We examine the effects of increases in risk on optimal loss control decision. We focus our attentions on the cases that the increases in risk take the form of both first degree and second degree stochastic dominance changes in risk. In particular, we derive a set of conditions, for each type of risk increases, that is sufficient for a risk averse decision maker to increase his investment level on loss control. For the case of risk change in type of first degree stochastic dominance the results of the comparative statics depend on Arrow-Pratt measures of risk aversion in a more or less complicated way. However in the case of risk change in type of second degree stochastic dominance Arrow-Pratt measures of risk aversion is no more useful tool to study the comparative statics. In essence, we obtain some meaningful comparative statics results by utilizing Kimball(1990)'s measures of Absolute and Relative Prudence.
The Government introduced the personal pension(PP) to induce a voluntary old-age income protection through the benefit of income tax deduction. Recently the lower rate of return(ROR) on the PP funds has become a big problem. But the problem may not be serious if the ROR effect of the income tax deduction on PPs can sufficiently recoup the lower ROR compared to that of similar financial products.
In order to examine the ROR effect this study computed the average annual rates of return over the period of 10 and 20 years by making the cumulative sum of the 10 and 20 years interest-adjusted after-tax savings equal the simple sum of 10 and 20 years savings. The result shows two things. One is that the ROR effect on both the old and the new PP becomes larger as the marginal tax rate increases and the ROR effect of the 20-year savings period becomes almost half that of the 10-year savings period. The other is that the ROR effect is unexpectedly lower compared to the decreased tax amount on the savings on the PPs. Especially with respect to the old PP the ROR effect is very low except the high income tax bracket and the income tax deduction effect on the savings is ignorable.
With respect to the new PP the ROR effect is more favorable to the higher income tax bracket than the lower income tax bracket. This result indicates that the current tax system on the PPs does not operate as an incentive to provide voluntary old-age income protection for the lower income tax bracket, so the system should be modified to provide all the PP participants with at least the same ROR effect.
Because of the long period of reverse mortgage loans, the mean values of housing price growth rates and interest rates which adapted to the model of reverse mortgages could be changed remarkably until the loan period is over. We confirmed the cycles of housing price growth rates and interest rates using several methods of time series analysis and then analyzed the market risk of reverse mortgages. In this analysis, we proposed a method of alleviating market risks resulting from cycles through using the modified values of housing. The result of this analysis shows us that we could alleviate the market risk of reverse mortgages considerably by using the smoothed housing prices on the model of reverse mortgages when we determine the levels of monthly payments.
Beneficiary certificates have gained popularity and acceptance not only by individuals but also by institutional investors such as banks, pension funds and insurers for diversifying stock and bond portfolios. For the appraisal of the performance of funds a variety of models have been suggested to complement or overcome the shortcomings of the traditional indices, such as Sharpe or Treynor indices. In this article we apply a mathematical programming approach called DEA to evaluate the performance of beneficiary certificates in Korea for the 5 quarters during the period of 2004~2005. This approach allows us to build fund performance indices that can take into account multiple inputs including several expenses related with funds. Another advantage of the DEA approach is that it avoids the benchmark problem that exists in the traditional indices.
The results show that the fees for marketing and managing funds have played an important role in the measurement of fund performance efficiency. We also find that there have been noticeable differences in the trends of efficiency scores and change between equity-type and mixed beneficiary certificates. The level of efficiency scores are different among different models, but the patterns of results are robust to model selection. Using DEA method can validate fund manager selection with other methodologies.