In this paper, we analytically derive the expected loss function associated with using sample means and the covariance matrix of returns to estimate the optimal portfolio. Our analytical results show ...that the standard plug-in approach that replaces the population parameters by their sample estimates can lead to very poor out-of-sample performance. We further show that with parameter uncertainty, holding the sample tangency portfolio and the riskless asset is never optimal. An investor can benefit by holding some other risky portfolios that help reduce the estimation risk. In particular, we show that a portfolio that optimally combines the riskless asset, the sample tangency portfolio, and the sample global minimum-variance portfolio dominates a portfolio with just the riskless asset and the sample tangency portfolio, suggesting that the presence of estimation risk completely alters the theoretical recommendation of a two-fund portfolio.
This paper investigates the comparative statics of "more ambiguity aversion" as defined by Klibanoff, Marinacci and Mukerji (2005, "A Smooth Model of Decision Making under Ambiguity", Econometrica, ...73 (6), 1849-1892). The analysis uses the static two-asset portfolio problem with one safe asset and one uncertain one. While it is intuitive that more ambiguity aversion would reduce demand for the uncertain asset, this is not necessarily the case. We derive sufficient conditions for a reduction in the demand for the uncertain asset and for an increase in the equity premium. An example that meets the sufficient conditions is when the set of plausible distributions for returns on the uncertain asset can be ranked according to their monotone likelihood ratio. It is also shown how ambiguity aversion distorts the price kernel in the alternative portfolio problem with complete markets for contingent claims.
We study whether investors can exploit serial dependence in stock returns to improve out-of-sample portfolio performance. We show that a vector-autoregressive (VAR) model captures stock return serial ...dependence in a statistically significant manner. Analytically, we demonstrate that, unlike contrarian and momentum portfolios, an arbitrage portfolio based on the VAR model attains positive expected returns regardless of the sign of asset return cross-covariances and autocovariances. Empirically, we show, however, that both the arbitrage and mean-variance portfolios based on the VAR model outperform the traditional unconditional portfolios only for transaction costs below ten basis points.
This study examines whether local stock returns vary with local business cycles in a predictable manner. We find that U.S. state portfolios earn higher future returns when state-level unemployment ...rates are higher and housing collateral ratios are lower. During the 1978 to 2009 period, geography-based trading strategies earn annualized risk-adjusted returns of 5%. This abnormal performance reflects time-varying systematic risks and local-trading induced mispricing. Consistent with the mispricing explanation, the evidence of predictability is stronger among firms with low visibility and high local ownership. Nonlocal domestic and foreign investors arbitrage away the predictable patterns in local returns in 1 year.
The heuristic <inline-formula><tex-math notation="LaTeX">1/N</tex-math></inline-formula> (i.e., equally weighted) portfolio and heuristic quintile portfolio are both popular simple strategies in ...financial investment. In the <inline-formula><tex-math notation="LaTeX">1/N</tex-math></inline-formula> portfolio, a fraction of <inline-formula><tex-math notation="LaTeX">1/N</tex-math></inline-formula> of the wealth is allocated to each of the <inline-formula><tex-math notation="LaTeX">N</tex-math></inline-formula> available assets. In the quintile portfolio, first the assets are sorted according to some characteristics, e.g., expected returns, and then the strategy equally longs the top 20% (i.e., top quintile) and perhaps shorts the bottom 20% (i.e., bottom quintile). Although they have been criticized for their lack of mathematical justification when proposed by practitioners, they have shown great advantage over more sophisticated portfolios in terms of stable performance and easy deployment. In this paper, we reinterpret the <inline-formula><tex-math notation="LaTeX">1/N</tex-math></inline-formula> and quintile portfolios as solutions to a mathematically sound robust portfolio optimization under different levels of robustness level in the stocks' characteristics. A variance-adjusted robustness uncertainty set is also proposed, leading to the inverse-volatility portfolios, whose nonzero weights are inversely proportional to their standard deviation.
We propose a high dimensional minimum variance portfolio estimator under statistical factor models, and show that our estimated portfolio enjoys sharp risk consistency. Our approach relies on ...properly integrating ℓ1 constraint on portfolio weights with an appropriate covariance matrix estimator. In terms of covariance matrix estimation, we extend the theoretical results of POET (Fan et al., 2013) to a setting that is coherent with principal component analysis. Simulation and extensive empirical studies on S&P 100 Index constituent stocks demonstrate favorable performance of our MVP estimator compared with benchmark portfolios.
We trace the impact of formative experiences on portfolio choice. Plausibly exogenous variation in workers' exposure to a depression allows us to identify the effects and a new estimation approach ...makes addressing wealth and income effects possible. We find that adversely affected workers are less likely to invest in risky assets. This result is robust to a number of control variables and it holds for individuals whose income, employment, and wealth were unaffected. The effects travel through social networks: individuals whose neighbors and family members experienced adverse circumstances also avoid risky investments.
The portfolio optimization model has limited impact in practice because of estimation issues when applied to real data. To address this, we adapt two machine learning methods, regularization and ...cross-validation, for portfolio optimization. First, we introduce
performance-based regularization
(PBR), where the idea is to constrain the sample variances of the estimated portfolio risk and return, which steers the solution toward one associated with less estimation error in the performance. We consider PBR for both mean-variance and mean-conditional value-at-risk (CVaR) problems. For the mean-variance problem, PBR introduces a quartic polynomial constraint, for which we make two convex approximations: one based on rank-1 approximation and another based on a convex quadratic approximation. The rank-1 approximation PBR adds a bias to the optimal allocation, and the convex quadratic approximation PBR shrinks the sample covariance matrix. For the mean-CVaR problem, the PBR model is a combinatorial optimization problem, but we prove its convex relaxation, a quadratically constrained quadratic program, is essentially tight. We show that the PBR models can be cast as robust optimization problems with novel uncertainty sets and establish asymptotic optimality of both sample average approximation (SAA) and PBR solutions and the corresponding efficient frontiers. To calibrate the right-hand sides of the PBR constraints, we develop new, performance-based
k
-fold cross-validation algorithms. Using these algorithms, we carry out an extensive empirical investigation of PBR against SAA, as well as L1 and L2 regularizations and the equally weighted portfolio. We find that PBR dominates all other benchmarks for two out of three Fama–French data sets.
This paper was accepted by Yinyu Ye, optimization
.
Bitcoin has been increasingly viewed as a new form of investment, yet its role as an asset in a diversified industry portfolio is not well understood. In this paper, we explore the dynamic ...interdependence between Bitcoin and the ten global industry sectors classified by the Global Industry Classification Standard. We find, in accordance with previous literature, that Bitcoin is relatively isolated from traditional industries. While the near-zero correlation with traditional financial assets offers some diversification benefits to investors, these benefits are counterbalanced by the volatility of the asset. Bitcoin’s optimal presence in a minimum variance portfolio is only about 1 percent – a weight that is robust to various methods for estimating the return covariance matrix. Bitcoin’s optimal weight in portfolios maximizing Sharpe and Sortino ratios are on the magnitude of 10 to 20 percent. Hence, the value of Bitcoin as an asset in a diversified portfolio critically depends on investors’ views about the future of Blockchain technology.
•We explore dynamic interdependence between Bitcoin and ten global industry sectors.•Results indicate that Bitcoin is relatively isolated from traditional industries.•Hence, Bitcoin offers some diversification benefits to investors.•However, these benefits are counterbalanced by the volatility of the asset.
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