This paper solves the equilibrium problem in a pure-exchange, continuous-time economy in which some agents face information costs or other types of frictions effectively preventing them from investing in the stock market. Under the assumption that the restricted agents have logarithmic utilities, the existence of an equilibrium is demonstrated, and a complete characterization of equilibrium prices and consumption/investment policies is provided. The restricted agents' consumption volatility is shown to be decreased in comparison to the benchmark economy in which all agents have free access to the stock market, while the unrestricted agents' consumption volatility is increased. The impact of restricted participation on equilibrium prices is also discussed. A simple calibration shows that the model can help resolve some of the empirical asset pricing puzzles. In the special case of both classes of agents having logarithmic preferences, it is shown that restricted participation unambiguously decreases the real interest rate and increases the stock risk premium, as compared to a benchmark economy with cost less access to the stock market.

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Value at Risk (VaR) has emerged in recent years as a standard tool to measure and control the risk of trading portfolios. Yet, existing theoretical analyses of the optimal behavior of a trader subject to VaR limits have produced a negative view of VaR as a risk-control tool. In particular, VaR limits have been found to induce increased risk exposure in some states and an increased probability of extreme losses. However, these conclusions are based on models that are either static or dynamically inconsistent. In this paper we formulate a dynamically consistent model of optimal portfolio choice subject to VaR limits and show that the conclusions of earlier papers are incorrect if, consistently with common practice, the VaR is reevaluated dynamically making full use of conditioning information. In particular, we find that the risk exposure of a trader subject to a VaR limit is always lower than that of an unconstrained trader and that the probability of extreme losses is also lower. We also consider the Tail Conditional Expectation (TCE), a coherent risk measure often advocated as an alternative to VaR, and show that in our dynamic setting it is always possible to transform a TCE limit into an equivalent VaR limit, and conversely.

This paper examines the optimal consumption and investment problem for a 'large' investor, whose portfolio choices affect the instantaneous expected returns on the traded assets. Alternatively, our analysis can be interpreted in terms of an optimal growth problem with nonlinear technologies. Existence of optimal policies is established using martingale and duality techniques under general assumptions on the securities' price process and the investor's preferences. As an illustration of our characterization result, explicit solutions are provided for specific examples involving an agent with logarithmic utilities and a generalized two-factor version of the CCAPM is derived. The analogy of the consumption problem examined in this paper to the consumption problem with constraints on the portfolio choices is emphasized.

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SUMMARYThis paper tests the Cox, Ingersoll and Ross model using the prices of Italian Treasury bonds in the secondary market. The model is estimated daily for the period 30 December 1983 to 13 March 1989. The resulting term structures of interest rates are compared with those obtained using interpolation techniques (the cubic splines method). The daily estimation of the yield curves also makes it possible to analyze the changes in Treasury bond prices, determine the turning points and obtain useful indications regarding the efficiency of the secondary market and the consistency between the primary and the secondary markets.