The Center performs and disseminates research on the most important and pressing issues in risk and portfolio management in financial markets.

**Konstantin Magin's Risk Center working paper (# 2009-01 and 2013-04), "Equity Risk Premium and Insecure Property Rights," has been published in Economic Theory Bulletin. The final publication is available here.**

**The Consortium for Data Analytics in Risk (CDAR) is an industry partnership working in close collaboration with the Risk Center, and funded by State Street Bank and Trust. The CDAR website went live on 8/28/15.**

**Yuriy Gorodnichenko and Michael Weber's Risk Center working paper, "Are Sticky Prices Costly? Evidence from the Stock Market" has been accepted by the American Economic Review.**

*PAST EVENTS*

**Alex Shkolnik** will present "Systemic Risk in the Repo Market" at the upcoming Consortium for Systemic Risk Meeting (CSRA) December 15th Meeting

**Samim Ghamami** will present “Static Models of Central Counterparty Risk” at the upcoming “Regulating Systemic Risk: Insights from Mathematical Modeling” workshop at the Isaac Newton Institute for Mathematical Sciences at University of Cambridge from December 15th to December 19th

**Northfield Conference
Speaker: Lisa Goldberg
Date: **October 8

"What Would Yale Do if it Were Taxable"

**Stanford University**

**Speaker: Lisa
Goldberg
Date:** November 5

Center for Financial and Risk Analytics Seminar

"Futures Financing Rates"

**Global Derivatives USA**

**Speaker: Lisa
Goldberg
Date**: November 17

"On a Convex Measure of Drawdown Risk"

Wednesday, May 28, 2014

Real Estate: The Case for U.S. Real

Estate Investment Trusts in

The award was for his presentation based on Center Working Paper #2012-09, joint with Lisa R. Goldberg. **The paper is forthcoming in The Journal of Derivatives.**

"Autocorrelation and Partial Price Adjustment" is a revision of Working Paper 2007-03, by Anderson, Eom, Hahn and Park.

A commentary entitled "The Dynamics of Rising Interest Rates," by Anderson, Bianchi and Goldberg, was published in the August 26 issue of Thomson Reuters Westlaw Journal Bank and Lender Liability. The commentary was based on "The Decision to Lever" and "Will My Risk Parity Strategy Outperform?"

"The Decision to Lever"is featured in *Asset International's* *Chief Investment Officer *and is the #1 download on SSRN's Risk Management and Analysis in Financial Institutions category as of 9/6/2013; it is in the top 10 downloads in four other SSRN categories.

**Martin Lettau**, **Matteo Maggiori** and **Michael Weber** win the First Prize 2013 AQR Insight Award for their Center Working Paper, "Conditional Risk Premia in Currency Markets and Other Asset Classes," which is now forthcoming in the * Journal of Financial Economics.*

On March 1, 2013, "Will My Risk Parity Strategy Outperform?" received the **Graham and Dodd Scroll Award**. The award, given by *Financial Analysts Journal*, recognizes excellence in research and financial writing.

**Asness, Frazzini** and **Pedersen** publish a long Letter to the Editor in the March/April 2013 issue of the Financial Analysts Journal contesting our findings. Read their letter and our response.

Stochastic Taxation and Money Supply

Robert H. Edelstein and Konstantin Magin

This paper examines three issues relating to US REITs pricing. First, using a modified Consumption Capital Asset Pricing Model (CCAPM) with stochastic taxation and money supply, we compute the fundamental values for United States Real Estate Investment Trusts (REITs) for our data sample, 1972-2013. Our empirical analysis for US REIT pricing is statistically consistent with the CCAPM with stochastic taxation and monetary policy. Second, for our purposes, for publicly traded equity REITs, we define a bubble at a point in time to be the difference between the actual stock market price and the fundamental value derived from our theoretical model. United States REITs have, among other corporate structural features, special rules governing dividend distributions and corporate taxation treatment that make them an especially attractive and preferred vehicle for testing for the presence of pricing bubbles. Our study suggests that during the sample time horizon, United States REITs experienced many price bubbles, some of which were quite large. Third, our empirical results imply that monetary policy, in the short run, plays a role in the formation of these pricing bubbles. more...

Konstantin Magin

This paper derives the infinite 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. more...

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. more...

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. more...

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. more...

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. more ...

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. more ...

Yuriy Gorodnichenko and Michael Weber

We show that after monetary policy announcements, the conditional volatility of stock market returns rises more for firms with stickier prices than for firms with more flexible prices. This differential reaction is economically large as well as strikingly robust to a broad array of checks. These results suggest that menu costs---broadly defined to include physical costs of price adjustment, informational frictions, and so on---are an important factor for nominal price rigidity at the micro level. We also show that our empirical results are qualitatively and, under plausible calibrations, quantitatively consistent with New Keynesian macroeconomic models in which firms have heterogeneous price stickiness. Because our framework is valid for a wide variety of theoretical models and frictions preventing firms from price adjustment, we provide "model-free" evidence that sticky prices are indeed costly for firms. more ...

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. more...

Enrico G. De Giorgi

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. more...

Robert H. Edelstein

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. more...

The UC Berkeley Center for Risk Management Research was established on July 1, 2013 as the successor to the Coleman Fung Risk Management Research Center. (more)