>> This series is available on the Internet at http://socrates.berkeley.edu/~schwrtz
 
 

After a lengthy somnolence, the UC President has directed his top staff to review and respond to my published critiques of last year's "Investment Strategy Study", which was produced for The Regents by the consultants from Wilshire Associates Inc.

In this paper I will present a recent exchange of letters, show and evaluate the responses provided so far, and report a newly discovered discrepancy in the outside experts' calculations of the future fiscal health of the University of California's $40 Billion Retirement Fund.
 
 

During October, a series of short papers, titled "What's Happening with the Pension Fund? - Parts 1-5", was produced, circulated to regents and others throughout the University and posted on the internet site http://socrates.berkeley.edu/~schwrtz. This independent analysis examined the "Investment Strategy Study - March 16, 2000" (also called the "Wilshire report") which was officially adopted by The Regents last year as their new policy on investments. A large number of serious flaws were found in the Wilshire report, including:

On this basis, one is drawn to severe conclusions about the competence and the integrity of Wilshire Associates; and these conclusions, if not rebutted, reflect badly upon the fiduciary performance of The Regents. These are whistleblower critiques, not based upon personal opinions about what may be good or bad investment strategies. The flaws in the Wilshire report are of their own making - errors in math and logic, and a glaring lack of objectivity. However embarrassing it may be for The Regents to acknowledge mistakes, trying to ignore them is worse.

Starting September 1, I wrote several times to President Atkinson with specific questions, complaints and requests for further documentation in connection with this independent analysis of the Wilshire report. The only response has been one letter from Vice President Mullinix, in which he promised that answers and assistance would be forthcoming. Alas, none of that has materialized. Lacking any shred of rebuttal - from the UC President's Office, from any regent, or from Wilshire Associates - I believe that this extensive critique stands validated.

The current agenda for The Regents includes consideration of contract renewal for a General Investment Consultant; and I hope that Wilshire Associates will not even be considered for that job without a satisfactory response to these criticisms.

Sincerely yours,
Charles Schwartz
Professor Emeritus

This letter was sent by mail and also presented in person at the regents' meeting on January 17, to no apparent effect. A while later, however, I received the following letter from the University Auditor, Mr. Patrick Reed, with some encouraging news.

Your letter of January 8, 2001 to the members of the Board of Regents has been forwarded to me. This response is not intended to provide answers to the various questions you have posed for several months but to advise you of the University's intended course of action in relation to your requests.

I have reviewed the history of correspondence referred to in your January 8th letter and additionally, have downloaded and read your five part series regarding pension plan matters, principally the Wilshire asset allocation plan. In addition, I have made inquiries of those to whom your questions and correspondence have been referred in the past.

I am informed that it continues to be the University's intent to provide additional information and responses that will attempt to address the questions and concerns you have raised. Senior Vice President Joseph Mullinix is coordinating that effort, with support from the Treasurer's Office and input from Wilshire Associates as to certain technical matters and calculations.

I expect that you will be hearing from the University in the near future. I hope this process can clarify and resolve the matters in question.

Sincerely,

Patrick V. Reed
University Auditor

cc: President Atkinson
Senior Vice President Mullinix
Vice President and General Counsel Holst
Interim Vice President and Treasurer Bowman

Next comes a letter (dated February 15, 2001) from UC's Senior Vice President Joseph P. Mullinix, which transmits Wilshire Associates' response to three issues I had raised in my earlier papers; and this new material will be studied below. The rest of Mullinix' letter is hardly more than a parade of platitudes, addressing none of the particular issues I have raised; so I have put it elsewhere on my website for any interested readers. ( Mullinix1 )
 
 

I had charged that Wilshire made errors in basic arithmetic when they calculated values of the Expected Returns for the alternative asset allocation policies considered in their Study. (See my paper: Part 2, "Step Zero". I note a typographical error in this citation: the fourth word in the second sentence of the first paragraph should be "Return" and not "Risk".)

There is a standard textbook formula for calculating the expected return E(r) for a portfolio composed of several different classes of assets (US stocks, non-US stocks, bonds, etc.):

                        E(r_p) = S_i w_i E(r_i)                                               Equation (1)

where w_i are the weights for each asset class. My notation here is taken from the widely used textbook, "Investments," by Bodie, Kane and Marcus. For later reference, I'll also write down the companion formula for the variance (variance equals the square of the standard deviation, s) for such a portfolio:

                        s_p² = S_i S_j w_i w_j Cov(r_i,r_j)                               Equation (2)

I had used Equation (1) in checking Wilshire's numbers. I also had confirmation from some academic experts I had spoken with that this was the correct formula to use and that Wilshire's results appeared to be in error. Here, now , is Wilshire's response.
 

"Mr Schwartz is confused because the expected returns for Alternative Asset Policies (Exhibit 5 of March 16, 2000 Investment Strategy Study) are not a simple weighted-average of the individual asset class returns (Exhibit 4). The calculation, unfortunately, is somewhat more complicated because the individual asset class expected returns are "geometric" means rather than "arithmetic" means. As a result, it is incorrect to arithmetically weight geometric means. The proper calculation first involves converting the geometric returns to arithmetic; take the weighted-average of arithmetic asset class returns; and finally convert to geometric returns. The conversion formula is straightforward. The geometric mean equals the arithmetic mean minus one-half the variance. While this may sound unnecessarily complicated - after all, why not just give arithmetic forecasts - the arithmetic returns overstate likely future returns. That is why the investment industry uses geometric averages. For example, performance measurement relies upon geometric, not arithmetic returns."

Whether or not I was confused before, I am certainly confused by this response from Wilshire Associates. It would help if they had given some mathematical definitions or some reference to an authoritative book or other publication. The best sense I can make out of the paragraph above is that they are talking about how to compound the returns on any investment over a number of years in order to calculate the "annualized return." That is a standard calculational procedure. (Wilshire's formulation, "The geometric mean equals the arithmetic mean minus one-half the variance," is an approximation to the exact formula.) But the compounding of sequential returns is a very different process from the combining of simultaneous returns due to the various components of a given portfolio. (The question of how often one rebalances the portfolio, if not once per year, may affect the calculation somewhat; but Wilshire says nothing about this issue.)

As it stands, Wilshire's Response #1 appears to be either unintelligible or wrong.
 
 

After finding the error in Wilshire's calculation of Expected Returns, just discussed, I had wanted to check their calculation of Expected Risk (standard deviation) for the same portfolios. The input data needed for that calculation was not given in the Wilshire Report and so I had written to them requesting the pertinent data. (See the correspondence, from last September, shown in Part 2, "Step Zero".) Now, at last, we get that data from Wilshire.
 

"Mr. Schwartz also wants to see Wilshire's individual asset class risk assumptions so he can verify the risk forecasts Wilshire Uses for the Alternative Asset Policies in Exhibit 5. Those risk calculations come from our 2000 Asset Allocation Assumption Report. Those risk and correlation forecasts are attached as a separate file."

The original calculation by Wilshire was based upon their data Assumptions as of June 30, 1999; while the data they have sent me now are effective as of December 31, 2000. Comparing this new data with the data in Exhibit 4 of Wilshire's previous Study, I see changes (amounting to 0.5% for each asset class) in the Expected Return numbers. However, assuming that the Risk data (standard deviations and correlation matrix) have not changed, I can do the calculation to get the standard deviation for each portfolio, using Equation (2) presented above.

The result: My calculations agree very well with the Expected Risk numbers given by Wilshire in their Exhibit 5. How nice that we can agree on something!

Since this agreement seems to confirm that I am using the correct formula for calculating Expected Risk, it supports the idea that my formula for Expected Return (which is based upon the same mathematical model) is also correct. That is, the agreement here serves to reinforce my position in the previous dispute.
 
 

One of my sharper criticisms was that the Wilshire Study was very misleading in its assertion that investment returns "are more predictable over 20 year periods than any individual year." (See my Part 1, just before "Conclusions".) Here is Wilshire's response.
 

"Mr. Schwartz objects to Wilshire's characterization of stocks as being less risky over long time periods. He correctly points out that "accumulated uncertainty gets larger the farther into the future." But Wilshire's point is that stock performance, relative to bonds, becomes less risky so that a higher stock allocation is warranted the longer the time horizon. That notion is general industry gospel."

This new explanation simply does not fit the facts. Here is the quotation from the Wilshire Study which I said, "appears to be very misleading to an average reader":
 

"A number of academic studies examining the 200 year history of the U.S. financial markets have shown that equity and bond returns are more predictable over 20 year periods than any individual year." (emphasis added)

This quotation is clearly not about contrasting stocks v. bonds, as Wilshire's new explanation claims. This quote explicitly puts equity and bond returns on the same footing in making their claim about greater predictability over long periods of time. Also, one can check the original context of this quotation - See page 6 of the Wilshire Study, "Investment Assumptions" - and see that their new explanation is baloney.
 
 

What is the score, for now, on the responses to my earlier criticisms of Wilshire's work? Out of three items covered so far, one is satisfactory and two are very unsatisfactory. One can only wonder at this point whether the failures are due to simple incompetence (or perhaps due to some failure to communicate clearly) or are part of a clumsy attempt by Wilshire to cover its previous mistakes by deliberate obfuscation.

I also wonder about UC's Senior Vice President Joseph Mullinix, who transmitted Wilshire's responses to me with this added comment,
"Hopefully this will assure you that the recommendations made in the study were soundly based."
He is reputed to be knowledgable on investment matters and should have easily seen the shortcomings in the responses provided by Wilshire. The net result is that my confidence in Wilshire had sunk even lower than it was before.

But it is still too early for a final judgment. There are many more issues that have been raised and not yet answered at all; and I wait to see what UC officials will have to say next.
 
 

As we all know, the excellent investment performance of UCRP over the past several years has left it with an enviable surplus and the University has been interested in making good use of that money. In January, The Regents approved a couple of policy changes that provide increased benefits for some old and new retirees; and these changes were judged to be very safe based upon a detailed quantitative study performed by the University's actuary, Towers Perrin, Inc.

A summary of the data presented by Towers Perrin is shown in Table 1. Working with a statistical model that explores predictions of the financial climates over the next 20 years, they calculate the expected ratio of Assets to Liabilities for the UC Retirement system. In the second part of Table 1 I have put, for comparison, the results of a similar calculation done by Wilshire Associates last year (from Exhibit 9 of their Study).
 
 

Towers Perrin's Forecasts of UCRP Assets/Liabilities  (page 13 of 1/01 report)

Year	2000	2004	2009	2014	2019
Ratio	154%	176%	184%	191%	204%	Net Change = + 50%

 

Wilshire's Forecasts of UCRP Assets/Liabilities  (page 10 of 3/00 report)

Year	2000	2005	2010	2015	2020
Ratio	170%	156%	140%	126%	118%	Net Change = - 52%

There are some minor differences in the two companies' methods which are readily noted: Towers Perrin starts with a more modest initial value of UCRP assets; Wilshire's dates are one year later; Wilshire calculates the ratio of the expected values of assets and liabilities projected separately while Towers Perrin calculates the expected value (mean) of the ratio assets/liabilities projected for each statistical scenario. Thus, some minor differences between the two sets of results are to be expected.

What we see in Table 1, however, is a huge discrepancy between the two sets of experts' forecasts. Over the next 20 years:

I was present at the regents meetings in January when the Towers Perrin report was presented. The Towers Perrin representative acknowledged the close relation between their work and Wilshire's study; and the Wilshire representative affirmed that their two sets of calculations were based upon consistent assumptions. Nobody seemed to be aware of this huge discrepancy in their results.

Several days after that regents' meeting, I wrote to UC officials pointing out this problem and I have since been assured that it is being looked into (although my requests to meet with competent officials to discuss this problem have been ignored). Now, more than two months later, I have still gotten no substantive response.

This is a very serious situation. It poses doubts about the reliability of some very prominent consulting firms, the competence of UC finance officials, the fiduciary responsibilities of The Regents, and, of course, the soundness of the current plans for managing the University's pension fund.