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.

This paper presents a framework for analyzing an economy's resilience to exchange rate risk using the balance sheet approach (BSA), which is gaining prominence worldwide in the surveillance of financial stability. The framework is applied to Israel's economy, by using an unique and extensive dataset: a combination of new national balance sheet data and foreign currency balance sheet data. The analysis using the BSA shows that Israel's economy was highly vulnerable to a depreciation of the shekel in 1997, but from then until 2005 it became more resilient. The improvement was due mainly to the lowering of the business sector's high level of exposure to depreciation and its greater financial strength. This, together with higher capital adequacy in the banking system, made the latter more resilient to indirect damage that could be caused by depreciation. The analysis shows further that despite the heavy exposure of the economy as a whole and most sectors within it to appreciation of the shekel at the end of 2005, the economy was quite resilient to such appreciation, as the private sector and the banks suffered little direct or indirect damage through it. The analysis stresses the central, but not exclusive, role played by the banks’ resilience in the economy's financial stability, and thus also favors the continuation of the process of reducing the banks’ dominance in financing the business sector, so that their indirect exposure to financial risks will fall. The findings yielded by the BSA are highly significant, because an analysis using the traditional approach leads to very different results, viz., that in 1997 the economy was not vulnerable to changes in the exchange rate, and that in 2005 it was highly vulnerable to shekel appreciation. The conclusions in the paper support the use of the balance sheet approach as an important instrument in surveillance of financial stability, the formulation of other similar frameworks for analyzing financial risks, and the provision of more detailed data in the national balance sheet that would enable a deeper analysis of overall economic risks and the risks in the major sectors.

Applying stochastic dominance rules with borrowing and lending at the risk‐free interest rate, we derive upper and lower values for an option price for all unconstrained utility functions and alternatively for concave utility functions. The derivation of these bounds is quite general and fits any kind of stock price distribution as long as it is characterized by a “nonnegative beta.” Transaction costs and taxes can be easily incorporated in the model presented here since investors are not required to revise their portfolios continuously. The “price” that is paid for this generalization is that a range of values rather than a unique value is obtained.

We develop closed-form expressions for the path and speed of stock price discovery in a utility-based CAPM with wealth effects. Two investors with uniquely bounded risk-preferences always apply opposite portfolio rebalancing trades. These trades determine the intra-period path and speed of price discovery in a Walrasian, tâtonnement setup. While conditions for maximum speed exist, convergence is rapid over a wide range of endowments and preferences. Convergence to equilibrium is exponential, and its speed depends on endowments, risk-preferences, firm size, and market price for risk. Convergence is not guaranteed, and the conditions for divergence are specified.

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.