World Income Components: Measuring and Exploiting International Risk Sharing Opportunities

We provide methods of decomposing the variance of world national incomes into components in such a way as to indicate the most important risk-sharing opportunities, and, therefore, the most important missing international risk markets to establish. One method uses a total variance reduction criterion, and identified risk-sharing opportunities in terms of eigenvectors of a variance matrix of residuals produced when country incomes are regressed on world income. Another method uses a mean-variance utility-maximizing criterion and identifies risk-sharing opportunities in terms of eigenvectors of a variance matrix of deviations of country incomes from their respective contract-year shares of world income. The two methods are applied using Summers-Heston [1991] data on national incomes for large countries 1950-1990, each using two different methods of estimating variances. While these data are not sufficient to provide accurate estimates of the requisite variance matrices of (transformed) national incomes, the results are suggestive of important new markets that could actually be created, and show that there may be large welfare gains to creating some of these markets.

The Significance of the Market Portfolio

The market portfolio (world portfolio) is in one sense a least important portfolio to provide to investors; there is always a better portfolio for social planners to make available to them. In a J-agent one-period stochastic endowment economy, where preferences are quadratic, the market portfolio is never spanned by the optimal markets a social planner would create. With identical preferences, the market portfolio is orthogonal to all J - 1 portfolios which achieve a first best solution. These conclusions rely on the assumption that the social planner has perfect information about agents' utilities. We also show that as the contract designer's information about agents' utilities becomes more imperfect, the optimal contracts approach contracts that weight individual endowments in proportion to elements of eigenvectors of the variance matrix of endowments. If there is a substantial market component to endowments than a social planner, for reasons of robustness and simplicity, may conclude that creating a contract to allow trading the market portfolio would be a significant innovation.

Growth Uncertainty and Risksharing

How large are potential benefits from global risksharing? In order to answer this question we propose a new methodology that is closely connected with the empirical growth literature. We obtain estimates of residual risk (growth uncertainty) at various horizons from regressions of country-specific growth in deviation from, world growth on a wide set of variables in the information set. Since this residual risk can be entirely hedged through risksharing, we use it to obtain a measure of the potential welfare gain\u27for\u27 a representative country. We find that nations can reap very large benefits from, engaging in such risksharing arrangements

The Significance of the Market Portfolio

The market portfolio, the portfolio of all endowments in the world, has great significance in the capital asset pricing model (CAPM) in finance. The Sharpe-Lintner CAPM characterization of optimal risk sharing implies that in equilibrium no one will be subject to a random shock that is not shared by everyone else. ^ Thus, the CAPM gives us the mutual fund theorem, which asserts that only one risky portfolio need be available to individual investors, the mutual fund that holds the market portfolio. In this paper we seek further clarification of the significance of the market portfolio beyond the bounds of the restrictive assumptions of the CAPM

World Income Components: Measuring and Exploiting Risk-Sharing Opportunities

We provide a method for decomposing the variance of changes in incomes in the world into components, world income components (WICs), in such a way as to indicate the most important risk-sharing opportunities among people of the world. We develop a constant absolute risk premium model, an intertemporal general equilibrium model of the world that facilitates consideration of optimal contract design. We show that for a contract designer maximizing a social welfare function, the optimal risk-management contracts maximize the equilibrium world real interest rate. That is the contract designer achieves the risk-optimal interest rate. We show that these WIC securities are defined in terms of eigenvectors of a transformed variance matrix of income changes. The method is applied with a variance matrix estimated using Penn World Table data on the G-7 countries, 1950-92.Constant Absolute Risk Premium, risk-optimal interest rate, three-level income model, WIC securities, contract design, macro markets, hedging

World Income Components: Measuring and Exploiting Risk-Sharing Opportunities

We provide a method for decomposing the variance of changes in incomes in the world into components, world income components (WICs), in such a way as to indicate the most important risk-sharing opportunities among people of the world. We develop a constant absolute risk premium model, an intertemporal general equilibrium model of the world that facilitates consideration of optimal contract design. We show that for a contract designer maximizing a social welfare function, the optimal risk-management contracts maximize the equilibrium world real interest rate. That is the contract designer achieves the risk-optimal interest rate. We show that these WIC securities are defined in terms of eigenvectors of a transformed variance matrix of income changes. The method is applied with a variance matrix estimated using Penn World Table data on the G-7 countries, 1950-92

World Income Components: Measuring and Exploiting International Risk Sharing Opportunities

We provide a method for decomposing the variance of world national income (present values) into components in such a way as to indicate the most important risk-sharing opportunities among nations of the world. We identify risk-sharing opportunities in terms of eigenvectors of a variance matrix of deviations of the present value of country incomes from their respective shares (adjusted for population and risk aversion) of world income. The method is applied to data on national incomes of six large countries 1870-1992 (Maddison [1995]): Canada, France, Germany, Italy, United Kingdom and United States. The method reveals that, assuming symmetric risk aversions, the most important risk sharing contract to devise for these countries would be essentially a national income swap between the United States, and together on the other side, France, Germany and Italy, i.e., approximately a US-Europe national income swap. A contract that is essentially a France-Germany swap is the second most important risk-sharing contract

Asset Prices and Consumption in a Model of Perpetual Youth

I construct a general equilibrium overlapping generations model with heterogeneous agents and obtain analytical solutions to asset prices, consumption, and asset demands. Individuals have constant absolute risk aversion and a constant probability of dying. Agents have three stages in their lives. In the first stage, agents are young and constrained from investing in stocks. In the second stage they work, and in the third they retire. I analyze asset prices numerically and with comparative statics. Changing any exogenous parameter has large effects on asset prices when there are large demographic changes to the population constrained from investing in stocks.