Xpert Speak - Investments

Q1. Utility Theory:

a) As far as I can tell, the only numbers to use for "A" (using the AIMR equation for Utility Maximization) are 2,3 of 4.  Given the complexities of individuals’ risk tolerance, the value for A seems far too simple.  How is the Utility Theory (value for A) used in the real world?  Do FP's use decimal values such as 2.2, 2.3, 2.4 etc?  When I tried to plug in other values such as 5 or 6 the asset allocation solution suggests shorting one asset class in order to purchase over 100% of the other asset class.

b) What is the best way to assign a reasonable valuation to an individual based upon their level of risk to make appropriate use of the Risk Utility equation?

While utility theory is an important part of the theoretical foundation used by professional advisors when thinking about investors’ risk tolerance, specific implementations like the AIMR formula are rarely used in practice.  Advisors often use formal and informal tools to assess client risk tolerance – questionnaires, for example, that will ask clients to respond to various theoretical tradeoffs – but they apply whatever insights they glean to a limited set of “acceptable” portfolios rather than to all that might appear on the efficient frontier.  Advisors almost invariably constrain investment choices to exclude short selling (i.e. in addition to the necessary condition that all weights sum to 1, a further constraint is placed upon each asset (or asset class) such that its weight must be greater than or equal to zero).  Likewise, advisors will further constrain the available portfolios to exclude those falling on the far right of the frontier (the terminus of the frontier, after all, is a one-asset portfolio composed entirely of the asset with the highest expected return, which would hardly qualify as a “diversified” portfolio).    

Choosing an appropriate portfolio is often an iterative process that involves client feedback at successive stages.  In my own case, I will gather information about client risk tolerance by exploring their perceptions of what would constitute an unacceptable loss, as well as information about their personal history and experience with different types of investments.  I will then choose two or three portfolios that I believe might be appropriate and review the characteristics of each with the client.  In doing so, I pay special attention to the downside risk (in mean-variance terms, risk is often thought of as represented by a symmetrical distribution, but from a practical client perspective, only downside variability (semi-variance) qualifies as risk).  I illustrate the downside potential in terms of percentage loss (E(r) minus two-times the standard deviation), dollar loss (maximum percentage loss times current value of portfolio), and “tail of the distribution” risk (maximum actual losses in any rolling 12 month period over the past 30 years.  The reality, unfortunately, is that no matter how clients respond to these hypothetical measures of downside risk, their reaction when such a loss actually occurs will tend to be different; specifically, they tend to overestimate their ability to tolerate risk when the discussion is hypothetical.  The planner is well advised, therefore, to adjust her assessment accordingly.  Lastly, as this is all taking place within a financial planning context, we must also explore the tradeoffs with respect to achievement of client planning goals.  For example, with respect to retirement planning, choosing a lower-risk/lower-return portfolio may require a client to accept higher savings goals or the need to defer retirement for several years.  Placing the risk discussion within the context of the financial plan really helps clients to answer the question of why, all other things being equal, they would ever accept more risk rather than less. 


Q.2 Probabilities

a) Where do the probability percentages, in calculating the expected return and standard deviation for a security) come from? So far they have been given (e.g., bull market scenario 40%, bear market 20%, etc.). But where do they come from in the real world?

b) Is Monte Carlo simulation used in the financial planning community for portfolio optimizations? If so, how is it incorporated in determining the allocations?

First of all, most financial planners are optimizing portfolios at the asset class level, not the level of individual securities (or even individual mutual funds).  For those planners who use formal optimization approaches (by no means all of them) there are two broad approaches that are employed.  The first involves deriving the summary statistics needed for optimization (E(r), variance, covariance) from historical measures.  Here the question becomes what period to use when developing estimates.  Some have suggested that the longest period for which there is data should be used, since this incorporates many more possible states of the economy (Ibbotson), while others would suggest a shorter period, like 60 monthly returns, a period short enough to encompass current structural realities within the economy, yet long enough to yield valid summary statistics (Sharpe).    The second major approach involves developing optimizer inputs based on forward-looking assessments and here is where you might have to assign probabilities to the chance for a bull market or bear market environment going forward.  Most practitioners will develop these based on the forecasts of professional economists, allowing their own biases and “gut feelings” to influence which forecasters they pay attention to (since at any point in time professional forecasters can be found along the full spectrum of possible opinion).   Those employing the former approach (historically derived estimates) might argue that variances and covariances are stable enough to use historical estimates (and to the degree these variables exhibit heteroskedasticity, it doesn’t follow a predictable pattern), and that the mean return is the only unbiased estimate of expected return.  With respect to this last, it has also been argued that if the ordinal relationship among the expected returns to different asset classes is maintained, the actual levels won’t change optimal combinations significantly. 

b) Monte Carlo simulations are primarily used in the context of testing the viability of plans to achieve various goals, like retirement.  It isn’t so much used in developing optimal portfolios.  If Monte Carlo simulations suggest that a particular retirement plan has an unacceptably high failure rate, the planner and client can adjust by pushing the goal farther out, increasing the savings rate, decreasing the cost, or increasing the risk (and return) of the portfolio.  To this degree, it can affect which portfolio allocation is chosen.



David B. Yeske, CFP
Yeske & Company, Inc.
220 Montgomery Street, Suite 994
San Francisco, CA 94104
415-956-9686 Voice
415-956-9748 Fax


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