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Chapter 21 A NOTE ON THE RELATIONSHIP AMONG THE PORTFOLIO PERFORMANCE INDICES UNDER RANK TRANSFORMATION KEN HUNG, National Dong Hwa University, Taiwan CHIN-WEI YANG, Clarion University, USA DWIGHT B. MEANS, Jr., Consultant, USA Abstract This paper analytically determines the conditions under which four commonly utilized portfolio measures (the Sharpe index, the Treynor index, the Jensen alpha, and the Adjusted Jensen’s alpha) will be similar and different. If the single index CAPM model is appropriate, we prove theoretically that well-diversified portfolios must have similar rankings for the Treynor, Sharpe indices, and Adjusted Jensen’s alpha ranking. The Jensen alpha rankings will coincide if and only if the portfolios have similar betas. For multi-index CAPM models, however, the Jensen alpha will not give the same ranking as the Treynor index even for portfolios of large size and similar betas. Furthermore, the adjusted Jensen’s alpha ranking will not be identical to the Treynor index ranking. Keywords: Sharpe index; Treynor index; Jensen alpha; Adjusted Jensen alpha; CAPM; multiindex CAPM; performance measures; rank correlation; ranking; rank transformation 21.1. Introduction Measurement of a portfolio’s performance is of extreme importance to investment managers. That is, if a portfolio’s risk-adjusted rate of return exceeds (or is below) that of a randomly chosen portfolio, it may be said that it outperforms (or underperforms) the market. The risk–return relation can be dated back to Tobin (1958), Markowitz (1959), Sharpe (1964), Lintner (1965), and Mossin (1966). Evaluation measures are attributed to Treynor (1965), Sharpe (1966), and Jensen (1968, 1969). Empirical studies of these indices can be found in the work by Friend and Blume (1970), Black et al. (1972), Klemkosky (1973), Fama and MacBeth (1974), and Kim (1978). For instance, the rank correlation between the Sharpe and Treynor indices was found by Sharpe (1966) to be 0.94. Reilly (1986) found the rank correlation to be 1 between the Treynor and Sharpe indices; 0.975 between the Treynor index and Jensen alpha; and 0.975 between the Sharpe index and Jensen alpha. In addition, the sampling properties and other statistical issues of these indices have been carefully studied by Levy (1972), Johnson and Burgess (1975), Burgess and Johnson (1976), Lee (1976), Levhari and Levy (1977), Lee and Jen (1978), and Chen and Lee (1981, 1984, 1986). For example, Chen and Lee (1981, 1986) found that the statistical relationship between performance measures and their risk proxies would, in general, be affected by A NOTE ON THE RELATIONSHIP AMONG THE PORTFOLIO PERFORMANCE INDICES the sample size, investment horizon, and market conditions associated with the sample period. Notwithstanding these empirical findings, an analytical study of the relationship among these measures is missing in the literature. These performance measures may well be considered very ‘‘similar’’ owing to the unusually high rank correlation coefficients in the empirical studies. However, the empirical findings do not prove the true relationship. These measures can theoretically yield rather divergent rankings especially for the portfolios whose sizes are substantially less than the market. A portfolio size about 15 or more in which further decreases in risk is in general not possible (Evans and Archer, 1968; Wagner and Lau, 1971; Johnson and Shannon, 1974) can generate rather different rankings. In the case of an augmented CAPM, a majority of these performance measures, contrary to the conventional wisdom, can be rather different regardless of the portfolio sizes! In this note, it is our intention to (1) investigate such relationship, (2) clarify some confusing issues, and (3) provide some explanations as to the empirically observed high rank correlations among performance measures. The analysis is free from the statistical assumptions (e.g. normality) and may provide some guidance to portfolio managers. 21.2. The Relationship between Treynor, Sharpe, and Jensen’s Measures in the Simple CAPM Given the conventional assumptions, a typical CAPM formulation can be shown as1 yi ¼ ai þ bi x (21:1) where yi ¼ pp
pf , which is the estimated excess rate of return of portfolio i over the risk-free rate, x ¼ pm
pf , which is the excess rate of return of the market over the risk-free rate. The Treynor index is a performance measure which is expressed as the ratio of the average excess rate of return of a portfolio over the estimated beta or Ti ¼ yi bi (21:2) 471 Similarly, the Sharpe index is the ratio of the average excess rate of return of a portfolio over its corresponding standard deviation or Si ¼ yi Syi (21:3) A standard deviation, which is significantly larger than the beta, may be consistent with the lack of complete diversification. While the Sharpe index uses the total risk as denominator, the Treynor index uses only the systematic risk or estimated beta. Note that these two indices are relative performance measures, i.e. relative rankings of various portfolios. Hence, they are suitable for a nonparametric statistical analysis such as rank correlation. In contrast to these two indices, the Jensen alpha (or a) can be tested parametrically by the conventional t-statistic for a given significance level. However, the absolute Jensen alpha may not reflect the proper risk adjustment level for a given performance level (Francis, 1980). For instance, two portfolios with the identical Jensen’s alpha may well have different betas. In this case, the portfolio with lower beta is preferred to the one with higher beta. Hence, the adjusted Jensen alpha can be formulated as the ratio of the Jensen alpha divided by its corresponding beta (see Francis, 1980) or AJi ¼ ai bi (21:4) The close correlation between the Treynor and Sharpe indices is often cited in the empirical work of mutual fund performances. Despite its popular acceptance, it is appropriate to examine them analytically by increasing the portfolio size (n) to the number of securities of the market (N), i.e. the portfolio risk premium x approaches the market risk premium y. Rewriting the Treynor index, we have

 yi Var(x) yi  Ti ¼ ¼ y i ¼ : Var(x) Cov(x, yi ) bi Var(yi )
 yi Var(x) (21:5) ¼ Si  sx ¼ Syi Syi 472 ENCYCLOPEDIA OF FINANCE since Cov(x  yi ) ¼ Var(yi ) ¼ Var(x) forx ¼ y2i . Equation (21.5) indicates that the Treynor index, in general, will not equal the Sharpe index even in the case of a complete diversification, i.e. n ¼ N. It is evident from (21.5) that these two indices are identical only for sx ¼ 1, a highly unlikely scenario. Since neither the Treynor nor Sharpe index is likely to be normally distributed, a rank correlation is typically computed to reflect their association. Taking rank on both sides of Equation (21.5) yields Rank(Ti ) ¼ Rank(Si )  sx (21:6) since sx in a given period and for a given market is constant. As a result, the Treynor and the Sharpe indices (which must be different values) give identical ranking as the portfolio size approaches the market size as stated in the following propositions: Proposition #1: In a given period and for a given market characterized by the simple CAPM, the Treynor and Sharpe indices give exactly the same ranking on portfolios as the portfolio size (n) approaches the market size (N). This proposition explains high rank correlation coefficients observed in empirical studies between these indices. Similarly, Equation (21.5) also indicates that parametric (or Pearson Product) correlation between the Treynor and Sharpe indices approaches 1 as n approaches N for a constant sx , i.e. Ti is a nonnegative linear transformation of Si from the origin. In general, these two indices give similar rankings but may not be identical. The Jensen alpha can be derived from the CAPM for portfolio i: Ji ¼ ai ¼ yi
bi x (21:7) It can be seen from Equation (21.7) that as n ! N, yi ! x, and bi ! 1. Hence ai approaches zero. The relationship of the rankings between the Jensen alpha and the Treynor index ranking are equal can be proved as bi approaches 1 because: Rank(Ji ) ¼ Rank(ai )   ai ¼ Rank bi ¼ Rank( yi )
Rank(bi x)    yi ¼ Rank
Rank( x) bi (21:8) ¼ Rank(Ti ) Since x is a constant; yi =bi ! yi and bi x ! x. We state this relationship in the following proposition. Proposition #2: In a given period and for a given market characterized by the simple CAPM, as the portfolio size n approaches the market size N, the Jensen alpha ranking approaches the Treynor index ranking. However, the Jensen alpha will in general be dependent on the average risk premium for a given beta value for all portfolios since x) Rank (ai ) ¼ Rank(yi )
bi Rank( ¼ Rank(yi) 
constant (21:9) for a constant bi (for all i). In this case the Jensen alpha will give similar rank to the Treynor index for a set of portfolios with similar beta values since   yi Rank ¼ Rank( yi ) ¼ Rank(ai ) bi for a fairly constant set of bi0 ’s. Hence, we state the following proposition. Proposition #3: In a given period and for a given market characterized by the simple CAPM, the ranking of the Jensen alpha and that of the Treynor index give very close rankings for a set of fairly similar portfolio betas regardless of the portfolio size. Next, we examine the relationship between the adjusted Jensen alpha and the Treynor index in the form of the adjusted Jensen alpha (AJ). Since ai ¼ yi
bi x hence AJ ¼ ai yi ¼
x bi bi (21:10) A NOTE ON THE RELATIONSHIP AMONG THE PORTFOLIO PERFORMANCE INDICES It follows immediately from Equation (21.10) that Rank(AJ) ¼ Rank(T)
Rank( x) (21:11) The result is stated in the following proposition. Proposition #4: In a given period and for a given market characterized by the simple CAPM, the adjusted Jensen alpha gives precisely identical rankings as does its corresponding Treynor index regardless of the portfolio size. Clearly, it is the adjusted Jensen alpha that is identical to the Treynor index in evaluating portfolio performances in the framework of the simple CAPM. The confusion of these measures can lead to erroneous conclusions. For example, Radcliffe (1990, p. 209) stated that ‘‘the Jensen and Treynor measures can be shown to be virtually identical.’’ Since he used only the Jensen alpha in his text, the statement is not correct without further qualifications such as Proposition #3. The ranking of the Jensen alpha must equal that of the adjusted Jensen alpha for a set of similar betas, i.e. Rand(ai =bi ) ¼ Rank(ai ) for a constant beta across all i. All other relationships can be derived by the transitivity property as shown in Table 21.1. In the next section, we expand our analysis to the augumented CAPM with more than one independent variable. Table 21.1. Jenson Alpha (Ji ) Adjusted Jenson Alpha (AJi ) 21.3. The Relationship Between the Treynor, Sharpe, and Jensen Measures in the Augmented CAPM An augumented CAPM can be formulated without loss of generality, as yi ¼ ai þ bi x þ X cij zij (21:12) where zij is another independent variable and cij is the corresponding estimated coefficient. For instance, zij could be a dividend yield variable (see Litzenberger and Ramaswami, 1979, 1980, 1982). In this case again, the Treynor and Sharpe indices have the same numerators as in the case of a simple CAPM, i.e. the Treynor index still measures risk premium per systematic risk (or bi ) and the Sharpe index measures the risk premium per total risk or (sy ). However, if the portfolio beta is sensitive to the additional data on zij due to some statistical problem (e.g. multi-collinearity), the Treynor index may be very sensitive due to the instability of the beta even for large portfolios. In this case, the standard deviations of the portfolio returns and portfolio betas may not have consistent rankings. Barring this situation, these two measures will in general give similar rankings for well-diversified portfolios. Analytical rank correlation between performance measures: Simple CAPM Sharpe Index (Si ) Sharpe Index (Si ) Treynor Index (Ti ) 473 1 Rank(Ti ) ¼ Rank(Si )  SX Identical ranking as n ! N As n ! N Rank(Ji ) ! Rank (Si ) As n ! N Rank(AJi ) ! Rank (Si ) Treynor Index (Ti ) Jensen Alpha (Ji ) Adjusted Jensen Alpha AJi 1 Rank(Ji ) ! Rank(Ti ) as n ! N or b ! 1 or Rank(Ji ) ! Rank(Ti ) for similar bi ’s Rank (AJi ) ¼ Rank(Ti ) regardless of the portfolio size 1 Rank(ai =bi ) ¼ Rank(ai ) for similar bi ’s 1 474 ENCYCLOPEDIA OF FINANCE However, in the augmented CAPM framework, the Jensen alpha may very well differ from the Treynor index even for a set of similar portfolio betas. This can be seen from reranking (ai ) as: X Rank(ai ) ¼ Rank(yi )
bi Rank(x) 
Rank(cij zij )j j (21:13) It is evident from Equation (21.13) that the Jensen alpha does not give same rank as the Treynor index, i.e. Rank (ai ) 6¼ Rank yi =bi ¼ Rank ( yi ) for a set of constant portfolio beta bi0 ’s. This is because cij zij is no longer constant; they differ for each portfolio selected even for a set of constant bi ’s (hence bi Rank( x)) for each portfolio i as stated in the following proposition. Proposition #5: In a given period and for a given market characterized by the augmented CAPM, the Jensen alpha in general will not give the same rankings as will the Treynor index, even for a set of similar portfolio betas regardless of the portfolio size. Last, we demonstrate that the adjusted Jensen alpha is no longer identical to the Treynor index as shown in the following proposition. Proposition #6: In a given period and for a given market characterized by the augmented CAPM, the Table 21.2. Jenson Alpha Ji Adjusted Jenson Alpha AJi j X cij  ai yi zij ¼
x
bi bi bi j We have Rank(AJi ) ¼ Rank(Ti )
Rank(x) 
X   Rank cij =bi zij j (21:14) It follows immediately that Rank (AJ) 6¼ Rank (T) in general since the last term of Equation (21.14) is not likely to be constant for each estimated CAPM regression. It is to be noted that contrary to the case of the simple CAPM, the adjusted Jensen alpha and the Treynor index do not produce identical rankings. Likewise, for a similar set of bi ’s for all i, the rankings of the Jensen and adjusted Jensen alpha are closely related. Note that the property of transitivity, however, does not apply in the augmented CAPM since the pairwise rankings of Ti and Ji or AJi do not Analytical rank correlation between performance measures: Augmented CAPM Sharpe Index Si Sharpe Index Si Treynor Index Ti adjusted Jensen alpha is not identical to the Treynor index regardless of the portfolio size. We furnish the proof by rewriting Equation (21.12) for each portfolio i as: X cij zij implies Since ai ¼ yi
bi x
1 Rank (Ti ) and Rank (Si ) are similar barring severe multicollinearity or an unstable beta Rank(Ji ) 6¼ Rank (Si ) Rank(AJi ) 6¼ Rank(Si ) Treynor Index Ti Jensen Alpha Ji Adjusted Jensen Alpha AJi 1 Rank(Ji ) 6¼ Rank (Ti ) even for a similar beta and regardless of the portfolio size Rank(AJi ) 6¼ Rank (Ti ) regardless of the portfolio size 1 Rank (AJi ) ! Rank (Ji ) 1 for a set of similar bi ’s A NOTE ON THE RELATIONSHIP AMONG THE PORTFOLIO PERFORMANCE INDICES converge consistently (Table 21.2) even for large porfolios. 21.4. Conclusion In this note, we first assume the validity of the single index CAPM. The CAPM remains the foundation of modern portfolio theory despite the challenge from fractal market hypothesis (Peters, 1991) and long memory (Lo, 1991). However, empirical results have revalidated the efficient market hypothesis and refute others (Coggins, 1998). Within this domain, we have examined analytically the relationship among the four performance indices without explicit statistical assumptions (e.g. normality). The Treynor and Sharpe indices produce similar rankings only for well-diversified portfolios. In its limiting case, as the portfolio size approaches the market size, the ranking of the Sharpe index becomes identical to the ranking of the Treynor index. The Jensen alpha generates very similar rankings as does the Treynor index only for a set of comparable portfolio betas. In general, the Jensen alpha produces different ranking than does the Treynor index. Furthermore, we have shown that the adjusted Jensen alpha has rankings identical to the Treynor index in the simple CAPM. However, in the case of an augmented CAPM with more than one independent variable, we found that (1) the Treynor index may be sensitive to the estimated value of the beta; (2) the Jensen alpha may not give similar rankings as the Treynor index even with a comparable set of portfolio betas; and (3) the adjusted Jensen alpha does not produce same rankings as that of the Treynor index. The potential difference in rankings in the augmented CAPM suggests that portfolio managers must exercise caution in evaluating these performance indices. Given the relationship among these four indices, it may be necessary in general to employ each of them (except the adjusted Jensen alpha and the Treynor index are identical in ranking in the simple CAPM) since they represent different measures to evaluate the performance of portfolio investments. 475 NOTES 1. We focus our analysis on the theoretical relationship among these indices in the framework of a true characteristic line. The statistical distributions of the returns (e.g. normal or log normal), from which the biases of these indices are derived, and other statistical issues are discussed in detail by Chen and Lee (1981, 1986). We shall limit our analysis to a pure theoretical scenario where the statistical assumptions are not essential to our analysis. It is to be pointed out that the normality assumption of stock returns in general has not been validated in the literature. 2. This condition is guaranteed if the portfolio yi is identical to the market (x) or if n is equal to N. In this special case, if the portfolio is weighted according to market value weights, the portfolio is identical to the market so Cov(x, yi ) ¼ Var(yi ) ¼ Var(x). REFERENCES Black, F., Jensen, M.C., and Scholes, M. (1972). ‘‘The Capital Asset Pricing Model: Some empirical tests,’’ in M.C. Jensen (ed.) Studies in the Theory of Capital Markets, New York: Praeger Publishers Inc. Burgess, R.C. and Johnson, K.H. (1976). ‘‘The effects of sampling fluctuations on required inputs of security analysis.’’ Journal of Financial and Quantitative Analysis, 11: 847–854. Chen, S.N. and Lee, C.F. (1981). ‘‘The sampling relationship between sharpe’s performance measure and its risk proxy: sample size, investment horizon, and market conditions.’’ Management Science, 27(6): 607–618. Chen, S.N. and Lee, C.F. (1984). ‘‘On measurement errors and ranking of three alternative composite performance measures.’’ Quarterly Review of Economics and Business, 24: 7–17. Chen, S.N. and Lee, C.F. (1986). ‘‘The effects of the sample size, the investment horizon, and market conditions on the validity of composite performance measures: a generalization.’’ Management Science, 32(11): 1410–1421. Coggin, T.D. (1998). ‘‘Long-term memory in equity style index.’’ Journal of Portfolio Management, 24(2): 39–46. Evans, J.L. and Archer, S.H. (1968). ‘‘Diversification and reduction of dispersion: an empirical analysis.’’ Journal of Finance, 23: 761–767. 476 ENCYCLOPEDIA OF FINANCE Fama, E.F. and MacBeth, J.D. (1973). ‘‘Risk, return and equilibrium: empirical tests.’’ Journal of Political Economy, 81: 607–636. Francis, J.C. (1980). Investments: Analysis and Management, 3rd edn, New York: McGraw-Hill Book Company. Friend, I. and Blume, M.E. (1970). ‘‘Measurement of portfolio performance under uncertainty.’’ American Economic Review, 60: 561–575. Jensen, M.C. (1968). ‘‘The performance of mutual funds in the period 1945–1964.’’ Journal of Finance, 23(3): 389–416. Jensen, M.C. (1969). ‘‘Risk, the pricing of capital assets, and the evaluation of investment portfolio.’’ Journal of Business, 19(2): 167–247. Johnson, K.H. and Burgess, R.C. (1975). ‘‘The effects of sample sizes on the accuracy of E-V and SSD efficient criteria.’’ Journal of Financial and Quantitative Analysis, 10: 813–848. Johnson, K.H. and Shannon, D.S. (1974). ‘‘A note on diversification and reduction of dispersion.’’ Journal of Financial Economics, 4: 365–372. Kim, T. (1978). ‘‘An assessment of performance of mutual fund management.’’ Journal of Financial and Quantitative Analysis, 13(3): 385–406. Klemkosky, R.C. (1973). ‘‘The bias in composite performance measures.’’ Journal of Financial and Quantitative Analysis, 8: 505–514. Lee, C.F. (1976). ‘‘Investment horizon and functional form of the Capital Asset Pricing Model.’’ Review of Economics and Statistics, 58: 356–363. Lee, C.F. and Jen, F.C. (1978). ‘‘Effects of measurement errors on systematic risk and performance measure of a portfolio.’’ Journal of Financial and Quantitative Analysis, 13: 299–312. Levhari, D. and Levy, H. (1977). ‘‘The Capital Asset Pricing Model and investment horizon.’’ Review of Economics and Statistics, 59: 92–104. Levy, H. (1972). ‘‘Portfolio performance and investment horizon.’’ Management Science, 18(12): B645– B653. Litner, J. (1965). ‘‘The valuation of risk assets and the selection of risky investment in stock portfolios and capital budgets.’’ Review of Economics and Statistics, 47: 13–47. Litzenberger, R.H. and Ramaswami, K. (1979). ‘‘The effects of personal taxes and dividends on capital asset prices: theory and empirical evidence.’’ Journal of Financial Economics, 7(2): 163–196. Litzenberger, R.H. and Ramaswami, K. (1980). ‘‘Dividends, short selling restriction, tax induced investor clienteles and market equilibrium.’’ Journal of Finance, 35(2): 469–482. Litzenberger, R.H. and Ramaswami, K. (1982 ). ‘‘The effects of dividends on common stock prices tax effects or information effect.’’ The Journal of Finance, 37(2): 429–443. Lo, A.W. (1991) ‘‘Long-term memory in stock market prices.’’ Econometrica, 59(5): 1279–1313. Markowitz, H.M. (1959). Portfolio Selection Cowles Monograph 16. New York: Wiley, Chapter 14. Mossin, J. (1966). ‘‘Equilibrium in a capital market.’’ Econometrica, 34: 768–783. Peters, E.E. (1991). Chaos and Order in the Capital Markets: A New View of Cycles, Prices and Market Volatility. New York: John Wiley. Radcliffe, R.C. (1990). Investment: Concepts, Analysis, and Strategy, 3rd edn. Glenview, IL: Scott, Foresman. Reilly, F.K. (1986). Investments, 2nd edn. Chicago, IL: The Dryden Press. Sharpe, W.F. (1964). ‘‘Capital asset price: A theory of market equilibrium under conditions of risk.’’ The Journal of Finance, 19(3): 425–442. Sharpe, W.F. (1966). ‘‘Mutual fund performance.’’ Journal of Business Supplement on Security Prices, 39: 119–138. Tobin, J. (1958). ‘‘Liquidity preference as behavior toward risk.’’ The Review of Economic Studies, 26(1): 65–86. Treynor, J.L. (1965). ‘‘How to rate management of investment funds.’’ Harvard Business Review, 43: 63–75. Wagner, W.H. and Lau, S.T. (1971). ‘‘The effect of diversification on risk.’’ Financial Analysts Journal, 27(5): 48–53. Chapter 22 CORPORATE FAILURE: DEFINITIONS, METHODS, AND FAILURE PREDICTION MODELS JENIFER PIESSE, University of London, UK and University of Stellenbosch, South Africa CHENG-FEW LEE, National Chiao Tung University, Taiwan and Rutgers University, USA HSIEN-CHANG KUO, National Chi-Nan University and Takming College, Taiwan LIN LIN, National Chi-Nan University, Taiwan Abstract 22.1. Introduction The exposure of a number of serious financial frauds in high-performing listed companies during the past couple of years has motivated investors to move their funds to more reputable accounting firms and investment institutions. Clearly, bankruptcy, or corporate failure or insolvency, resulting in huge losses has made investors wary of the lack of transparency and the increased risk of financial loss. This article provides definitions of terms related to bankruptcy and describes common models of bankruptcy prediction that may allay the fears of investors and reduce uncertainty. In particular, it will show that a firm filing for corporate insolvency does not necessarily mean a failure to pay off its financial obligations when they mature. An appropriate risk-monitoring system, based on well-developed failure prediction models, is crucial to several parties in the investment community to ensure a sound financial future for clients and firms alike. The financial stability of firms is of concern to many agents in society, including investors, bankers, governmental and regulatory bodies, and auditors. The credit rating of listed firms is an important indicator, both to the stock market for investors to adjust stock portfolios, and also to the capital market for lenders to calculate the costs of loan default and borrowing conditions for their clients. It is also the duty of government and the regulatory authorities to monitor the general financial status of firms in order to make proper economic and industrial policy. Further, auditors need to scrutinize the going-concern status of their clients to present an accurate statement of their financial standing. The failure of one firm can have an effect on a number of stakeholders, including shareholders, debtors, and employees. However, if a number of firms simultaneously face financial failure, this can have a wide-ranging effect on the national economy and possibly on that of other countries. A recent example is the financial crisis that began in Thailand in July 1997, which affected most of the other Asia-Pacific countries. For these reasons, the development of theoretical bankruptcy prediction models, which can Keywords: corporate failure; bankruptcy; distress; receivership; liquidation; failure prediction; Discriminant Analysis (DA); Conditional Probability Analysis (CPA); hazard models; misclassification cost models 478 ENCYCLOPEDIA OF FINANCE protect the market from unnecessary losses, is essential. Using these, governments are able to develop policies in time to maintain industrial cohesion and minimize the damage caused to the economy as a whole. Several terms can be used to describe firms that appear to be in a fragile financial state. From standard textbooks, such as Brealey et al. (2001) and Ross et al. (2002), definitions are given of distress, bankruptcy, or corporate failure. Pastena and Ruland (1986, p. 289) describe this condition as when . Import penetration into the firm’s home markets . Deteriorating financial structures . Difficulties controlling new or geographically dispersed operations . Over-trading in relation to the capital base . Inadequate financial control over contracts . Inadequate control over working capital . Failure to eliminate actual or potential lossmaking activities . Adverse changes in contractual arrangements. 1. the market value of assets of the firm is less than its total liabilities; 2. the firm is unable to pay debts when they come due; 3. the firm continues trading under court protection. Apart from these, a new company is usually thought to be riskier than those with longer history. Blum (1974, p. 7) confirmed that ‘‘other things being equal, younger firms are more likely to fail than older firms.’’ Hudson (1987), examining a sample between 1978 and 1981, also pointed out that companies liquidated through a procedure of creditors’ voluntary liquidation or compulsory liquidation during that period were on average two to four years old and three-quarters of them less than ten years old. Moreover, Walker (1992, p. 9) also found that ‘‘many new companies fail within the first three years of their existence.’’ This evidence suggests that the distribution of the failure likelihood against the company’s age is positively skewed. However, a clear-cut point in age structure has so far not been identified to distinguish ‘‘new’’ from ‘‘young’’ firms in a business context, nor is there any convincing evidence with respect to the propensity to fail by firms of different ages. Consequently, the age characteristics of liquidated companies can only be treated as an observation rather than theory. However, although the most common causes of bankruptcy can be noted, they are not sufficient to explain or predict corporate failure. A company with any one or more of these characteristics is not certain to fail in a given period of time. This is because factors such as government intervention may play an important role in the rescue of distressed firms. Therefore, as Bulow and Shoven (1978) noted, the conditions under which a Of these, insolvency, or the inability to pay debts when they are due, has been the main concern in the majority of the early bankruptcy literature. This is because insolvency can be explicitly identified and also serves as a legal and normative definition of the term ‘‘bankruptcy’’ in many developed countries. However, the first definition is more complicated and subjective in the light of the different accounting treatments of asset valuation. Firstly, these can give a range of market values to the company’s assets and second, legislation providing protection for vulnerable firms varies between countries. 22.2. The Possible Causes of Bankruptcy Insolvency problems can result from endogenous decisions taken within the company or a change in the economic environment, essentially exogenous factors. Some of the most common causes of insolvency are suggested by Rees (1990): . Low and declining real profitability . Inappropriate diversification: moving into unfamiliar industries or failing to move away from declining ones CORPORATE FAILURE firm goes through liquidation are rather complicated. Foster (1986, p. 535) described this as ‘‘there need not be a one-to-one correspondence between the non-distressed=distressed categories and the non-bankrupt=bankrupt categories.’’ It is noticeable that this ambiguity is even more severe in the not-for-profit sector of the economy. 22.3. Methods of Bankruptcy As corporate failure is not only an issue for company owners and creditors but also the wider economy, many countries legislate for formal bankruptcy procedures for the protection of the public interest, such as Chapter VII and Chapter XI in the US, and the Insolvency Act in the UK. The objective of legislation is to ‘‘[firstly] protect the rights of creditors . . . [secondly] provide time for the distressed business to improve its situation . . . [and finally] provide for the orderly liquidation of assets’’ (Pastena and Ruland, 1986, p. 289). In the UK, where a strong rescue culture prevails, the Insolvency Act contains six separate procedures, which can be applied to different circumstances to prevent either creditors, shareholders, or the firm as a whole from unnecessary loss, thereby reducing the degree of individual as well as social loss. They will be briefly described in the following section. 22.3.1. Company Voluntary Arrangements A voluntary arrangement is usually submitted by the directors of the firm to an insolvency practitioner, ‘‘who is authorised by a recognised professional body or by the Secretary of State’’ (Rees, 1990, p. 394) when urgent liquidity problems have been identified. The company in distress then goes through the financial position in detail with the practitioner and discusses the practicability of a proposal for corporate restructuring. If the practitioner endorses the proposal, it will be put to the company’s creditors in the creditors’ meeting, requiring an approval rate of 75 percent of attendees. If the restructuring report is accepted, those notified will thus be bound by this agreement and the 479 practitioner becomes the supervisor of the agreement. It is worth emphasizing that a voluntary arrangement need not pay all the creditors in full but a proportion of their lending (30 percent in a typical voluntary agreement in the UK) on a regular basis for the following several months. The advantages of this procedure are that it is normally much cheaper than formal liquidation proceedings and the creditors usually receive a better return. 22.3.2. Administration Order It is usually the directors of the insolvent firm who petition the court for an administration order. The court will then assign an administrator, who will be in charge of the daily affairs of the firm. However, before an administrator is appointed, the company must convince the court that the making of an order is crucial to the survival of the company or for a better realization of the company’s assets than would be the case if the firm were declared bankrupt. Once it is rationalized, the claims of all creditors are effectively frozen. The administrator will then submit recovery proposals to the creditors’ meeting for approval within three months of the appointment being made. If this proposal is accepted, the administrator will then take the necessary steps to put it into practice. An administration order can be seen as the UK version of the US Chapter XI in terms of the provision of a temporary legal shelter for troubled companies. In this way, they can escape future failure without damaging their capacity to continue to trade (Counsell, 1989). This does sometimes lead to insolvency avoidance altogether (Homan, 1989). 22.3.3. Administrative Receivership An administration receiver has very similar powers and functions as an administrator but is appointed by the debenture holder (the bank), secured by a floating or fixed charge after the