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This chapter provides a short overview of the main concepts, ideas, and tools that have been produced by more than fifty years of research in the evaluation of risky projects and risky assets. It is devoted to the analysis of the risk premium for risky projects that should be added to the discount rate for safe projects. Here, valuing risky projects introduces a new dimension to the theory of investment. We have shown that this new dimension can be treated by transforming each future cash flow into its certainty equivalent. By doing this, one is back to the problem of evaluating a safe project, and the discount rates discussed in this book can be used.

Many proposals to reform the current social security system would permit the investment of retirement funds in risky assets such as equities. This chapter asks whether there is an important role for international financial assets in a privatized social security system. It shows that international equities provide significant diversification benefits and should be very attractive to retired investors who are currently holding either the real annuity provided by social security or a risky portfolio of domestic assets. The chapter first provides an overview of social security, focusing on the nature of its cash flows. It then explores the consequences of allowing individuals to add risky assets to their retirement portfolios, provides evidence on the behavior of labor income, and analyzes the benefits of a reformed social security system that allows retirees to earn returns on the basis of an optimal investment in the stock market during the retirement period. Finally, the chapter considers the issue of how retirement funds should be invested during the working years.

Chapter III explains and illustrates what it means for an economic theory to be empirically relevant. A theory’s empirical relevance depends on the empirical context in which it is tested and on the explication of empirical relevance. In present-day econometrics the empirical context of a test is determined by the characteristics of the data generating process. Also, the theory is empirically relevant if and only if the test gives the researcher no reason to reject the theory. In formal econometrics the empirical context of a test is determined by a probability distribution of the data - the MPD - that is induced by the probability distribution of the theory variables and the bridge principles. Also, the theory is empirically relevant if and only if there is a model of its axioms and a model of the bridge principles that determine a model of the MPD that belongs to a 95% confidence band around a meaningful statistical estimate of the MPD. Examples from experimental economics, consumer choice, simultaneous equations, and choice among safe and risky assets illustrate the contrasting characteristics of the notion of empirical relevance in present-day and formal econometrics.

This chapter examines public policy options to build wealth for America's middle class, such as increasing savings rates, minimizing individual risk exposure, and lowering the costs of building wealth. It first provides a historical overview of wealth building in the United States before turning to a discussion of three salient characteristics associated with recent patterns of wealth-holding: little savings, inequality, and concentration in risky assets. It then considers wealth-building measures that the government may implement, such as turning tax deductions for personal savings into refundable tax credits, streamlining tax incentives for savings, increasing the transparency of financial markets, offering incentives for more financial market competition, and offering directly supported loans.

The concept of market completeness is discussed in some detail and we prove that the Black–Scholes model is complete. We also discuss how completeness and absence of arbitrage is related to the number of risky assets and the number of random sources in the model.