Mixed data sampling expectile regression with applications to measuring financial risk

To avoid information loss or measurement error in traditional methods dealing with mixed frequency data, we develop a novel mixed data sampling expectile regression (MIDAS-ER) model to measure financial risk. We construct the MIDAS-ER model by introducing a MIDAS structure into expectile regressions. This enables us to perform an expectile regression on raw mixed frequency data directly. We apply the proposed MIDAS-ER model to estimate two popular financial risk measures, namely, Value at Risk and Expected Shortfall, with both simulated data and four stock indices, and compare the model's performance with those of several popular models. The outstanding performance of our model demonstrates that high-frequency information helps to improve the accuracy of risk measurement. In addition, the numerical results also imply that our model can be a significant tool for risk-averse investors to control risk losses and for financial institutions to implement robust risk management.     

Diversification in Portfolios of Individual Stocks: 100 Stocks Are Not Enough

We examine returns and ending wealth in portfolios selected from 1,000 large U.S. stocks over a 20‐year holding period. Shortfall risk, the possibility of ending wealth being below a target, is a useful metric for long horizon investors and is consistent with the Safety First criterion. Density functions obtained from simulations illustrate that shortfall risk reduction continues as portfolio size is increased, even above 100 stocks. A slightly lower risk can be achieved in small portfolios by diversifying across industries, but a greater reduction is obtained by simply increasing the number of stocks.     

The impact of mandatory IFRS reporting on institutional trading costs: Evidence from Australia

This study examines the impact of mandatory International Financial Reporting Standards (IFRS) on the market quality of the Australian Securities Exchange (ASX) 200 constituent stocks. Using traditional metrics that are consistent with prior literature (i.e., bid‐ask spreads), the first stage analysis confirms that stock liquidity has improved. However, when the analysis is extended to consider the trading costs incurred by market participants (i.e., execution shortfall), results suggest liquidity has not changed significantly. The paper utilizes rich unique datasets that contain detailed trade information, and findings are robust after controlling for trade difficulty and market conditions. In the era of High Frequency Trading (HFT) and occurrences of ‘fleeting’ liquidity, this paper provides some evidence that while IFRS may have enhanced ‘visible’ bid‐ask spreads, tangible liquidity for market participants, particularly global institutional investors, has not improved significantly.     

Estimating portfolio risk for tail risk protection strategies

We forecast portfolio risk for managing dynamic tail risk protection strategies, based on extreme value theory, expectile regression, copula‐GARCH and dynamic generalized autoregressive score models. Utilizing a loss function that overcomes the lack of elicitability for expected shortfall, we propose a novel expected shortfall (and value‐at‐risk) forecast combination approach, which dominates simple and sophisticated standalone models as well as a simple average combination approach in modeling the tail of the portfolio return distribution. While the associated dynamic risk targeting or portfolio insurance strategies provide effective downside protection, the latter strategies suffer less from inferior risk forecasts, given the defensive portfolio insurance mechanics.     

LIMIT THEOREMS FOR PARTIAL HEDGING UNDER TRANSACTION COSTS

We study shortfall risk minimization for American options with path‐dependent payoffs under proportional transaction costs in the Black–Scholes (BS) model. We show that for this case the shortfall risk is a limit of similar terms in an appropriate sequence of binomial models. We also prove that in the continuous time BS model, for a given initial capital, there exists a portfolio strategy which minimizes the shortfall risk. In the absence of transactions costs (complete markets) similar limit theorems were obtained by Dolinsky and Kifer for game options. In the presence of transaction costs the markets are no longer complete and additional machinery is required. Shortfall risk minimization for American options under transaction costs was not studied before.     

ASSET ALLOCATION AND ANNUITY-PURCHASE STRATEGIES TO MINIMIZE THE PROBABILITY OF FINANCIAL RUIN

In this paper, we derive the optimal investment and annuitization strategies for a retiree whose objective is to minimize the probability of lifetime ruin, namely the probability that a fixed consumption strategy will lead to zero wealth while the individual is still alive. Recent papers in the insurance economics literature have examined utility-maximizing annuitization strategies. Others in the probability, finance, and risk management literature have derived shortfall-minimizing investment and hedging strategies given a limited amount of initial capital. This paper brings the two strands of research together. Our model pre-supposes a retiree who does not currently have sufficient wealth to purchase a life annuity that will yield her exogenously desired fixed consumption level. She seeks the asset allocation and annuitization strategy that will minimize the probability of lifetime ruin. We demonstrate that because of the binary nature of the investor's goal, she will not annuitize any of her wealth until she can fully cover her desired consumption with a life annuity. We derive a variational inequality that governs the ruin probability and the optimal strategies, and we demonstrate that the problem can be recast as a related optimal stopping problem which yields a free-boundary problem that is more tractable. We numerically calculate the ruin probability and optimal strategies and examine how they change as we vary the mortality assumption and parameters of the financial model. Moreover, for the special case of exponential future lifetime, we solve the (dual) problem explicitly. As a byproduct of our calculations, we are able to quantify the reduction in lifetime ruin probability that comes from being able to manage the investment portfolio dynamically and purchase annuities.     

Risk measure pricing and hedging in incomplete markets

This article attempts to extend the complete market option pricing theory to incomplete markets. Instead of eliminating the risk by a perfect hedging portfolio, partial hedging will be adopted and some residual risk at expiration will be tolerated. The risk measure (or risk indifference) prices charged for buying or selling an option are associated to the capital required for dynamic hedging so that the risk exposure will not increase. The associated optimal hedging portfolio is decided by minimizing a convex measure of risk. I will give the definition of risk-efficient options and confirm that options evaluated by risk measure pricing rules are indeed risk-efficient. Relationships to utility indifference pricing and pricing by valuation and stress measures will be discussed. Examples using the shortfall risk measure and average VaR will be shown. The work of Mingxin Xu is supported by the National Science Foundation under grant SES-0518869. I would like to thank Steven Shreve for insightful comments, especially his suggestions to extend the pricing idea from using shortfall risk measure to coherent ones, and to study its relationship to utility based derivative pricing. The comments from the associate editor and the anonymous referee have reshaped the paper into its current version. The paper has benefited from discussions with Freddy Delbaen, Jan Večeř, David Heath, Dmitry Kramkov, Peter Carr, and Joel Avrin.     

Credit portfolios: What defines risk horizons and risk measurement?

The strong autocorrelation between economic cycles demands that we analyze credit portfolio risk in a multiperiod setup. We embed a standard one-factor model in such a setup. We discuss the calibration of the model to Standard & Poor’s ratings data in detail. But because single-period risk measures cannot capture the cumulative effects of systematic shocks over several periods, we define an alternative risk measure, which we call the time-conditional expected shortfall (TES), to quantify credit portfolio risk over a multiperiod horizon.     

沪深股市风险度量中半参数ES模型的实证检验

目前度量预期不足(Expected Shortfall, ES)的风险技术大多基于参数模型,其建模过程避免不了对收益的分布类型做出假定,但这些分布往往与现实相悖。为此,介绍两种重要半参数模型,即CARE模型和CARES模型,并应用我国2007-2016年上证综合指数与深证成分指数的相关数据评估模型优劣。结果表明：CARES模型与CARE模型在度量我国股市风险中都具有较好的效果,但两者比较,CARES模型明显优于CARE模型。因此,CARES模型能作为我国股市风险度量工具中的一个重要补充。