A reward–risk measure that accounts for systemic risk is proposed. In particular, the authors address the portfolio diversification problem when systemic risk is high by performing reward–risk portfolio optimization on simulated data. The profitability of several strategies based on the forecasted evolution of returns is examined.
The authors propose a reward–risk performance measure that considers the comovement of returns for financial assets. By simulating a large number of realistic scenarios, the proposed measure is estimated and applied to portfolio selection. The empirical analysis shows that, compared with other measures, the new measure offers the opportunity to generate better performance during periods of financial instability.
How Is This Research Useful to Practitioners?
During the recent financial crisis, asset managers had difficulty achieving diversification because of the increased level of systemic risk. The authors propose a reward–risk performance measure based on co-measures of risk and reward. On the basis of the Rachev ratio (see Biglova, Ortobelli, Rachev, and Styanov, Journal of Portfolio Management 2004), they suggest a co-expected tail loss (CoETL) measure, which they define as the average of the portfolio losses when all the assets are in distress. Because CoETL considers all assets, it is a good choice to measure the portfolio downside risk in the presence of systemic risk. Using the same logic, they suggest a co-expected tail profit (CoETP) measure to account for the co-reward of the portfolio return. What they call the “co-Rachev ratio,” which equals the CoETP measure divided by the CoETL measure, accounts for the comovements of losses and profits. The authors optimize a portfolio by maximizing the co-Rachev ratio.
To evaluate a robust estimator of a “tail” portfolio measure, a sufficient number of observations are needed when the portfolio return is in the tail. The authors propose a method to build scenarios based on a simulated copula.
Finally, they apply the proposed performance measure to portfolio selection. A portfolio maximized with the co-Rachev ratio performs better than one maximized with the Sharpe ratio, even after considering transaction costs. The co-Rachev ratio strategy appears to be able to account for systemic risk. Moreover, the co-Rachev ratio provides more portfolio diversification among the returns.
The empirical analysis shows that the co-Rachev ratio offers the opportunity to generate improved performance during periods of financial instability. The portfolio is characterized by a relatively high portfolio turnover because of the consideration of systemic risk.
How Did the Authors Conduct This Research?
The authors use empirical analysis to compare portfolio performance based on different risk measures. To start, they use stock indexes of the first 14 developed countries (as classified by MSCI Barra) with the highest nominal GDP according to the International Monetary Fund. The data include the daily MSCI stock index return series from 4 January 1988 to 15 March 2012, totaling 6,312 observations.
Because tail events are rare, the authors simulate a sufficiently large number of realistic scenarios. The algorithm to generate future return scenarios involves the following steps: First, the authors approximate each return for each country at each day with an ARMA(1,1)–GARCH(1,1) model process and then provide the marginal distributions for standardized innovations of each return used to simulate the next-period returns. Next, they estimate the dependence structure among the innovations with an asymmetrical t-copula. Finally, they combine the marginal distributions and the scenarios for the copula into scenarios for the vector of future standardized innovations. The generated future scenarios incorporate heavy tailness, volatility clustering, and the multivariate dependency structure of the return distribution.
On the basis of these generated scenarios, portfolio optimization problems in the presence of increased systemic risk can be solved. The authors compare the ex post wealth and total return obtained by maximizing the daily reward–risk performance measure.
Starting with 1 June 2007, the authors use a moving window of 5,062 daily historical return observations to evaluate the model’s parameters. The period of ex post analysis is from 1 June 2007 to 15 March 2015, which includes most of the recent financial crisis. After considering transaction costs, the total return and final wealth of the co-Rachev ratio strategy are 0.141 and 1.172, respectively, which outperforms the corresponding figures of –0.076 and 0.906 for the Sharpe ratio strategy.
In traditional portfolio theory, systemic risk is positively related to return. But during the recent financial crisis, the comovement of assets generated a contagion effect on portfolios. The authors make two contributions to address the systemic risk. First, they propose a measure that maximizes the return per unit of the systemic risk of the portfolio at the tail. Second, they propose a method to build scenarios based on a simulated copula, which is helpful to approximate the asymmetrical and heavy-tailed stock returns.