Expert: Dr. Joseph de Beauchamp - 3/12/2005

Question
The Third Restatement Of Trusts requires that a fiduciary officer use an investment strategy suitable to the trust's purposes.  So does the Uniform Prudent Investor Act.  The Restatement assumes (though it doesn't explicitly say) that a trustee will use MPT.  So does the Act.  As a practical matter, this means that the trustee must draw an "indifference curve" suitable to the trust's goals.  Once the curve has been drawn, life is easy, because MPT is mostly an application of conventional parametric statistics.  But how does not draw the curve in the first place?  Drawing of the curve is NOT merely an application of traditional statistical principles.  This means that there must be, somewhere, some modern books and articles on the subject.  I don't mean the kind of general blather set forth in the Restatement and in the Act.  I mean that someone must have written a step-by-step procedure, setting forth the method by which one can examine a trust instrument, and then deduce the indifference curve.  I have not found any such book or article, and the failure has not occurred for any lack of searching.  Can you send me a few citations, to helpful tomes?  Thank you.


Answer
Perhaps below is pasted some help to this. Prudent Investor Act actually states that you put no money more than 10% into one class of stock or sector, unless it has "no risk". I therefore do not see the application using the MPT to solve this problem. The curve might give you a range of things to select, but you would have to limit your choice to no more than 10%.

I am not a fan of technical analysis. I do not believe that measuring the history is going to yield performance for risk over time. I think curves change very fast and the only way to select positions is to do fundamental analysis. I am certain this flys against the technical people who believe that past performance equals the future performance. I am still waiting for them to be correct on technical analysis.

Dr. Joseph de Beauchamp

PS: you may wish to try the following for further reading, but I do not believe that you will find a meaningful solution to the "magic method" of making investment decisions on a stats basis:

Modern portfolio theory (MPT)—or portfolio theory—was introduced by Harry Markowitz with his paper "Portfolio Selection," which appeared in the 1952 Journal of Finance. Thirty-eight years later, he shared a Nobel Prize with Merton Miller and William Sharpe for what has become a broad theory for portfolio selection.

Prior to Markowitz's work, investors focused on assessing the risks and rewards of individual securities in constructing their portfolios. Standard investment advice was to identify those securities that offered the best opportunities for gain with the least risk and then construct a portfolio from these. Following this advice, an investor might conclude that railroad stocks all offered good risk-reward characteristics and compile a portfolio entirely from these. Intuitively, this would be foolish. Markowitz formalized this intuition. Detailing a mathematics of diversification, he proposed that investors focus on selecting portfolios based on their overall risk-reward characteristics instead of merely compiling portfolios from securities that each individually have attractive risk-reward characteristics. In a nutshell, inventors should select portfolios not individual securities.

If we treat single-period returns for various securities as random variables, we can assign them expected values, standard deviations and correlations. Based on these, we can calculate the expected return and volatility of any portfolio constructed with those securities. We may treat volatility and expected return as proxy's for risk and reward. Out of the entire universe of possible portfolios, certain ones will optimally balance risk and reward. These comprise what Markowitz called an efficient frontier of portfolios. An investor should select a portfolio that lies on the efficient frontier.

James Tobin (1958) expanded on Markowitz's work by adding a risk-free asset to the analysis. This made it possible to leverage or deleverage portfolios on the efficient frontier. This lead to the notions of a super-efficient portfolio and the capital market line. Through leverage, portfolios on the capital market line are able to outperform portfolio on the efficient frontier.

Sharpe (1964) formalized the capital asset pricing model (CAPM). This makes strong assumptions that lead to interesting conclusions. Not only does the market portfolio sit on the efficient frontier, but it is actually Tobin's super-efficient portfolio. According to CAPM, all investors should hold the market portfolio, leveraged or de-leveraged with positions in the risk-free asset. CAPM also introduced beta and relates a security's expected return to its beta.

Portfolio theory provides a broad context for understanding the interactions of systematic risk and reward. It has profoundly shaped how institutional portfolios are managed, and motivated the use of passive investment management techniques. The mathematics of portfolio theory is used extensively in financial risk management and was a theoretical precursor for today's value-at-risk measures.

Related Internal Links
  

capital asset pricing model—an influential model that concludes that all investors should hold the market portfolio.

capital market line—a set of portfolios obtainable by leveraging or deleveraging positions in a "super-efficient" portfolio.

efficient frontier—a set of portfolios that each maximize expected return for a given level of risk.

hedging and diversification Two techniques for reducing a portfolio's risk.

market risk Exposure to the uncertain market value of a portfolio.


Related Books
  

The following books offer different perspectives on portfolio theory. Bernstein (1993) is a must-read history of finance during the 20th century. Body, Kane and Marcus (2004) is the standard university text on finance. For the practitioner's perspective, see Fabozzi and Markowitz (2002). Now a classic, Markowitz (1959) is Harry Markowitz's original book on portfolio theory.

Capital Ideas

Peter L. Bernstein

quality  

technical   
1993
  


Investments

Zvi Bodie, Alex Kane, Alan J. Marcus

quality  

technical   
2004
  


Theory and Practice of Investment Management

Frank J. Fabozzi and Harry M. Markowitz

 quality  

technical   
2002
  


Portfolio Selection

Harry Markowitz

quality  

technical   
1959
  




Cited Papers
  

Markowitz, Harry M. (1952). Portfolio selection, Journal of Finance, 7 (1), 77-91.

Sharpe, William F. (1964). Capital asset prices: A theory of market equilibrium under conditions of risk, Journal of Finance, 19 (3), 425-442.

Tobin, James (1958). Liquidity preference as behavior towards risk, The Review of Economic Studies, 25, 65-86.