pension fund perspective: pension multiplier revisited

CFA Institute

Pension Fund Perspective: Pension Multiplier RevisitedAuthor(s): Michael KantorSource: Financial Analysts Journal, Vol. 44, No. 1 (Jan. - Feb., 1988), pp. 14-15+47Published by: CFA InstituteStable URL: http://www.jstor.org/stable/4479086 .

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Patrick J. Regan, VP, PENSION FUND PERSPECTIVE ~~~~~~~~~BEA Associates

Eleven years ago, Jack Treynor, Bill Priest and I wrote The Financial Reality of Pension Funding Under ERISA. The principal concept of that book was that ERISA had converted pension obligations into corporate obligations and that investors would have to utilize an "augmented" balance sheet approach in analyzing companies. Today this approach is widespread, with investment bankers looking for overfunded pension plans and reversions being commonplace.

A corollary concept developed in the book is the notion of the "pension multiplier" effect, which results from the fact that most

by Michael Kantor

Treynor, Regan and Priest have ar- gued that the stock market is becoming more volatile because most major corporations sponsor pension plans that hold common stock in other pension-sponsoring corporations.' When stock prices decline, the value of pension assets also declines, adversely af- fecting the future profitability of the sponsoring corporations. This reduces the stock prices of pension-sponsoring corporations, causing further declines in pension assets and creating a new round of stock price declines. When stock prices increase, the reverse is true.

The multiplier effect is becoming more significant as investors are be- ginning to consider how well pension plans are funded. FASB Statement No. 87 requires corporations to disclose more information about their pension obligations. In certain situations, corporations will have to include unfund- ed pension obligations on their balance sheets and possibly suffer a reduction in net worth. On the other side of the coin, corporations with overfunded pension plans have taken asset reversions. This has often caused

companies with pension funds tend to hold each other's stock in their pension portfo- lios. If pension assets are thought of as corporate assets, as in the augmented balance sheet approach, the sponsor's stock price should fall when the stock in the portfolio falls, assuming interest rates are unchanged. To the extent that the sponsor's pension assets are invested in the common stocks of companies that have their own pension funds invested in each other, a 1 per cent decline in the market will cause the sponsor's share price to drop by more than 1 per cent, the exact factor being the "pension multiplier."

Pension Multiplier Revisited

an increase in the price of their stock, especially when it has attracted the attention of corporate raiders .2 Treynor developed the "pension multiplier" to measure the impact of this vicious cycle. We reproduce the pension multiplier calculation for year-end 1974 and then recalculate it for year- end 1986. We will show that much of the improvement in pension funding ratios over these 12 years is illusory. This is because pension obligations were discounted at much higher rates in 1986 than in 1974, despite virtually identical prevailing interest rates.

Multipliers Then and Now

The Treynor multiplier is given by the following equation:

1.0 Multiplier = 1.0 (ie) = e/(e-l).

Here "1" is the present value of the vested liability less the value of the fixed income assets in the pension fund. (In other words, if bonds are held in a pension fund, the borrower is assumed to replace the pension sponsor as the one with responsibility for discharging that portion of the pension obligation.)

The definition of "e" is less straight- forward. Prior to ERISA, an employ-

Below, Michael Kantor shows how the pension multiplier has increased over the past decade and perhaps contributed to market volatility. In addition, he adjusts the interest rate assumptions and finds that they explain much of the improvement in funding ratios.

Michael Kantor is Vice President of SEI Corporation. He has written many papers in the field of portfolio theory, performance measurement and risk analysis. He is also an enrolled actuary and an Associate in the Society of Actuaries.

-P.J.R.

er's pension obligation was limited to the assets held in the pension fund. If these assets declined in value, the em- ployer had no obligation to make up for this shortfall. Thus the conventional definition of shareholders' equity ignored any provision for pension obligations. After ERISA became law, employers became liable for all pension benefits earned to date. If pension assets were insufficient, employees could look to corporate assets to satis- fy their claims. This led to the concept of augmenting the balance sheet with the pension assets and liabilities.

Treynor defined "new equity" to incorporate this augmentation, as follows:

New Equity = Conventional Eq- uity + Pension Assets - Pen- sion Liabilities.

However, pension assets invested in equities of companies that are not pension sponsors behave as conventional equity. Thus Treynor defined "adjusted conventional equity" as follows:

e = Conventional Equity + Pen- sion Assets Invested in Equities of Non-Sponsors.

The pension multiplier calculated at the end of 1974 was derived from the following data on the 20 most widely held corporations: 1. Footnotes appear at end of article.

FINANCIAL ANALYSTS JOURNAL / JANUARY-FEBRUARY 1988 O 14



Pension Assets = $21.7 billion Debt = 9.5 Equity (sponsors) = 6.1 Equity (non-sponsors) = 6.1

This breakdown was based on the assumption that 44 per cent of pension assets were invested in debt and that half the equity holdings were in pension-sponsor corporations.

Vested pension liabilities at that time totaled $29 billion. The market value of the 20 corporations equaled $145.8 billion. This would have been based on the new equity calculation, as ERISA was already in effect, making pension obligations into a corporate obligation. Transforming this equity value into its conventional equity equivalent and adjusting the liability figure for pension portfolio debt gives us the following values for the calculation of the pension multiplier:

Adjusted Liability = 1 = $29.0 - $9.5 = $19.5 billion,

Conventional Equity = $145.8 + $7.3 = $153.1 billion,

Adjusted Conventional Equity - e = $153.1 + $6.1 = $159.2 billion.

The original multiplier calculated by Treynor, Regan and Priest was thus:

1.0 e 159.2

1.0 - l/e e-l 159.2-19.5

= 1.14.

If all equity holdings were invested in pension-sponsoring corporations, we would not have to adjust conventional equity. However, the multiplier would change slightly, to 1.146.

Has the multiplier changed since the passage of ERISA? According to Pen- sions & Investment Age's reported se- lected financial statistics on the For- tune 100 as of December 31, 1986, pension assets can be broken down as follows:

Pension Assets = $273.9 billion Debt = 123.3 Equity (sponsors) = 105.4 Equity (non-sponsors) = 45.2

The allocation of pension assets is based on SEI's statistics showing that

approximately 45 per cent of pension assets are in fixed income securities. Also, among large plans in SEI's uni- verse, over 70 per cent of the equity holdings are concentrated in 260 corporations with capitalizations exceed- ing $2 billion. As virtually every major corporation sponsors a pension plan, we assume that 70 per cent of the equity portion of pension assets is invested in other sponsoring corporations.

For 1986, vested pension liabilities totaled $209.7 billion. The market value (new equity calculation) of the corporations equaled $770.2 billion. Con- ventional equity equaled $706.0 billion ($770.2 - $64.2). (Pension liabilities were overfunded by $64.2 billion; the conventional (unaugmented) equity is derived by subtracting the amount of overfunding.)

We thus have the following values to use in calculating the multiplier:

Adjusted Liability (1) = $209.7 - $123.3 = $86.4 billion,

Adjusted Conventional Equity (e) = $706.0 + $45.2 - $751.2 billion.

Calculating the new multiplier, we obtain:

e 751.2 = = ~~~~1. 13.

e-1 751.2-86.4

Discount Rate Dilemma The multiplier seems to have changed little over the past 12 years. There is, however, a major inconsistency be- tween the liabilities reported in 1974 and those reported in 1986. The discount rates used in 1974 were general- ly 5 to 6 per cent, compared with an average rate of 8.75 per cent in 1986. Yet prevailing interest rates were virtually identical at those points in time; the difference in discount rates is artifi- cial. There are two reasons why such different discount rates were used.

In 1974, sponsors were discounting at rates they perceived to be long-run rates of return. As they hadn't experi- enced the double-digit interest rates of the late '70s and early '80s, 5 to 6 per cent was a reasonable expectation. FASB No. 87 now requires sponsors to discount liabilities at prevailing market

rates, rather than long-run rates of return. Thus sponsors must value their liabilities at these higher rates.

We want to calculate a pension multiplier that is consistent with the earli- er calculation. Suppose we discount current liabilities at 6.50 per cent, rather than 8.75 per cent. This approxi- mates the Pension Benefit Guarantee Corporation's (PBGC) rates as of De- cember 31, 1986. The PBGC uses these rates to price liabilities of terminated pension plans. Assuming that vested benefits have an approximate duration of 12 years, reducing the discount rate by 2.25 percentage points increases the value of liabilities until it is virtually identical to the value of assets.

We can now recalculate the current pension multiplier, using the following values:

Pension Assets = Pension Liabil- ity = $273.9 billion,

Conventional (Unaugmented) Eq- uity = New (Augmented) Equi- ty = $770.2 billion,

Adjusted Liability (1) = $273.9 - $123.3 = $150.6 billion,

Adjusted Conventional Equity (e) = $770.2 + $45.2 = $815.4 billion.

The revised multiplier becomes:

e 815.4 = 1.23.

e-l 815.4-150.6

The pension multiplier is signifi- cantly greater today than at the time ERISA became law. This is because pension assets have grown from 15 to 35 per cent of the sponsoring corporation's market value.3 Over the past 12 years, pension sponsors have made significant contributions to their pen-. sion funds to comply with ERISA's funding requirements, to prefund for plan amendments and to cover actuar- ial losses due to unfavorable investment and salary-increase experience that occurred in the early 1980s.

Corporate pension funding ratios have not improved drastically over the last 12 years. The raw statistics suggest that corporate pension plans have gone from being underfunded to being overfunded. We have shown that much of this improvement in funding

Concluded on page 47.

FINANCIAL ANALYSTS JOURNAL / JANUARY-FEBRUARY 1988 El 15



index options on the S&P 100 or S&P 500 on one side of the market is limited to 15,000 contracts in the near maturity.'0 This limit severely reduces the interest of the largest investors in implementation of portfolio insurance with options.

Implications Under post-crash conditions, successful im-

plementation of a systematic dynamic strategy is more difficult, requiring a mixture of trading in the underlying spot assets, in futures and in options. Uncertainty about the level of trans- action costs, potential discontinuities in market prices and uncertainty in the regulatory environment increase the difficulty of predicting the outcome from any type of dynamic strategy. Understandably, the demand for portfolio insurance has fallen off. Moving forward, we are likely to see increased technological sophistica- tion and a more balanced variety of dynamic strategies in the future. E

Footnotes 1. See M. Rubinstein and H. Leland, "Replicating

Options with Positions in Stock and Cash," Fi- nancial Analysts Joumal, July/August 1981, p. 66.

2. The capital of program traders able to take arbitrage positions by selling stock they already owned was for the most part absorbed by positions taken prior to the crash. Other program traders who rely on short selling were largely shut out by the short-sale up-tick rule. In addition, trading delays substantially increased the risk of arbitrage-related transactions.

3. For a much more detailed analysis of single-price auctions, see Steven Wunsch's discussion in Kid- der, Peabody's Stock Index Futures commentary dated October 29, 1987.

4. See J. Cox and M. Rubinstein, Options Markets (Englewood Cliffs, NJ: Prentice-Hall, 1985), p. 86.

5. Prior to October 19, futures hedgers were re- quired to deposit $5,000 per contract; now the requirement has been raised to $15,000 per contract.

6. Compared with investors who buy and hold, buyers (sellers) of insurance adopt strategies that systematically transfer wealth toward (away from) risky assets and away from (toward) less risky assets as the relative values of risky assets rise (fall), and do the opposite as risky asset values fall.

7. Well before the crash, investors were moving in this direction by selecting longer-term policies (which also tend to moderate trading in the early years of the policy), but even these investors would be faced with taking extreme positions near the end of the policy. Some insurance ven- dors have attempted to replicate these more complex policies with minimum and maximum exposures, but potential clients seemed to prefer the simplicity of the more extreme forms of insurance.

8. Surplus is defined as the difference or the ratio of the market values of the assets and liabilities of the pension fund.

9. In a Black-Scholes environment, options are priced as if investors are risk-neutral. But, by their assumption, price movements are continu- ous. In discontinuous markets, it is possible that options may be priced relative to their underlying assets with built-in risk premiums. This could raise the market prices of most options above their Black-Scholes values.

10. The limits are 25,000 contracts irrespective of maturity. However, longer-maturity options have poor liquidity, and positions greater than 15,000 contracts must be reduced to that number when the options become the nearest maturity contracts.

Pension Fund Perspective concluded from page 15.

ratios is attributable to the higher dis- ally identical to those used in 1974. rates used in 1974, we find that pen- count rates being used today even When we discount current liabilities at sion assets barely cover the liabilities. though overall interest rates are virtu-

Footnotes

1. J. Treynor, P. J. Regan and W. Priest, The Financial Reality of Pen- sion Funding Under ERISA (Home- wood, IL: Dow Jones-Irwin, 1976).

2. According to ERISA, pension assets legally belong to the participants, not the sponsoring organization.

However, the sponsor derives eco- nomic benefit from these assets because gains (losses) reduce (increase) contributions, which come out of earnings. Also, corporations have terminated overfunded pension plans and taken asset reversions.

3. The sharp increase in bond and equity prices in recent years affects both pension assets and the market value of the sponsoring corporation. Thus it should have no major impact on this ratio.

FINANCIAL ANALYSTS JOURNAL / JANUARY-FEBRUARY 1988 0J 47



pension fund perspective: pension multiplier revisited

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