In my article, I have discussed the relationship between the internal rate of return, K, and Kp which denotes the reciprocal of the payoff period under several alternative assumptions.

The Capital Asset Pricing Model (CAPM), an equilibrium model for the price determination of risky assets, was developed by Sharpe [16], Lintner [9, 10] and Treynor [21], following the pioneering work of Markowitz [12, 13] and Tobin [20]. In spite of the tremendous impact of this model on the profession, the CAPM still raises many questions, and is inconsistent with a considerable body of empirical evidence.

Two measures of investment worth: the discounted-rate-of-return and the payback method will be compared here. Many examples can be found in the literature illustrating the serious limitations of the payback method.According to these examples, an investment proposal may be judged economically undesirable when in actual fact it is highly profitable. This happens when the annual cash flow is not equal, and the investment project promises a relatively large cash flow after the cut-off period.

Most research dealing with portfolio selection under uncertain inflation is carried out by assuming either one of the following two approximations: a linear or a quadratic approximation. In this paper, we analyze the general case, namely assume that the nominal return is the product of the real return and one plus the rate of inflation. We demonstrate that the general analysis leads to the following results that are not found in the two approximations: (1) even if we assume that nominal returns are independent of inflation, the nominal and real efficient sets will not necessarily coincide. Mean-Variance (M-V) analysis leads to a nominal efficient set, that is, a subset of the real M-V efficient set, whereas the opposite holds assuming investors maximize expected utility of real wealth. (2) Similar results are obtained when real returns are independent of inflation (the Fisher hypothesis). Assuming normality of nominal returns, we derive the CAPM in real terms or its zero beta counterpart.

Studies which deal with portfolio efficiency analysis can be divided into two main categories: (a) those concerned with the development of normative decision rules; and (b) those that discuss the application of the normative rules to empirical data. Most of the research on portfolio efficiency analysis uses some set of empirical data, without considering the possible errors which may arise when a sample rather than the entire population is examined. The prevailing neglect of the sampling errors is a clear reflection of the complexity of the issue.

The assumption that investors can borrow and lend at a riskless interest rate reduces the Mean-Variance (M-V) efficient set to only one optimal unlevered portfolio. However, once we realize that the market is generally imperfect and that the borrowing rate is higher than the lending rate, we can no longer use the mean-variance Separation Theorem. Instead, a number of unlevered portfolios must be included in the efficient set, while the optimal unlevered portfolio is selected on the basis of the investor's preference. The size of the efficient set of unlevered portfolios is a function of the type of empirical data used and of the disparity between the borrowing and lending interest rates.

Investment decision making under conditions of uncertainty, and in particular portfolio selection, is carried out mainly in the Mean-Variance framework which has been developed by Markowitz [29], [30] and Tobin [42]. By assuming the lending and borrowing of money at a given riskless interest rate, Sharpe [39], [40], Lintner [27], [28], Mossin [34], and others derived and extended the Capital Asset Pricing Model, under which an equilibrium price of each risky asset is determined. However, though the mean variance rule is quite convenient to apply, its limitations are well known, i.e., one must assume either normal probability distributions with risk aversion or quadratic utility functions.

The theory of choice under conditions of certainty has been extended by Von Neumann and Morgenstern [8], Friedman and Savage [5], Marschak [13], and others to conditions involving risk by assuming that individuals maximize their expected utility. The application of this theory to portfolio selection, to efficiency criteria, and to the explanation of the well-known phenomenon of diversification of assets has been carried further by Markowitz [11 and 12], Tobin [17], Samuelson [15], Sharpe [16], and Lintner [10], and more recently by Hadar and Russell [5] and Hanoch and Levy [8].

Efficiency analysis is concerned with isolating the efficient subset of investments (portfolios) for all investors belonging to a specified group. In order to construct a meaningful efficiency criterion, i.e., one which holds for more than one investor, care must be exercised to ensure that the investors' efficient set is independent of their wealth.

Individual decisions about investment may be regarded as choices among alternative probability distributions of net returns. It is assumed that these distributions are completely known and independent of initial wealth positions, and that individuals determine the preferred portfolio of investment in accordance with a given, consistent set of preferences.