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Despite its significance for Finance as an academic field, mean-variance optimization has yet to be broadly accepted as an investment opportunity in practicedue to the crippling effects estimation errors have on the out-of-sample performance of such portfolios. In this paper we offer a novel approach that aims at resolving this issue. More precisely, we propose optimizing portfolios based on forecasted ranking information instead of historical data. The main idea behind this approach is that reducing the informational content of input parameters eliminates outliers caused by estimation errors which in turn means mean-variance optimization suggests less extreme weights resulting in an overall better diversified and less concentrated portfolio. Our results confirm that our approach has a higher risk-adjusted performance compared to the plug-in mean-variance approach and also outperforms naively diversified portfolios. Furthermore, our approach is more effective when estimation errors are expected to be larger.
Mean monthly Sharpe ratios for rank-based mean-variance portfolios (yellow) optimized according to our forecasted ranks, plug-in mean variance portfolios (pink) where parameters are based on the past 120 monthly returns and equally-weighted portfolios (brown). All portfolios are based on randomly drawn samples from the 49 industry cross-section. The number of portfolios within each sample starts at 5 and increases in steps of 5 up to 45 portfolios.
Cumulative abnormal benchmarked returns (vs. IPO), equally weighted, full sample (solid line: only breakpoints, dashed line: including IPOs, dotted line: including break points as of break dates)
Estimating parameter inputs for portfolio optimization has been shown to be notoriously difficult and gets further complicated by structural breaks and regime shifts in financial data. We argue that these structural breaks ultimately result in parameter uncertainty, to which investors are averse. On an aggregate market level, this ambiguity-aversion gives rise to a premium for parameter uncertainty as stocks with high (low) parameter uncertainty are avoided/sold (more attractive/bought). We propose a novel measure called break-(adjusted stock-) age that proxies for parameter uncertainty and is based on detecting structural breaks in stock returns using unsupervised machine learning techniques. Our measure reveals (i) that break-age is priced significantly in the cross-section of stock returns and (ii) that break-age is a powerful proxy for parameter uncertainty.
We analyze the characteristics of 22 leading equity indices and discuss common biases relative to their respective national equity markets. Findings demonstrate systematic risk-factor exposures on a universally consistent basis in form of a large-cap, low beta, growth and contrarian tilt. These systematic biases are also relevant given their knock-on effect on public changes in consumption due to a changes in net wealth, especially as more private investors are utilizing ETFs on the basis of these indices rather than delegated mandates in form of mutual or pension funds.
Three-year rolling CAPM betas. Figure shows the three-year rolling CAPM betas of leading stock market indices versus their respective national market portfolios. The observation period is between 07/1997–03/2017 and corresponds to 238 monthly observations
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