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In this paper we consider a problem, called convex projection, of projecting a convex set onto a subspace. We will show that to a convex projection one can assign a particular multiobjective convex optimization problem, such that the solution to that problem also solves the convex projection (and vice versa), which is analogous to the result in the polyhedral convex case considered in Löhne and Weißing (Math Methods Oper Res 84(2):411–426, 2016). In practice, however, one can only compute approximate solutions in the (bounded or selfbounded) convex case, which solve the problem up to a given error tolerance. We will show that for approximate solutions a similar connection can be proven, but the tolerance level needs to be adjusted. That is, an approximate solution of the convex projection solves the multiobjective problem only with an increased error. Similarly, an approximate solution of the multi-objective problem solves the convex projection with an increased error. In both cases the tolerance is increased proportionally to amultiplier. Thesemultipliers are deduced and shown to be sharp. These results allow to compute approximate solutions to a convex projection problem by computing approximate solutions to the corresponding multi-objective convex optimization problem, for which algorithms exist in the bounded case. For completeness, we will also investigate the potential generalization of the following result to the convex case. In Löhne and Weißing (Math Methods Oper Res 84(2):411–426, 2016), it has been shown for the polyhedral case, how to construct a polyhedral projection associated to any given vector linear program and how to relate their solutions. This in turn yields an equivalence between polyhedral projection, multi-objective linear programming and vector linear programming. We will show that only some parts of this result can be generalized to the convex case, and discuss the limitations.

Based on a large panel of listed firms from 52 countries in the period 2002–2020, we inves-tigate the relationship between corporate social responsibility (CSR) and equity risk. We confirm previous evidence that higher CSR scores are related to lower risk measures, con-sidering all types of risks: total, systematic, and idiosyncratic. Analyzing a large interna-tional sample allows us to investigate the role of country and company characteristics in the relationship between CSR scores and risk measures. The risk-reducing effect is more pronounced in weaker institutional environments. It is stronger in civil-law countries, in countries with low security regulation or disclosure requirement levels and where financial information is less widespread. Firms in high impact or high profile industries benefit more from CSR than firms in other industries as do firms that are not cross-listed. The financial crisis has increased the risk-reducing effect of CSR. The main results are confirmed in the COVID-19 period.

The aim of this paper is to study the optimal investment problem by using coherent acceptability indices (CAIs) as a tool to measure the portfolio performance. We call this problem the acceptability maximization. First, we study the one-period (static) case, and propose a numerical algorithm that approximates the original problem by a sequence of risk minimization problems. The results are applied to several important CAIs, such as the gain-to-loss ratio, the risk-adjusted return on capital and the tail-value-at-risk based CAI. In the second part of the paper we investigate the acceptability maximization in a discrete time dynamic setup. Using robust representations of CAIs in terms of a family of dynamic coherent risk measures (DCRMs), we establish an intriguing dichotomy: if the corresponding family of DCRMs is recursive (i.e. strongly time consistent) and assuming some recursive structure of the market model, then the acceptability maximization problem reduces to just a one period problem and the maximal acceptability is constant across all states and times. On the other hand, if the family of DCRMs is not recursive, which is often the case, then the acceptability maximization problem ordinarily is a time-inconsistent stochastic control problem, similar to the classical mean-variance criteria. To overcome this form of time-inconsistency, we adapt to our setup the set-valued Bellman's principle recently proposed in \cite{KovacovaRudloff2019} applied to two particular dynamic CAIs - the dynamic risk-adjusted return on capital and the dynamic gain-to-loss ratio. The obtained theoretical results are illustrated via numerical examples that include, in particular, the computation of the intermediate mean-risk efficient frontiers., 31 pages, 3 figures

Important dimensions of dividend behavior are not well understood. How do dividends behave in extreme states of the world? Why is the risk premium on dividend claims so high? Would dividend bans in crisis states have plausible effects on firms' cost of capital? In this paper we use evidence from the ongoing Corona pandemic to shed light on these questions. We find that, contrary to the folklore that near-future dividends are smoother than earnings or share prices, the opposite is true in disaster states. It appears that firms do not fulfill their role as liquidity intermediaries for their shareholders in precisely those states, in which predictable cash payments would be valued most highly. This is consistent with the apparent puzzle that near-maturity dividend futures have provided investors with "anomalously" high returns in the past years. In light of the recent Corona disaster, these risk premia are consistent with compensation for negative co-skewness and exposure to disaster risk. Our findings imply that policy setters who consider banning dividends in a crisis should take into account the potential effect this is likely to have on firms' future cost of capital.

We introduce implied volatility duration (IVD) as a new measure for the timing of uncertainty resolution, with a high IVD corresponding to late resolution. Portfolio sorts on a large cross-section of stocks indicate that investors demand, on average, more than 5% return per year as a compensation for a late resolution of uncertainty. In a general equilibrium model, we show that “late” stocks can only have higher expected returns than “early” stocks if the investor exhibits a preference for early resolution of uncertainty. Our empirical analysis thus provides a purely market-based assessment of the timing preferences of the marginal investor.

In this paper we present results on dynamic multivariate scalar risk measures, which arise in markets with transaction costs and systemic risk. Dual representations of such risk measures are presented. These are then used to obtain the main results of this paper on time consistency; namely, an equivalent recursive formulation of multivariate scalar risk measures to multiportfolio time consistency. We are motivated to study time consistency of multivariate scalar risk measures as the superhedging risk measure in markets with transaction costs (with a single eligible asset) (Jouini and Kallal (1995), Löhne and Rudloff (2014), Roux and Zastawniak (2016)) does not satisfy the usual scalar concept of time consistency. In fact, as demonstrated in (Feinstein and Rudloff (2021)), scalar risk measures with the same scalarization weight at all times would not be time consistent in general. The deduced recursive relation for the scalarizations of multiportfolio time consistent set-valued risk measures provided in this paper requires consideration of the entire family of scalarizations. In this way we develop a direct notion of a “moving scalarization” for scalar time consistency that corroborates recent research on scalarizations of dynamic multi-objective problems (Karnam, Ma and Zhang (2017), Kováčová and Rudloff (2021)).

We study whether firms spread out debt maturity dates, which we call "granularity of corporate debt.'' In our model, firms that are unable to roll over expiring debt need to liquidate assets. If multiple small asset sales are less inefficient than a single large one, it can be optimal to diversify debt rollovers across time. Using a large sample of corporate bond issuers during the 1991-2012 period, we establish novel stylized facts and evidence consistent with our model's predictions. There is substantial heterogeneity, i.e., firms have both concentrated and dispersed debt structures. Debt maturities are more dispersed for larger and more mature firms, for firms with better investment opportunities, with higher leverage, and with lower profitability. During the recent financial crisis firms with valuable investment opportunities implemented more dispersed maturity structures. Finally, firms manage granularity actively and adjust toward target levels.

This paper shows with a formal model that under monopoly regulation, OPEX-risk can be a source for a CAPEX-bias. If OPEX and CAPEX are substitutes, the regulated firm can reduce the risk of the firm and thereby reduce the true cost of capital by rebalancing OPEX and CAPEX. If the regulated rate-of-return on capital is not influenced by the firm’s actions, this creates a margin between the regulated rate-of-return and the true cost of capital; this causes a CAPEX-bias. We examine the so-called fixed-OPEX-CAPEX-share (FOCS), which is a variation of TOTEX-regulation, as a promising remedy to address the CAPEX-bias. We argue that FOCS is effective to address the CAPEX-bias, while it can easily be implemented.

For incomplete preference relations that are represented by multiple priors and/or multiple -- possibly multivariate -- utility functions, we define a certainty equivalent as well as the utility buy and sell prices and indifference price bounds as set-valued functions of the claim. Furthermore, we motivate and introduce the notion of a weak and a strong certainty equivalent. We will show that our definitions contain as special cases some definitions found in the literature so far on complete or special incomplete preferences. We prove monotonicity and convexity properties of utility buy and sell prices that hold in total analogy to the properties of the scalar indifference prices for complete preferences. We show how the (weak and strong) set-valued certainty equivalent as well as the indifference price bounds can be computed or approximated by solving convex vector optimization problems. Numerical examples and their economic interpretations are given for the univariate as well as for the multivariate case.

Optimization plays an important role in many methods routinely used in statistics, machine learning and data science. Often, implementations of these methods rely on highly specialized optimization algorithms, designed to be only applicable within a specific application. However, in many instances recent advances, in particular in the field of convex optimization, make it possible to conveniently and straightforwardly use modern solvers instead with the advantage of enabling broader usage scenarios and thus promoting reusability. This paper introduces the R optimization infrastructure ROI which provides an extensible infrastructure to model linear, quadratic, conic and general nonlinear optimization problems in a consistent way. Furthermore, the infrastructure administers many different solvers, reformulations, problem collections and functions to read and write optimization problems in various formats.

Using unsecured bond spreads over the 2007 to mid‐2014 period, we test investors’ ability to price bank loan risk. We use a new measure of loan risk that incorporates forward‐looking information embedded in ratings assigned by external rating agencies to bank loan portfolios. Only Italian banks are required to systematically disclose this specific information. We find that investors do price forward‐looking information inherent in bank loan portfolios. This finding reflects the increase in risk perception following the sovereign debt crisis, which had the strongest effects on peripheral countries, with tensions in the lending market. Overall, these results suggest that our new forward‐looking measure provides an additional channel through which market discipline can operate.

This paper shows that low‐risk anomalies in the capital asset pricing model and in traditional factor models arise when investors require compensation for coskewness risk. Empirically, we find that option‐implied ex ante skewness is strongly related to ex post residual coskewness, which allows us to construct coskewness factor‐mimicking portfolios. Controlling for skewness renders the alphas of betting‐against‐beta and betting‐against‐volatility insignificant. We also show that the returns of beta‐ and volatility‐sorted portfolios are driven largely by a single principal component, which in turn is explained largely by skewness.

We propose a novel framework for credit risk modeling, where default or failure information and rating or expert information are jointly incorporated in the model. These sources of information are modeled as response variables in a multivariate ordinal regression model estimated by a composite likelihood procedure. The proposed framework provides probabilities of default conditional on the rating information observed at the beginning of a predetermined period and is able to account for missing failure or credit rating information. Our approach is, to the best of our knowledge, the first that consistently combines failure-prediction models, where default indicators are used as responses, with so-called shadow rating models, where the responses are estimates of default probabilities usually derived from the leading credit rating agencies. In our empirical analysis we apply the proposed framework to a data set of US firms over the period from 1985 to 2014. Different sets of financial ratios constructed from financial statements and market information are selected as bankruptcy predictors in line with the standard literature in failure-prediction modeling. We find that the joint model of failures and credit ratings outperforms state-of-the-art failure-prediction models and shadow rating approaches in terms of prediction accuracy and discriminatory power

We find that bond issues increased substantially since the onset of the COVID-19 crisis in week 12 (March 16-20). This is the case for bonds rated A or higher, but also for bonds rated BBB or lower, although to a lesser extent. We find that the earliest issuers, issuing in weeks 12 and 13, have mostly ratings A or better, have substantial experience from previous bond issues, and are larger. Over the subsequent crisis weeks, the average issue rating deteriorates, issuers are less experienced and they are smaller. This may be partly due to Fed programs which were announced in week 13, and may have reduced market stress, thereby enabling a broader segment of firms to access the bond market. Compared to their previous issues, firms choose longer maturities during the crisis. Determinants of corporate bond spreads change substantially during COVID-19. Before, asset tangibility has a highly significant negative effect on spreads, but this is not the case in the crisis. Also, in contrast to normal periods, being a dividend payer has a significant spread-increasing effect during the crisis. Finally, experience from past bond issues significantly reduces credit spreads during the crisis, but not in normal periods. We also provide descriptive statistics for equity issuance activities during the COVID-19 crisis. Here a different picture emerges. Issuance activity slowed considerably during the crisis, both in terms of numbers and capital raised, and only recovered in the first two weeks of May.

Based on a unique data set of driving behavior we test whether private in- formation in driving characteristics has significant effects on contract choice and risk in automobile insurance. We define a driving factor based on over- all distance driven, number of car rides, and speeding. Using local weather conditions, we account for the endogeneity of the driving factor. While this driving factor has an effect on risk, there is no significant evidence for se- lection effects in the level of third-party liability and first-party insurance coverage.

We show that the effect of regulation on credit rating informativeness depends on asset complexity. Using the Dodd-Frank Act as a shock to the rating industry, we analyze the impact of rating changes on market prices, conditioning on various measures of complexity. Rating informativeness improves after Dodd-Frank, but not for assets with high complexity. Our results are robust to alternative measures of informativeness and provide strong evidence that the impact of regulation varies in the cross-section of securities. Our findings are consistent with models combining rating shopping with rating agencies that strategically decide on information acquisition and rating inflation. (JEL, G12, G32) Received July 23, 2020; editorial decision November 10, 2021 by editor Andrew Ellul. Authors have furnished an Internet Appendix, which is available on the Oxford University Press Web site next to the link to the final published paper online.

This paper presents empirical evidence that the maturity structure of financial leverage affects the cross-section of equity returns. We find that short-term leverage is associated with a positive premium, whereas long-term leverage is not. The premium for short-term compared to long-term leverage reflects higher exposure of equity to systematic risk. To rationalize our findings, we show that the same patterns emerge in a model of debt rollover risk with endogenous leverage and debt maturity choice. Our results suggest that analyses of leverage effects in asset prices and corporate financial applications should account for the maturity structure of debt.

We investigate how volatility shocks affect investors’ risk-taking, risk perception and forecasts. We run artefactual field experiments with two participant pools (finance professionals and students), differing in (i) the direction of the shock (down, up, or a neutral case) and (ii) the presentation format of the time series (prices or returns). Professionals’ investments are negatively associated with the price change and performance of the stock and their perceived risk increases to a similar extent following shocks of all directions. Students’ risk perception, in contrast, is more closely related to the frequency of negative returns rather than an increase in volatility.

We study asset management decisions of three competing student managed funds in Vienna Austria for a 10 year period. This real-world experience allows us to precisely test the tournament effect of fund management, the disposition effect and managerial team size. We find support for risk taking by the trailing funds in an annual tournament, and risk reductions by leading funds. The disposition effect usually observed in the case of retail investors is reversed. Finally, we find that smaller management teams outperform larger ones. Using a partly controlled setting, we relate the results to practice in the areas of institutional client evaluation of managers and the social and organizational structure of asset management companies.

The paper studies structural credit risk models with incomplete information of the asset value. It is shown that the pricing of typical corporate securities such as equity, corporate bonds or CDSs leads to a nonlinear filtering problem. This problem cannot be tackled with standard techniques as the default time does not have an intensity under full information. We therefore transform the problem to a standard filtering problem for a stopped diffusion process. This problem is analyzed via SPDE results from the filtering literature. In particular we are able to characterize the default intensity under incomplete information in terms of the conditional density of the asset value process. Moreover, we give an explicit description of the dynamics of corporate security prices. Finally, we explain how the model can be applied to the pricing of bond and equity options and we present results from a number of numerical experiments.

In fixed exchange rate systems, default risks tend to have devastating effects on currencies, usually leading to sharp devaluations. However, little is known about the relationship between default expectations and exchange rates in floating rate regimes. This column uses data from a broad set of currencies to uncover a strong link between exchange rate movements and sovereign risk across all exchange rate regimes. This relationship is largely caused by countries’ exposure to global sovereign risk factors and shown to be driven by changes in default expectations.

An increase in a country's sovereign risk, as measured by credit default swap spreads, is accompanied by a contemporaneous depreciation of its currency and an increase of its volatility. The relation between currency excess returns and sovereign risk is mainly driven by default expectations (rather than distress risk premia) and exposure to global sovereign risk shocks, and also emerges in a predictive setting for currency risk premia. We show that a sovereign risk factor is priced in the cross-section of currency returns and that it is not subsumed by the carry factor., Christian Wagner acknowledges support from the Center for Financial Frictions (FRIC), grant no. DNRF102

We find that US public firms spread out their debt more across different sources in recession quarters, making measures of debt concentration move pro-cyclically. There is substantial cross-sectional variation in these dynamics. Firms with less leverage and higher debt concentration further decrease leverage and increase debt concentration in recessions. The opposite is true for firms with higher leverage and lower debt concentration. The latter (former) group consists of firms that are larger (smaller), less risky (riskier), have fewer (more) growth options and lower (higher) cash levels. While the fraction of total assets funded by bank debt increases in the recession by approximately 18% of its average non-recession level, the equivalent measure for market debt drops by approximately 7%. Bank debt, in particular, term loans, appears to become more attractive during recession quarters, especially for borrowers characterized by high profitability while firm size, in contrast, has a positive effect on the use of market debt in recessions. A cluster analysis shows that a substantial fraction of firms changes its debt policy over the business cycle. For example, 12% of the firms that exclusively use bond-financing pre-recession switch to bank-financing during recessions.

This paper investigates whether security markets price the effect of social distancing on firms’ operations. We document that firms that are more resilient to social distancing significantly outperformed those with lower resilience during the COVID-19 outbreak, even after controlling for the standard risk factors. Similar cross-sectional return differentials already emerged before the COVID-19 crisis: the 2014-19 cumulative return differential between more and less resilient firms is of similar size as during the outbreak, suggesting growing awareness of pandemic risk well in advance of its materialization. Finally, we use stock option prices to infer the market’s return expectations after the onset of the pandemic: even at a two-year horizon, stocks of more pandemic-resilient firms are expected to yield significantly lower returns than less resilient ones, reflecting their lower exposure to disaster risk. Hence, going forward, markets appear to price exposure to a new risk factor, namely, pandemic risk.