The safety first expected utility model: Experimental evidence and economic implications

Roy’s [Roy, A., 1952. Safety first and the holding of assets. Econometrica 20 (3), 431–449] safety first criterion advocates the minimization of the probability of outcomes below a certain “disaster” level. This paper examines safety first theoretically and experimentally. We find that safety first plays a crucial role in decision-making, inducing choices that cannot be explained by, and even contradict, risk-aversion, Prospect Theory, and loss-aversion in general. Yet, safety first alone cannot explain individual choice. Therefore, we propose an expected utility – safety first (EU–SF) model where decisions are made based on a weighted average of the safety first criterion and standard expected utility maximization. We experimentally estimate these relative weights, and discuss their economic implications.     

ON THE LINKAGE BETWEEN FINANCIAL RISK TOLERANCE AND RISK AVERSION

We explore the linkage between financial risk tolerance (FRT) and risk aversion. To do this, we obtain FRT scores from a psychometrically validated survey and conduct a battery of online lottery choice experiments involving the same nonstudent participants. We contrast: real and hypothetical payoffs, low and high stakes, decisions involving gains and losses, and order effects. Our key finding is that the two approaches to analyzing decision making under uncertainty are strongly aligned. We present evidence that this is particularly the case for the female participants in our sample and when high‐stake gambles are employed.     

The impact of risk and uncertainty on expected returns

We study asset pricing in economies featuring both risk and uncertainty. In our empirical analysis, we measure risk via return volatility and uncertainty via the degree of disagreement of professional forecasters, attributing different weights to each forecaster. We empirically model the typical risk-return trade-off and augment these models with our measure of uncertainty. We find stronger empirical evidence for an uncertainty-return trade-off than for the traditional risk-return trade-off. Finally, we investigate the performance of a two-factor model with risk and uncertainty in the cross section.     

Does the choice of performance measure influence the evaluation of hedge funds?

The Sharpe ratio is adequate for evaluating investment funds when the returns of those funds are normally distributed and the investor intends to place all his risky assets into just one investment fund. Hedge fund returns differ significantly from a normal distribution. For this reason, other performance measures for hedge fund returns have been proposed in both the academic and practice-oriented literature. In conducting an empirical study based on return data of 2763 hedge funds, we compare the Sharpe ratio with 12 other performance measures. Despite significant deviations of hedge fund returns from a normal distribution, our comparison of the Sharpe ratio to the other performance measures results in virtually identical rank ordering across hedge funds.     

Sufficient conditions for expected utility to imply drawdown-based performance rankings

The least restrictive sufficient condition for expected utility to imply Sharpe ratio rankings is the location and scale (LS) property (see [Sinn, 1983] and [Meyer, 1987]). The normal, the extreme value, and many other distributions commonly used in finance satisfy this property. We argue that the LS property is also sufficient for expected utility to imply drawdown-based performance measure rankings, because for investment funds satisfying the LS condition, the Sharpe ratio and drawdown-based performance measures result in identical rankings. Hence, the same conditions that provide an expected utility foundation for the Sharpe ratio also provide a foundation for drawdown-based performance measures. We conclude that from a decision-theoretic perspective, drawdown-based performance measures are as good as the Sharpe ratio.     

A decision-theoretic foundation for reward-to-risk performance measures

In this paper we prove that partial-moments-based performance measures (e.g., Omega, Kappa, upside-potential ratio, Sortino–Satchell ratio, Farinelli–Tibiletti ratio), value-at-risk-based performance measures (e.g., VaR ratio, CVaR ratio, Rachev ratio, generalized Rachev ratio), and other admissible performance measures are a strictly increasing function in the Sharpe ratio. The theoretical basis of this result is the location and scale property and two other plausible and mild conditions. Our result provides a decision-theoretic foundation for all these frequently used performance measures. Moreover, it might explain the empirical finding that all these measures typically lead to very similar rankings.     

Short-selling constraints as cause for price distortions: An experimental study

In this paper we explore the influence of the possibility to short stocks and/or borrow money in laboratory markets. A key innovation of our study is that subjects can simultaneously trade two risky assets on two double-auction markets, allowing us to differentiate between assets with relatively high versus low capitalization. Divergence of opinions is created by providing each trader with noisy information on the intrinsic values of both assets. We find that when borrowing money or shorting stocks is restricted prices are systematically distorted. Specifically, stocks with high (low) capitalization are traded at lower (higher) prices than their fundamental value. Lifting the restrictions leads to more efficient prices and more liquidity, thereby also lowering volatility and bid-ask spreads.     

The 1/N investment strategy is optimal under high model ambiguity

The 1/N investment strategy, i.e. the strategy to split one’s wealth uniformly between the available investment possibilities, recently received plenty of attention in the literature. In this paper, we demonstrate that the uniform investment strategy is rational in situations where an agent is faced with a sufficiently high degree of model uncertainty in the form of ambiguous loss distributions. More specifically, we use a classical risk minimization framework to show that, for a broad class of risk measures, as the uncertainty concerning the probabilistic model increases, the optimal decisions tend to the uniform investment strategy.To illustrate the theoretical results of the paper, we investigate the Markowitz portfolio selection model as well as Conditional Value-at-Risk minimization with ambiguous loss distributions. Subsequently, we set up a numerical study using real market data to demonstrate the convergence of optimal portfolio decisions to the uniform investment strategy.     

Spectral risk measures and portfolio selection

This paper deals with risk measurement and portfolio optimization under risk constraints. Firstly we give an overview of risk assessment from the viewpoint of risk theory, focusing on moment-based, distortion and spectral risk measures. We subsequently apply these ideas to an asset management framework using a database of hedge funds returns chosen for their non-Gaussian features. We deal with the problem of portfolio optimization under risk constraints and lead a comparative analysis of efficient portfolios. We show some robustness of optimal portfolios with respect to the choice of risk measure. Unsurprisingly, risk measures that emphasize large losses lead to slightly more diversified portfolios. However, risk measures that account primarily for worst case scenarios overweight funds with smaller tails which mitigates the relevance of diversification.     

Nonlinearly weighted convex risk measure and its application

We propose a new class of risk measures which satisfy convexity and monotonicity, two well-accepted axioms a reasonable and realistic risk measure should satisfy. Through a nonlinear weight function, the new measure can flexibly reflect the investor’s degree of risk aversion, and can control the fat-tail phenomenon of the loss distribution. A realistic portfolio selection model with typical market frictions taken into account is established based on the new measure. Real data from the Chinese stock markets and American stock markets are used for empirical comparison of the new risk measure with the expected shortfall risk measure. The in-sample and out-of-sample empirical results show that the new risk measure and the corresponding portfolio selection model can not only reflect the investor’s risk-averse attitude and the impact of different trading constraints, but can find robust optimal portfolios, which are superior to the corresponding optimal portfolios obtained under the expected shortfall risk measure.     

Optimal life insurance purchase and consumption/investment under uncertain lifetime

In this paper, we consider optimal insurance and consumption rules for a wage earner whose lifetime is random. The wage earner is endowed with an initial wealth, and he also receives an income continuously, but this may be terminated by the wage earner’s premature death. We use dynamic programming to analyze this problem and derive the optimal insurance and consumption rules. Explicit solutions are found for the family of CRRA utilities, and the demand for life insurance is studied by examining our solutions and doing numerical experiments.     

On the role of the estimation error in prediction of expected shortfall

In the estimation of risk measures such as Value at Risk and Expected shortfall relatively short estimation windows are typically used rendering the estimation error a possibly non-negligible component. In this paper we build upon previous results for the Value at Risk and discuss how the estimation error comes into play for the Expected Shortfall. We identify two important aspects where it may be of importance. On the one hand there is in the evaluation of predictors of the measure. On the other there is in the interpretation and communication of it. We illustrate magnitudes numerically and emphasize the practical importance of the latter aspect in an empirical application with stock market index data.     

An empirical analysis of the factors impacting discount rates: Evidence from the U.S. Marine Corps

This analysis examines the impact of age, race, marital status, number of dependents, education, rank, years of service, and occupational code on personal discount rates. The study focuses on 3241 Marine Corps officers/enlisted personnel between 1992 and 1997 who separated from the Marine Corps through the VSI program (an annuity payment) or the SSB program (lump-sum payment). The analysis finds that, although the degree of statistical significance varied between the officer model and the enlisted model, holding other factors constant, females and individuals with more years of service or education were less likely to take the lump-sum payment, and that blacks and individuals with more dependents were more likely to take the lump-sum payment. Across all demographic factors, enlisted personnel had statistically significantly higher average discount rates than officers, as is consistent with prior studies. The estimated personal discount rates averaged 14.9% for officers and 24% for enlisted Marines. This study contributes to the literature in that it is the only study to examine the Marines during this time period. Many of the results can be generalized to the civilian sector to assist in formulation of savings/retirement policies.     

Sentiment and stock prices: The case of aviation disasters

Behavioral economic studies reveal that negative sentiment driven by bad mood and anxiety affects investment decisions and may hence affect asset pricing. In this study we examine the effect of aviation disasters on stock prices. We find evidence of a significant negative event effect with an average market loss of more than $60 billion per aviation disaster, whereas the estimated actual loss is no more than $1 billion. In two days a price reversal occurs. We find the effect to be greater in small and riskier stocks and in firms belonging to less stable industries. This event effect is also accompanied by an increase in the perceived risk: implied volatility increases after aviation disasters without an increase in actual volatility.     

Assessing the risk-return trade-off in loan portfolios

This paper proposes a methodology to analyse the risk and return of large loan portfolios in a joint setting. I propose a tractable model to obtain the distribution of loan returns from observed interest rates and default frequencies. I follow a sectoral approach that captures the heterogeneous cyclical features of different kinds of loans and yields moments in closed form. I investigate the validity of mean–variance analysis with a value at risk constraint and study its relationship with utility maximisation. Finally, I study the efficiency of corporate and household loan portfolios in an empirical application to the Spanish banking system.     

Portfolio credit-risk optimization

This paper evaluates several alternative formulations for minimizing the credit risk of a portfolio of financial contracts with different counterparties. Credit risk optimization is challenging because the portfolio loss distribution is typically unavailable in closed form. This makes it difficult to accurately compute Value-at-Risk (VaR) and expected shortfall (ES) at the extreme quantiles that are of practical interest to financial institutions. Our formulations all exploit the conditional independence of counterparties under a structural credit risk model. We consider various approximations to the conditional portfolio loss distribution and formulate VaR and ES minimization problems for each case. We use two realistic credit portfolios to assess the in- and out-of-sample performance for the resulting VaR- and ES-optimized portfolios, as well as for those which we obtain by minimizing the variance or the second moment of the portfolio losses. We find that a Normal approximation to the conditional loss distribution performs best from a practical standpoint.     

Equity and fixed income markets as drivers of securitised real estate

This paper re-examines the sensitivity and importance of interest rates and stock market price behavior on securitised property by decomposing their long-run impact between transient and permanent effects. This is achieved in a framework that accounts for endogenously determined structural breaks within the data. The results provide a different perspective on the relationship securitised property has with these markets and sheds new light on their long-run interaction. Once structural breaks are accounted for the results show that securitised property is driven by both interest rate and stock market changes, regardless of the type of securitised property being examined. Evidence also points to companies with increased debt-to-asset ratios and companies that are tax-exempt entities are still all influenced by both the equity and fixed income markets over the long-run period, although the influence these factors have do vary across time.     

PORTFOLIO OPTIMIZATION UNDER TRACKING ERROR AND WEIGHTS CONSTRAINTS

The performance of active portfolio managers who must comply with a weights constraint is often assessed against a benchmark. The weights constraint is common as the funds are committed by their own prospectus to a minimum (or maximum) portfolio concentration. We characterize the optimal asset allocation and analyze the implications of the weights constraint on the manager's performance and on the relevance of the information ratio. We obtain that because of the weights constraint, at the optimum, the information ratio often decreases when the manager is free to deviate more from the benchmark.