Mitigating Estimation Risk in Asset Allocation: Diagonal Models Versus 1/N Diversification

Recent literature suggests that optimal asset‐allocation models struggle to consistently outperform the 1/N naïve diversification strategy, which highlights estimation‐risk concerns. We propose a dichotomous classification of asset‐allocation models based on which elements of the inverse covariance matrix that a model uses: diagonal only versus full matrix. We argue that parsimonious diagonal‐only strategies, which use limited information such as volatility or idiosyncratic volatility, are likely to offer a good tradeoff between incorporating limited information while mitigating estimation risk. Evaluating five sets of portfolios over 1926–2012, we find that 1/N is generally not optimal when compared with these diagonal strategies.     

Tail risk of coal futures in China's market

This study evaluates the downside tail risk of coal futures contracts (coke, coking coal and thermal coal) traded in the Chinese market between 2011 and 2021, measured by value at risk (VaR). We examine the one-day-ahead VaR forecasting performance with a hybrid econometric and deep learning model (GARCH-LSTM), GARCH family models, extreme value theory models, quantile regression models and two naïve models (historical simulation and exponentially weighted moving average). We use four backtesting techniques and the model confidence set to identify the optimal models. The results suggest that the models focusing on tail risk or utilising long short-term memory generate more effective risk management.     

Diversification benefits of risk portfolio models: a case of Taiwan’s stock market

How to construct effective investment strategies is a core issue for modern finance. In this paper, we investigate the benefits of various models by rebalancing portfolios using the daily stock return data in Taiwan. We further consider investment constraints in portfolios to ensure the feasibility of their applications. Using five performance criteria, we find the risk models, particularly the CVaR, yield higher ex ante and ex post performance than a naïve buy-and-hold portfolio. The two-stage regressions show that high return benefits are associated with a bear market while high reduction in risk is positively related to high volatility. Though VaR is regarded as a standard model applied in the real world, our findings suggest that CVaR can serve as a good alternative.     

Volatility timing: How best to forecast portfolio exposures

This paper investigates how best to forecast optimal portfolio weights in the context of a volatility timing strategy. It measures the economic value of a number of methods for forming optimal portfolios on the basis of realized volatility. These include the traditional econometric approach of forming portfolios from forecasts of the covariance matrix. Both naïve forecasts using simple historical averages, and those generated from econometric models are considered. A novel method, where a time series of optimal portfolio weights are constructed from observed realized volatility and direct forecast is also proposed. A number of naïve forecasts and the approach of directly forecasting portfolio weights show a great deal of merit. Resulting portfolios are of similar economic benefit to a number of competing approaches and are more stable across time. These findings have obvious implications for the manner in which volatility timing is undertaken in a portfolio allocation context.     

Naïve Buying Diversification and Narrow Framing by Individual Investors

We provide the first tests to distinguish whether individual investors equally balance their overall portfolios (naïve portfolio diversification, NPD) or, in contrast, equally balance the values of same-day purchases of multiple assets (naïve buying diversification, NBD). We find NBD in purchases of multiple stocks, and in mixed purchases of individual stocks and funds. In contrast, there is little evidence of NPD. Evidence suggests that NBD arises due to stock picking behavior and neglect of diversification. These findings suggest that behavioral finance theory should incorporate transaction, as well as portfolio, framing.     

How to build a factor portfolio: Does the allocation strategy matter?

Factor-based allocation embraces the idea of factors, as opposed to asset classes, as the ultimate building blocks of investment portfolios. We examine whether there is a superior way of combining factors in a portfolio and provide a comparison of factor-based allocation strategies within a multiple testing framework. Factor-based allocation is profitable beyond exploiting genuine risk premia, even when applying multiple testing corrections. Investment portfolios can be efficiently diversified using factor-based allocation strategies, as demonstrated by robust economic performance over various economic scenarios. The naïve equally weighted factor portfolio, albeit simple and cost-efficient, cannot be outperformed by more sophisticated allocation strategies.     

Cross-commodity hedging for illiquid futures: Evidence from China's base metal futures market

This paper evaluates the effectiveness of cross-commodity hedging between China's base metal spot and futures markets, using daily data of metal spot and futures prices in the Shanghai Futures Exchange. The main findings suggest that, compared to unhedged spot portfolios, a naïve hedge increases risk exposure, while static and dynamic hedges can significantly reduce the risk of holding spot assets. Zinc futures and nickel futures outperform other base metal futures in individually hedging lead spot and tin spot respectively, while copper futures constitute a moderately optimal instrument to hedge both lead and tin spot assets.     

Market share and risk taking: the role of collateral asset managers in the collapse of the arbitrage CDO market

Asset pricing theory predicts that if credit ratings do not reflect all relevant aspects of a CDO debt tranche’s risk profile (i.e., its total and systematic risk), then ratings-based tranche pricing by some naïve investors creates incentives for CDO arrangers to take excessive non-priced risk. CDO managers’ desire for repeat issuance makes them part of this risk taking strategy to exploit naïve investors. The implication is that the credit quality of CDOs run by large market share managers has a higher tendency to deteriorate in bad times. This paper finds empirical evidence for large market share manager’s conflicts of interest.     

Investigating tail-risk dependence in the cryptocurrency markets: A LASSO quantile regression approach

We construct the complete network of tail risk spillovers among major cryptocurrencies using the Least Absolute Shrinkage and Selection Operator (LASSO) quantile regression. We capture important features of the network, including major risk-driving and major risk-receiving currencies, and the evolution of the tail dependence among the currencies over time. Importantly, we reveal a striking finding that the right tail dependence among the cryptocurrencies is significantly stronger than the left tail counterpart. This unique characteristic may have contributed to the rise in popularity of cryptocurrencies over the last few years. Our portfolio analysis reveals that diversification in cryptocurrency investment can be accomplished simply by employing the naïve equal-weighted scheme even when transaction costs are taken into account.     

Can tail risk explain size,book‐to‐market,momentum, and idiosyncratic volatility anomalies?

We examine the impact of tail risk on the return dynamics of size, book‐to‐market ratio, momentum and idiosyncratic volatility sorted portfolios. Our time‐series analyses document significant portfolio return exposures to aggregate tail risk. In particular, portfolios that contain small, value, high idiosyncratic volatility and low momentum stocks exhibit negative and statistically significant tail risk betas. Our cross‐sectional analyses at the individual stock level suggest that tail risk helps in explaining the four pricing anomalies, particularly size and idiosyncratic volatility anomalies.     

Empirical estimation of tail dependence using copulas: application to Asian markets

This paper introduces non-parametric estimators for upper and lower tail dependence whose confidence intervals are obtained with a bootstrap method. We call these estimators ‘naïve estimators’ as they represent a discretization of Joe's formulae linking copulas to tail dependence. We apply the methodology to an empirical data set composed of three composite indexes for the three Tigers (Thailand, Malaysia and Indonesia). The extremes show a dependence structure which is symmetric for the Thai and Malaysian markets and asymmetric for the Thai and Indonesian markets and for the Malaysian and the Indonesian markets. Using these results we estimate the copula (which belongs to the Student or Archimedean copula families) for each pair of markets by two methods. Finally, we provide risk measurements using the best copula associated with each pair of markets.     

Multi-asset portfolio optimization and out-of-sample performance: an evaluation of Black–Litterman,mean-variance,and naïve diversification approaches

The Black–Litterman model aims to enhance asset allocation decisions by overcoming the problems of mean-variance portfolio optimization. We propose a sample-based version of the Black–Litterman model and implement it on a multi-asset portfolio consisting of global stocks, bonds, and commodity indices, covering the period from January 1993 to December 2011. We test its out-of-sample performance relative to other asset allocation models and find that Black–Litterman optimized portfolios significantly outperform naïve-diversified portfolios (1/N rule and strategic weights), and consistently perform better than mean-variance, Bayes–Stein, and minimum-variance strategies in terms of out-of-sample Sharpe ratios, even after controlling for different levels of risk aversion, investment constraints, and transaction costs. The BL model generates portfolios with lower risk, less extreme asset allocations, and higher diversification across asset classes. Sensitivity analyses indicate that these advantages are due to more stable mixed return estimates that incorporate the reliability of return predictions, smaller estimation errors, and lower turnover.     

Optimal transaction filters under transitory trading opportunities: Theory and empirical illustration

If transitory profitable trading opportunities exist, transaction filters mitigate trading costs. We use a dynamic programming framework to design an optimal filter that maximizes after-cost expected returns. The filter size depends crucially on the degree of persistence of trading opportunities, transaction cost, and standard deviation of shocks. For daily dollar–yen exchange trading, the optimal filter can be economically significantly different from a naïve filter equal to the transaction cost. The candidate trading strategies generate positive returns that disappear after transaction costs. However, when the optimal filter is used, returns after costs remain positive and higher than for naïve filters.     

Analyzing the impact of credit migration in a portfolio setting

Credit migration is an essential component of credit portfolio modeling. In this paper, we outline a framework for gauging the effects of credit migration on portfolio risk measurements. For a typical loan portfolio, we find credit migration can explain as much as 51% of volatility and 35% of economic capital. We compare through-the-cycle migration effects, implied by agency rating transitions, with point-in-time migration, implied by EDF? (Expected Default Frequency) transitions, and find that migration of point-in-time credit quality accounts for a greater fraction of total portfolio risk when compared with through-the-cycle dynamics. In a stylized analytic setting, we show that, when controlling for PD term structure effects, higher likelihood of moving away from the current credit state does not necessarily imply greater risk. Finally, we review methods for generating high-frequency transition matrices, needed for analyzing instruments with cash flows or contingencies whose frequencies are asynchronous to an available transition matrix. We further demonstrate that the naïve application of such methods can result in material deviations to portfolio analytics.     

Twenty‐five years of the Taffler z‐score model: Does it really have predictive ability?

Although copious statistical failure prediction models are described in the literature, appropriate tests of whether such methodologies really work in practice are lacking. Validation exercises typically use small samples of non‐failed firms and are not true tests of ex ante predictive ability, the key issue of relevance to model users. This paper provides the operating characteristics of the well‐known Taffler (1983) UK‐based z‐score model for the first time and evaluates its performance over the 25‐year period since it was originally developed. The model is shown to have clear predictive ability over this extended time period and dominates more naïve prediction approaches. This study also illustrates the economic value to a bank of using such methodologies for default risk assessment purposes. Prima facie, such results also demonstrate the predictive ability of the published accounting numbers and associated financial ratios used in the z‐score model calculation.     

Momentum strategies based on reward–risk stock selection criteria

In this paper, we analyze momentum strategies that are based on reward–risk stock selection criteria in contrast to ordinary momentum strategies based on a cumulative return criterion. Reward–risk stock selection criteria include the standard Sharpe ratio with variance as a risk measure, and alternative reward–risk ratios with the expected shortfall as a risk measure. We investigate momentum strategies using 517 stocks in the S&P 500 universe in the period 1996–2003. Although the cumulative return criterion provides the highest average monthly momentum profits of 1.3% compared to the monthly profit of 0.86% for the best alternative criterion, the alternative ratios provide better risk-adjusted returns measured on an independent risk-adjusted performance measure. We also provide evidence on unique distributional properties of extreme momentum portfolios analyzed within the framework of general non-normal stable Paretian distributions. Specifically, for every stock selection criterion, loser portfolios have the lowest tail index and tail index of winner portfolios is lower than that of middle deciles. The lower tail index is associated with a lower mean strategy. The lowest tail index is obtained for the cumulative return strategy. Given our data-set, these findings indicate that the cumulative return strategy obtains higher profits with the acceptance of higher tail risk, while strategies based on reward–risk criteria obtain better risk-adjusted performance with the acceptance of the lower tail risk.     

Immunization using a stochastic-process independent multi-factor model: The Portuguese experience

In this paper, we evaluate the relative immunization performance of the M-vector proposed by Nawalkha and Chambers (1997) [Nawalkha, S.K., Chambers, D.R., 1997. The M-vector model: derivation and testing of extensions to M-squared. The Journal of Portfolio Management 23, 92–98], using data for the Portuguese government debt market. Empirical results show that: (i) immunization models (single- and multi-factor) remove most of the interest rate risk underlying a more naïve maturity strategy; (ii) duration-matching portfolios constrained to include the maturity bond and formed using a single-factor model provide the best immunization performance overall, particularly in highly volatile term structure environments and shorter holding periods; (iii) varying the rebalancing frequency and the investment horizon shows that these results are less robust for Portugal than for other countries.     

Trapped in diversification – another look at the risk of fund of hedge funds

Recent literature implies that despite being more diversified, fund of hedge funds (FOFs) are exposed to tail risk. We propose an explanation for this phenomenon; tail risk is a systematic risk factor for hedge funds, which by construction, explains the higher portion of the returns in the diversified portfolios. Our study suggests that not only an additional tail risk factor improves the explanatory power of the factor model, the relative importance of tail risk factor increases with the number of underlying hedge funds in an FOF portfolio. Furthermore, we demonstrate that FOFs with a short history, higher management fees, leverage and requiring shorter lockup periods are more sensitive to tail risk.     

Decomposing the VIX: Implications for the predictability of stock returns

The VIX index is not only a volatility index but also a polynomial combination of all possible higher moments in market return distribution under the risk-neutral measure. This paper formulates the VIX as a linear decomposition of four fundamentally different elements: the realized variance (RV), the variance risk premium (VRP), the realized tail (RT), and the tail risk premium (TRP), respectively. Using an innovative and nonparametric tail risk measure, we find that approximately one-third of the VIX's formation is attributed to the TRP. In addition to VRP, RT and TRP are crucial components for predicting future returns on equity portfolios.     

Fast simulations in credit risk

We consider the problem of simulating tail loss probabilities and expected losses conditioned on exceeding a large threshold (expected shortfall) for credit portfolios. Our new idea, called the geometric shortcut, allows an efficient simulation for the case of independent obligors. It is even possible to show that, when the average default probability tends to zero, its asymptotic efficiency is higher than that of the naive algorithm. The geometric shortcut is also useful for models with dependent obligors and can be used for dependence structures modeled with arbitrary copulae. The paper contains the details for simulating the risk of the normal copula credit risk model by combining outer importance sampling with the geometric shortcut. Numerical results show that the new method is efficient in assessing tail loss probabilities and expected shortfall for credit risk portfolios. The new method outperforms all known methods, especially for credit portfolios consisting of weakly correlated obligors and for evaluating the tail loss probabilities at many thresholds in a single simulation run.