Midterm Exam:Answer Sheet
|
|
- Prosper Dennis
- 8 years ago
- Views:
Transcription
1 Econ 497 Barry W. Ickes Spring 2007 Midterm Exam:Answer Sheet 1. (25%) Consider a portfolio, c, comprised of a risk-free and risky asset, with returns given by r f and E(r p ), respectively. Let y be the proportion of the portfolio invested in the risky asset. Let the utility function of the agent be given by where A is a constant. U = E(r) 1 2 Aσ2 (1) (a) Why does (1) make sense? What does it mean if A<0? IfA =0?Drawtheindifference curves of an agent who has the preferences described by (1) for each of the three cases: A<0,A=0,A>0. Which case is the most sensible? brief answer Utility depends on positively on expected return and negatively on the risk. This makes sense if people are risk averse or risk loving. Indeed, this equation can even represent preferences for risk-neutral agents (A = 0). In the latter case indifference curves will have zero slope: the agent cares only about expected return, and is indifferent to risk. For A>0indifference curves will be positively sloped: the agent is risk averse, implying that higher expected return is required to get her to hold more risk. If A<0 the indifference curves are negatively sloped as the agent is arisklover. A>0 makes more sense given that agents typically purchase insurance. (b) Denote the standard deviation of the risky asset as σ p. What will the standard deviation of the portfolio, σ c, be equal to? What will the variance of the portfolio, σc, 2 be equal to? brief answer The risk-free asset must have zero variance. So σ c = yσ P. Then σc 2 = y 2 σc. 2 (c) What will the expected return on the complete portfolio, E(r c ) be equal to? brief answer E(r c )=ye(r P )+(1 y)r f (d) How will the optimal choice of y vary with (i) the variance of the risky asset; (ii) the excess return on the risky asset; (iii) the value of A? brief answer If σp 2 increases, then y will decrease given A>0; this is the case of the capital allocation line becoming flatter. If E(r P ) r f increases then y will increase; this is equivalent to the capital allocation line becoming steeper. If A rises then the agent is more risk averse, so he will hold less y. Think of it as the indifference curve becoming steeper. 2. (20%) When Kendall first showed that prices in financial markets evolved randomly he took this to be disturbing new for economists. It seemed to imply that stock markets are erratic and irrational. Today this conclusion seems exactly backwards. Why might we expect price changes in a well-functioning market to evolve randomly? Explain. 1
2 brief answer If markets function efficiently then any information agents have will be incorporated in the price. If you know the price will rise tomorrow, you bid more today. Hence, arbitrage causes the current price to reveal all available information. If the current price reveals all available information, then prices change only on new information. New information by definition is not yet known. So prices are just as likely to rise or fall. (a) If asset prices are determined by some theory (CAPM, APT, etc.) how can price changes be random? Explain. brief answer Asset pricing theories explain the current price. They are based on available current information. New information causes prices to change. So it makes sense that prices will evolve randomly. Think about p t = E t [m t+1 x t+1 ]. If we obtain new information about future payoffs this will change the price. Since we do not know what the new information will reveal, we cannot know how the price will change. (b) Suppose changes in stock returns were evolving randomly as in an efficient market. At some date, t 1, the risk premium rises (people become more risk averse). What would happen to stock prices at t 1?Aftert 1 what will happen to stock prices? Does this mean that the market is inefficient? Explain. brief answer If the risk premium rises stock prices will fall. This is necessary so that expected returns can rise. (You can think of this as a higher value of A in problem 1. If A rises agents hold less of the risky asset, so its price must fall today given the supply). With a higher risk premium assets require higher expected returns to be held. But if prices fall today to reflect the higher risk premium, prices will be expected to rise in the future returning to where they were. Indeed, if prices were not expected to rise in the future returns would not be higher and people would not hold the assets (this phenomenon is called overshooting). So it seems that prices are predictable. But this is not a violation of efficient markets. Although the next period s price will be a function of the current price, this is because it is the only way for markets to clear. It is fully compatible with fully informed agents and full arbitrage. Indeed, there is no way to make excess returns, since the predictable price is precisely what is required to match the higher risk premium that agents now demand. Returns are only truly random if agents are risk neutral, or if the risk premium is uncorrelated with past prices. In this case they are not. (c) Samuelson convincingly argued that in properly functioning markets it is the change in the log of the price (e.g., the percentage change in prices), rather than the change in the absolute price ( P t ) itself that evolves randomly. Why would a random walk in the level (as opposed to the log) of the price of a security be incompatible with economics? brief answer If P were random then prices could be negative, but asset prices are bounded below by zero. Negative asset prices make no sense for securities. But if the growth rate of prices is random then prices no longer can become negative. 3. (30%) Assume the agent is a price taker in the asset (i.e., she can purchase or sell as much of the payoff x t+1 as she wants at the price p t ).Letx t+1 be the payoff of this asset in period 2
3 t +1. The solution to the consumer s optimal consumption problem yields p t = E t [m t+1 x t+1 ] (2) where m t+1 = β u0 (c t+1 ) u 0 (c t ), β is the discount factor, and u0 (c i ) is the marginal utility of consumption in period i. (a) Explain the logic behind the expression (2). Why does this represent optimal behavior? brief answer h It is useful to substitute the definition of m in expression (2): p t = E t β u 0 (c t+1 ) x i u 0 (c t ) t+1.iknowu 0 (c t ) today, so I can write this as u 0 (c t )p t = E t [βu 0 (c t+1 )x t+1 ]. The left-hand side is the cost of buying a unit of the asset today. It reduces my consumption by p t and the utility cost of that is u 0 (c t )p t. The right-hand side is the expected gain from buying more of the asset. I get the payoff x t+1 and the utility of that is u 0 (c t+1 )x t+1, but it is in the future, so I discount it by β. Ifthisequationdid not hold true I could raise my utility by rearranging my consumption. One can see this at point C in figure 1. If we were at point E, condition (2) is not satisfied, and utility can be raised by reducing current consumption and having higher expected future consumption. Figure 1: Optimal Consumption (b) Why is expression (2) useful (indeed cool)? brief answer The stochastic discount factor, m t+1, can be used to price any asset. Indeed, the same discount factor can be used to price any asset. That is cool. (c) Suppose an asset s payoff, x t+1, positively covaries with m t+1. What does (2) imply about the price of this asset (about your desire to hold it in your portfolio)? brief answer If the payoff covaries with m t+1 you would like to hold more of it, so its price will be higher. A higher m means lower future consumption, since marginal utility decreases with consumption. You would like an asset that pays off higher when consumption is lower. That is insurance. This is obvious from expression (2) but it is nice to know why. 3
4 (d) Suppose the asset s payoff has zero correlation with m t+1. What does this imply about the rate of return that this asset will bear? Explain. brief answer It must pay the risk-free rate. Only risk correlated with market risk bears higher return. One could show this formally from the basic price equation again, p = E(mx). Recall the definition of covariance: cov(m, x) = E(mx) E(m)E(x).So p = E(m)E(x)+ cov(m, x) Now we can divide through by p to obtain 1 = E t [m t+1 R t+1 ]or R f = 1 is a risk-free asset. Thus we have: E(m), since it p = E(x) R f + cov(m, x) (3) the first term on RHS is discounted present value, second term is risk adjustment. Now if the covariance is zero, as in this question last term on the RHS drops off. So E(x) = E(R p t+1 )=R f. We could let σ 2 (x) equal a billion, but if cov(m, x) =0,it will still yield only the risk-free rate. Even if people are totally risk averse. (e) What relationship, if any, does (2) have with the CAPM? Explain. brief answer Everything! Suppose that m is inversely related to the return on the market portfolio, R P (This makes sense: when consumption is high, returns are less valuabletoyouthanwhenitislow.). Specifically, let m = a br P.Thenm and R P are perfectly negatively correlated. So an asset s payoff depends on its correlation with the market portfolio. So the CAPM follows from the assumption that investor s marginal utility declines linearly when the market goes up. The CAPM says that the risk premium we require to add asset A to our portfolio is proportional to its β. If an asset s return is uncorrelated with the market return its beta is zero. Such a risky asset is riskless in the market portfolio so its expected return is the risk-free interest rate. 4. (25%) Let X U be the future operating income (payoff) oftheunleveredfirm, and X L be the same for the levered firm. Assume that they are of the same risk class, i.e., X = X U = X L. The value of the unlevered firm is equal to the value of the firms equity: V U S U. For the levered firm the value is equal to debt plus equity, V L S L + D L,whereS is the current value oftheequityandd L is the current value of the debt. Let r be the rate of return on this debt. (a) Consider the portfolio that consists of holding α% of the shares of the unlevered firm. What is the current cost of this portfolio? What is the future payoff equal to? brief answer It costs you αs U. Its future payoff is αx. (b) Consider an alternative portfolio that consists of α% of the bonds of the levered firm, and α% of the equity of the levered firm. What is the current cost of this portfolio? What is the future payoff of this portfolio equal to? brief answer The bonds cost you αd L and the equity costs you αs L,orα(S L +D L ). The payoff from the bonds is the αmin[x, rd L ], since bondholders receive interest unless the payoff is insufficient to cover this. The equity holders receive the rest, so their 4
5 payoff is αmax[x rd L, 0], since there is limited liability. Adding these two terms we have αmin[x, rd L ]+αmax[x rd L, 0] = α [Min[X, rd L ]+Max[X rd L, 0]] = αx. (c) Compare the payoffs from the two portfolios. What can you conclude about the current costs? What does this imply about the relationship between V U and V L? brief answer The payoffs from the two portfolios are the same, so the law of one price says they must cost the same. So α(s L +D L )=αs U.SoS L +D L = S U = V L = V U. In words, the value of the firm is independent of its capital structure. (d) Why is this an important result? Explain. brief answer We have shown that capital structure is irrelevant. This is the M-M theorem. This theorem is important because it shows that what matters for firm value are the firm s prospects, X, nothowitisfinanced. If leverage does matter for valuation some assumption of the theorem must be violated. So the theorem makes us think about what must be true if leverage matters. It also shows us the power of the LOP. It tells us that if leverage does matter, then the LOP must not hold, or there must be tax considerations, or costs of bankruptcy. We use 4 assumptions: (i) No arbitrage (equal-sized bites of the pie have the same taste ). (ii) Operating income (from assets) is not affected by capital structure. (iii) The proportion of operating income that is jointly allocated to stocks and bonds is not affected by the firm s capital structure ( only stockholders and bondholders eat the pie ). (iv) The present value function (economy-wide state prices) is not affected by capital structure( tasteperbiteofthepieisfixed ). Notice that assumption (ii) rules out bankruptcy costs, differential transaction costs, peculiar managerial incentive schemes based on capital structure. Assumption (iii) rules out differential taxes for income from stocks and bonds. Assumption (iv) rules out the possibility of creating or destroying desired patterns of returns not otherwise existing in the market by changing capital structure. 5
t = 1 2 3 1. Calculate the implied interest rates and graph the term structure of interest rates. t = 1 2 3 X t = 100 100 100 t = 1 2 3
MØA 155 PROBLEM SET: Summarizing Exercise 1. Present Value [3] You are given the following prices P t today for receiving risk free payments t periods from now. t = 1 2 3 P t = 0.95 0.9 0.85 1. Calculate
More informationSAMPLE MID-TERM QUESTIONS
SAMPLE MID-TERM QUESTIONS William L. Silber HOW TO PREPARE FOR THE MID- TERM: 1. Study in a group 2. Review the concept questions in the Before and After book 3. When you review the questions listed below,
More informationTPPE17 Corporate Finance 1(5) SOLUTIONS RE-EXAMS 2014 II + III
TPPE17 Corporate Finance 1(5) SOLUTIONS RE-EXAMS 2014 II III Instructions 1. Only one problem should be treated on each sheet of paper and only one side of the sheet should be used. 2. The solutions folder
More informationCapital Allocation Between The Risky And The Risk- Free Asset. Chapter 7
Capital Allocation Between The Risky And The Risk- Free Asset Chapter 7 Investment Decisions capital allocation decision = choice of proportion to be invested in risk-free versus risky assets asset allocation
More informationChapter 17 Corporate Capital Structure Foundations (Sections 17.1 and 17.2. Skim section 17.3.)
Chapter 17 Corporate Capital Structure Foundations (Sections 17.1 and 17.2. Skim section 17.3.) The primary focus of the next two chapters will be to examine the debt/equity choice by firms. In particular,
More informationFIN-40008 FINANCIAL INSTRUMENTS SPRING 2008
FIN-40008 FINANCIAL INSTRUMENTS SPRING 2008 Options These notes consider the way put and call options and the underlying can be combined to create hedges, spreads and combinations. We will consider the
More informationChapter 17 Does Debt Policy Matter?
Chapter 17 Does Debt Policy Matter? Multiple Choice Questions 1. When a firm has no debt, then such a firm is known as: (I) an unlevered firm (II) a levered firm (III) an all-equity firm D) I and III only
More informationTest3. Pessimistic Most Likely Optimistic Total Revenues 30 50 65 Total Costs -25-20 -15
Test3 1. The market value of Charcoal Corporation's common stock is $20 million, and the market value of its riskfree debt is $5 million. The beta of the company's common stock is 1.25, and the market
More informationHomework Assignment #1: Answer Key
Econ 497 Economics of the Financial Crisis Professor Ickes Spring 2012 Homework Assignment #1: Answer Key 1. Consider a firm that has future payoff.supposethefirm is unlevered, call the firm and its shares
More informationIntroduction to Options. Derivatives
Introduction to Options Econ 422: Investment, Capital & Finance University of Washington Summer 2010 August 18, 2010 Derivatives A derivative is a security whose payoff or value depends on (is derived
More informationUse the table for the questions 18 and 19 below.
Use the table for the questions 18 and 19 below. The following table summarizes prices of various default-free zero-coupon bonds (expressed as a percentage of face value): Maturity (years) 1 3 4 5 Price
More informationLeverage. FINANCE 350 Global Financial Management. Professor Alon Brav Fuqua School of Business Duke University. Overview
Leverage FINANCE 35 Global Financial Management Professor Alon Brav Fuqua School of Business Duke University Overview Capital Structure does not matter! Modigliani & Miller propositions Implications for
More informationOptions: Valuation and (No) Arbitrage
Prof. Alex Shapiro Lecture Notes 15 Options: Valuation and (No) Arbitrage I. Readings and Suggested Practice Problems II. Introduction: Objectives and Notation III. No Arbitrage Pricing Bound IV. The Binomial
More informationPractice Set #4 and Solutions.
FIN-469 Investments Analysis Professor Michel A. Robe Practice Set #4 and Solutions. What to do with this practice set? To help students prepare for the assignment and the exams, practice sets with solutions
More informationModels of Risk and Return
Models of Risk and Return Aswath Damodaran Aswath Damodaran 1 First Principles Invest in projects that yield a return greater than the minimum acceptable hurdle rate. The hurdle rate should be higher for
More informationThe Binomial Option Pricing Model André Farber
1 Solvay Business School Université Libre de Bruxelles The Binomial Option Pricing Model André Farber January 2002 Consider a non-dividend paying stock whose price is initially S 0. Divide time into small
More informationThe Assumptions and Math Behind WACC and APV Calculations
The Assumptions and Math Behind WACC and APV Calculations Richard Stanton U.C. Berkeley Mark S. Seasholes U.C. Berkeley This Version October 27, 2005 Abstract We outline the math and assumptions behind
More informationCAPITAL STRUCTURE [Chapter 15 and Chapter 16]
Capital Structure [CHAP. 15 & 16] -1 CAPITAL STRUCTURE [Chapter 15 and Chapter 16] CONTENTS I. Introduction II. Capital Structure & Firm Value WITHOUT Taxes III. Capital Structure & Firm Value WITH Corporate
More informationChapter 14 Capital Structure in a Perfect Market
Chapter 14 Capital Structure in a Perfect Market 14-1. Consider a project with free cash flows in one year of $130,000 or $180,000, with each outcome being equally likely. The initial investment required
More informationCAPM, Arbitrage, and Linear Factor Models
CAPM, Arbitrage, and Linear Factor Models CAPM, Arbitrage, Linear Factor Models 1/ 41 Introduction We now assume all investors actually choose mean-variance e cient portfolios. By equating these investors
More information1 Pricing options using the Black Scholes formula
Lecture 9 Pricing options using the Black Scholes formula Exercise. Consider month options with exercise prices of K = 45. The variance of the underlying security is σ 2 = 0.20. The risk free interest
More informationTwo-State Option Pricing
Rendleman and Bartter [1] present a simple two-state model of option pricing. The states of the world evolve like the branches of a tree. Given the current state, there are two possible states next period.
More informationFIN 3710. Final (Practice) Exam 05/23/06
FIN 3710 Investment Analysis Spring 2006 Zicklin School of Business Baruch College Professor Rui Yao FIN 3710 Final (Practice) Exam 05/23/06 NAME: (Please print your name here) PLEDGE: (Sign your name
More informationAFM 472. Midterm Examination. Monday Oct. 24, 2011. A. Huang
AFM 472 Midterm Examination Monday Oct. 24, 2011 A. Huang Name: Answer Key Student Number: Section (circle one): 10:00am 1:00pm 2:30pm Instructions: 1. Answer all questions in the space provided. If space
More informationFinal Exam Practice Set and Solutions
FIN-469 Investments Analysis Professor Michel A. Robe Final Exam Practice Set and Solutions What to do with this practice set? To help students prepare for the final exam, three practice sets with solutions
More informationDUKE UNIVERSITY Fuqua School of Business. FINANCE 351 - CORPORATE FINANCE Problem Set #7 Prof. Simon Gervais Fall 2011 Term 2.
DUKE UNIVERSITY Fuqua School of Business FINANCE 351 - CORPORATE FINANCE Problem Set #7 Prof. Simon Gervais Fall 2011 Term 2 Questions 1. Suppose the corporate tax rate is 40%, and investors pay a tax
More information15.433 Investments. Assignment 1: Securities, Markets & Capital Market Theory. Each question is worth 0.2 points, the max points is 3 points
Assignment 1: Securities, Markets & Capital Market Theory Each question is worth 0.2 points, the max points is 3 points 1. The interest rate charged by banks with excess reserves at a Federal Reserve Bank
More informationOption Valuation. Chapter 21
Option Valuation Chapter 21 Intrinsic and Time Value intrinsic value of in-the-money options = the payoff that could be obtained from the immediate exercise of the option for a call option: stock price
More informationFour Derivations of the Black Scholes PDE by Fabrice Douglas Rouah www.frouah.com www.volopta.com
Four Derivations of the Black Scholes PDE by Fabrice Douglas Rouah www.frouah.com www.volopta.com In this Note we derive the Black Scholes PDE for an option V, given by @t + 1 + rs @S2 @S We derive the
More informationRate of Return. Reading: Veronesi, Chapter 7. Investment over a Holding Period
Rate of Return Reading: Veronesi, Chapter 7 Investment over a Holding Period Consider an investment in any asset over a holding period from time 0 to time T. Suppose the amount invested at time 0 is P
More informationCHAPTER 7: OPTIMAL RISKY PORTFOLIOS
CHAPTER 7: OPTIMAL RIKY PORTFOLIO PROLEM ET 1. (a) and (e).. (a) and (c). After real estate is added to the portfolio, there are four asset classes in the portfolio: stocks, bonds, cash and real estate.
More informationReview for Exam 2. Instructions: Please read carefully
Review for Exam 2 Instructions: Please read carefully The exam will have 25 multiple choice questions and 5 work problems You are not responsible for any topics that are not covered in the lecture note
More informationPractice Questions for Midterm II
Finance 333 Investments Practice Questions for Midterm II Winter 2004 Professor Yan 1. The market portfolio has a beta of a. 0. *b. 1. c. -1. d. 0.5. By definition, the beta of the market portfolio is
More informationCHAPTER 11: ARBITRAGE PRICING THEORY
CHAPTER 11: ARBITRAGE PRICING THEORY 1. The revised estimate of the expected rate of return on the stock would be the old estimate plus the sum of the products of the unexpected change in each factor times
More informationEC247 FINANCIAL INSTRUMENTS AND CAPITAL MARKETS TERM PAPER
EC247 FINANCIAL INSTRUMENTS AND CAPITAL MARKETS TERM PAPER NAME: IOANNA KOULLOUROU REG. NUMBER: 1004216 1 Term Paper Title: Explain what is meant by the term structure of interest rates. Critically evaluate
More informationFinancial Options: Pricing and Hedging
Financial Options: Pricing and Hedging Diagrams Debt Equity Value of Firm s Assets T Value of Firm s Assets T Valuation of distressed debt and equity-linked securities requires an understanding of financial
More informationOne Period Binomial Model
FIN-40008 FINANCIAL INSTRUMENTS SPRING 2008 One Period Binomial Model These notes consider the one period binomial model to exactly price an option. We will consider three different methods of pricing
More informationCHAPTER 13 Capital Structure and Leverage
CHAPTER 13 Capital Structure and Leverage Business and financial risk Optimal capital structure Operating Leverage Capital structure theory 1 What s business risk? Uncertainty about future operating income
More informationCh. 18: Taxes + Bankruptcy cost
Ch. 18: Taxes + Bankruptcy cost If MM1 holds, then Financial Management has little (if any) impact on value of the firm: If markets are perfect, transaction cost (TAC) and bankruptcy cost are zero, no
More information1 Capital Asset Pricing Model (CAPM)
Copyright c 2005 by Karl Sigman 1 Capital Asset Pricing Model (CAPM) We now assume an idealized framework for an open market place, where all the risky assets refer to (say) all the tradeable stocks available
More informationCHAPTER 10 RISK AND RETURN: THE CAPITAL ASSET PRICING MODEL (CAPM)
CHAPTER 10 RISK AND RETURN: THE CAPITAL ASSET PRICING MODEL (CAPM) Answers to Concepts Review and Critical Thinking Questions 1. Some of the risk in holding any asset is unique to the asset in question.
More informationTHE FINANCING DECISIONS BY FIRMS: IMPACT OF CAPITAL STRUCTURE CHOICE ON VALUE
IX. THE FINANCING DECISIONS BY FIRMS: IMPACT OF CAPITAL STRUCTURE CHOICE ON VALUE The capital structure of a firm is defined to be the menu of the firm's liabilities (i.e, the "right-hand side" of the
More informationAdditional Practice Questions for Midterm I
1 Finance 333 Investments Additional Practice Questions for Midterm I Winter 2004 Professor Yan 1. Financial assets. A) directly contribute to the country's productive capacity *B) indirectly contribute
More informationSolution: The optimal position for an investor with a coefficient of risk aversion A = 5 in the risky asset is y*:
Problem 1. Consider a risky asset. Suppose the expected rate of return on the risky asset is 15%, the standard deviation of the asset return is 22%, and the risk-free rate is 6%. What is your optimal position
More informationHolding Period Return. Return, Risk, and Risk Aversion. Percentage Return or Dollar Return? An Example. Percentage Return or Dollar Return? 10% or 10?
Return, Risk, and Risk Aversion Holding Period Return Ending Price - Beginning Price + Intermediate Income Return = Beginning Price R P t+ t+ = Pt + Dt P t An Example You bought IBM stock at $40 last month.
More informationLecture Notes: Basic Concepts in Option Pricing - The Black and Scholes Model
Brunel University Msc., EC5504, Financial Engineering Prof Menelaos Karanasos Lecture Notes: Basic Concepts in Option Pricing - The Black and Scholes Model Recall that the price of an option is equal to
More informationBINOMIAL OPTION PRICING
Darden Graduate School of Business Administration University of Virginia BINOMIAL OPTION PRICING Binomial option pricing is a simple but powerful technique that can be used to solve many complex option-pricing
More informationMid-Term Spring 2003
Mid-Term Spring 2003 1. (1 point) You want to purchase XYZ stock at $60 from your broker using as little of your own money as possible. If initial margin is 50% and you have $3000 to invest, how many shares
More informationFIN 432 Investment Analysis and Management Review Notes for Midterm Exam
FIN 432 Investment Analysis and Management Review Notes for Midterm Exam Chapter 1 1. Investment vs. investments 2. Real assets vs. financial assets 3. Investment process Investment policy, asset allocation,
More informationDUKE UNIVERSITY Fuqua School of Business. FINANCE 351 - CORPORATE FINANCE Problem Set #4 Prof. Simon Gervais Fall 2011 Term 2.
DUK UNIRSITY Fuqua School of Business FINANC 351 - CORPORAT FINANC Problem Set #4 Prof. Simon Gervais Fall 2011 Term 2 Questions 1. Suppose the corporate tax rate is 40%. Consider a firm that earns $1,000
More informationFinancial Markets and Valuation - Tutorial 6: SOLUTIONS. Capital Structure and Cost of Funds
Financial Markets and Valuation - Tutorial 6: SOLUTIONS Capital Structure and Cost of Funds (*) denotes those problems to be covered in detail during the tutorial session (*) Problem 1. (Ross, Westerfield
More informationBlack Scholes Merton Approach To Modelling Financial Derivatives Prices Tomas Sinkariovas 0802869. Words: 3441
Black Scholes Merton Approach To Modelling Financial Derivatives Prices Tomas Sinkariovas 0802869 Words: 3441 1 1. Introduction In this paper I present Black, Scholes (1973) and Merton (1973) (BSM) general
More informationFIN-40008 FINANCIAL INSTRUMENTS SPRING 2008. Options
FIN-40008 FINANCIAL INSTRUMENTS SPRING 2008 Options These notes describe the payoffs to European and American put and call options the so-called plain vanilla options. We consider the payoffs to these
More informationForward Contracts and Forward Rates
Forward Contracts and Forward Rates Outline and Readings Outline Forward Contracts Forward Prices Forward Rates Information in Forward Rates Reading Veronesi, Chapters 5 and 7 Tuckman, Chapters 2 and 16
More informationChoice under Uncertainty
Choice under Uncertainty Part 1: Expected Utility Function, Attitudes towards Risk, Demand for Insurance Slide 1 Choice under Uncertainty We ll analyze the underlying assumptions of expected utility theory
More informationLecture 6: Option Pricing Using a One-step Binomial Tree. Friday, September 14, 12
Lecture 6: Option Pricing Using a One-step Binomial Tree An over-simplified model with surprisingly general extensions a single time step from 0 to T two types of traded securities: stock S and a bond
More informationCall Price as a Function of the Stock Price
Call Price as a Function of the Stock Price Intuitively, the call price should be an increasing function of the stock price. This relationship allows one to develop a theory of option pricing, derived
More informationChapter 1: The Modigliani-Miller Propositions, Taxes and Bankruptcy Costs
Chapter 1: The Modigliani-Miller Propositions, Taxes and Bankruptcy Costs Corporate Finance - MSc in Finance (BGSE) Albert Banal-Estañol Universitat Pompeu Fabra and Barcelona GSE Albert Banal-Estañol
More informationCHAPTER 21: OPTION VALUATION
CHAPTER 21: OPTION VALUATION 1. Put values also must increase as the volatility of the underlying stock increases. We see this from the parity relation as follows: P = C + PV(X) S 0 + PV(Dividends). Given
More informationRisk and Return Models: Equity and Debt. Aswath Damodaran 1
Risk and Return Models: Equity and Debt Aswath Damodaran 1 First Principles Invest in projects that yield a return greater than the minimum acceptable hurdle rate. The hurdle rate should be higher for
More informationCHAPTER 15 Capital Structure: Basic Concepts
Multiple Choice Questions: CHAPTER 15 Capital Structure: Basic Concepts I. DEFINITIONS HOMEMADE LEVERAGE a 1. The use of personal borrowing to change the overall amount of financial leverage to which an
More informationThe cost of capital. A reading prepared by Pamela Peterson Drake. 1. Introduction
The cost of capital A reading prepared by Pamela Peterson Drake O U T L I N E 1. Introduction... 1 2. Determining the proportions of each source of capital that will be raised... 3 3. Estimating the marginal
More information1 Portfolio mean and variance
Copyright c 2005 by Karl Sigman Portfolio mean and variance Here we study the performance of a one-period investment X 0 > 0 (dollars) shared among several different assets. Our criterion for measuring
More informationPractice Exam (Solutions)
Practice Exam (Solutions) June 6, 2008 Course: Finance for AEO Length: 2 hours Lecturer: Paul Sengmüller Students are expected to conduct themselves properly during examinations and to obey any instructions
More informationBond Valuation. Capital Budgeting and Corporate Objectives
Bond Valuation Capital Budgeting and Corporate Objectives Professor Ron Kaniel Simon School of Business University of Rochester 1 Bond Valuation An Overview Introduction to bonds and bond markets» What
More informationCorporate Finance, Fall 03 Exam #2 review questions (full solutions at end of document)
Corporate Finance, Fall 03 Exam #2 review questions (full solutions at end of document) 1. Portfolio risk & return. Idaho Slopes (IS) and Dakota Steppes (DS) are both seasonal businesses. IS is a downhill
More informationLecture 1: Asset Allocation
Lecture 1: Asset Allocation Investments FIN460-Papanikolaou Asset Allocation I 1/ 62 Overview 1. Introduction 2. Investor s Risk Tolerance 3. Allocating Capital Between a Risky and riskless asset 4. Allocating
More informationExpected default frequency
KM Model Expected default frequency Expected default frequency (EDF) is a forward-looking measure of actual probability of default. EDF is firm specific. KM model is based on the structural approach to
More informationBlack-Scholes Equation for Option Pricing
Black-Scholes Equation for Option Pricing By Ivan Karmazin, Jiacong Li 1. Introduction In early 1970s, Black, Scholes and Merton achieved a major breakthrough in pricing of European stock options and there
More informationCHAPTER 6: RISK AVERSION AND CAPITAL ALLOCATION TO RISKY ASSETS
CHAPTER 6: RISK AVERSION AND CAPITAL ALLOCATION TO RISKY ASSETS PROBLEM SETS 1. (e). (b) A higher borrowing is a consequence of the risk of the borrowers default. In perfect markets with no additional
More informationCost of Capital, Valuation and Strategic Financial Decision Making
Cost of Capital, Valuation and Strategic Financial Decision Making By Dr. Valerio Poti, - Examiner in Professional 2 Stage Strategic Corporate Finance The financial crisis that hit financial markets in
More informationChapter 3: Commodity Forwards and Futures
Chapter 3: Commodity Forwards and Futures In the previous chapter we study financial forward and futures contracts and we concluded that are all alike. Each commodity forward, however, has some unique
More informationOption Pricing Applications in Valuation!
Option Pricing Applications in Valuation! Equity Value in Deeply Troubled Firms Value of Undeveloped Reserves for Natural Resource Firm Value of Patent/License 73 Option Pricing Applications in Equity
More informationFinal Exam MØA 155 Financial Economics Fall 2009 Permitted Material: Calculator
University of Stavanger (UiS) Stavanger Masters Program Final Exam MØA 155 Financial Economics Fall 2009 Permitted Material: Calculator The number in brackets is the weight for each problem. The weights
More informationLecture 6: Arbitrage Pricing Theory
Lecture 6: Arbitrage Pricing Theory Investments FIN460-Papanikolaou APT 1/ 48 Overview 1. Introduction 2. Multi-Factor Models 3. The Arbitrage Pricing Theory FIN460-Papanikolaou APT 2/ 48 Introduction
More informationLesson 5. Risky assets
Lesson 5. Risky assets Prof. Beatriz de Blas May 2006 5. Risky assets 2 Introduction How stock markets serve to allocate risk. Plan of the lesson: 8 >< >: 1. Risk and risk aversion 2. Portfolio risk 3.
More informationChapter 1: Financial Markets and Financial Derivatives
Chapter 1: Financial Markets and Financial Derivatives 1.1 Financial Markets Financial markets are markets for financial instruments, in which buyers and sellers find each other and create or exchange
More informationThe Capital Asset Pricing Model (CAPM)
Prof. Alex Shapiro Lecture Notes 9 The Capital Asset Pricing Model (CAPM) I. Readings and Suggested Practice Problems II. III. IV. Introduction: from Assumptions to Implications The Market Portfolio Assumptions
More informationThe value of tax shields is NOT equal to the present value of tax shields
The value of tax shields is NOT equal to the present value of tax shields Pablo Fernández * IESE Business School. University of Navarra. Madrid, Spain ABSTRACT We show that the value of tax shields is
More informationCHAPTER 22: FUTURES MARKETS
CHAPTER 22: FUTURES MARKETS PROBLEM SETS 1. There is little hedging or speculative demand for cement futures, since cement prices are fairly stable and predictable. The trading activity necessary to support
More informationEC372 Bond and Derivatives Markets Topic #5: Options Markets I: fundamentals
EC372 Bond and Derivatives Markets Topic #5: Options Markets I: fundamentals R. E. Bailey Department of Economics University of Essex Outline Contents 1 Call options and put options 1 2 Payoffs on options
More informationNote: There are fewer problems in the actual Final Exam!
HEC Paris Practice Final Exam Questions Version with Solutions Financial Markets Fall 2013 Note: There are fewer problems in the actual Final Exam! Problem 1. Are the following statements True, False or
More informationThe Tangent or Efficient Portfolio
The Tangent or Efficient Portfolio 1 2 Identifying the Tangent Portfolio Sharpe Ratio: Measures the ratio of reward-to-volatility provided by a portfolio Sharpe Ratio Portfolio Excess Return E[ RP ] r
More informationCurrent Accounts in Open Economies Obstfeld and Rogoff, Chapter 2
Current Accounts in Open Economies Obstfeld and Rogoff, Chapter 2 1 Consumption with many periods 1.1 Finite horizon of T Optimization problem maximize U t = u (c t ) + β (c t+1 ) + β 2 u (c t+2 ) +...
More informationRethinking Fixed Income
Rethinking Fixed Income Challenging Conventional Wisdom May 2013 Risk. Reinsurance. Human Resources. Rethinking Fixed Income: Challenging Conventional Wisdom With US Treasury interest rates at, or near,
More informationFund Manager s Portfolio Choice
Fund Manager s Portfolio Choice Zhiqing Zhang Advised by: Gu Wang September 5, 2014 Abstract Fund manager is allowed to invest the fund s assets and his personal wealth in two separate risky assets, modeled
More informationFinance 2 for IBA (30J201) F. Feriozzi Re-sit exam June 18 th, 2012. Part One: Multiple-Choice Questions (45 points)
Finance 2 for IBA (30J201) F. Feriozzi Re-sit exam June 18 th, 2012 Part One: Multiple-Choice Questions (45 points) Question 1 Assume that capital markets are perfect. Which of the following statements
More informationChapter 11 Options. Main Issues. Introduction to Options. Use of Options. Properties of Option Prices. Valuation Models of Options.
Chapter 11 Options Road Map Part A Introduction to finance. Part B Valuation of assets, given discount rates. Part C Determination of risk-adjusted discount rate. Part D Introduction to derivatives. Forwards
More informationOption Pricing Theory and Applications. Aswath Damodaran
Option Pricing Theory and Applications Aswath Damodaran What is an option? An option provides the holder with the right to buy or sell a specified quantity of an underlying asset at a fixed price (called
More informationChapter 7: Capital Structure: An Overview of the Financing Decision
Chapter 7: Capital Structure: An Overview of the Financing Decision 1. Income bonds are similar to preferred stock in several ways. Payment of interest on income bonds depends on the availability of sufficient
More informationChap 3 CAPM, Arbitrage, and Linear Factor Models
Chap 3 CAPM, Arbitrage, and Linear Factor Models 1 Asset Pricing Model a logical extension of portfolio selection theory is to consider the equilibrium asset pricing consequences of investors individually
More information11 Option. Payoffs and Option Strategies. Answers to Questions and Problems
11 Option Payoffs and Option Strategies Answers to Questions and Problems 1. Consider a call option with an exercise price of $80 and a cost of $5. Graph the profits and losses at expiration for various
More informationThe Equity Premium in India
The Equity Premium in India Rajnish Mehra University of California, Santa Barbara and National Bureau of Economic Research January 06 Prepared for the Oxford Companion to Economics in India edited by Kaushik
More informationHow Dilution Affects Option Value
How Dilution Affects Option Value If you buy a call option on an options exchange and then exercise it, you have no effect on the number of outstanding shares. The investor who sold the call simply hands
More informationOption Values. Determinants of Call Option Values. CHAPTER 16 Option Valuation. Figure 16.1 Call Option Value Before Expiration
CHAPTER 16 Option Valuation 16.1 OPTION VALUATION: INTRODUCTION Option Values Intrinsic value - profit that could be made if the option was immediately exercised Call: stock price - exercise price Put:
More informationOptions Pricing. This is sometimes referred to as the intrinsic value of the option.
Options Pricing We will use the example of a call option in discussing the pricing issue. Later, we will turn our attention to the Put-Call Parity Relationship. I. Preliminary Material Recall the payoff
More informationChapter 5 Risk and Return ANSWERS TO SELECTED END-OF-CHAPTER QUESTIONS
Chapter 5 Risk and Return ANSWERS TO SELECTED END-OF-CHAPTER QUESTIONS 5-1 a. Stand-alone risk is only a part of total risk and pertains to the risk an investor takes by holding only one asset. Risk is
More informationCapital budgeting & risk
Capital budgeting & risk A reading prepared by Pamela Peterson Drake O U T L I N E 1. Introduction 2. Measurement of project risk 3. Incorporating risk in the capital budgeting decision 4. Assessment of
More informationThe Black-Scholes Formula
FIN-40008 FINANCIAL INSTRUMENTS SPRING 2008 The Black-Scholes Formula These notes examine the Black-Scholes formula for European options. The Black-Scholes formula are complex as they are based on the
More information