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Kamakura Corporation Named to World Finance 100

August 26, 2014
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August 18, 2014
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August 13, 2014
Liquidity At Risk – A stochastic look at cashflows

August 12, 2014
Five of Seven Regional Banks Trade at Credit Spreads Better than the Too Big to Fail Banks

August 12, 2014
Kinder Morgan Energy Partners Leads the 20 Best Value Bond Trades with Maturities of 10 Years or More

August 11, 2014
Measuring the Funding Costs of the Too Big to Fail Banks:
The U.S. Dollar Cost of Funds Index™

August 8, 2014
Forward 1 Month T-Bill Rates Plunge 0.26% in 2 Years but Forward 10 Year U.S. Treasury Yield Drops Only 0.04% from Last Week

August 6, 2014
Credit Spreads and Default Probabilities: A Simple Model Validation Example

August 5, 2014
Vodafone Group PLC: Default Risk is Down Sharply But Value Ranks in the Bottom 10% of Bonds

July 30, 2014
American International Group Inc. Bonds:
A Reward to Risk Ratio Twice as High as the Median Bond Issue

July 29,2014
AT&T Inc. Bonds: Ten Times the Risk of IBM and Below Average Value

July 15, 2014
Brazil, Italy, Spain, Credit Default Swaps and the
European Commission Short Sale Ban, 2010-2014

July 14, 2014
Bank of America and MBIA Lead U.S. Bank Credit Default Swap Trading Volume, 2010-2014

March 19, 2014
Stress Testing and Interest Rate Risk Models: A Multi-Factor Stress Testing Example

March 13, 2014
Stress Testing: A Credit Spread Ranking of 12 U.S. and 12 International Banks



Kamakura Blog

Jan 27

Written by: Donald van Deventer
1/27/2013 10:54 PM 

At a major risk management conference in Geneva in December 2002, Nobel Prize winner Robert C. Merton told this story before an audience of 400 risk experts:

“A major pension fund manager was approached by a Wall Street salesman who made this suggestion. ‘You have most of your portfolio in fixed income securities, yet your fund has a very long life.  If you shifted your entire portfolio to equity securities, you’d have more money in 40 years 99% of the time.’  The fund manager thought quietly for a moment and then replied, ‘Well, if you are right, your firm should be willing to write my pension fund a 40 year put option at its current market value for a very cheap price.  Why don’t you speak to your colleagues about the pricing on the put option?  If the pricing is as cheap as your story would lead me to believe, we’ll buy the put and make the portfolio shift that you suggest.”  Merton finished by saying “Of course, the pension fund manager never heard from the salesman again” and the audience burst into laughter.  Sadly, few adherents to conventional wisdom in the public pension fund arena understand this joke. In this blog, we explain why there is an immediate need to reform disclosure and risk management to protect voters, taxpayers and the beneficiaries of public pension funds.

Merton’s story illustrates one of the tried and true strategies of Wall Street firms: to get a naïve client to focus exclusively on expected returns and to ignore the relevant risks.  Merton’s audience laughed because they knew that portfolio insurance which would protect the market value of a common stock portfolio for 40 years would be enormously expensive because the risk of price declines is so great.  Indeed, after peaking mid-day at 38,957.44 on December 29, 1989, Japan’s Nikkei 225 stock price index traded today at 10,487, a full 73.1% below its peak value after a holding period of 23 years.  This translates into a 23 year annualized compound return on Japanese equities of MINUS 5.53%.

Unfortunately, an obsessive focus on expected return and inattention to risk management is typical in the public pension fund arena. The results have been disastrous, and they may well get worse.  This blog summarizes the reforms in disclosure and risk management of public pension funds necessary if fund beneficiaries and taxpayers are to be protected and if plan sponsors are to avoid bankruptcy.

There are notable exceptions to the conventional wisdom at public pension funds.  A number of public funds in Canada have been using leading-edge risk management techniques for more than a decade.  In the United States, Rhode Island General Treasurer Gina M. Raimondo has led the way in accurately analyzing the pension fund risk for the State of Rhode Island:

General Treasurer Raimondo’s white paper “Truth in Numbers” is a masterpiece that explains in plain English what went wrong in Rhode Island and how to fix it:

For most public pension funds in the United States, however, a candid assessment of the true state of public pension fund value and risk and a concrete plan to resolve the issues are nowhere to be seen.

Japanese Snow and “Public Pension Funds are Different”

In the late 1980s a Japanese Minister of International Trade and Industry ended his career by stating publicly that “Japanese snow is different, and foreign ski makers are incapable of delivering high quality skis to the Japanese market.”  In a similar way, probably with a similar outcome, long time participants in public pension funds and public pension fund consulting sometimes argue that the basic principles of finance and economics do not apply to public pension fund analysis and that “non-members” of the “public pension club” cannot possibly understand the rules that do apply.  Of course, that argument is nonsense.  The perception of differences stems from another fixation common in the sector, a focus on government accounting standards with no regard for true economics and true risk assessment.

Government Accounting Standards and Real Risk Management

In the banking and insurance industries, government bodies and accounting bodies specify a number of calculations: generally accepted accounting principles and required capital adequacy standards.  These calculations vary by geography and legal jurisdiction.  All regulated institutions conform to these requirements but they do not make the mistaken presumption that no other calculations are necessary or useful.  In fact, for the most part, calculations mandated by accounting bodies or government capital rules are not key calculations in accurately measuring the true risk and value of an institution.  In this blog

van Deventer, Donald R. “A 4 Question Pass/Fail Test on Risk Management for CEOs and Members of the Board of Directors,” Kamakura blog, www.kamakuraco.com, April 27, 2009. Redistributed on www.riskcenter.com, April 28, 2009.

we outlined four simple questions that a CEO and Board of Directors should be able to answer. The word “firm” should be taken to mean public pension fund and “net income” can be read as cash flow:

Question 1: What happens to the market capitalization and net income of the firm if any of these risk factors change: home prices, foreign exchange rates, commercial real estate prices, stock index levels, interest rates, commodity prices?

Question 2: Using an insider's knowledge of the assets and liabilities of the firm, both "on balance sheet" and "off balance sheet," what is the best estimate, monthly for the next ten years, of the probability that the firm will fail in each of these 120 monthly periods?

Question 3: Using only information available to an outsider, what is the best estimate of the probability of the failure of the firm in both the short run and the long run?

Question 4: If the firm is able to answer Questions 1, 2, and 3, what hedging position is necessary to insure that the macro factor sensitivity of the firm and default probability of the firm reach the target levels set by the Board of Directors?

True believers in the “public pension club” argue that public pensions are different because public bodies “exist in perpetuity.”  In fact, the bankruptcies of Orange County (1994), Vallejo (2008), Stockton (2012) and San Bernardino (2012) provide ample recent evidence to the contrary.  Kamakura Risk Information Services has proven that even sovereign entities fail at four times the rate of publicly listed corporations over the period from 1990 to the present.  A complete listing of the 31 municipal bankruptcies since January 1, 2010 is available here:

A second series of arguments by true believers of the public pension club is more basic.  They say the following:

a. Government accounting standards and state statutes require us to use expected returns to discount pension liabilities
b. Statutes require amortization of securities gains and losses and changes in actuarial assumptions in determining unfunded pension liabilities
c. The statutory calculation of unfunded pension liabilities drives the contribution of the sponsoring municipal entity.
d. We seek to outperform the mandated expected return
e. Therefore nothing else is required for risk management or disclosure purposes.


We agree that this is common practice among public pension funds. Unfortunately, it has led to serious impairment of the ability of public pension funds to meet their obligations to beneficiaries current and future.  We begin our explanation of why this is the case with a simple example for background.

A Simple Example of a One-Beneficiary Pension Fund

The riskiness of the common practice pension fund strategy is easiest to illustrate if we take one typical future beneficiary of “the fund.”  We call that beneficiary Ms. Thomas and assume the following stylized details:

Current Date

January 17, 2013


January 17, 1963

Age at Retirement


Pension Credit per Years of Service

2% of salary for each year

Employment Start Date

January 17, 1993

Pension Inflation Adjustment


Current Annual Salary


Assumed Real Salary Change (Percent)


Assumed Inflation Rate (Percent)


Date of Retirement

January 17, 2018

We assume that Ms. Thomas will not retire early, that she will not quit and that she will pass away at age 75.  We ignore all other variations in the pension scheme.

If our assumptions about the real and inflation components of her salary are perfect, her new salary level will be set on these dates, and the last salary level will determine her pension amount:

January 17, 2014


January 17, 2015


January 17, 2016


January 17, 2017


She will receive her pension at an annual rate of 25 years x 2.00% x $57,409, or an annual rate of $28,704.71. This is $2,392.06 per month starting on February 17, 2018 and ending on the 240th month, January 17, 2038.

Before retirement, Ms. Thomas and her employer will make contributions to the pension fund. We assume typical rates of 11% of salary by Ms. Thomas and 30% of salary by the employer.  This means that there will be 60 months of contributions at the rates starting on these dates:

February 17, 2013 


February 17, 2014


February 17, 2015


February 17, 2016


February 17, 2017


How much money will need to be in this one person pension fund when Ms. Thomas retires?  The naïve answer is that the answer depends on the expected return on the pension fund.  A more sophisticated reply would be that it depends on the risk level of the assets of the fund and the expected return at that risk level.  Let’s look at two different decisions by Ms. Thomas:

Case 1: “No risk” investment strategy
Case 2: 7.75% expected return investment strategy, risk is ignored

What if Ms. Thomas chooses to take the zero risk investment strategy?  Let’s assume that the U.S. government is riskless, even though trading in the credit default swap market on the United States of America indicates that is slightly optimistic.  This graph gives the continuously compounded yields to maturity that Ms. Thomas could earn as of January 17, 2013.


To match the maturity of the cash flows on her pension with U.S. Treasury investments, the pension fund would need to hold U.S. Treasury bonds with a market value equal to $419,435.10 on January 17, 2018.  In Case 2, there is an asset class with an expected return of 7.75% (we assume this is compounded monthly).  If we ignore the risk of this asset class and focus only on expected return, the value of assets that the pension fund needs to have is $291,884.44 on January 17, 2018.

Case 2 describes what the typical California public pension fund is doing now, with some slight variations we discuss below.  See Bornstein et al (2010), Nation (2010), Long (2013), and Storms and Nation (2012) for examples. What is wrong with Case 2?  In a nutshell, it’s a very dangerous strategy.  What if Ms. Thomas becomes uncomfortable with the asset class in Case 2 on January 18, 2013 and demands that the chief investment officer of the pension fund move 100% of the portfolio into U.S. Treasury securities?  If the rates for January 17, 2018 still prevail, an investment of only $291,884.44 GUARANTEES THAT THE FUND WILL DEFAULT ON ITS OBLIGATIONS TO MS. THOMAS UNLESS IT DECIDES TO ADD TO THE FUND. At the $291,884.44 level, full pension payments to Ms. Thomas will end in month 144 (on January 17, 2030) and there will be a partial payment in month 145 (on February 17, 2030).

The typical California public pension fund investment strategy is like the Hotel California.  You can check out but you can never leave.  You cannot change your mind and switch to a lower risk investment strategy without one of two things taking place: the bankruptcy of the fund or a large infusion of cash that was unplanned. Unlike General Treasurer Raimondo in Rhode Island, most public pension funds in California do not have estimates of (a) when they will run out of cash and (b) how much additional asset value is needed today to reduce the risk of failure to zero.

We now turn to a more formal summary of the risk management problems and disclosure problems of the typical public pension fund.

A Summary of Risk Management Problems at Public Pension Funds

Our simple example in the previous section shows clearly that the typical public pension fund has fallen victim to the Wall Street salesman in the Robert Merton story.  They have provided assets to the fund on the basis of an expected return that is in fact uncertain, and that decision has left the funds facing certain bankruptcy if they shifted to a low risk strategy without a huge injection of additional funds.  In this section, we briefly list the risk management decisions that have left the funds in this position.  We close the section with suggestions on additional disclosure which would make the true risk of the funds more apparent to beneficiaries, taxpayers and voters.

Problem 1: Management of the pension funds has focused on the asset side and ignored the liabilities of the fund in setting a “benchmark portfolio.”

The example above shows that that true zero-risk benchmark is the portfolio of U.S. Treasury securities that meets the fund’s obligations with 100% certainty.  This is the investment strategy of the U.S. Social Security Administration.  King and Soneji (2012) and the Annual Report of the Trustees (2012) have shown that, even with a zero risk investment strategy, the Social Security fund has been underfunded and will run out of funds in the 2031-2033 time period.  In large part this due both to consistent intentional underfunding and to unhedged longevity risk that we discuss later.  One of the largest university endowments in the United States also ignored the potential liabilities of the endowment in setting its benchmark portfolio.  In 2006, I asked the chief risk officer of the endowment, “Did you ask the university to outline the cash flows that they expect to withdraw from the endowment in the years ahead?”  The answer was “Well, we probably should have talked to them but we didn’t.” After the crash in 2008, the university endowment began explicitly incorporating its implicit liabilities to the university in its benchmark planning.

Problem 2: Management’s defined benchmark is a high risk benchmark, and the risk of that strategy has received minimal disclosure.

The pension funds are using 100% borrowed funds.  Typically less than 25% of the fund’s assets are in fixed income instruments that match the interest rate risk characteristics of its obligations to pension beneficiaries.  The funds, effectively, are operating with zero equity and 100% margin with 75% of their assets in the form of common stock, hedge fund investments, commodities, venture capital and other high risk investments. This level of leverage is extraordinarily risky:

  • It is prohibited to commercial banks by regulators

  • It is prohibited to insurance companies by regulators

  • It would be prohibited to the pension beneficiaries if they sought to implement this strategy as individual investors

Problem 3: Management’s high risk investment strategy involves the highest fees to fund management firms, since hedge funds, venture firms and common stock funds charge much higher management fees than managers of more conservative fixed income funds.

There is no need to elaborate here.   Not a single hedge fund investment would be approved if put to a vote of the pension beneficiaries with full disclosure of the fee schedules and the compensation of the hedge fund’s top management.

Problem 4: Management’s statutory valuation of liabilities makes no economic sense, and a correct valuation for risk purposes should be done frequently but usually it isn’t done at all.

Nation (2010), Bornstein et al (2010), Long (2013) and Storms and Nation (2012) explain this at length.  The lack of integrated asset and liability management of public pension funds, common practice in banking for 45 years, is astonishing.

Problem 5: Mortality rates used in valuing liabilities are based on long historical time series averages and don’t reflect current mortality rates.

King and Soneji (2013) summarize this problem at the Social Security Administration: “Remarkably, since Social Security was created in 1935, the government’s forecasting methods have barely changed, even as a revolution in big data and statistics has transformed everything from baseball to retailing. This omission can be explained by the fact that the Office of the Chief Actuary, the branch of the Social Security Administration that is responsible for the forecasts, is almost exclusively composed of, well, actuaries — without any serious representation of statisticians or social science methodologists. While these actuaries are highly responsible and careful and do excellent work curating and describing the data that go into the forecasts, their job is not to make statistical predictions. Yet the agency badly needs such expertise.”

King and Soneji (2013) continue: ”...the Social Security Administration underestimates how long Americans will live and how much the trust funds will need to pay out — to the tune of $800 billion by 2031, more than the current annual defense budget — and that the trust funds will run out, if nothing is done, two years earlier than the government has predicted.”

At least the Social Security system has a relatively precise estimate of their default date.  The same cannot be said of most public pension funds.

Problem 6: Public Pension Fund Boards have a conflict of interest in setting the expected return on their funds.

By leaving the expected return on their funds at levels from 7.75% to 7.25%, well above reasonable low risk return levels, the boards of public pension funds lower the statutory valuation of their liabilities and minimize the amount of perceived underfunding.  These high expected returns “kick the can down the road” rather than dealing with the problem while it is still manageable, as Kotlikoff and Burns (2012) passionately recommend.

If returns fall below the target, disaster is just around the corner.  The 23 year compounded return on the Japanese Nikkei 225 stock index is MINUS 5.53%, and anyone who assumes it can’t happen in the United States has ignored the parallel drops in residential real estate in the two countries.

Another critical problem with the setting of expected returns is that the estimation of the risk premium over the risk-free rate of interest, given the fund’s risk profile, is an unsolved problem in financial theory.  A Board of Directors has no established, consensus methodology to rely on, as Jarrow (2012) explains:

“Estimating such a risk premium is a non-trivial exercise. It is equivalent to estimating the expected return on [all assets in the portfolio], a procedure that requires an equilibrium asset pricing model including a complete specification of the economy. Financial economists, over 50 years after the initial discovery of the capital asset pricing model, still have not reached a consensus on how to do this… Indeed, the estimation of the risk premium is very difficult. The reason for this difficulty is that the empirical finance literature has documented that risk premiums are nonstationary. They vary across time according to both changing tastes and changing economic fundamentals. This nonstationarity makes problematic both the modeling of risk premiums and their estimation.”

Problem 7: Assuming expected returns are achievable leads to wasteful transactions like pension obligation bonds.

A January 2013 issuance of pension obligation bonds was accompanied by a press release arguing that $20 million of pension costs were saved because the fund gave a discount to the plan sponsor at 600 basis points higher than the market yield on the pension obligation bonds for early payment of pension expenses to the fund.  The fund, in effect, drank its own Kool-Aid.  The net result was simple: $20 million of value was transferred from the pension fund to the sponsoring municipality, and $600,000 was wasted in underwriting, legal and other expenses of the bond issue.  It is hard to imagine that a well-informed board would have approved such a transaction.  See Munnell (2010) for more on the problems of pension obligation bonds.

Problem 8: High default risk equities under-perform low default risk equities, but default probabilities are almost never used in asset selection and risk analysis.

Campbell, Hilscher and Szilagyi (2008, 2011) show persuasively that high default risk equity portfolios under-perform low default risk portfolios by all standard measures of risk-adjusted performance.  In spite of that, the typical public pension fund completely ignores default probabilities in asset selection and risk management.  They still rely on legacy credit ratings, even though the government’s banking regulations now define “investment grade” in terms of default probabilities, not ratings.

Where are we now?

Nation (2010) nicely summarizes the high risk positions that most independent public pension funds in California find themselves in today.  At realistic discount rates for pension liabilities, the true economic unfunded actuarial liabilities are multiples of the statutory calculation (“UAAL”), and there is a very high risk of failure of many funds without extraordinarily favorable market conditions or a major injection of funds:


Enhancements in Risk Management and Disclosure are Essential to Solving the Public Pension Fund Problems

Early in this paper, we discussed the short job tenure of the Japanese cabinet minister who denied that foreign skis would be of use in Japan.  In a similar way, traditional approaches to the management of public pension funds have failed and an injection of more modern analytical methods and financial disclosure are essential to solving the current public pension fund problems:

  • A regular mark to market of liabilities should be done using best practice financial economics and modern mortality forecasting as in King and Soneji (2012, 2013)

  • Liabilities of the pension fund should define the benchmark for asset management purposes, not vice-versa

  • Daily risk analysis and reporting is essential. This risk analysis should include valuation of all assets and liabilities, projections of cash flows, stress testing, value at risk, and simulations that address the four key questions that the pension fund CEO and Board of Directors should be able to answer below.

  • Detailed solvency analysis should be reviewed with the Board monthly and communicated explicitly to the beneficiaries just as the Trustees of the Social Security system do in their annual reports (2009-2012)

  • Fund management should explicitly model the high fee levels on current high risk asset classes and the impact of these fees on historical and simulated returns

  • Fund management should terminate the use of pension obligation bonds, which are a form of welfare for lawyers and municipal bond underwriters

  • The fund should make complete disclosure to voters, taxpayers and pension fund beneficiaries on an economic basis, not just on a statutory basis

  • Liability analysis should be done at the individual beneficiary level at frequent intervals by the fund itself.  An annual actuarial review is insufficient to solve the current problems with speed and accuracy.

For more information and a copy of the example used for Ms. Thomas, please contact us at info@kamakuraco.com.

Donald R. van Deventer
Kamakura Corporation
Honolulu, Hawaii
January 29, 2013

Copyright © 2013 by Donald R. van Deventer. All Rights Reserved.


Board of Trustees of the Federal Old-Age and Survivors Insurance and Federal Disability Trust Funds, “The 2012 Annual Report of the Board of Trustees of the Federal Old-Age and Survivors Insurance and Federal Disability Trust Funds,” U.S. Government Printing Office, 2012.

Board of Trustees of the Federal Old-Age and Survivors Insurance and Federal Disability Trust Funds, “The 2011 Annual Report of the Board of Trustees of the Federal Old-Age and Survivors Insurance and Federal Disability Trust Funds,” U.S. Government Printing Office, 2011.

Board of Trustees of the Federal Old-Age and Survivors Insurance and Federal Disability Trust Funds, “The 2010 Annual Report of the Board of Trustees of the Federal Old-Age and Survivors Insurance and Federal Disability Trust Funds,” U.S. Government Printing Office, 2010.

Board of Trustees of the Federal Old-Age and Survivors Insurance and Federal Disability Trust Funds, “The 2009 Annual Report of the Board of Trustees of the Federal Old-Age and Survivors Insurance and Federal Disability Trust Funds,” U.S. Government Printing Office, 2009.

Bornstein, Howard, Stan Markuze, Cameron Percy, Lisha Wang, and Moritz Zander, “Going for Broke: Reforming California’s State Pension System,” Stanford Institute for Policy Research, May 13, 2010.

Campbell, John Y., Jens Hilscher and Jan Szilagyi, "In Search of Distress Risk," Journal of Finance, December 2008, pp. 2899-2939.

Campbell, John Y., Jens Hilscher and Jan Szilagyi, "Predicting Financial Distress and the Performance of Distressed Stocks," Journal of Investment Management, 2011, pp. 1-21.

Davis, Roger, “An Introduction to Pension Obligation Bonds and Other Post-Employment Benefits, Third Edition, Orrick, Herrington & Sutcliffe LLP, 2006.

Jarrow, Robert A. “Problems with Using CDS to Infer Default Probabilities,” Journal of Fixed Income, 21 (4), Spring 2012.

King, Gary and Samir Soneji, “Statistical Security for Social Security,” Harvard University Memorandum, 2012.

King, Gary and Samir Soneji, ”Social Security: It’s Worse Than You Think,” New York Times, January 5, 2013.

Kotlikoff, Laurence J. and Scott Burns, The Clash of Generations: Saving Ourselves, Our Kids, and Our Economy, MIT Press, Cambridge, MA., 2012.

Long, Cate, “Pension reform: Litigate, negotiate or go bankrupt,” www.reuters.com, January 11, 2013.

Munnell, Alicia H., Thad Calabrese, Ashby Monk, and Jean-Pierre Aubry, “Pension Obligation Bonds: Financial Crisis Exposes Risks,” Center for Pension Research, Boston College, January 2010.

Nation, Joe, “The Funding Status of Independent Public Employee Pension Systems in California” Stanford Institute for Economic Policy Research, November 2010.

Raimondo, Gina M. “Truth in Numbers: The Security & Sustainability of Rhode Island’s Retirement System,” Office of the General Treasurer, State of Rhode Island, June 2011.

Storms, Evan and Joe Nation, “More Pension Math: Funded Status, Benefits, and Spending Trends for California’s Largest Independent Public Employee Pension Systems,” Stanford Institute for Economic Policy Research, February 21, 2012.