Methodology
The aim of efficient indexation is to improve the risk-reward ratio of a broadly diversified stock market portfolio compared to the cap-weighted index. To generate such an efficient index, we resort to mean-variance optimisation. Although our aim to maximise risk-return efficiency is fully consistent with financial theory, successful implementation of the theory depends not only on its conceptual grounds but also on the reliability of the input to the model. In our case, the results depend greatly on the quality of the parameter estimate (the covariance matrix and the expected returns of all stocks in the index).
The standard CAPM theory, as it happens, is a poor guide to the input parameters. For the CAPM, expected returns should be proportional to the stock's beta, though it has in fact been shown that such a relationship does not hold. Likewise, the single-factor nature of the CAPM would mean that there is a single (market) factor driving the correlation of stocks, whereas the consensus in both academe and business is that multifactor models do a better job capturing the common drivers behind stock comovements.
We generate proxies for tangency portfolios that rely on robust input parameters for both the covariance matrix and expected returns. One challenge is the estimation of expected return parameters. Instead of relying purely on statistics, which is known to generate poor expected return estimates, we use a common sense estimate of expected returns that relies on a risk-reward trade-off. We use the insight that the return on a given stock in excess of the risk-free rate is proportional to the riskiness of the stock. Investors are often underdiversified and averse not only to systematic risk but also the specific risk of a stock. Investors shun the volatility, negative skewness, and kurtosis of a stock's returns. We use a suitably designed risk measure that integrates these aspects and estimate expected returns by sorting stocks into high risk and low risk categories. The second central ingredient in the tangency portfolio is an estimate of the covariance of stock returns. We use a robust estimation procedure that first extracts the common factors of stock returns and then uses these factors to model the comovement of individual stocks. This efficient indexation procedure allows us to construct indices whose risk/reward ratio is significantly better than that of cap-weighted indices.
 | "Efficient Indexation: An Alternative to Cap-Weighted Indices" |
