Optimal market indices using value-at-risk : a first empirical approach for three stock markets

Since Fama's Efficient Market Hypothesis (EMH), numerous authors have argued that it is impossible to constantly beat the market. The best an investor can do is buy and hold 'the market' through a market index. Taking into account the important role of market indices as benchmarks against which we compare performance and as tools to prove efficiency or calculate Capital Asset Pricing Model (CAPM), few articles have studied how we should build, weigh or incorporate Modern Portfolio Theory into market index construction. Everybody accepts market indices as an essential part of finance, but nobody seems to care about them. In this article, we propose a different way of calculating market indices, which uses characteristics of optimal portfolios and risk control to establish the components' weights. We present the minimum risk indices using a Value-at-Risk (VaR) minimization problem and prove that they have less risk than current market indices, and that in some markets they beat the actual market index.