Predictability of VRP: A Comparison Study

Empirical evidence suggests that excess bond returns are forecastable by financial indicators such as forward spreads and yield spreads, a violation of the expectations hypothesis based on constant risk premia. But existing evidence does not tie the forecastable variation in excess bond returns to underlying macroeconomic fundamentals, as would be expected if the forecastability were attributable to time variation in risk premia. We use the methodology of dynamic factor analysis for large datasets to investigate possible empirical linkages between forecastable variation in excess bond returns and macroeconomic fundamentals. We find that several common factors estimated from a large dataset on U.S. economic activity have important forecasting power for future excess returns on U.S. government bonds. Following Cochrane and Piazzesi (2005), we also construct single predictor state variables by forming linear combinations of either five or six estimated common factors. The single state variables forecast excess bond returns at maturities from two to five years, and do so virtually as well as an unrestricted regression model that includes each common factor as a separate predictor variable. The linear combinations we form are driven by both "real" and "inflation" macro factors, in addition to financial factors, and contain important information about one year ahead excess bond returns that is not captured by forward spreads, yield spreads, or the principal components of the yield covariance matrix.

VIX Decomposed Tail Risk Premia and the Tail Risk Factor

We measure “good” and “bad” variance premia that capture risk compensations for the realized variation in positive and negative market returns, respectively. The two variance premium components jointly predict excess returns over the next one and two years with statistically significant positive (negative) coefficients on the good (bad) component. The R2s reach about 10% for aggregate equity and portfolio returns and 20% for corporate bond returns. To explain the new empirical evidence, we develop a model that highlights the differential impact of upside and downside risk on equity and variance risk premia. The online appendix is available at https://doi.org/10.1287/mnsc.2017.2890 . This paper was accepted by Neng Wang, finance.

Credit default swap spreads and variance risk premia

In this paper, we analyse, modify, and apply one of the most widely used measures of systemic risk, SRISK, developed by Brownlees and Engle (in Rev Financ Stud 30:48–79, 2016). The measure is defined as the expected capital shortfall of a firm conditional on a prolonged market decline. We argue that segregated funds, also known as separate accounts in the US, should be excluded from actuarial liabilities when SRISK is calculated for insurance companies. We also demonstrate the importance of careful analysis of accounting standards when specifying the prudential capital ratio used in SRISK methodology. Based on the proposed adjustments to SRISK, we assess the systemic risk of the Canadian banking and insurance industries. It is shown that in its current implementation, the SRISK methodology substantially overestimates the systemic risk of Canadian insurance companies.

The recombining binomial tree approach, which has been initiated by Cox et al. (J Financ Econ 7: 229–263, 1979) and extended to arbitrary diffusion models by Nelson and Ramaswamy (Rev Financ Stud 3(3): 393–430, 1990) and Hull and White (J Financ Quant Anal 25: 87–100, 1990a), is applied to the simultaneous evaluation of price and Greeks for the amortized fixed and variable rate mortgage prepayment option. We consider the simplified binomial tree approximation to arbitrary diffusion processes by Costabile and Massabo (J Deriv 17(3): 65–85, 2010) and analyze its numerical applicability to the mortgage valuation problem for some Vasicek and CIR-like interest rate models. For fixed rates and binomial trees with about thousand steps, we obtain very good results. For the Vasicek model, we also compare the closed-form analytical approximation of the callable fixed rate mortgage price by Xie (IAENG Int J Appl Math 39(1): 9, 2009) with its binomial tree counterpart. With respect to the binomial tree values one observes a systematic underestimation (overestimation) of the callable mortgage price (prepayment option price) analytical approximation. This numerical discrepancy increases at longer maturities and becomes impractical for a valuable estimation of the prepayment option price.

Variance risk: A bird’s eye view

This paper proposes a stochastic optimization model for generating the optimal price-maker trading strategy for a wind power producer using virtual bidding, which is a kind of financial tool available in most electricity markets of the United States. In the proposed model, virtual bidding is used to improve the wind power producer's market power in the day-ahead (DA) market by trading at multiple buses, which are not limited to the locations of the wind units. The optimal joint wind power and virtual trading strategy is generated by solving a bi-level nonlinear stochastic optimization model. The upper-level problem maximizes the total expected profit of the wind power and virtual bidding while using the conditional value at risk (CVaR) for risk management. The lower-level problem represents the clearing process of the DA market. By using the Ka-rush-Kuhn-Tucker (KKT) conditions, duality theory, and big- <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$M$</tex> method, the bi-level nonlinear stochastic model is firstly transferred into an equivalent single-level stochastic mathematical program with the equilibrium constraints (MPEC) model and then a mixed-integer linear programming (MILP) model, which can be solved by existing commercial solvers. To reduce the computational cost of solving the proposed stochastic optimization model for large systems, a method of reducing the number of buses considered for virtual bidding is proposed to simplify the stochastic MPEC model by reducing its decision variables and constraints related to virtual bidding. Case studies are performed to show the effectiveness of the proposed model and the method of reducing the number of buses considered for virtual bidding. The impacts of the transmission limits, wind unit location, risk aversion parameters, wind power volatility, and wind and virtual capacities on the price-maker trading strategy are also studied through case studies.

Growth and Inflation Implications of Systemic Risk in the Euro Area Banking Industry: Lessons from the Financial Crisis

This article sought to understand the behavior of young low-income university students through an experiment based on prospect and hyperbolic discounting theory, with risk and time preferences, and their relationships with financial literacy with regard to choice probability distortions. There is a notable lack of studies that simultaneously address risk and time preferences in low-income urban groups, relating experiments based on prospect theory to capture probability distortions in choice processes. This study opens the doors for the question of the relationship between poverty and risk and time preferences to be better discussed in Brazil with the aim of providing evidence that supports national financial literacy plans. The study shows the importance of financial education as a means of reducing agents’ probability distortion. This is crucial, given that probability distortion is one of the pillars of prospect theory. This experiment was based on prospect and hyperbolic discounting theory and used value, weight, and quasi-hyperbolic discounting functions within a maximum likelihood methodology to estimate the risk and time parameters with sociodemographic variables, and with the Financial Literacy Index moderating variable, in a private HEI, with 54 students and 5,940 lotteries. It was observed that low-income urban populations in emerging economies have similar risk and loss aversion parameters to rural populations in developing countries. Low-income students have a greater preference for the present, with it being perceived that a small increase in income is associated with a higher level of patience, making decisions more rational. A better financial education could lead to a smaller probability distortion.

&lt;p&gt;The contemporary risk management practice emphasizes the interplay of multilevel risks, of which the systematic and systemic risks are considered the main culprits of catastrophic losses. With this in mind, this thesis investigates three important topics in quantitative risk management, in which the systematic and systemic risks play a devastating role.&lt;/p&gt;&lt;p&gt;First of all, we center on the design of reinsurance policies that accommodate the joint interests of the insurer and reinsurer by drawing upon the celebrated notion of Pareto optimality in the context of a distortion-risk-measure-based model. Such a topic is of considerable practical interest in the current post financial crisis era when people have witnessed the significant systemic risk posed by the insurance industry and the vulnerability of insurance companies to systemic events. Specifically, we characterize the set of Pareto-optimal reinsurance policies analytically and introduce the Pareto frontier to visualize the insurer-reinsurer trade-off structure geometrically. Another enormous merit of developing the Pareto frontier is the considerable ease with which Pareto-optimal reinsurance policies can be constructed even in the presence of the insurer's and reinsurer's individual risk constraints. A strikingly simple graphical search of these constrained policies is performed in the special cases of value-at-risk and tail value-at-risk.&lt;/p&gt;&lt;p&gt;Secondly, we propose probabilistic and structural characterizations for insurance indemnities that are universally marketable in the sense that they appeal to both policyholders and insurers irrespective of their risk preferences and risk profiles. We begin with the univariate case where there is a single risk facing the policyholder, then extend our results to the case where multiple possibly dependent risks co-exist according to a mixture structure capturing policyholder's exposure to systematic and systemic risks.&lt;/p&gt;&lt;p&gt;Next, we study the asymptotic behavior of the loss from defaults of a large credit portfolio. We consider a static structural model in which latent variables governing individual defaults follow a mixture structure incorporating idiosyncratic, systematic, and systemic risks. The portfolio effect, namely the decrease in overall risk due to the portfolio size increase, is taken into account. We derive sharp asymptotics for the tail probability of the portfolio loss as the portfolio size becomes large and our main finding is that the occurrence of large losses can be attributed to either the common shock variable or systematic risk factor, whichever has a heavier tail.&lt;/p&gt;&lt;p&gt;Finally, we extend the asymptotic study of loss from defaults of a large credit portfolio under an amalgamated model. Aiming at investigating the dependence among the risk components of each obligor, we propose a static structural model in which each obligor's default indicator, loss given default, and exposure at default are respectively governed by three dependent latent variables with exposure to idiosyncratic, systematic, and systemic risks. The asymptotic distribution as well as the asymptotic value-at-risk and expected shortfall of the portfolio loss are obtained. The results are further refined when a specific mixture structure is employed for latent variables.&lt;/p&gt;

We consider the practical investment consequences of implementing the two most popular formulations of the scalarization (or risk-aversion) parameter in the time-consistent dynamic mean–variance (MV) portfolio optimization problem. Specifically, we compare results using a scalarization parameter assumed to be (i) constant and (ii) inversely proportional to the investor’s wealth. Since the link between the scalarization parameter formulation and risk preferences is known to be nontrivial (even in the case where a constant scalarization parameter is used), the comparison is viewed from the perspective of an investor who is otherwise agnostic regarding the philosophical motivations underlying the different formulations and their relation to theoretical risk-aversion considerations, and instead simply wishes to compare investment outcomes of the different strategies. In order to consider the investment problem in a realistic setting, we extend some known results to allow for the case where the risky asset follows a jump-diffusion process, and examine multiple sets of plausible investment constraints that are applied simultaneously. We show that the investment strategies obtained using a scalarization parameter that is inversely proportional to wealth, which enjoys widespread popularity in the literature applying MV optimization in institutional settings, can exhibit some undesirable and impractical characteristics.

Agriculture's potential to reduce poverty assumes that income from crops can significantly increase per capita income of small farm households. Using nationally representative data on the value and variable costs of production of 10 crops (rice, maize, blackgram, chickpea, pigeonpea, mustard, groundnut, soybean, sunflower, sesamum) commonly grown in India, we calculated the mean benefit: cost (B:C) ratios and profit per hectare for each crop in seven three-year periods between 2000 and 2020. All crops were profitable (B:C &gt; 1) in all periods but B:C varied widely and unpredictably, both between crops and with time. We then calculated, for the maximum and minimum observed national level values of B:C for each crop, the relation between household land per capita (LPC) over the range 0–1.0 hectares per person, and the crop personal daily income (CPDI) in PPP $ per person per day that would be generated by growing that crop. Only three out of a possible 100 combinations of crop and LPC (chickpea, 2005–2008, LPC = 1.0 and mustard (2008–2011, LPC = 0.9 or 1.0) generated CPDI values greater than a poverty line of $2.15 per person per day. A large survey confirmed that 96.9% of farming households in India had LPC values of 1.0 hectares per person or less. The majority of farming households could not have generated enough income from growing any of these crops during this twenty-year period to reach a poverty line of $2.15 per person per day. Most farms in India do not have enough land to benefit much from intensifying their crop production. Such small incentives and uncertainty about expected returns on investment (and increased exposure to risk) might contribute to low adoption of best practices, and more in-depth studies of rural household livelihood portfolios are needed to clarify that assumption.

We consider a political economy in which government cares about risk-averse farmers’ loss of income but incurs political cost if it provides monetary support to farmers. Farmers’ expectations of government disaster aid and overconfidence (optimism bias) regarding their risk prevent farmers from purchasing full insurance under actuarially fair rates. Considering this conclusion, government prefers to subsidize farmers’ purchases of insurance ex ante rather than solely relying on disaster aid ex post. The resulting subsidy rate depends on the political environment, the degree of systemic risk, the distribution of farmers’ risk preferences, and the nature and distribution of farmers’ risk perceptions.

The measurement and determination of risk have received considerable attention in recent years. One measure of risk is systematic risk, defined in terms of the covariance of a security's return with the return from the market portfolio. The relationship is often standardized by dividing the covariance by the variance of return from the market portfolio. Hereafter, this measure of standardized systematic risk shall be referred to as beta.