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.     

Performance evaluation of portfolio insurance strategies using stochastic dominance criteria

This paper evaluates the performance of the stop-loss, synthetic put and constant proportion portfolio insurance techniques based on a block-bootstrap simulation. We consider not only traditional performance measures, but also some recently developed measures that capture the non-normality of the return distribution (value-at-risk, expected shortfall, and the Omega measure). We compare them to the more comprehensive stochastic dominance criteria. The impact of changing the rebalancing frequency and level of capital protection is examined. We find that, even though a buy-and-hold strategy generates higher average excess returns, it does not stochastically dominate the portfolio insurance strategies, nor vice versa. Our results indicate that a 100% floor value should be preferred to lower floor values and that daily-rebalanced synthetic put and CPPI strategies dominate their counterparts with less frequent rebalancing.     

HEDGING FIXED-RATE PREFERRED STOCK INVESTMENTS

Corporations seeking to maximize the return on their cash reserve resources have an incentive to invest in traditional preferred stock because of their right to exclude 70% of the dividends from taxation. Nevertheless, fixed-rate preferred stock investments may contribute significantly to the return volatility of a cash portfolio and cause unacceptable losses to the corporate investors. As a result, many corporations might consider such higher-return investments only if they can hedge away a sufficient amount of risk. The research presented in this article seeks to evaluate how much of the return variation of fixed-rate preferred equity portfolios can be reduced with various hedging strategies.
This research shows that it is possible to reduce the risk of preferred stock investments significantly through the use of hedges employing some combination of fixed income futures and/or options. Although some risk remains even with the hedged preferred stock portfolio, the author demonstrates that money market assets can be combined with a hedged preferred stock portfolio to create a position that has no material chance of loss but expected after-tax returns higher than those on money market investments. In addition, the article also shows the high level of profitability associated with a strategy of increasing the size of liquid reserves in order to allow for losses related to an unhedged preferred stock component of those reserves.     

The effectiveness of the VaR-based portfolio insurance strategy: An empirical analysis

This paper proposes an approach to constructing the insured portfolios under the VaR-based portfolio insurance strategy (VBPI) and provides a comprehensive analysis of its hedging effectiveness in comparison with the buy-and-hold (B&H) as well as the constant proportion portfolio insurance (CPPI) strategies in the context of the Chinese market. The results show that both of the insurance strategies are able to limit the downward returns while retaining certain upside returns, and their capabilities of reshaping the return distributions increase as the guarantee or the confidence level rises. In general, the VBPI strategy tends to outperform the CPPI strategy in terms of both the degree of downside protection and the return performance.     

Discretely adjusted option hedges

This paper analyses the distribution of returns on a hedged portfolio, consisting of a European call option and its associated stock, when the portfolio is rebalanced at discrete time intervals. Under the assumptions of the Black-Scholes model this distribution is particularly skew. In tests of the average return on a hedged portfolio this skewness leads to biased t-statistics. The paper explores the nature and extent of this bias and suggests procedures for overcoming it. Other aspects of discrete hedging are also discussed.     

OPTIMAL PORTFOLIO SELECTION WITH A SHORTFALL PROBABILITY CONSTRAINT: EVIDENCE FROM ALTERNATIVE DISTRIBUTION FUNCTIONS

We propose a new approach to optimal portfolio selection in a downside risk framework that allocates assets by maximizing expected return subject to a shortfall probability constraint, reflecting the typical desire of a risk-averse investor to limit the maximum likely loss. Our empirical results indicate that the loss-averse portfolio outperforms the widely used mean-variance approach based on the cumulative cash values, geometric mean returns, and average risk-adjusted returns. We also evaluate the relative performance of the loss-averse portfolio with normal, symmetric thin-tailed, symmetric fat-tailed, and skewed fat-tailed return distributions in terms of average return, risk, and average risk-adjusted return.     

Swap variance hedging and efficiency: The role of high moments

In this article, we propose a new theoretical approach for developing hedging strategies based on swap variance (SwV). SwV is a generalized risk measure equivalent to a polynomial combination of all moments of a return distribution. Using the S&P 500 index and West Texas Intermediate (WTI) crude oil spot and futures price data, as well as simulations by varying the distribution of asset returns, we investigate the dynamic differences between hedge ratios and portfolio performances based on SwV (with high moments) and variance (without high moments). We find that, on average, the minimizing-SwV hedging suggests more short futures contracts than minimizing-variance hedging; however, when market conditions deteriorate, the minimizing-SwV hedging suggests fewer short positions in futures. The superior posthedge performances of the mean-SwV hedged portfolios over the mean-variance hedged portfolios in highly volatile or extremely calm markets confirm the efficiency of the mean-SwV hedging strategy.     

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.     

Pension Fund Design under Long-term Fairness Constraints

We consider optimal portfolio insurance for a mutually owned with-profits pension fund. First, intergenerational fairness is imposed by requiring that the pension fund is driven towards a steady state. Subject to this condition the optimal asset allocation is identified among the class of constant proportion portfolio insurance strategies by maximising expected power utility of the benefit. For a simple contract approximate analytical results are available and accurate, whereas for a more involved contract Monte Carlo methods must be applied to pick out the best design. The main insights are (i) aggressive investment strategies are disastrous for the clients; (ii) in most cases it is optimal to gear the bonus reserve; and (iii) the results are far less sensitive to the agent's risk aversion than in the classical case of Merton (1969), and as opposed to Merton horizon matters even with constant investment opportunities (because of the serial dependence between bonuses).     

Data-driven robust mean-CVaR portfolio selection under distribution ambiguity

In this paper, we present a computationally tractable optimization method for a robust mean-CVaR portfolio selection model under the condition of distribution ambiguity. We develop an extension that allows the model to capture a zero net adjustment via a linear constraint in the mean return, which can be cast as a tractable conic programme. Also, we adopt a nonparametric bootstrap approach to calibrate the levels of ambiguity and show that the portfolio strategies are relatively immune to variations in input values. Finally, we show that the resulting robust portfolio is very well diversified and superior to its non-robust counterpart in terms of portfolio stability, expected returns and turnover. The results of numerical experiments with simulated and real market data shed light on the established behaviour of our distributionally robust optimization model.     

Pension Benefit Security: A Comparison of Solvency Requirements,a Pension Guarantee Fund,and Sponsor Support

Developed countries apply different security mechanisms in regulation to protect pension benefits: solvency requirements, a pension guarantee fund (PGF), and sponsor support. We compare these mechanisms for a generalized form of hybrid pension schemes. We calculate the expected log return for the beneficiaries, the shortfall probability, that is, the likelihood of the pension payment falling below the promised level and the expected loss given shortfall. Comparing solvency requirements to a pension guarantee system or sponsor support involves trading off risk and return. Additional spending on default insurance reduces the shortfall probability and the expected loss given shortfall but also lowers the probability of high positive returns as are feasible under solvency requirements.     

Analysis of Participating Life Insurance Contracts: A Unification Approach

Fair pricing of embedded options in life insurance contracts is usually conducted by using risk‐neutral valuation. This pricing framework assumes a perfect hedging strategy, which insurance companies can hardly pursue in practice. In this article, we extend the risk‐neutral valuation concept with a risk measurement approach. We accomplish this by first calibrating contract parameters that lead to the same market value using risk‐neutral valuation. We then measure the resulting risk assuming that insurers do not follow perfect hedging strategies. As the relevant risk measure, we use lower partial moments, comparing shortfall probability, expected shortfall, and downside variance. We show that even when contracts have the same market value, the insurance company's risk can vary widely, a finding that allows us to identify key risk drivers for participating life insurance contracts.     

Fair valuation of cliquet-style return guarantees in (homogeneous and) heterogeneous life insurance portfolios

Participating life insurance contracts allow the policyholder to participate in the annual return of a reference portfolio. Additionally, they are often equipped with an annual (cliquet-style) return guarantee. The current low interest rate environment has again refreshed the discussion on risk management and fair valuation of such embedded options. While this problem is typically discussed from the viewpoint of a single contract or a homogeneous* insurance portfolio, contracts are, in practice, managed within a heterogeneous insurance portfolio. Their valuation must then – unlike the case of asset portfolios – take account of portfolio effects: Their premiums are invested in the same reference portfolio; the contracts interact by a joint reserve, individual surrender options and joint default risk of the policy sponsor. Here, we discuss the impact of portfolio effects on the fair valuation of insurance contracts jointly managed in (homogeneous and) heterogeneous life insurance portfolios. First, in a rather general setting, including stochastic interest rates, we consider the case that otherwise homogeneous contracts interact due to the default risk of the policy sponsor. Second, and more importantly, we then also consider the case when policies are allowed to differ in further aspects like the guaranteed rate or time to maturity. We also provide an extensive numerical example for further analysis.     

Exploiting the “Win But Does Not Cover” Phenomenon in College Basketball

Wolfers (2006) was the first to document that heavy favorites in college basketball win but fail to cover the pre‐game point spread at a statistically higher rate than expected. We generate a hedged strategy to exploit the “win but does not cover” phenomenon using two wagers: a bet on the underdog sides line and a bet on the favorite money line. While one bet is guaranteed to win regardless of the outcome, both bets win if the favorite wins but does not cover. We show that the minimum‐variance portfolio best exploits this anomaly, yielding an average return of 0.34% per game and a positive return in five of the seven seasons of college basketball analyzed.     

Efficient Hedge Fund Strategy Allocations – Systematic Framework for Investors that Incorporates Higher Moments

In this paper, we provide a realistic framework that investors can use to optimize hedge fund portfolio strategy allocations. Our approach includes important aspects that investors need to address in the real world, such as how limited resources can restrict the ability to conduct multiple due diligences. Additionally, our approach is not based on a utility function, but on an easily quantifiable preference parameter, lambda. We need to account for higher moments of the return distribution within our optimization and approximate a best‐fit distribution. Thus we replace the empirical return distributions, which are often skewed or exhibit excess kurtosis, with two normal distributions. We then use the estimated return distributions in the strategy optimization. Our dataset comes from the Lipper TASS Hedge Fund Database and covers the June 1996‐December 2008 time period. Our results show in‐ and out‐of‐sample that our framework yields superior results to the Markowitz framework. It is also better able to manage regime switches, which tend to occur frequently during crises. Lastly, to test our results for stability, we use robustness tests, which allow for the time‐varying correlation structures of the strategies.     

Estimating the Cost of Equity for Property-Liability Insurance Companies

Due to the highly skewed and heavy‐tailed distributions associated with the insurance claims process, we evaluate the Rubinstein‐Leland (RL) model for its ability to improve the cost of equity estimates of insurance companies because of its distribution‐free feature. Our analyses show that there is as large as a 94‐basis‐point difference in the estimated cost of insurance equity between the RL model and the capital asset pricing model (CAPM) for the sample of property‐liability insurers with more severe departures from normality. In addition, consistent with our hypotheses, significant differences in the market risk estimates are found for insurers with return distributions that are asymmetrically distributed, and for small insurers. Third, we find significant performance improvements from using the RL model by showing smaller values of excess return of the expected return of the portfolio to the model return for a portfolio of insurers with returns that are more skewed and for a portfolio of small insurers. Finally, our panel data analysis shows the differences in the market risk estimates are significantly influenced by firm size, degree of leverage, and degree of asymmetry. The implication is that insurers should use the RL model rather than the CAPM to estimate its cost of capital if the insurer is small (assets size is less than $2,291 million), and/or its returns are not symmetrical (the value of skewness is greater than 0.509 or less than ?0.509).     

International Diversification Strategies for Direct Real Estate

This paper will disentangle the performance of international real estate into property type performance and region selection. This helps to create an international diversification strategy for direct real estate. We use constrained cross-section regression with dummy variables for regions and property types to measure the best risk reducer. We analyze the impact of currency changes on total returns by looking at a hedged and un-hedged portfolio, both stock and equally weighted. The findings show that geographic factors have the largest influence on the volatility of international real estate returns. The average variance of the regional effects is higher than the property type effects and therefore the regional effects have a higher influence on the variation of the total portfolio. However, the regional effects are less stable through time, compared with the variance and correlation of the property type effects. Also the property type effect seems to become a more important factor for the return over time, especially when the return is expressed in local currency.     

Pricing and managing risks of ruin contingent life annuities under regime switching variance gamma process

We propose a model for valuing ruin contingent life annuities under the regime-switching variance gamma process. The Esscher transform is employed to determine the equivalent martingale measure. The PIDE approach is adopted for the pricing formulation. Due to the path dependency of the payoff of the insurance product and the non-existence of a closed-form solution for the PIDE, the finite difference method is utilized to numerically calculate the value of the product. To highlight some practical features of the product, we present a numerical example. Finally, we examine numerically the performance of a simple hedging strategy by investigating the terminal distribution of hedging errors and the associated risk measures such as the value at risk and the expected shortfall. The impacts of the frequency of re-balancing the hedging portfolio on the quality of hedging are also discussed.     

A bootstrap-based comparison of portfolio insurance strategies

This study presents a systematic comparison of portfolio insurance strategies. We implement a bootstrap-based hypothesis test to assess statistical significance of the differences in a variety of downside-oriented risk and performance measures for pairs of portfolio insurance strategies. Our comparison of different strategies considers the following distinguishing characteristics: static versus dynamic protection; initial wealth versus cumulated wealth protection; model-based versus model-free protection; and strong floor compliance versus probabilistic floor compliance. Our results indicate that the classical portfolio insurance strategies synthetic put and constant proportion portfolio insurance (CPPI) provide superior downside protection compared to a simple stop-loss trading rule and also exhibit a higher risk-adjusted performance in many cases (dependent on the applied performance measure). Analyzing recently developed strategies, neither the TIPP strategy (as an ‘improved’ CPPI strategy) nor the dynamic VaR-strategy provides significant improvements over the more traditional portfolio insurance strategies.     

“KLICing” there and back again: Portfolio selection using the empirical likelihood divergence and Hellinger distance

Stutzer (2000, 2003) proposes the decay-rate maximizing portfolio selection rule wherein the investor selects the asset mix that maximizes the rate at which the probability of shortfall decays to zero. A close examination of this rule reveals that it ranks portfolios by computing the divergence, in the Kullback-Leibler sense, between the unweighted portfolio return distribution and a tilted distribution meaned at the predetermined target or benchmark rate of return selected by or imposed upon the investor. This result implies, in the IID case, that Stutzer's rules can be written as a benchmark constrained Kullback-Leibler-based optimization problem with an endogenous utility interpretation. Here we expand on this idea by introducing two closely related portfolio selection rules based on the empirical likelihood divergence and the Hellinger-Matusita distance. The first of these is the reversed Kullback-Leibler divergence and the second is proportional to the average of the two divergences. The theoretical and in-sample properties of the new criteria suggest them to be competitive with and in some cases better than existing methods, especially in terms of skewness preference.