Dr. Krzysztof Ostaszewski, FSA, CFA, MAAA Actuarial Program Director Illinois State University, Normal, IL , U.S.A.

Transcription

1 Dr. Krzysztof Ostaszewski, FSA, CFA, MAAA Actuarial Program Director Illinois State University, Normal, IL , U.S.A. Hans-Joachim Zwiesler Sektion Aktuarwissenschaften University of Ulm D Ulm, Germany The German State Pension System in relation to German Capital Markets Abstract The state pension system in Germany is one the largest social insurance systems in the world, and an important instrument of public policy. In this work we analyze it also as a part of the overall market of capital assets. This perspective is largely ignored in the existing literature on the system. In this work, we look at the capital assets created within the system and how their pricing by the system relates to the capital markets within the private sector. The first author has completed this research while holding a visiting position at the University of Ulm.

2 Introduction. One of the fundamental concepts of financial economics is that of a financial asset, also known as capital asset, or security. Bodie, Kane and Marcus (1999) discuss it. They note that the wealth of a society is determined ultimately by the productive capacity of its economy, i.e., the goods and services that can be produced. This productive capacity is derived from the real assets of the economy, i.e., the land, buildings, machines, and knowledge, which are used in the entire production process. On the other hand, wealth produced with the use of real assets is claimed through financial assets. Financial, or capital, assets are defined as such claims to the output. Their existence allows consumers to exchange current consumption for future consumption. Current income not consumed and instead used to purchase a capital asset is effectively exchanged for the future claims derived from that asset. Standard examples of capital assets include stocks and bonds issued by corporations seeking financing for their operations. Other capital assets are mortgages, government bonds, and assets created by financial intermediaries, such as bank deposits or annuity contracts. The last three decades saw an unprecedented growth in derivative securities, which have their cash flows derived from cash flows of primary securities listed above. Examples of derivative securities include options, futures, collateralized mortgage obligations, swaps, etc. Determination of the market price, and the market rate of return, of capital assets, and derivative securities in particular, has been the central issue in modern financial theory, with central roles played by the Capital Asset Pricing Model (Sharpe, 1964, Lintner, 1965, and Mossin, 1966), Arbitrage Pricing Theory (Ross, 1976), and the option valuation theory (Black and Scholes, 1973, Merton, 1973). All of the pricing methodologies indicate that capital assets, defined as rights to future income produced by real assets, have values determined by a systematic, dynamic market process. Marketable capital assets coexist with other entities within the national economy, which provide future income streams. For example, education is an investment in human capital, resulting in the creation of a future income stream. This paper is concerned with another mode of acquisition of future income stream, in the form of state pension benefits. Rights to future pension benefits, usually related to wages, can be acquired in Germany within the national system of social insurance for retirement, disability and death. This is a defined benefit pension system. While participants in defined benefit systems acquire their pension rights on a group basis, their benefits are individual. Other (marketable) capital assets are purchased with a current income expenditure on individual basis. From the economic standpoint, the price paid for a capital asset is the current consumption foregone in return for future consumption acquired. While on the apparent monetary basis the funding for the pension system is obtained from group premium paid, the individual worker pays for future benefits with current consumption foregone, i.e., on an individual basis. In this work we study the relationship of marketable capital assets obtained with direct monetary payments to non-marketable pension benefit rights, obtained with indirect payment through consumption foregone.

3 We will term the capital asset held by pension system participants, paid for with consumption foregone, and sold for benefits received, the pension system participation. We want to ask two key questions: - How does the price of pension system participation compare with prices of comparable marketable capital assets? What is the role of pension system participation in the context of personal investment portfolio choices? - If there are significant discrepancies between the price of pension system participation and marketable capital assets, what would the effect of such a situation be on the capital markets and the pension system, or the national economy in general? In particular, the recent debate about pension system reform has included many arguments about the rate of return realized by the system participants. This work proposes evaluating such a rate of return in an organized, systematic fashion, in the context of a portfolio of other investments available to participants. 1. Pricing Pension System Participation. In the seminal paper that began the science of modern finance, Markowitz (1952) pointed out that pricing capital assets is tacitly linked not only to rates of return earned by such assets, but also to the uncertainty of the return. The term risk encompasses such uncertainty. Technically, risk of a capital asset is a measure of uncertainty of utility of future consumption provided by such asset, and it is only the marginal utility of future consumption specifically provided by the said asset that matters. But in practice we usually settle for the standard deviation of the rate of return as the measure of risk, as in the work of Markowitz (1952). The Capital Asset Pricing Model (see Sharpe, 1964 and Lintner, 1965, also Bodie, Kane and Marcus, 1999) added a new perspective to risk measurement. In CAPM only the systematic risk, and not the security specific risk, is the measure of risk which affects the rate of return. The systematic risk is the overall market risk remaining after all of the security specific risk has been eliminated through diversification. In CAPM it is measured by security s beta, defined as the ratio of the covariance of that security s return with the return of the market to the variance of the return of the market. The rate of return is modeled as a random variable, whose expected value is a measure of return. Our interest lies in understanding the rate of return earned by participants in a social insurance retirement system. When analyzing such rate of return, several approaches have been proposed. One could, for example, calculate the internal rate of return for an identifiable group of participants. This approach has all the known problems of using the internal rate of return for comparing financial projects, and it is widely rejected in finance. Another alternative is to discount the cash flows using certain market rates, and calculate the money s-worth for participants (Myers and Schobel, 1992, give a very comprehensive presentation of this methodology). Martin Feldstein (see, for example, Feldstein and Liebman, 2001/2002) has consistently argued that in the long run a pay-as-you-go system can only offer retirees the rate of return corresponding to the rate of growth of the economy, derived from work force growth plus productivity growth. What we propose here is a variation on Feldstein s idea. Samuelson (1958) analyzed the stable-state relationship between present and future consumption in relation to the rate of growth of the economy. Samuelson s

4 analysis implies that the natural rate of return within a social insurance retirement system is the overall rate of growth of payroll tax receipts. Let us try to explain this reasoning within the simplest context of a stable population. Social insurance is designed as a payas-you-go system, which in its steady state pays out all of its receipts in benefits. Assume that a stable population has a natural growth rate of r, with constant wages and all workers working from age 25 and retiring at age 65. Let the payroll tax rate be set at a constant amount π, and the pension system be designed to function on a pay-as-you-go basis, with each beneficiary receiving a unit benefit continuously from age 65 to death. Then (Keyfitz and Beekman, 1984, Chapter 3) the payroll tax premium is: = where ω is the limiting age, and l x is the population aged x. On the other hand, if instead of pay-as-you-go the system was funded with marketable securities having earned exactly the rate δ, then the continuous annual premium, which pays for a unit benefit payable continuously for life, starting at age 65, is = e rx l x dx, e rx l x dx e x l x dx, e x l x dx and since these are essentially the same payments and benefits, the rate of return for a pay-as-you-go participant is exactly the rate δ earned by the marketable alternative, which must equal the rate of growth r. As Keyfitz and Beekman (1984) astutely observe, this simple observation generalizes naturally to a situation when the population is replaced by the taxable payroll, and growth observed is calculated on an after-inflation basis, so that the continuous life annuity paid in benefit is a real annuity, constant only after inflation adjustment. This, of course, assumes a constant payroll tax rate. Effectively, the rate of return becomes the rate of growth of payroll tax collected. Admittedly, pension system participation is not a marketable security, and its payments are, for current workers, deferred into the very distant future. Furthermore, participants do not have any choice about the purchase, and cannot directly trade their benefits. What this traditional perspective misses is that while pension system participation security may not move in price towards other capital assets, other capital assets can, and will, move in response to statutory pricing of pension system participation. The Arbitrage Pricing Theory (Ross, 1976, see also Panjer, 1997) shows us that any set of future cash flows, if it can be replicated by marketable sets of cash flows, is priced by the market. The dynamics between pension system participation and private retirement annuities and securities markets are somewhat similar to the relationship that the Federal Reserve s monetary policy (or any central bank s monetary policy) has with the bond market in dealing with interest rates, or the Federal Reserve and the Treasury Department have with the foreign exchange markets in dealing with the foreign

5 currencies rates of exchange for the U.S. dollar. While hard, direct, arbitrage is not always possible in interest rates or foreign exchange, the work of Krugman (1991) showed the relationship of government foreign exchange targets to the market dynamics, while Cook and Hahn (1989) studied similar dynamics for the interest rates markets. Bass and Farnsworth (2000) show that Arbitrage Pricing Theory can be in fact applied to the interest rates markets in the presence of the official policy targets set by the central bank. The situation of pension system participation vis-à-vis marketable capital assets is quite similar, given stated payroll tax rates and benefit formula. How can arbitrage be performed in the case of pension system participation? The simplest argument goes as follows. If pension system participation is cheap, i.e., it grants large benefits in relation to payroll taxes paid, other capital assets are relatively expensive and will be sold until the relationship between the statutory asset, pension system participation, and the market assets, is more reasonable. In full arbitrage, one would expect participants to purchase more pension system participation. This is not always possible, but can be partially achieved by investing in one s future wages, i.e., education. This is, in fact, exactly the argument advanced by Mueller (1997 and 1999), who claims that the U.S. Social Security System has contributed to productivity growth by creating incentives for investment in education. There is, however, a limit to the indirect pension system participation purchases through education, and any greater degree of arbitrage can only be attained by selling capital assets and purchasing consumption assets (indeed, one could argue that excessive consumption could be a form of investment in human capital: after all, a happy worker may be a more productive worker ). On the other hand, if the social insurance system grants benefits which are exceedingly small in relation to payroll taxes paid (many Third World or former communist economies provide examples of such a situation), there are two ways to arbitrage against the government: avoid paying the payroll tax, and increase investments in marketable assets with relatively lower prices. Increasing participation in an un-taxed underground economy is one common arbitragetype response to such situation. Schneider and Enste (2002) point out that the United States has among the lowest rates of underground economy participation rates in the world, a finding consistent with relative generosity of the U.S. social insurance system, while the country with the smallest underground economy overall, Switzerland, also has relatively small state sector in the national economy. In Germany, the share of the underground economy was relatively stable in the 8%-12% range in the period , but over the next 16 years, simultaneously with the decline in relative attractiveness of the state pension system returns, it has doubled, to 22% in The study of the relationship between prices of capital assets and the price of pension system participation is a complicated one. In addition to the redistribution between age cohorts (which is exactly the same function as the capital markets perform), social insurance has intra-cohort redistribution mechanisms (although taxation of investment income and income support programs have the same effect on capital markets). However, excessive arbitrage opportunities created by statutory pricing of pension system participation may cause significant economic and social dislocations. We do have an easy direct way to compare capital assets and pension system participation in spite of the fact that the latter is not marketable. There is also the issue of risk. While pension system participation enjoys a government guarantee of payment comparable to that of public debt, in the long run it does undergo fluctuations in value,

6 due to fluctuations in wages and productivity levels, demographics, economy s ability to carry the payroll tax burden, and political influences. When comparing it to other assets, we not only should seek some proxy for pension system participation, but also account for its risk relative to other securities. In this work, we propose the rate of growth of payroll taxes collected as the proxy for the rate of return on pension system participation, with its volatility as the measure of risk. This is, we agree, an imperfect proxy. It is derived as a long-term rate of return to cohorts only, under a restrictive model. But it does catch the essence of the inter-cohort transfer structure, it can be calculated, and it can be compared to statistics available for marketable securities, which perform the same intercohort transfer function. While a perfect design for arbitrage between the pension system and capital markets cannot be determined based on this proxy, we propose a comparison based on the contribution of the pension system participation in an efficient portfolio of a German investor, based on historical data, and we believe that our conclusions suggest that such arbitrage may have indeed been taking place. The rate of return earned by the pay-as-you-go social insurance participants is a central issue in many debates related to reform or privatization of existing systems. Proponents of privatization argue that if the existing social insurance is replaced with private accounts invested in marketable securities, such private accounts will earn a higher rate of return (Timmins, 1998, and Palacios and Whitehouse, 1998). What is the reality of rates of return to pension system participation and what are the exact sources of those returns? How does the pension system participation compare to marketable securities? We will attempt to answer this question in more detail now in a way, which incorporates both returns and risks of pension system participation, in the investment portfolio context. 2. Risk and Return of Social Security Participation The rate of return enjoyed by an individual social insurance participant can be affected by that individual s special circumstances and by redistribution features of the system (the benefit formula is tilted in favor of low income participants). On the other hand, rates of return to generational cohorts are naturally determined by the growth rate of taxable payroll. There is, however, a way to change this balance. The system may not only redistribute income within a generation, but between generations, beyond the redistribution (or, actually, relative pricing of current consumption in terms of future uncertain consumption) achieved by the equilibrium of capital markets. A first standard method of artificially increasing returns is to increase tax rates (so that early participants pay low taxes but receive benefits based on higher tax rates). One more method of increasing rates of return is to increase work force coverage. This way workers previously covered, who were then a part of a smaller system, can enjoy higher benefits due to greater tax collections from wider workforce coverage now. The third standard way to artificially increase payroll tax growth is to increase the portion of wages covered by payroll taxes. All of these features increase rates of return to past generational cohorts. We will attempt to make appropriate adjustments in the growth rate of payroll taxes for these three factors: tax rate increase, coverage increase, and contribution base increase. One more special way in which the German pension system changed the natural balance of rates of return was the addition of East Germany to the system fully implemented in This has suddenly increased the number of workers available to pay payroll taxes.

7 Of course, this also increased benefits payable, but if we adjust growth of payroll taxes collected for the increase in the number of workers 1, the balance of analysis is restored. What is the experience in that rate of growth of payroll taxes Germany? We will now show that experience since 1980, discuss it in the context of other capital assets - stocks (DAX index total return) and bonds (public bonds average annual yields) - and study the most efficient capital allocations within such context of historical experience. The German Social Security Administration 2 provides information about the amount of payroll tax receipts annually as well as about the historical and current tax rates and workers coverage. Intrinsic (adjusted for the growth in coverage and tax rates) growth rate g of the payroll tax receipts can be estimated from that data as g = 1+ g H ( 1+ g C )( 1+ g T )( 1+ g W )( 1+ g DDR ) 1 (1) where g H is the actual growth rate of payroll tax receipts, g C is the growth rate of coverage (percentage of workers paying payroll tax), g T is the growth rate of the tax rate, and g W is the growth rate of portion of wages taxed (we use the growth of maximum contribution base, adjusted for inflation 3. 4 Let us note here that (1) makes a simplifying assumption that all changes in appropriate rates take place on anniversaries (this approximation is imperfect, but since it is common for politically imposed changes, we believe that we can use it, with a caveat about its imperfections). This natural rate of return of pension system participation can be appropriately compared to rates of return of other securities. The purpose of such a comparison is to attempt to create an efficient portfolio incorporating pension system participation prospectively. We also look at these data in relation to inflation, considering real returns of all of these assets. Appendix A presents the data on rates of return of Social Security participation (as adjusted in (1)) and the asset classes listed, while Appendix B presents analogous data on real returns of all of them. Returns are annual, for years Let us first note that the arithmetic average annual rate of growth of payroll taxes for without adjustments in formula (1) was % with a standard deviation of %. With adjustments from (1) we observe that the pension system participation has an arithmetic average annual return of %, with standard deviation of %. The actual earned rate of return, i.e., geometric average, was %. These are nominal rates. The real (inflation adjusted) return arithmetic average was %, with standard deviation of %, and the actual compound real annual return (geometric average) was %. Figure 1 shows the nominal pension participation rates of return. 1 This factor will be called g DDR in formula (1). 2 Bundesversicherungsanstalt fuer Angestellte (BfA, 3 Since there is no consistent wage index published by BfA, we use inflation as a replacement. 4 For g DDR see above.

8 Figure 1. Historical nominal rates of return of pension system participation. Nominal Pension Return % % % % % % % Figures 2 shows historical real rates of return (inflation adjusted). Figure 2. Historical real rates of return on pension system participation security. Real Pension Return % % % % % % Figure 3 shows the rates of return for the German pension system participation in comparison with German stocks and bonds. Figure 4 contains the same information about real rates of return.

9 Figure 3. Summary statistics of nominal rates of return. Pension system participation Stocks (DAX Index) Public bonds Mean return Standard deviation Correlation with pension return 1.81% 5.13% % 26.04% % 1.59% Figure 4. Summary statistics of real rates of return. Pension system participation Stocks (DAX Index) Public bonds Mean return Standard deviation Correlation with the pension system -0.40% 4.75% % 25.91% % 1.34% Some rather interesting relationships should be noted in the statistics listed. Pension system participation is negatively correlated with stocks, and with both stocks and bonds on the basis of real returns. Any security, which has positive returns, but negative correlation with an existing portfolio provides diversification benefits to such a portfolio (Bodie, Kane and Marcus, 1999). Unfortunately, German pension system participation has negative returns on real basis. From the point of view of public policy, increasing those returns to positive level would make pension system participation valuable from a diversification perspective. But this would require that either wages grow faster than in the data studied or that employment increases. This data seems to point towards increasing employment as a major goal for public policy not just for its own sake, but also to make the pension system more attractive to participants. 3. Efficient Frontier Analysis Markowitz (1952) defined the efficient frontier of investment portfolios as the set of those portfolios which offer the highest level of expected return for a given level of standard deviation of returns (or, in general, highest degree of return for a given level of risk). His analysis, rewarded with the 1990 Nobel Prize in Economics, initiated modern finance theory, which was the precursor of the Capital Asset Pricing Model and Arbitrage Pricing Theory. Based on historical returns of asset classes analyzed in this work we can estimate the efficient frontier for German investors, and study the role of pension system participation in it.

10 The efficient frontier can be calculated either with or without allowing short (i.e., negative) positions in asset classes. We will perform our analysis using both assumptions, for nominal and real returns. Figure 5. Efficient frontier of German asset classes. Nominal asset returns. No short sales. (downward-sloping curve represents optimal portfolio allocation to pension system security) In the above Figure 5, the horizontal axis shows the volatility (standard deviation) of portfolio returns. The upward sloping curve is the efficient frontier, showing portfolios with highest level of expected return for the given level of volatility, as given on the horizontal axis. For the efficient frontier graph, the vertical axis shows the expected return of the portfolio. The downward-sloping curve is the allocation to the German pension system in an efficient portfolio, for a given level of volatility, as shown on the horizontal axis. For the graph of the efficient portfolio allocation to the German pension system, the vertical axis gives the portion of the portfolio invested in the German pension system. Figure 6 shows the same graphs, but with short sales allowed in portfolio optimization. The axes are labeled in the same fashion as in the Figure 6. Figure 7 shows the efficient frontier of German asset classes for real asset returns without short sales, while Figure 8 also uses real returns but allows short sales.

11 Figure 6. Efficient frontier of German asset classes. Nominal asset returns. Short sales allowed. (downward sloping curve represents optimal portfolio allocation to pension system security) Figure 7. Efficient frontier of German asset classes. Real asset returns. No short sales. (downward sloping curve represents optimal portfolio allocation to pension system security)

12 Figure 8. Efficient frontier of German asset classes. Real asset returns. Short sales allowed. (downward-sloping curve represents optimal portfolio allocation to pension system security) In Figure 8 allocation to the German pension system security attains large negative values, even reaching the level of nearly 200% for the volatility of 9%. As in the previous figures, in Figure 8, the upward sloping curve is the efficient frontier, and the downward-sloping curve is the optimal portfolio allocation to the German pension system security. The horizontal axis shows the level of volatility (standard deviation of returns), for the efficient frontier graph the vertical axis gives the level of expected return, and for the allocation graph, the vertical axis is the actual portfolio allocation to the German pension system security. The striking feature of optimal portfolios for a German investor is very low efficient allocation to the pension system security. Of course, payroll taxes are mandatory. But the system itself is unattractive as an investment, and it encourages escaping paying the payroll taxes. Also, optimal allocations to bonds are quite high. If personal credit at rates below bond rates were available (this is the case in the United States, where mortgage interest is tax-deductible, and as a result, borrowing at effective rates below bond yields is possible), this would encourage borrowing against future income (i.e., excessive consumption) and investing in bonds. Given limited availability of low interest credit, this is not a viable strategy. However, not paying payroll taxes and investing in bonds (through a high savings rate) is, and this may shed a new light on the combined high unemployment rate and high savings rate in Germany. Ostaszewski (2003) performed a similar analysis for the U.S. Social Security system. Unlike in the German system, U.S. investors, especially low risk investors, generally do include their state pension (i.e., Social Security) in optimal portfolios, but only for lower ranges of volatility. The riskiest U.S. portfolios have very large stock

13 allocations, while social insurance pension is shorted. In contrast with the U.S., in Germany, in optimal portfolios bonds dominate and state pension should be shorted. Conclusions This work indicates that German state pension system participation is an unattractive security, with a negative real rate of return. We believe that such information may be valuable to policy makers. Optimal portfolio allocation would include no state pension allocation, and if possible, short position in the pension system with high bond allocation. While some may believe this asset allocation to be unrealistic, implications of its optimality should not be underestimated. Arbitrage opportunities created by sub-optimal portfolios will be exploited. We believe this work to be the first step, opening new avenues into the study of the relationship of the German state pension system and capital markets. Results obtained here indicate that this relationship may have profound effects on the investment portfolio selection by German workers, and on the German economy. State pension does provide an alternative to traditional capital assets, and for that reason alone we should, and indeed we can, based on this work, expect the capital assets to affect state pensions (in the political arena), and state pensions to affect capital assets (in the economic arena). One natural extension of this line of research is to include other non-marketable assets in the analysis. In the United States, one such notable asset is real estate: home ownership is widespread. But in Germany, individual home ownership is less common, and while in the long run such analysis may be beneficial, we hope to leave its scope to future investigators.

14 References Bass, Richard, and Heber Farnsworth, The Term Structure with Semi-credible Targeting, Washington University, John M. Olin School of Business Working Paper, June Black, Fischer and Myron Scholes, The Pricing of Options and Corporate Liabilities, Journal of Political Economy, 81, May-June Bodie, Zvi, Alex Kane, and Alan J. Marcus, Investments, 4 th Edition, Irwin/McGraw-Hill, Boston, Massachusetts, Cook, T., and T. Hahn, The effect of changes in the federal funds rate target on market interest rates in the 1970 s, Journal of Monetary Economics, Martin Feldstein and Jeffrey Liebman, "Social Security," National Bureau of Economic Research Working Paper No. 8451, September 2001, chapter in "The Handbook of Public Economics," edited with Alan Auerbach, Vol. 4, Keyfitz, Nathan and John A. Beekman, Demography Through Problems, Springer- Verlag, New York, Krugman, P. R., Target zones and exchange rate dynamics, Quarterly Journal of Economics, Lintner, John, The Valuation of Risk Assets and the Selection of Risky Investments in Stock Portfolios and Capital Budgets, Review of Economics and Statistics, February Markowitz, Harry, Portfolio Selection, Journal of Finance, 7, 1952, pp Merton, Robert C., Theory of Rational Option Pricing, Bell Journal of Economics and Management Science, 4, Spring Mossin, Jan, Equilibrium in a Capital Asset Market, Econometrica, October Mueller, John, The Economics of Pay-as-you-go Social Security and the Economic Cost of Ending It, National Committee to Preserve Social Security and Medicare, Washington, D.C., October Mueller, John, Winner and Losers from Privatizing Social Security, National Committee to Preserve Social Security and Medicare, Washington, D.C., March Robert J. Myers and Bruce D. Schobel, "An Updated Money's-Worth Analysis of Social Security Retirement Benefits", Transactions of Society of Actuaries, Vol. 44 (1992), pp (including discussions). Ostaszewski, Krzysztof, Social Security system as a part of capital markets, Illinois State University working paper. Palacios, Robert, and Edward Whitehouse, The role of choice in the transition to a funded pension system, World Bank Social Protection Division, 1998, page 5. Panjer, Harry, editor, Financial Economics, The Actuarial Foundation, Schaumburg, Illinois, Ross, Stephen A., Return, Risk and Arbitrage, in I. Friend and J. Bicksler, editors, Risk and Return in Finance, Ballinger, Cambridge, Massachusetts, Samuelson, Paul, An Exact Consumption Loan Model of Interest With or Without the Social Contrivance of Money, Journal of Political Economy 66(1958), pp

15 Schneider, Friedrich and Dominik Enste, Hiding in the Shadows: The Growth of the Underground Economy, Economic Issues, No. 30, International Monetary Fund, March Sharpe, William, Capital Asset Prices: A Theory of Market Equilibrium, Journal of Finance, September Timmins, Nicholas, The biggest question in town: America faces critical choices over the future of its most popular spending program, Financial Times, March 20, 1998, page 23.

16 APPENDIX A Nominal returns data Year State Pension Return Stocks Bonds % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % %

17 APPENDIX B Real returns data % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % %