**Newest Working Papers**

**Submodular Risk Allocation**

Samim Ghamami and Paul Glasserman

We analyze the optimal allocation of trades to portfolios when the cost associated with an allocation is proportional to each portfolio's risk. Our investigation is motivated by changes in the over-the-counter derivatives markets, under which some contracts may be traded bilaterally or through central counterparties, splitting a set of trades into two or more portfolios. A derivatives dealer faces risk-based collateral and capital costs for each portfolio, and it seeks to minimize these costs through its allocation of trades to portfolios. When margin requirements are submodular, the problem becomes a submodular intersection problem. Its dual provides per-trade margin attributions, and assigning trades to portfolios based on the lowest attributed costs yields an optimal allocation. As part of this investigation, we derive conditions under which standard deviation and other risk measures are submodular functions of sets of trades. We compare systemwide optimality with individually optimal allocations in a market with multiple dealers.

**Equilibrium Comparative Statics in Finite Horizon Finance Economies with Stochastic Taxation**

Konstantin Magin

This paper studies equilibrium comparative statics of Financial Markets (FM) equilibria in the ﬁnite horizon General Equilibrium with Incomplete Markets (GEI) model with respect to changes in stochastic tax rates imposed on agents’ endowments and dividends. We show that under reasonable assumptions, without assuming CRRA and identical agents, an increase in the current dividend tax rate unambiguously reduces current asset prices. The paper also ﬁnds that there exists a bound B such that for a coeﬃcient of relative risk aversion less than B, an increase in a future dividend tax rate reduces current price of tradable assets. At the same time, for a coeﬃcient of relative risk aversion greater than B, an increase in a future dividend tax rate boosts the current price of tradable assets. Finally, for a coeﬃcient of relative risk aversion equal to B, an increase in a future dividend tax rate leaves current price of tradable assets unchanged. As a special case, under additional assumptions, B is equal to 1. Also, under reasonable assumptions, an increase in the current endowment tax rate reduces current asset prices, while an increase in a future endowment tax rate boosts current asset prices.

**Controlling shareholders’ value, long-run firm value and short-term performance**

Hyung Cheol Kang, Robert M. Anderson, Kyong Shik Eom, and Sang Koo Kang

We propose a new determinant of firm value within a business group: controlling shareholders’ value (CSV), the value of controlling shareholders’ stake in an affiliate divided by their stake in all affiliates. We posit that controlling shareholders focus attention on the high-CSV affiliates. Using data on Korean family-controlled business groups, we find that CSV has greater explanatory power for firm performance than traditional cash flow rights (CFR). We also find that, among affiliates with non-family CEOs, higher CSV is associated with higher Tobin’s Q and lower EBITDA, indicating that controlling shareholders and non-family CEO have successfully addressed their principal-agent problem.

**The effect of listing switches from a growth market to a main board: An alternative perspective**

Jong-Ho Park, Ki Beom Binh, and Kyong Shik Eom

We examine whether firms switching listings from the Korean growth market (KOSDAQ) to the main board (KOSPI) experienced improved trading-related market quality. We focus on market macrostructure and use a difference-in-difference technique with nearest matching. Contrary to previous research and practitioners’ opinions, we find that trading-related market quality mostly deteriorated or remained unchanged following the switch, indicating that the specific market macrostructure of a country matters. Listing switches produce a negative externality by weakening KOSDAQ and thereby impairing funding for innovative new firms, suggesting that policymakers should encourage firms whose characteristics fit the standalone growth market to remain listed there.

**Comparative Statics in Finite Horizon Finance Economies with Stochastic Taxation**

**Konstantin Magin**

This paper studies comparative statics of Financial Markets (FM) equilibria in the finite horizon General Equilibrium with Incomplete Markets (GEI) model with respect to changes in stochastic tax rates imposed on agent’s endowments and dividends. We show that under reasonable assumptions, without assuming CRRA and identical agents, an increase in the current dividend tax rate unambiguously reduces current asset prices. The paper also finds that there exists a bound B such that for a coefficient of relative risk aversion less than B, an increase in a future dividend tax rate reduces current price of tradable assets. At the same time, for a coefficient of relative risk aversion greater than B, an increase in a future dividend tax rate boosts the current price of tradable assets. Finally, for a coefficient of relative risk aversion equal to B, an increase in a future dividend tax rate leaves current consumption and current price of tradable assets unchanged. As a special case, under additional assumptions, B is equal to 1. Also, under reasonable assumptions, an increase in the current endowment tax rate reduces current asset prices, while an increase in a future endowment tax rate boosts current asset prices.

**Infinite Horizon CCAPM with Stochastic Taxation and Monetary Policy**

Konstantin Magin

This paper derives the infnite horizon CCAPM with heterogeneous agents, stochastic dividend taxation and monetary policy. I find that under reasonable assumptions on assets' dividends and probability distributions of the future dividend taxes and consumption, the model implies the constant price/after-tax dividend ratios. I also obtain that the higher current and expected dividend tax rates imply lower current asset prices. Finally, contrary to popular belief, monetary policy is neutral, in the long run, with respect to the real equilibrium asset prices.

**Generic Existence of Equilibria in Finite Horizon Finance Economies with Stochastic Taxation**

**Konstantin Magin**

The paper proves the existence of equilibria in the finite horizon general equilibrium with incomplete markets (GEI) model with insecure property rights. Insecure property rights come in the form of the stochastic taxes imposed on agents’ endowments and assets’ dividends. This paper finds that under reasonable assumptions, Financial Markets (FM) equilibria exist for most of the stochastic tax rates. Moreover, sufficiently small changes in stochastic taxation preserve the existence and completeness of FM equilibria.

**Understanding Systematic Risk: A High-Frequency Approach**

Markus Pelger

Under a large dimensional approximate factor model for asset returns, I use high-frequency data for the S&P 500 firms to estimate the latent continuous and jump factors. I estimate four very persistent continuous systematic factors for 2007 to 2012 and three from 2003 to 2006. These four continuous factors can be approximated very well by a market, an oil, a finance and an electricity portfolio. The value, size and momentum factors play no significant role in explaining these factors. For the time period 2003 to 2006 the finance factor seems to disappear. There exists only one persistent jump factor, namely a market jump factor. Using implied volatilities from option price data, I analyze the systematic factor structure of the volatilities. There is only one persistent market volatility factor, while during the financial crisis an additional temporary banking volatility factor appears. Based on the estimated factors, I can decompose the leverage effect, i.e. the correlation of the asset return with its volatility, into a systematic and an idiosyncratic component. The negative leverage effect is mainly driven by the systematic component, while it can be non-existent for idiosyncratic risk.

**Large-Dimensional Factor Modeling Based on High-Frequency Observations**

Markus Pelger

This paper develops a statistical theory to estimate an unknown factor structure based on financial high-frequency data. I derive a new estimator for the number of factors and derive consistent and asymptotically mixed-normal estimators of the loadings and factors under the assumption of a large number of cross-sectional and high-frequency observations. The estimation approach can separate factors for normal “continuous” and rare jump risk. The estimators for the loadings and factors are based on the principal component analysis of the quadratic covariation matrix. The estimator for the number of factors uses a perturbed eigenvalue ratio statistic. The results are obtained under general conditions, that allow for a very rich class of stochastic processes and for serial and cross-sectional correlation in the idiosyncratic components.

**Derivatives Pricing under Bilateral Counterparty Risk**

Peter Carr and Samim Ghamami

We consider risk-neutral valuation of a contingent claim under bilateral counterparty risk in a reduced-form setting similar to that of Duffie and Huang [1996] and Duffie and Singleton [1999]. The probabilistic valuation formulas derived under this framework cannot be usually used for practical pricing due to their recursive path-dependencies. Instead, finite-difference methods are used to solve the quasi-linear partial differential equations that equivalently represent the claim value function. By imposing restrictions on the dynamics of the risk-free rate and the stochastic intensities of the counterparties’ default times, we develop path-independent probabilistic valuation formulas that have closed-form solution or can lead to computationally efficient pricing schemes. Our framework incorporates the so-called wrong way risk (WWR) as the two counterparty default intensities can depend on the derivatives values. Inspired by the work of Ghamami and Goldberg [2014] on the impact of WWR on credit value adjustment (CVA), we derive calibration-implied formulas that enable us to mathematically compare the derivatives values in the presence and absence of WWR. We illustrate that derivatives values under unilateral WWR need not be less than the derivatives values in the absence of WWR. A sufficient condition under which this inequality holds is that the price process follows a semimartingale with independent increments.

**The Temporal Dimension of Drawdown**

**Ola Mahmoud**

Multi-period measures of risk account for the path that the value of an investment portfolio takes. The most widely used such path-dependent indicator of risk is drawdown, which is a measure of decline from a historical peak in cumulative returns. In the context of probabilistic risk measures, the focus has been on one particular dimension of drawdown, its magnitude, and not on its temporal dimension, its duration. In this paper, the concept of temporal path-dependent risk measure is introduced to capture the risk associated with the temporal dimension of a stochastic process. We analyze drawdown duration, which measures the length of excursions below a running maximum, and liquidation stopping time, which denotes the first time drawdown duration exceeds a subjective liquidation threshold, in the context of coherent temporal path-dependent risk measures and show that they, unlike drawdown magnitude, do not satisfy any of the axioms for coherent risk measures. Despite its non-coherence, we illustrate through an empirical example some of the insights gained from analyzing drawdown duration in the investment process and discuss the challenges of path-dependent risk estimation in practice.

**Diversification Preferences in the Theory of Choice**

Enrico G. De Giorgi and Ola Mahmoud

Diversification represents the idea of choosing variety over uniformity. Within the theory of choice, desirability of diversification is axiomatized as preference for a convex combination of choices that are equivalently ranked. This corresponds to the notion of risk aversion when one assumes the von-Neumann-Morgenstern expected utility model, but the equivalence fails to hold in other models. This paper reviews axiomatizations of the concept of diversification and their relationship to the related notions of risk aversion and convex preferences within different choice theoretic models. The survey covers model-independent diversification preferences, preferences within models of choice under risk, including expected utility theory and the more general rank-dependent expected utility theory, as well as models of choice under uncertainty axiomatized via Choquet expected utility theory. Remarks on interpretations of diversication preferences within models of behavioral choice are given in the conclusion.

**Stochastic Taxation and REITS Pricing Bubbles: A Statistical Analysis**

Robert H. Edelstein and Konstantin Magin

Using a modified Consumption Capital Asset Pricing Model (CCAPM) with stochastic taxation, we create estimates of fundamental values and fundamental overall rates of returns for United States Real Estate Investment Trusts (REITs) for our data sample, 1972 — 2013. Comparing actual, observed REITs prices (and overall rates of return) with model-generated fundamental values (and fundamental overall rates of return), we examine the presence of bubbles. For our purposes, for publicly traded equity REITs, we define a bubble to be the difference between actual stock market price (overall rates of return) and fundamental value (fundamental overall rate of return). United States REITs have, among other features, special rules governing dividend distributions and corporate taxation treatment that makes them an especially attractive and a preferred vehicle to test the presence of pricing and rate of return bubbles. Using this notion for bubbles, our study suggests that during the sample time horizon, United States REITs experienced statistically significant price and rates of return bubbles for a preponderance of the time.

**Static Models of Central Counterparty Risk**

**Samim Ghamami**

Following the 2009 G-20 clearing mandate, international standard setting bodies (SSBs) have outlined a set of principles for central counterparty (CCP) risk management; they have also devised formulaic CCP risk capital requirements on clearing members for their central counterparty exposures. There is still no consensus among CCP regulators and bank regulators on how central counterparty risk should be measured coherently in practice. A conceptually sound and logically consistent definition of the CCP risk capital in the absence of a unifying CCP risk measurement framework is challenging. Incoherent CCP risk capital requirements may create an obscure environment disincentivizing the central clearing of over the counter (OTC) derivatives transactions. Based on novel applications of well-known mathematical models in finance, this paper introduces a risk measurement framework that coherently specifies all layers of the default waterfall resources of typical derivatives CCPs. The proposed framework gives the first risk sensitive definition of the CCP risk capital based on which less risk sensitive non-model-based methods can be evaluated.