Intraday Empirical Analysis and Modeling of Diversified World Stock Indices

This paper proposes an approach to the intraday analysis of diversified world stock accumulation indices. The growth optimal portfolio (GOP) is used as reference unit or benchmark in a continuous financial market model. Diversified portfolios, covering the world stock market, are constructed and shown to approximate the GOP, providing the basis for a range of financial applications. The normalized GOP is modeled as a time transformed square root process of dimension four. Its dynamics are empirically verified for several world stock indices. Furthermore, the evolution of the transformed time is modeled as the integral over a rapidly evolving mean-reverting market activity process with deterministic volatility. The empirical findings suggest a rather simple and robust model for a world stock index that reflects the historical evolution, by using only a few readily observable parameters.world stock index; intraday analysis; growth optimal portfolio; diversified portfolio; market activity; deseasonalization; square root process

Carbon portfolio management

The aim of the European Union's Emissions Trading Scheme (EU ETS) is that by 2020, emissions from sectors covered by the EU ETS will be 21% lower than in 2005. In addition to large CO 2 emitting companies covered by the scheme, other participants have entered the market with a view of using emission allowances for the diversification of their investment portfolios. The performance of this asset as a stand alone investment and its portfolio diversification implications will be investigated in this paper. Our results indicate that the market views Phases 1, 2, and 3 European Union allowance futures as unattractive as stand alone investments. In a portfolio context, in Phase 1, once the short-selling option is added, there are considerable portfolio benefits. However, our results indicate that these benefits only existed briefly during the pilot stage of the EU ETS. There is no evidence to suggest portfolio diversification benefits exist for Phase 2 or the early stages of Phase 3

Robust Portfolios and Weak Incentives in Long-Run Investments

When the planning horizon is long, and the safe asset grows indefinitely, isoelastic portfolios are nearly optimal for investors who are close to isoelastic for high wealth, and not too risk averse for low wealth. We prove this result in a general arbitrage-free, frictionless, semimartingale model. As a consequence, optimal portfolios are robust to the perturbations in preferences induced by common option compensation schemes, and such incentives are weaker when their horizon is longer. Robust option incentives are possible, but require several, arbitrarily large exercise prices, and are not always convex