Domenico Cuoco

Optimal Dynamic Trading Strategies with Risk Limits

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 portfolio VaR is reevaluated dynamically making use of available conditioning information. In particular, we ?nd 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 risk limits formulated in terms of 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.

Optimal Consumption of a Divisible Durable Good

We examine the intertemporal optimal consumption and investment problem in a continuous-time economy with a divisible durable good. Consumption services are assumed to be proportional to the stock of the good held and adjustment of the stock is costly, in that it involves the payment of a proportional transaction cost. For the case in which the investor has an isoelastic utility function and asset prices follow a geometric Brownian motion, we establish the existence of an optimal policy and provide an explicit representation for the value function. We show that the investor acts so as to maintain the ratio of the stock of the durable to total wealth in a fixed (nonstochastic) range and that the optimal investment policy involves stochastic portfolio weights. The dependence of the optimal policies on the parameters of the model is also discussed.