SANTA MONICA, Calif., Jan. 25, 2005 (PRIMEZONE) -- Research announced today by Wilshire Associates Incorporated, a global leader in investment technology, investment consulting and investment management, concludes that conventional quantitative methods of portfolio analysis in wide use by fund managers can systematically understate the risks in both passively managed and actively managed investment portfolios.
"The biases are such that the standard deviation of return in a pension fund's equity portfolio may be understated by 40% or more. As a result, the excess value at risk for a conventional equity portfolio may be as much as five percent of the portfolio. For a typical individual investor with a $500,000 retirement nest egg, this could amount to an unintended exposure to loss of as much as $25,000 during a one year period," noted Robert Kuberek, a senior managing director at Wilshire Associates who supervises quantitative research and software development for the Equity Management, Fixed Income Management, Total Fund Management and Asset Allocation products offered by the firm.
To reduce or eliminate these kinds of biases in risk estimation, Wilshire Analytics, a business unit of Wilshire Associates that develops and markets asset allocation, risk management and accounting analytical solutions, has developed sophisticated, new technology and has incorporated it into the most recent versions of Wilshire's analytical systems provided to investment professionals, Mr. Kuberek said. Among the technology solutions utilizing the new technology are The Wilshire Atlas, The Wilshire Axiom, The Wilshire Spectrum and The Wilshire iQuantum, the next generation in analytical solutions.
Traditionally, portfolio managers estimate risk in a portfolio using the statistical notion of variance, a measure of randomness in the dispersion of payoffs that was pioneered in the 1950's by Nobel laureate Harry Markowitz. Since the mid-1970's analytics firms like Wilshire have used this powerful and highly successful idea to measure investment risk in institutional portfolios such as pension funds that focus on total return. Since the early 1990's, J. P. Morgan has used an essentially equivalent approach, characterized Value-at-Risk, for financial institutions such as banks and brokerage firms that focus on dollar exposure. Both approaches are based on the same underlying mathematics and measure essentially the same thing.
According to Mr. Kuberek, a critical step in the risk measurement process is estimation of the variances and covariances for the variables that drive changes in portfolio value. This set of numbers, arranged in an array called a matrix, summarizes the risk level of the underlying variables, taking into account the tendency of some of the variables to move together. Frequently, the matrix of variances and covariances is estimated using historical returns. However, he noted that when historical returns are used to estimate variances and covariances, noise in the particular sample employed results in errors in the estimated covariance matrix. This means that some of the sample covariances will be smaller, and some larger, than they really are.
"On average, these errors in the sample covariance matrix will tend to cancel: the sample covariance matrix is said to be an unbiased estimator for the true covariance matrix. However, if optimization is applied to the portfolio with the objective of minimizing risk, using the sample covariance matrix as an input, the resulting 'optimized' portfolio will almost always appear to be less risky than it really is: optimization tends to favor portfolios for which risk is underestimated," said Peter Matheos, Ph.D., a managing director at Wilshire and the lead researcher for this study. "The amount of the bias will depend on the number and magnitudes of the underlying true covariances and on the length of the historical sample used to estimate them."
"The tendency for optimization to result in portfolios for which estimation errors are greatest is known. However, what may not be as well appreciated is that even if optimization is not used to construct portfolios explicitly, it could often be the case that optimization is used implicitly. This would happen if in considering trades portfolio managers cannot resist the temptation to "peek" at their risk estimates," said Mr. Kuberek. "The tendency would be to attribute higher reward/risk ratios to trades which produce value-added at what appears to be low marginal risk. Since such trades appear attractive, chances are good that the trades will be executed, and the resulting positions will reflect a preponderance of the trades. However, unless the portfolio manager has a lot of data from which to estimate variances and covariances, what is "low risk" will likely depend on exactly the same covariance matrix that is used to report risk on the portfolio after the trades are done. This more insidious form of risk estimation bias may be less pronounced than in the case where optimization is used explicitly, but likely will still be present."
Using mathematics that have only been known for a few years, Wilshire's SHaPTSE estimator explicitly corrects for the bias in the estimate of portfolio risk that results from the use the sample covariance matrix. (SHaPTSE stands for Structured Hadamard Product Target Shrinkage Estimator.) The SHaPTSE estimator works by adjusting the sample covariance matrix in a way that takes account of things that are known (or can be assumed) about the true covariance matrix. In this respect, the SHaPTSE estimator resembles a Bayesian estimator.
"From the point of view of the ultimate investor, the issue is a technical one," Mr. Kuberek acknowledged. "However, it is a little like a computer virus: the technical details of how computers are infected with a virus and how a virus works are obscure to many of us, but the effects are obvious, and sometimes disastrous, to most of us."
"For investors the main concern likely will be the possibility of underestimating risk in the portfolio -- in particular, being caught off-guard by portfolios whose true risks are large but whose estimated risks are small. SHaPTSE directly addresses that possibility by optimally adjusting the measured risk in the portfolio and offering a better characterization of that risk. This is a material step forward in practical modern risk management," said Dr. Matheos.
About Wilshire Associates
Wilshire Associates is a leading global investment technology, investment consulting and investment management firm with four business units including Wilshire Analytics, Wilshire Funds Management, Wilshire Consulting, and Wilshire Private Markets.
The firm was founded in 1972 revolutionizing the industry by pioneering the application of investment analytics and research for investment managers in the institutional marketplace. Wilshire also is credited with helping to develop the field of quantitative investment analysis that uses mathematical tools to analyze market risks. All other business units evolved from Wilshire's strong analytics foundation. Wilshire developed the index now known as the Dow Jones Wilshire 5000 Total Market Index, the first asset/liability models for pension funds, the first U.S. equity style metrics work and many other "firsts" as the firm grew to more than 300 employees serving the investment needs of institutional and high net worth clients around the world.
Based in Santa Monica, CA, Wilshire provides services to clients in more than 20 countries representing in excess of 600 organizations with assets totaling more than $12.5 trillion. With eight offices on four continents, Wilshire Associates and its affiliates are dedicated to providing clients with the highest quality counsel, products and services. For more information go to www.wilshire.com