Financial Analysis and Quantitative Risk Management (M.S.) About the Program
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Essays in Macro-Finance and Asset Pricing
University of Pennsylvania ScholarlyCommons Publicly Accessible Penn Dissertations 2017 Essays In Macro-Finance And Asset Pricing Amr Elsaify University of Pennsylvania, [email protected] Follow this and additional works at: https://repository.upenn.edu/edissertations Part of the Economics Commons, and the Finance and Financial Management Commons Recommended Citation Elsaify, Amr, "Essays In Macro-Finance And Asset Pricing" (2017). Publicly Accessible Penn Dissertations. 2268. https://repository.upenn.edu/edissertations/2268 This paper is posted at ScholarlyCommons. https://repository.upenn.edu/edissertations/2268 For more information, please contact [email protected]. Essays In Macro-Finance And Asset Pricing Abstract This dissertation consists of three parts. The first documents that more innovative firms earn higher risk- adjusted equity returns and proposes a model to explain this. Chapter two answers the question of why firms would choose to issue callable bonds with options that are always "out of the money" by proposing a refinancing-risk explanation. Lastly, chapter three uses the firm-level evidence on investment cyclicality to help resolve the aggregate puzzle of whether R\&D should be procyclical or countercylical. Degree Type Dissertation Degree Name Doctor of Philosophy (PhD) Graduate Group Finance First Advisor Nikolai Roussanov Keywords Asset Pricing, Corporate Bonds, Leverage, Macroeconomics Subject Categories Economics | Finance and Financial Management This dissertation is available at ScholarlyCommons: https://repository.upenn.edu/edissertations/2268 ESSAYS IN MACRO-FINANCE AND ASSET PRICING Amr Elsaify A DISSERTATION in Finance For the Graduate Group in Managerial Science and Applied Economics Presented to the Faculties of the University of Pennsylvania in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy 2017 Supervisor of Dissertation Nikolai Roussanov, Moise Y. -
Stochastic Discount Factors and Martingales
NYU Stern Financial Theory IV Continuous-Time Finance Professor Jennifer N. Carpenter Spring 2020 Course Outline 1. The continuous-time financial market, stochastic discount factors, martingales 2. European contingent claims pricing, options, futures 3. Term structure models 4. American options and dynamic corporate finance 5. Optimal consumption and portfolio choice 6. Equilibrium in a pure exchange economy, consumption CAPM 7. Exam - in class - closed-note, closed-book Recommended Books and References Back, K., Asset Pricing and Portfolio Choice Theory,OxfordUniversityPress, 2010. Duffie, D., Dynamic Asset Pricing Theory, Princeton University Press, 2001. Karatzas, I. and S. E. Shreve, Brownian Motion and Stochastic Calculus, Springer, 1991. Karatzas, I. and S. E. Shreve, Methods of Mathematical Finance, Springer, 1998. Merton, R., Continuous-Time Finance, Blackwell, 1990. Shreve, S. E., Stochastic Calculus for Finance II: Continuous-Time Models, Springer, 2004. Arbitrage, martingales, and stochastic discount factors 1. Consumption space – random variables in Lp( ) P 2. Preferences – strictly monotone, convex, lower semi-continuous 3. One-period market for payo↵s (a) Marketed payo↵s (b) Prices – positive linear functionals (c) Arbitrage opportunities (d) Viability of the price system (e) Stochastic discount factors 4. Securities market with multiple trading dates (a) Security prices – right-continuous stochastic processes (b) Trading strategies – simple, self-financing, tight (c) Equivalent martingale measures (d) Dynamic market completeness Readings and References Duffie, chapter 6. Harrison, J., and D. Kreps, 1979, Martingales and arbitrage in multiperiod securities markets, Journal of Economic Theory, 20, 381-408. Harrison, J., and S. Pliska, 1981, Martingales and stochastic integrals in the theory of continuous trading, Stochastic Processes and Their Applications, 11, 215-260. -
Consumption-Based Asset Pricing
CONSUMPTION-BASED ASSET PRICING Emi Nakamura and Jon Steinsson UC Berkeley Fall 2020 Nakamura-Steinsson (UC Berkeley) Consumption-Based Asset Pricing 1 / 48 BIG ASSET PRICING QUESTIONS Why is the return on the stock market so high? (Relative to the "risk-free rate") Why is the stock market so volatile? What does this tell us about the risk and risk aversion? Nakamura-Steinsson (UC Berkeley) Consumption-Based Asset Pricing 2 / 48 CONSUMPTION-BASED ASSET PRICING Consumption-based asset pricing starts from the Consumption Euler equation: 0 0 U (Ct ) = Et [βU (Ct+1)Ri;t+1] Where does this equation come from? Consume $1 less today Invest in asset i Use proceeds to consume $ Rit+1 tomorrow Two perspectives: Consumption Theory: Conditional on Rit+1, determine path for Ct Asset Pricing: Conditional on path for Ct , determine Rit+1 Nakamura-Steinsson (UC Berkeley) Consumption-Based Asset Pricing 3 / 48 CONSUMPTION-BASED ASSET PRICING 0 0 U (Ct ) = βEt [U (Ct+1)Ri;t+1] A little manipulation yields: 0 βU (Ct+1) 1 = Et 0 Ri;t+1 U (Ct ) 1 = Et [Mt+1Ri;t+1] Stochastic discount factor: 0 U (Ct+1) Mt+1 = β 0 U (Ct ) Nakamura-Steinsson (UC Berkeley) Consumption-Based Asset Pricing 4 / 48 STOCHASTIC DISCOUNT FACTOR Fundamental equation of consumption-based asset pricing: 1 = Et [Mt+1Ri;t+1] Stochastic discount factor prices all assets!! This (conceptually) simple view holds under the rather strong assumption that there exists a complete set of competitive markets Nakamura-Steinsson (UC Berkeley) Consumption-Based Asset Pricing 5 / 48 PRICES,PAYOFFS, AND RETURNS Return is defined as payoff divided by price: Xi;t+1 Ri;t+1 = Pi;t where Xi;t+1 is (state contingent) payoff from asset i in period t + 1 and Pi;t is price of asset i at time t Fundamental equation can be rewritten as: Pi;t = Et [Mt+1Xi;t+1] Nakamura-Steinsson (UC Berkeley) Consumption-Based Asset Pricing 6 / 48 MULTI-PERIOD ASSETS Assets can have payoffs in multiple periods: Pi;t = Et [Mt+1(Di;t+1 + Pi;t+1)] where Di;t+1 is the dividend, and Pi;t+1 is (ex dividend) price Works for stocks, bonds, options, everything. -
Foundations of High-Yield Analysis
Research Foundation Briefs FOUNDATIONS OF HIGH-YIELD ANALYSIS Martin Fridson, CFA, Editor In partnership with CFA Society New York FOUNDATIONS OF HIGH-YIELD ANALYSIS Martin Fridson, CFA, Editor Statement of Purpose The CFA Institute Research Foundation is a not- for-profit organization established to promote the development and dissemination of relevant research for investment practitioners worldwide. Neither the Research Foundation, CFA Institute, nor the publication’s editorial staff is responsible for facts and opinions presented in this publication. This publication reflects the views of the author(s) and does not represent the official views of the CFA Institute Research Foundation. The CFA Institute Research Foundation and the Research Foundation logo are trademarks owned by The CFA Institute Research Foundation. CFA®, Chartered Financial Analyst®, AIMR- PPS®, and GIPS® are just a few of the trademarks owned by CFA Institute. To view a list of CFA Institute trademarks and the Guide for the Use of CFA Institute Marks, please visit our website at www.cfainstitute.org. © 2018 The CFA Institute Research Foundation. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the copyright holder. This publication is designed to provide accurate and authoritative information in regard to the subject matter covered. It is sold with the understanding that the publisher is not engaged in rendering legal, accounting, or other professional service. If legal advice or other expert assistance is required, the services of a competent professional should be sought. -
The Peculiar Logic of the Black-Scholes Model
The Peculiar Logic of the Black-Scholes Model James Owen Weatherall Department of Logic and Philosophy of Science University of California, Irvine Abstract The Black-Scholes(-Merton) model of options pricing establishes a theoretical relationship between the \fair" price of an option and other parameters characterizing the option and prevailing market conditions. Here I discuss a common application of the model with the following striking feature: the (expected) output of analysis apparently contradicts one of the core assumptions of the model on which the analysis is based. I will present several attitudes one might take towards this situation, and argue that it reveals ways in which a \broken" model can nonetheless provide useful (and tradeable) information. Keywords: Black-Scholes model, Black-Scholes formula, Volatility smile, Economic models, Scientific models 1. Introduction The Black-Scholes(-Merton) (BSM) model (Black and Scholes, 1973; Merton, 1973) estab- lishes a relationship between several parameters characterizing a class of financial products known as options on some underlying asset.1 From this model, one can derive a formula, known as the Black-Scholes formula, relating the theoretically \fair" price of an option to other parameters characterizing the option and prevailing market conditions. The model was first published by Fischer Black and Myron Scholes in 1973, the same year that the first U.S. options exchange opened, and within a decade it had become a central part of Email address: [email protected] (James Owen Weatherall) 1I will return to the details of the BSM model below, including a discussion of what an \option" is. The same model was also developed, around the same time and independently, by Merton (1973); other options models with qualitatively similar features, resulting in essentially the same pricing formula, were developed earlier, by Bachelier (1900) and Thorp and Kassouf (1967), but were much less influential, in part because the arguments on which they were based made too little contact with mainstream financial economics. -
Mathematical Finance: Tage's View of Asset Pricing
CHAPTER1 Introduction In financial market, every asset has a price. However, most often than not, the price are not equal to the expectation of its payoff. It is widely accepted that the pricing function is linear. Thus, we have a first look on the linearity of pricing function in forms of risk-neutral probability, state price and stochastic discount factor. To begin our analysis of pure finance, we explain the perfect market assumptions and propose a group of postulates on asset prices. No-arbitrage principle is a cornerstone of the theory of asset pricing, absence of arbitrage is more primitive than equilibrium. Given the mathematical definition of an arbitrage opportunity, we show that absence of arbitrage is equivalent to the existence of a positive linear pricing function. 1 2 Introduction § 1.1 Motivating Examples The risk-neutral probability, state price, and stochastic discount factor are fundamental concepts for modern finance. However, these concepts are not easily understood. For a first grasp of these definitions, we enter a fair play with elementary probability and linear algebra. Linear pricing function is the vital presupposition on financial market, therefore, we present more examples on it, for a better understanding of its application and arbitrage argument. 1.1.1 Fair Play Example 1.1.1 (fair play): Let’s play a game X: you pay $1. I flip a fair coin. If it is heads, you get $3; if it is tails, you get nothing. 8 < x = 3 −−−−−−−−−! H X0 = 1 X = : xL = 0 However, you like to play big, propose a game Y that is more exciting: where if it is heads, you get $20; if it is tails, you get $2. -
The Capital Asset Pricing Model (CAPM) of William Sharpe (1964)
Journal of Economic Perspectives—Volume 18, Number 3—Summer 2004—Pages 25–46 The Capital Asset Pricing Model: Theory and Evidence Eugene F. Fama and Kenneth R. French he capital asset pricing model (CAPM) of William Sharpe (1964) and John Lintner (1965) marks the birth of asset pricing theory (resulting in a T Nobel Prize for Sharpe in 1990). Four decades later, the CAPM is still widely used in applications, such as estimating the cost of capital for firms and evaluating the performance of managed portfolios. It is the centerpiece of MBA investment courses. Indeed, it is often the only asset pricing model taught in these courses.1 The attraction of the CAPM is that it offers powerful and intuitively pleasing predictions about how to measure risk and the relation between expected return and risk. Unfortunately, the empirical record of the model is poor—poor enough to invalidate the way it is used in applications. The CAPM’s empirical problems may reflect theoretical failings, the result of many simplifying assumptions. But they may also be caused by difficulties in implementing valid tests of the model. For example, the CAPM says that the risk of a stock should be measured relative to a compre- hensive “market portfolio” that in principle can include not just traded financial assets, but also consumer durables, real estate and human capital. Even if we take a narrow view of the model and limit its purview to traded financial assets, is it 1 Although every asset pricing model is a capital asset pricing model, the finance profession reserves the acronym CAPM for the specific model of Sharpe (1964), Lintner (1965) and Black (1972) discussed here. -
Mortgage-Backed Securities Jesper Lund May 12, 1998 the Danish
Fixed Income Analysis Mortgage-Backed Securities The Danish mortgage market Problems with pricing mortgage-backed b onds The prepayment function Price-yield relationship for MBB's Mo deling burnout and borrower heterogeneity Jesp er Lund May 12, 1998 1 The Danish mortgage market We fo cus on the Danish market for MBS | but there are many similarities to the US xed-rate loan with prepayment option. Mortgage-backed b onds are used for real-estate nance up to 80 of value in Denmark. Each MBS is backed by thousands of individual mortgages widely di erent sizes | corp orate as well as single-family borrowers Fixed coup on, annuity loans, 20{30 years to maturity at issue. Except for a small fee to the mortgage institution, all payments are passed through to the investors pass-through securities. Borrowers can prepay their mortgage at any time. They have an option to re nance the loan if interest rates drop. Payments from a given borrower: scheduled payments interest and principal and prepayments remaining principal. 2 Problems with pricing MBS { 1 N MBS: xed-income derivative with payments, fB t g at times i i=1 N ft g , dep ending on the future evolution of interest rates. i i=1 General expression for the value to day t = 0 of the MBS: " R N t X i Q r ds s 0 e B t : 1 E V = i 0 0 i=1 If the mortgage is non-callable, payments are non-sto chastic and the value is given by: N X V = B t P 0;t : 2 0 i i i=1 Danish MBS are callable b orrowers have a prepayment option. -
8 Consumption-Based Asset Pricing
8 Consumption-based asset pricing Purpose of lecture: 1. Explore the asset-pricing implications of the neoclassical model 2. Understand the pricing of insurance and aggregate risk 3. Understand the quantitative limitations of the model 8.1 The fundamental asset pricing equation Consider and economy where people live for two periods ... • max u (ct)+βEtu (ct+1) ct,ct+1,at+1 { } { } subject to yt = ct + ptat+1 ct+1 = yt+1 +(pt+1 + dt+1) at+1, where yt is income in period t, pt is the (ex-dividend) price of the asset in period t,anddt is the dividend from the asset in period t. Substitute the two constraints into the utility function: • max u (yt ptat+1)+βEtu (yt+1 +(pt+1 + dt+1) at+1) at+1 { − } and differentiate w.r.t. how much of the asset to purchase, at+1: 0= pt u (yt ptat+1)+βEt u (yt+1 +(pt+1 + dt+1) at+1) (pt+1 + dt+1) − · − { · } ⇒ pt u (ct)=βEt u (ct+1) (pt+1 + dt+1) . · { · } Interpretation: the left-hand side is the marginal cost of purchasing one • additional unit of the asset, in utility terms (so price * marginal utility), while the right-hand side is the expected marginal gain in utility terms (i.e., next-period marginal utility time price+dividend). Rewrite to get the fundamental asset-pricing equation: • βu (ct+1) pt = Et (pt+1 + dt+1) , u (c ) · t where the term βu(ct+1) is the (stochastic) discount factor (or the “pricing u(ct) kernel”). 46 Key insight #1: Suppose the household is not borrowing constrained • and suppose the household has the opportunity to purchase an asset. -
An Analysis and Description of Pricing and Information Sources in the Securitized and Structured Finance Markets
An Analysis and Description of Pricing and Information Sources in the Securitized and Structured Finance Markets The Bond Market Association and The American Securitization Forum October 2006 ANALYsis AND DESCRipTION OF PRiCING AND INFORmaTION SOURCES IN THE SECURITIZED AND STRUCTURED FINANCE MARKETS TABLE OF CONTENTS Executive Summary ................................................................................................. 1 I. Introduction and Methodology ............................................................................. 9 Study Objective ............................................................................................................................. 9 What Does the Study Cover ....................................................................................................... 9 The Pricing and Information Sources Covered in this Report .............................................10 II. Broad Observations and Conclusions ................................................................10 Each product sector is unique, though some general conclusions may be drawn ..........10 Structured Finance Products Trade in Dealer Markets .................................................10 Types of Pricing ..........................................................................................................................11 Primary Market vs. Secondary Pricing ....................................................................................11 Pricing Information Contexts and Applications ................................................................. -
Asset Prices and Real Investment
Asset Prices and Real Investment Leonid Kogan∗ This Draft: October, 2003 Abstract This paper analyzes the links between the firms investment technology and financial asset prices within a general equilibrium production economy. The model assumes that real investment is irreversible and subject to convex adjustment costs. It shows how these basic features of real investment naturally generate rich dynamics of stock returns. Firm investment activity and firm characteristics, particularly the market- to-book ratio, or q, are functions of the state of the economy and therefore contain information about the dynamic behavior of stock returns. The model implies that the relation between real investment, q, and stock returns is conditional in nature. During low-q periods when the irreversibility constraint is binding, the relation between the conditional volatility and expected returns on one hand, and the market-to-book ratio and investment rate on the other hand should be negative. During high-q periods when the constraint on the rate of investment is binding, the relation should change sign to positive. Empirical tests based on industry portfolios are supportive of the model predictions for the behavior of conditional return volatility, but provide no evidence in favor of the implications for expected return. JEL classification: G1, D5, E2, C0 Keywords: Investment; Irreversibility; General equilibrium; Leverage effect; Book-to-market ∗Sloan School of Management, Massachusetts Institute of Technology, Cambridge, MA 02142. Phone: (617) 253-2289. -
Interest Rate Volatility IV
The LMM methodology Dynamics of the SABR-LMM model Covariance structure of SABR-LMM Interest Rate Volatility IV. The SABR-LMM model Andrew Lesniewski Baruch College and Posnania Inc First Baruch Volatility Workshop New York June 16 - 18, 2015 A. Lesniewski Interest Rate Volatility The LMM methodology Dynamics of the SABR-LMM model Covariance structure of SABR-LMM Outline 1 The LMM methodology 2 Dynamics of the SABR-LMM model 3 Covariance structure of SABR-LMM A. Lesniewski Interest Rate Volatility The LMM methodology Dynamics of the SABR-LMM model Covariance structure of SABR-LMM The LMM methodology The main shortcoming of short rate models is that they do not allow for close calibration to the entire volatility cube. This is not a huge concern on a trading desk, where locally calibrated term structure models allow for accurate pricing and executing trades. It is, however, a concern for managers of large portfolios of fixed income securities (such as mortgage backed securities) which have exposures to various segments of the curve and various areas of the vol cube. It is also relevant in enterprise level risk management in large financial institutions where consistent risk aggregation across businesses and asset classes is important. A methodology that satisfies these requirements is the LIBOR market model (LMM) methodology, and in particular its stochastic volatility extensions. That comes at a price: LMM is less tractable than some of the popular short rate models. It also tends to require more resources than those models. We will discuss a natural extension of stochastic volatility LMM, namely the SABR-LMM model.