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082079 (E50) Simultane optimierung von versicherungsbestand and kapitalanlage — kapitalmarkttheoretische überlegungen
Abstracts and Reviews reliable estimates of underwriting betas do not exist. It also demonstrates the inapplicability of the CAPM to the yield to maturity of a bond or portfolio of bonds. Finally, it demonstrates that the assumption that the yield on a U.S. Treasury bill is risk-free for purposes of applying the CAPM implies that all U.S. Treasury securities, regardless of maturity, have betas of zero. Keywords: CAPM.
082078 (E50, E53, B51) Pension fund assets valuation and investment. Dyson A.C.L., Exley C.J., British Actuarial Journal, Volume 1, N ° 3, 1995, pp. 471-540 The theoretical basis for, and practical application of, the discounted income method for valuing U.K. pension fund assets is discussed with particular reference to the widely adopted application to variable income (equity type) assets, as proposed by Day & McKelvey (1964), in the context of both the management and compliance objectives of pension fund valuation. An alternative methodology is proposed in which consistency with assets, liabilities, and market values is demanded, with smoothing of the valuation result achieved on an explicit rather than implicit basis. It is then demonstrated that the explicit smoothing parameter can be set so as to achieve the historic smoothness of the discounted income asset valuation method and that the overall approach leads to a rational framework for establishing pension fund investment policy. In conclusion the paper suggests greater emphasis on market-related methodologies for compliance valuations and leaves open the choice of methodology for management valuations and monitoring purposes, on the grounds that there is a large subjective clement in any realistic basis. However, it is demonstrated that while smoother than unadjusted market-related methods, other aspects of the dynamics of the funding level under the method of Day & McKelvey can be perverse and it is suggested that this method should not be allowed to dictate investment decisions. Keywords: Assets, Pension Schemes, Disclosure, Solvency, Funding, Investment, Management. 082079 (E50) Simultane Optimierung yon Versicherungsbestand and Kapitalanlage kapitalmarkttheoretische tlberlegungen. Nickel A., Zeitschrift far die gesamte Versicherungswissenschaft, Volume 84, 1995, pp. 407-428
245
Insurance companies need to design and organize their insurance portfolios, as well as to invest the prepaid insurance premiums of their policyholders. For optimal results these objectives should be analyzed concurrently. Portfolio decisions are analyzed according to how insurance companies can be diversified efficiently. Given the considerable risks with which insurance companies are encountered, the risk aspect is central to the analysis. To get a better understanding of the subject, the Capital Asset Pricing Model (CAPM) is briefly explained. The assumptions of the CAPM are analysed with respect to insurance companies. The analysis of the assumption of a uniform interest rate, at which unlimited borrowing and lending is allowed leads to particularly interesting results. Moreover, separability of investment and finance is drawn from this assumption in the CAPM. This is known as the Separation Theorem of Tobin. For companies which produce physical goods this assumption is not generally met because their creditors (banks etc.) require credit limits or credit linked risk premiums. These restrictions are not valid in the same way for insurance companies that invest their prepaid insurance premiums which in this context can be considered debts. Another reason for a favorable presupposition for insurance companies is their broader investment opportunities which stem from high and continuous supplies of investable funds. Although the Separation Theorem of Tobin is a very limiting and unrealistic assumption for almost all other companies, insurance companies are more able to meet this assumption. The existing restrictions concerning the interdependence of finance and investment of insurance companies are mainly due to regulations of capital investments and insurance business. It is postulated that the concurrent analyzing of the insurance and the capital asset portfolios is an instrument to meet future objectives through the development of a combined actuarial and capital investment technique. The goal of this technique is the simultaneous optimization of risk and return. According to this goal, the asset/liability structure of insurance companies has to be derived. Therefore, different models are developed. Each of these different models intellectually integrates the insurance portfolio into the capital asset portfolio. Subsequently, a new CAPM based simultaneous approach is presented and compared with other models. A positive feature of this approach is the relatively small data amount and complexity. The actuarial input data is, via capital market transactions,
246
Abstracts and Reviews
transformed into capital market data. This data generating process implies that only capital market data have to be included in the objective of the simultaneous asset/liability management. The capital market transaction of contracts written on the development of the insurers own claim payments (loss experience) is the generator for this data. The value of the information of such a data transformation is not yet known. In contrast to Germany at the American Chicago Board of Trade (CBoT), an organized trade of contracts written on claim payments is developing. It started in December 1992 with so called Catastrophe Insurance Futures (CAT Futures). The contracts written in claim payments can also be used to generate synthetical reinsurance. Reflections of actuarial data in the capital market as well as the insertion of modem financial instruments in the actuarial technique are to be expected. Both will have great influence on the risk and diversification management o f insurance companies in the future. After further theoretical developments and appropriate insertion in praxi, the simultaneous asset/liability management can lead to positive results in form of a broader and optimized basis for diversification, which improves the insurer's capacity and lowers the costs for risk transformation. The modified perception of capital market theory should be taken more into consideration by insurance law and the insurance companies. Keywords: CAPM.
E53: INVESTMENT 082080 (E53) Modelling skewness and kurtosis in the London Stock Exchange FT-SE index return distributions. Millst T. C., The Statistician, Volume 44, N ° 3, 1995, pp. 323-332 This paper provides an empirical examination of the distribution of daily returns to the three London Stock Exchange indices, the FT-SE 100, Mid 250 and the 350, over the period 1986-92. Empirical densities are fitted to each o f the return distributions before their shapes are explored by using Tukey's a- and hdistributions. The returns are characterized by highly non-Gaussian behavior, being both skewed and extremely kurtotic, although the shapes of the distributions depend on whether data from 1986 and 1987 are included or not. Some implications for portfolio analysis are drawn. Keywords: Empirical densities, g- and h-distributions,
Portfolio analysis, Skewness and kurtosis, Stock Returns. 082081 (E53) Modelling asymmetry in stock returns by a threshold autoregressive conditional heteroscedastic model. Li W.K., Lam K., The statistician, Volume 44, N ° 3. p p 333-341 Possible asymmetric behavior of stock prices during bear and bull markets are studied by using a threshold type non-linear time series model with conditional heteroscedastic variance. Using Hong Kong data it is demonstrated that the return series could have a conditional mean structure which depends on the rise and fall of the market on a previous day. The findings also shed some light on why it could be difficult to reject the efficient market hypothesis. The threshold model with conditional changing variance is also of interest in other financial applications. Keywords: Autoregressive conditional heteroscedastic model, Efficient market hypothesis, Self-excitedthreshold autoregressive models, Skewness, Threshold autoregressive conditional heteroscedastic model.
082082 (E53) The Risk Premium on Ordinary Shares. Wilkie A.D., British ActuarialJournal, Volume 1. N ° 1, 1995, pp. 251-283 The risk premium on ordinary shares is investigated, by studying the total returns on ordinary shares, and on both long-term and short-term fixedinterest investments over the period 1919 to 1994, and by analyzing the various components of that return. The total returns on ordinary shares exceeded those on fixedinterest investments by over 5% p.a. on a geometric mean basis and by over 7% p.a. on an arithmetic mean basis, but it is argued that these figures are misleading, because most of the difference can be accounted for by the fact that price inflation turned out to be about 4.5% p.a. over the period, whereas investors had been expecting zero inflation. Quotations from contemporary authors are brought forward to demonstrate what contemporary attitudes were. Simulations are used along with the Wilkie stochastic asset model to show what the results would be if investors make various assumptions about the future, but the true model turns out to be different from what they expected. The differences between geometric means of the data and arithmetic means are shown to correspond to differences between using medians or means of the distribution of future returns, and it is
082078 (E50, E53, B51) Pension fund assets valuation and investment. Dyson A.C.L., Exley C.J., British Actuarial Journal, Volume 1, N ° 3, 1995, pp. 471-540 The theoretical basis for, and practical application of, the discounted income method for valuing U.K. pension fund assets is discussed with particular reference to the widely adopted application to variable income (equity type) assets, as proposed by Day & McKelvey (1964), in the context of both the management and compliance objectives of pension fund valuation. An alternative methodology is proposed in which consistency with assets, liabilities, and market values is demanded, with smoothing of the valuation result achieved on an explicit rather than implicit basis. It is then demonstrated that the explicit smoothing parameter can be set so as to achieve the historic smoothness of the discounted income asset valuation method and that the overall approach leads to a rational framework for establishing pension fund investment policy. In conclusion the paper suggests greater emphasis on market-related methodologies for compliance valuations and leaves open the choice of methodology for management valuations and monitoring purposes, on the grounds that there is a large subjective clement in any realistic basis. However, it is demonstrated that while smoother than unadjusted market-related methods, other aspects of the dynamics of the funding level under the method of Day & McKelvey can be perverse and it is suggested that this method should not be allowed to dictate investment decisions. Keywords: Assets, Pension Schemes, Disclosure, Solvency, Funding, Investment, Management. 082079 (E50) Simultane Optimierung yon Versicherungsbestand and Kapitalanlage kapitalmarkttheoretische tlberlegungen. Nickel A., Zeitschrift far die gesamte Versicherungswissenschaft, Volume 84, 1995, pp. 407-428
245
Insurance companies need to design and organize their insurance portfolios, as well as to invest the prepaid insurance premiums of their policyholders. For optimal results these objectives should be analyzed concurrently. Portfolio decisions are analyzed according to how insurance companies can be diversified efficiently. Given the considerable risks with which insurance companies are encountered, the risk aspect is central to the analysis. To get a better understanding of the subject, the Capital Asset Pricing Model (CAPM) is briefly explained. The assumptions of the CAPM are analysed with respect to insurance companies. The analysis of the assumption of a uniform interest rate, at which unlimited borrowing and lending is allowed leads to particularly interesting results. Moreover, separability of investment and finance is drawn from this assumption in the CAPM. This is known as the Separation Theorem of Tobin. For companies which produce physical goods this assumption is not generally met because their creditors (banks etc.) require credit limits or credit linked risk premiums. These restrictions are not valid in the same way for insurance companies that invest their prepaid insurance premiums which in this context can be considered debts. Another reason for a favorable presupposition for insurance companies is their broader investment opportunities which stem from high and continuous supplies of investable funds. Although the Separation Theorem of Tobin is a very limiting and unrealistic assumption for almost all other companies, insurance companies are more able to meet this assumption. The existing restrictions concerning the interdependence of finance and investment of insurance companies are mainly due to regulations of capital investments and insurance business. It is postulated that the concurrent analyzing of the insurance and the capital asset portfolios is an instrument to meet future objectives through the development of a combined actuarial and capital investment technique. The goal of this technique is the simultaneous optimization of risk and return. According to this goal, the asset/liability structure of insurance companies has to be derived. Therefore, different models are developed. Each of these different models intellectually integrates the insurance portfolio into the capital asset portfolio. Subsequently, a new CAPM based simultaneous approach is presented and compared with other models. A positive feature of this approach is the relatively small data amount and complexity. The actuarial input data is, via capital market transactions,
246
Abstracts and Reviews
transformed into capital market data. This data generating process implies that only capital market data have to be included in the objective of the simultaneous asset/liability management. The capital market transaction of contracts written on the development of the insurers own claim payments (loss experience) is the generator for this data. The value of the information of such a data transformation is not yet known. In contrast to Germany at the American Chicago Board of Trade (CBoT), an organized trade of contracts written on claim payments is developing. It started in December 1992 with so called Catastrophe Insurance Futures (CAT Futures). The contracts written in claim payments can also be used to generate synthetical reinsurance. Reflections of actuarial data in the capital market as well as the insertion of modem financial instruments in the actuarial technique are to be expected. Both will have great influence on the risk and diversification management o f insurance companies in the future. After further theoretical developments and appropriate insertion in praxi, the simultaneous asset/liability management can lead to positive results in form of a broader and optimized basis for diversification, which improves the insurer's capacity and lowers the costs for risk transformation. The modified perception of capital market theory should be taken more into consideration by insurance law and the insurance companies. Keywords: CAPM.
E53: INVESTMENT 082080 (E53) Modelling skewness and kurtosis in the London Stock Exchange FT-SE index return distributions. Millst T. C., The Statistician, Volume 44, N ° 3, 1995, pp. 323-332 This paper provides an empirical examination of the distribution of daily returns to the three London Stock Exchange indices, the FT-SE 100, Mid 250 and the 350, over the period 1986-92. Empirical densities are fitted to each o f the return distributions before their shapes are explored by using Tukey's a- and hdistributions. The returns are characterized by highly non-Gaussian behavior, being both skewed and extremely kurtotic, although the shapes of the distributions depend on whether data from 1986 and 1987 are included or not. Some implications for portfolio analysis are drawn. Keywords: Empirical densities, g- and h-distributions,
Portfolio analysis, Skewness and kurtosis, Stock Returns. 082081 (E53) Modelling asymmetry in stock returns by a threshold autoregressive conditional heteroscedastic model. Li W.K., Lam K., The statistician, Volume 44, N ° 3. p p 333-341 Possible asymmetric behavior of stock prices during bear and bull markets are studied by using a threshold type non-linear time series model with conditional heteroscedastic variance. Using Hong Kong data it is demonstrated that the return series could have a conditional mean structure which depends on the rise and fall of the market on a previous day. The findings also shed some light on why it could be difficult to reject the efficient market hypothesis. The threshold model with conditional changing variance is also of interest in other financial applications. Keywords: Autoregressive conditional heteroscedastic model, Efficient market hypothesis, Self-excitedthreshold autoregressive models, Skewness, Threshold autoregressive conditional heteroscedastic model.
082082 (E53) The Risk Premium on Ordinary Shares. Wilkie A.D., British ActuarialJournal, Volume 1. N ° 1, 1995, pp. 251-283 The risk premium on ordinary shares is investigated, by studying the total returns on ordinary shares, and on both long-term and short-term fixedinterest investments over the period 1919 to 1994, and by analyzing the various components of that return. The total returns on ordinary shares exceeded those on fixedinterest investments by over 5% p.a. on a geometric mean basis and by over 7% p.a. on an arithmetic mean basis, but it is argued that these figures are misleading, because most of the difference can be accounted for by the fact that price inflation turned out to be about 4.5% p.a. over the period, whereas investors had been expecting zero inflation. Quotations from contemporary authors are brought forward to demonstrate what contemporary attitudes were. Simulations are used along with the Wilkie stochastic asset model to show what the results would be if investors make various assumptions about the future, but the true model turns out to be different from what they expected. The differences between geometric means of the data and arithmetic means are shown to correspond to differences between using medians or means of the distribution of future returns, and it is