the IPS and based on risk and return expectations produced by an Efficient Frontier analysis.  After all, targets should reflect the best possible allocation under the circumstances and upper and lower limits associated with the final allocation decision are nothing more than a guide to portfolio rebalancing.

2.  Determination of the Target Rate of Return for the Portfolio.  Many factors enter into the selection of the target rate of return, some controllable by the IDM and others dependent on factors outside the IDM's control.  Examples of the latter include expected inflation and a minimum level of administrative expenses.  Controllable factors include the: withdrawal rate from the portfolio, desired real growth in portfolio value (return above the rate of inflation and after withdrawals), and, ultimately, risk.  As will be shown, determination of the target rate of return is subject to change once the risk level associated with this rate of return is estimated.

3.  Determination of the Risk Tolerance for the Portfolio.  Perhaps there is no more vexing problem for an IDM than determining an appropriate risk level for a portfolio.  It is well known that all investors desire high returns and low risk.  It is an axiom of finance that return and risk move together; the higher the desired return, the higher the necessary exposure to risk.  Thus, there is a tradeoff between desired return and risk.  As demonstrated in the following sections of this article, an IDM can estimate the investor's risk tolerance through an iterative process.  This process involves determining initially the desired rate of return consistent with the IPS and then assessing the risk level required to achieve that return.  If the risk is higher than a tolerable level, then the desired return must be adjusted downward to accommodate a lowering of the risk.  It is possible the opposite occurs.  The initial desired rate of return may suggest a risk level that is below a tolerable level.  In this instance, elements of the desired return controllable by the IDM can be increased.

III.    The Appropriate Level of Risk for a Portfolio

A.  The Portfolio's Target Rate of Return. 
Let us assume we have a well-considered IPS for a family.  This document would specify the portfolio's target rate of return consistent with the family's goals and objectives.  For example the investment policy of a portfolio with a specified withdrawal rate for income purposes for the older generation and the remaining portfolio value after their death allocated to the younger generation would be initially designed to provide periodic income desired by the older generation.  To be sustainable, the income target would have to be consistent with the life expectancy of the older generation, the initial portfolio value, consideration of the remaining amount available to the younger generation, and the expected rates of return on the constituent asset classes to produce the specified level of return.  Assuming all parties have agreed on the portfolio's initial target rate of return, we can proceed to analyze the appropriate risk level.  That risk level, in turn, provides feedback for the IDM's construction of the investment portfolio.  Finally, the risk level may need to be adjusted in light of the family's risk tolerance.

B.  Risk and Rate of Return.  In the first article in this series we introduced the Efficient Frontier.  This technique finds the best possible combination of asset classes - best in the sense the portfolios along the Efficient Frontier all offer the lowest risk for their level of expected return.  This collection of best portfolios is produced by examining all combinations of assets in the appropriate set - those asset classes the IDM deems suitable possible investments.  Although IDMs who are experienced investment professionals could forecast and justify their own independent asset class returns, risks, and correlations, historical records are probably the best source for these forecasts.  The same history of asset class performance is widely available to everyone.  For purposes of this article we will assume the IDM has determined departures from these numbers are unwarranted.

C.  Using the Historical Record.  Historical rates of return on seven popular asset classes are shown in Figure 3.   Assume the IDM has selected these seven asset classes as appropriate for the portfolio.  The column labeled average return shows the average annual return (including dividends and capital appreciation) produced by these seven asset classes.

Figure 3
Annual Historical Returns on Seven Indices*
All statistics in %

Average Return    Standard Deviation
Small Stocks     17.45            22.71
Foreign Stocks    9.48            15.78
Large Stocks     11.49            14.83
Real Estate       16.72            15.36
Corp Bonds         8.41             7.92
Govt Bonds         8.56             9.61
T-bills                  3.83             0.47

* Figure 3 is based on actual annual returns from 1972 through 2006.

This Figure makes three main points:

1.  Lessons from the Historical Record.  First, this historical experience sets the range of returns that have occurred and, therefore under our assumptions, are likely to occur on average in the future.  An IDM seeking a 17.45% rate of return, for example, would have to invest the entire portfolio in small stocks.  This approach, of course, would be contrary to the importance of diversification in portfolio construction.  A diversified portfolio would have to accept a more modest return objective.

2.  Asset Class Risk and Return.  Second, every target rate of return carries some risk.  Even a portfolio dedicated to Treasury bills carries some risk, as the standard deviation column in Figure 3 suggests.  The standard deviation indicates the amount of variation around the annual average return.  Every asset class has a standard deviation.  Common investment practice is to take this standard deviation statistic as a measure of risk.  This statistic produces an intuitive ranking of returns to these asset classes in that most people recognize bonds are more risky than Treasury bills, real estate is more risky than bonds, and stocks become more risky as one moves from large stocks, to foreign stocks, to small stocks.   Experience with the capital markets reflects the interaction of millions of investors and billions of dollars over many years.  We can, therefore, use this historical information to translate the portfolio's expected return requirement into a risk level.

3.  An Alternative Portfolio.  If we assume the portfolio's desired rate of return is 12% per year we could construct a portfolio that was invested 43% in real estate and 57% in corporate bonds (.43 x 16.72% + .57 x 8.41% = 12%).  This portfolio, however, would carry more risk (i.e., be less efficient) than other portfolios that are expected to produce a rate of return of 12%.  The IDM should initially use the Efficient Frontier to discover the portfolio that provides the least risk with an expected return of 12%.  Figure 4 shows such an Efficient Frontier.

D.  Using an Efficient Frontier.  The Efficient Frontier shown in Figure 4 was developed following the process discussed in the first article of this series.  To find the risk level associated with the efficient portfolio that produces an expected return of 12%, locate the portfolio on the Efficient Frontier that produces 12% (labeled "12% Portfolio") and read down to determine the risk level.  In this example the 12% Portfolio has the asset allocation shown in Figure 5 with an expected standard deviation of 11.8%.
Figure 4
Efficient Frontier Using Historical Annual Returns for Seven Indices*


* Figure 4 is based on actual annual returns from 1972 through 2006.

Figure 5
Allocation of the Efficient Portfolio
with an Expected return of 12%

Asset Class    Allocation
Small Stocks       0%
Foreign Stocks    21%
Large Stocks       0%
Real Estate         52%
Corp Bonds        22%
Govt Bonds        0%
T-bills                 5%

While this portfolio is mathematically the best (least risk) portfolio that produces an expected return of 12%, it is not well-diversified in the sense that it does not contain all the asset classes the IDM judged to be consistent with the IPS.  This problem can be addressed, however, by nearly efficient portfolios that have the same risk but somewhat less expected return.  In other words the IDM is willing to trade some expected return for better diversification.

E.  Nearly Efficient Portfolios.  The Efficient Portfolio in Figures 4 and 5 has an expected return of 12% and an expected standard deviation of 11.8%.  The vertical line in Figure 4 that connects this portfolio on the Efficient Frontier and the horizontal axis describes another set of portfolios, all of which have a standard deviation of 11.8% and returns progressively less than 12%.  By inspecting these portfolios the IDM can select one that has acceptable diversification and an expected return as close to 12% as possible.  One of these portfolios is shown in Figure 6.

Figure 6
Allocation of Nearly Efficient Portfolio
with Expected Return of 11.4%

Asset Class    Allocation
Small Stocks        14%
Foreign Stocks     17%
Large Stocks          7%
Real Estate           23%
Corp Bonds           15%
Govt Bonds           13%
T-bills                    12%

This portfolio has an expected return of 11.4% and an expected standard deviation of 11.8%.  Assume that the IDM selects this portfolio for risk analysis.

F.  Assessing the Portfolio's Risk.   The IDM can now review the Nearly Efficient Portfolio and form a judgment as to whether the risk implied by the original desired rate of return, 11.8%, is suitable.  For many individuals the concept of risk is more difficult than the concept of return.  Figure 7 shows how the portfolio displayed in Figure 6 can be recast to assess the risk.
Figure 7
Forecast Range of Nearly Efficient Portfolio's Wealth
from One to Twenty Years in the Future

 Figure 7 shows forecast wealth for one through five, ten, and twenty years into the future for the Nearly Efficient Portfolio shown in Figure 6.  The portfolio is assumed to start with $1 million today.   The bars above each year represent the likely dollar range covering 90% of possible outcomes, i.e., from the 5th to the 95th percentile of the distribution.  The horizontal line represents the 50th percentile.  The dollar figures are fifth and ninety-fifth percentiles for representative Years 1, 10 and 20.  For example, the wealth forecasts for Year 1 range between $968,600 (at the 5% level) and $1,271,800 (at the 95% level).  Note that the fifth percentile stays close to the $1 million assumed starting value for many years, and does not exceed $2 million until after year ten.  Representing the Nearly Efficient Portfolio this way often helps individuals understand the implications of the asset allocation decision.

G.  Adjusting the Portfolio's Risk.  Assume after evaluating the wealth ranges for the Nearly Efficient Portfolio, the conclusion is reached that the range of wealth values over the years is too large and represents too much risk.  In this case, the IDM might choose a different portfolio, close to the original Efficient Portfolio, that has less risk, and, therefore, less expected return than the Nearly Efficient Portfolio.  This portfolio, shown in Figures 8 and 9, is labeled the Alternative Nearly Efficient Portfolio.  This portfolio has an expected return of 11.2% and an expected standard deviation of 10.3%, placing it slightly below and to the left of the 12% Efficient Portfolio shown in Figure 4.
Figure 8
Allocation of Alternative Nearly Efficient Portfolio
with Expected Return of 11.2%

Asset Class    Allocation
Small Stocks        10%
Foreign Stocks     10%
Large Stocks        25%
Real Estate          15%
Corp Bonds          25%
Govt Bonds          10%
T-bills                     5%

Figure 9
Forecast Range of the Alternative Nearly Efficient Portfolio's Wealth
from One to Twenty Years in the Future


With this portfolio, the IDM can point out the comparisons with the Nearly Efficient Portfolio's risk and return.  Notice that the range of wealth for the Alternative Nearly Efficient Portfolio is less than that for the Nearly Efficient Portfolio for all years.  For example in Year 1 the Alternative Portfolio has a higher 5th%-tile ($988,400) compared to the Nearly Efficient Portfolio in Figure 7 ($968,600) and a lower 95th%-tile ($1,219,300 versus $1,271,800).  The differences are easiest to see over long periods of time with Year 20 demonstrating the biggest difference.  This approach can help individuals understand the risk-return trade-off inherent in a more aggressive portfolio.

F.  The Optometrist Approach.   This process of moving to lower risk portfolios near the Efficient Frontier (or to higher risk portfolios if the desire is to increase risk) can be repeated until an appropriate level of risk tolerance is found.  Once a risk comfort level is established, the portfolio's asset composition is also determined.  Like an optometrist alternating lenses and asking, "Can you see the chart better now?" the IDM continues to adjust the portfolio's risk up or down until the range of wealth values for a portfolio near the Efficient Frontier meets the family's risk preference.

IV. Conclusions

A. The Investment Policy Statement.
  A well constructed and implemented IPS is an important step in an IDM's management of a portfolio.  It provides a guide for consistent implementation of an investment strategy based on circumstances associated with a particular portfolio and prevents irrational reactions to events in the market place.  The appropriate contents of an IPS are well documented in the literature.  When constructing an IPS, the IDM should pay particular attention (in the following order) to selection of the appropriate set of assets to be included in the portfolio, determination of the target return and assessment of the appropriate risk tolerance. 

The selection of the portfolio's potential assets determines the appropriate set which in turn determines the Efficient Frontier.  Estimation of the target return established in the IPS identifies the appropriate portfolio on the Efficient Frontier.  The location of the portfolio on the Efficient Frontier can be used to assess the portfolio's expected risk for that return. 

B.  Diversification and the Efficient Frontier Portfolio.  It is possible, perhaps likely, that the Efficient Frontier Portfolio will not meet the diversification requirements of the IDM.  In this instance, the IDM can establish a better diversified portfolio by forming a portfolio below the expected return of the Efficient Portfolio.  The portfolio, which we have identified as a Nearly Efficient Portfolio, will have the same risk level as the Efficient Portfolio.

C.  Determining the Appropriate Level of Risk.  The desired return and risk are inextricably related; the higher the required return of a portfolio the higher the risk exposure of the portfolio.  Using the targeted return established in the IPS to locate an Efficient Portfolio allows the IDM to identify the expected risk of the portfolio expressed in terms of its standard deviation.  The Nearly Efficient Portfolio will have the same standard deviation as the Efficient Portfolio.  While the standard deviation is a common indicator of risk used by academics it can be difficult for individuals to appreciate its significance.  Using a simulation it is possible to convert this risk measure into potential ending dollar values for the portfolio.  The higher the risk level the larger the potential future fluctuations in the portfolio's dollar value.  The IDM can determine whether the ranges of potential ending dollar values are acceptable.  If the potential ranges of portfolio values are deemed to be unacceptable, then the target return of the portfolio must be reduced in increments until an acceptable level of risk is determined.  It is also possible the initial target return estimation results in potential portfolio value fluctuation estimations that are below a level of tolerance.  In this case, the target return can be increased resulting in higher portfolio risk.  This process, increasing or decreasing the target return, is repeated until the risk tolerance of the portfolio is established.

D.  Strategic Asset Allocation.  After the target rate of return and corresponding risk level has been determined, the portfolio's strategic asset allocation can be established.  If the strategic asset allocation and the upper and lower limits around the allocation for portfolio rebalancing guidelines are created prior to establishing the Efficient Frontier, a Constrained Efficient Portfolio will be created, with limited asset allocation opportunities for the IDM.