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Research Papers

A Brief Introduction to the Basics of Game Theory

by Matthew O. Jackson; Stanford University

I provide a (very) brief introduction to game theory. I have developed these notes to provide quick access to some of the basics of game theory; mainly as an aid for students in courses in which I assumed familiarity with game theory but did not require it as a prerequisite.


A Quantitative Approach to Tactical Asset Allocation

by Mebane T. Faber; Cambria Investment Management

In this paper we update our 2006 white paper “A Quantitative Approach to Tactical Asset Allocation” with new data from the 2008-2012 period. How well did the purpose of the original paper – to present a simple quantitative method that improves the risk-adjusted returns across various asset classes – hold up since publication? Overall, we find that the models have performed well in real-time, achieving equity like returns with bond like volatility and drawdowns. We also examine the effects of departures from the original system including adding more asset classes, introducing various portfolio allocations, and implementing alternative cash management strategies.


Understanding the Modern Monetary System

by Cullen O. Roche; Orcam Financial Group, LLC

This paper provides a broad understanding of the workings of the modern fiat monetary system in the United States. The work is primarily descriptive in nature and takes an operational perspective of the modern fiat monetary system using the understandings of Monetary Realism.


Equity Risk Premiums (ERP): Determinants, Estimations and Implications – The 2013 Edition

by Aswath Damodaran; New York University – Stern School of Business

Equity risk premiums are a central component of every risk and return model in finance and are a key input in estimating costs of equity and capital in both corporate finance and valuation. Given their importance, it is surprising how haphazard the estimation of equity risk premiums remains in practice. We begin this paper by looking at the economic determinants of equity risk premiums, including investor risk aversion, information uncertainty and perceptions of macroeconomic risk. In the standard approach to estimating equity risk premiums, historical returns are used, with the difference in annual returns on stocks versus bonds over a long time period comprising the expected risk premium. We note the limitations of this approach, even in markets like the United States, which have long periods of historical data available, and its complete failure in emerging markets, where the historical data tends to be limited and volatile. We look at two other approaches to estimating equity risk premiums – the survey approach, where investors and managers are asked to assess the risk premium and the implied approach, where a forward-looking estimate of the premium is estimated using either current equity prices or risk premiums in non-equity markets. In the next section, we look at the relationship between the equity risk premium and risk premiums in the bond market (default spreads) and in real estate (cap rates) and how that relationship can be mined to generated expected equity risk premiums. We close the paper by examining why different approaches yield different values for the equity risk premium, and how to choose the “right” number to use in analysis.


Option Traders Use (very) Sophisticated Heuristics, Never the Black-Sholes-Merton Formula

by Espen Gaarder Haug and Nassim Nichalos Taleb; NYU-Poly

Option traders use a heuristically derived pricing formula which they adapt by fudging and changing the tails and skewness by varying one parameter, the standard deviation of a Gaussian. Such formula is popularly called “Black–Scholes–Merton” owing to an attributed eponymous discovery (though changing the standard deviation parameter is in contra- diction with it). However, we have historical evidence that: (1) the said Black, Scholes and Merton did not invent any formula, just found an argument to make a well known (and used) formula compatible with the economics establishment, by removing the “risk” parameter through “dynamic hedging”, (2) option traders use (and evidently have used since 1902) sophisticated heuristics and tricks more compatible with the previous versions of the formula of Louis Bachelier and Edward O. Thorp (that allow a broad choice of probability distributions) and removed the risk parameter using put-call parity, (3) option traders did not use the Black–Scholes–Merton formula or similar formulas after 1973 but continued their bottom-up heuristics more robust to the high impact rare event. The paper draws on historical trading methods and 19th and early 20th century references ignored by the finance literature. It is time to stop using the wrong designation for option pricing.


The Capital Asset Pricing Model: Some Empirical Tests

by Michael C. Jensen, Fischer Black and Myron Scholes; Harvard Business School, Sloan School of Management and Platinum Grove Asset Management L.P.

Considerable attention has recently been given to general equilibrium models of the pricing of capital assets. Of these, perhaps the best known is the mean-variance formulation originally developed by Sharpe (1964) and Treynor (1961), and extended and clarified by Lintner (1965a; 1965b), Mossin (1966), Fama (1968a; 1968b), and Long (1972). In addition Treynor (1965), Sharpe (1966), and Jensen (1968; 1969) have developed portfolio evaluation models which are either based on this asset pricing model or bear a close relation to it. In the development of the asset pricing model it is assumed that (1) all investors are single period risk-averse utility of terminal wealth maximizers and can choose among portfolios solely on the basis of mean and variance, (2) there are no taxes or transactions costs, (3) all investors have homogeneous views regarding the parameters of the joint probability distribution of all security returns, and (4) all investors can borrow and lend at a given riskless rate of interest. The main result of the model is a statement of the relation between the expected risk premiums on individual assets and their “systematic risk.” Our main purpose is to present some additional tests of this asset pricing model which avoid some of the problems of earlier studies and which, we believe, provide additional insights into the nature of the structure of security returns.

The evidence presented in Section II indicates the expected excess return on an asset is not strictly proportional to its B, and we believe that this evidence, coupled with that given in Section IV, is sufficiently strong to warrant rejection of the traditional form of the model given by (1). We then show in Section III how the cross-sectional tests are subject to measurement error bias, provide a solution to this problem through grouping procedures, and show how cross-sectional methods are relevant to testing the expanded two-factor form of the model. We show in Section IV that the mean of the beta factor has had a positive trend over the period 1931-65 and was on the order of 1.0 to 1.3% per month in the two sample intervals we examined in the period 1948-65. This seems to have been significantly different from the average risk-free rate and indeed is roughly the same size as the average market return of 1.3 and 1.2% per month over the two sample intervals in this period. This evidence seems to be sufficiently strong enough to warrant rejection of the traditional form of the model given by (1). In addition, the standard deviation of the beta factor over these two sample intervals was 2.0 and 2.2% per month, as compared with the standard deviation of the market factor of 3.6 and 3.8% per month. Thus the beta factor seems to be an important determinant of security returns.


We Don’t Quite Know What We are Talking About When We Talk About Volatility

by Daniel G. Goldstein and Nassim Nicholas Taleb; London Business School and NYU-Poly

Finance professionals, who are regularly exposed to notions of volatility, seem to confuse mean absolute deviation with standard deviation, causing an underestimation of 25% with theoretical Gaussian variables. In some fat tailed markets the underestimation can be up to 90%. The mental substitution of the two measures is consequential for decision making and the perception of market variability.


Value Investing: Investing for Grown Ups?

by Aswath Damodaran; New York University – Stern School of Business

Value investors generally characterize themselves as the grown ups in the investment world, unswayed by perceptions or momentum, and driven by fundamentals. While this may be true, at least in the abstract, there are at least three distinct strands of value investing. The first, passive value investing, is built around screening for stocks that meet specific characteristics – low multiples of earnings or book value, high returns on projects and low risk – and can be traced back to Ben Graham’s books on security analysis. The second, contrarian investing, requires investing in companies that are down on their luck and in the market. The third, activist value investing, involves taking large positions in poorly managed and low valued companies and making money from turning them around. While value investing looks impressive on paper, the performance of value investors, as a whole, is no better than that of less “sensible” investors who chose other investment philosophies and strategies. We examine explanations for why “active” value investing may not provide the promised payoffs.


Market Efficiency, Long-Term Returns, and Behavioral Finance

by Eugene F. Fama; University of Chicago

Market efficiency survives the challenge from the literature on long-term return anomalies. Consistent with the market efficiency hypothesis that the anomalies are chance results, apparent over-reaction to information is about as common as under-reaction. And post-event continuation of pre-event abnormal returns is about as frequent as post-event reversal. Consistent with the market efficiency prediction that apparent anomalies can also be due to methodology, the anomalies are sensitive to the techniques used to measure them, and many disappear with reasonable changes in technique.


Private Equity Performance: What Do We Know?

by Robert S. Harris, Tim Jenkinson and Steven N. Kaplan; University of Virginia - Darden School of Business , University of Oxford – Said Business School and University of Chicago – Booth School of Business

We study the performance of nearly 1400 U.S. buyout and venture capital funds using a new dataset from Burgiss. We find better buyout fund performance than has previously been documented – performance consistently has exceeded that of public markets. Outperformance versus the S&P 500 averages 20% to 27% over a fund’s life and more than 3% annually. Venture capital funds outperformed public equities in the 1990s, but underperformed in the 2000s. Our conclusions are robust to various indices and risk controls. Performance in Cambridge Associates and Preqin is qualitatively similar to that in Burgiss, but is lower in Thomson Venture Economics.


Bitcoin: A Peer-to-Peer Electronic Cash System by Satoshi Nakamoto

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