CHAPTER 5. Introduction to Risk, Return, and the Historical Record INVESTMENTS BODIE, KANE, MARCUS. McGraw-Hill/Irwin

Size: px
Start display at page:

Download "CHAPTER 5. Introduction to Risk, Return, and the Historical Record INVESTMENTS BODIE, KANE, MARCUS. McGraw-Hill/Irwin"

Transcription

1 CHAPTER 5 Introduction to Risk, Return, and the Historical Record McGraw-Hill/Irwin Copyright 2011 by The McGraw-Hill Companies, Inc. All rights reserved.

2 5-2 Interest Rate Determinants Supply Households Demand Businesses Government s Net Supply and/or Demand Federal Reserve Actions

3 5-3 Real and Nominal Rates of Interest Nominal interest rate: Growth rate of your money Real interest rate: Growth rate of your purchasing power (how many Big Macs can I buy with my money?) Let R = nominal rate, r = real rate and i = inflation rate. Then: r R i 1 Solve: r r 1 1 R i R i 1 i

4 5-4 Equilibrium Real Rate of Interest Determined by: Supply Demand Government actions Expected rate of inflation

5 5-5 Figure Real Rate of Interest Equilibrium

6 5-6 Equilibrium Nominal Rate of Interest As the inflation rate increases, investors will demand higher nominal rates of return If E(i) denotes current expectations of inflation, then we get the Fisher Equation: Nominal rate = real rate + expected inflation R r E() i

7 5-7 Taxes and the Real Rate of Interest Tax liabilities are based on nominal income Given a tax rate (t) and nominal interest rate (R), the real after-tax rate of return is: R1 t i r i1 t i r1 t i t after tax inflation-adjusted As intuition suggests, the after-tax, real rate of return falls as the inflation rate rises.

8 Rates of Return for Different Holding Periods 5-8 Zero Coupon Bond Par = $100 T = maturity P = price r f (T) = total risk free return P r f T r f 100 T 1 P

9 Example 5.2 Time Does Matter: Use Annualized Rates of Return 5-9

10 5-10 Equation 5.7 EAR Time matters use EAR to annualize Effective Annual Rate definition: percentage increase in funds invested over a 1-year horizon f T EAR T 1 r 1 1 EAR 1 r f T 1 T

11 5-11 Equation 5.8 APR Annual Percentage Rate (APR): annualizing using simple interest 1 APR T 1 APR T EAR T 1 EAR 1 T

12 Investment End Value End Value with APR=5.0% End Value with EAR=5.0% (years)

13 5-13 Table 5.1 APR vs. EAR

14 5-14 Continuous Compounding Frequency of compounding matters At the limit to (compounding time) 0: 1 EAR e r cc

15 Investment End Value End Value with APR=5.0% End Value with EAR=5.0% End Value with Rcc=5.0% (years)

16 Let r =rate and x =compounding time End Value Make x very small. Then use A=e ln(a) How to derive R cc x0 lim 1 T N * x N T / 1 r * x1 r * x 1 r * x N compounding N times N r * x lim e ln 1r* x N S x0 x Substitute N=T/x lim x0 T e ln 1r* x x 1 T r 1r* x 1 lime e x0 Looks like 0/0. Use de l Hôpital rt Q.E.D. lime x0 d dx T ln Checks: r=0 End Value=1 T=0 End Value=1 d dx 1r* x x

17 Table 5.2 Statistics for T-Bill Rates, Inflation Rates and Real Rates,

18 5-18 Bills and Inflation, Moderate inflation can offset most of the nominal gains on low-risk investments. One dollar invested in T-bills from grew to $20.52, but with a real value of only $1.69. Negative correlation between real rate and inflation rate means the nominal rate responds less than 1:1 to changes in expected inflation.

19 Figure 5.3 Interest Rates and Inflation,

20 5-20 Risk and Risk Premiums Rates of Return: Single Period HPR P P 1 P 0 0 D HPR = Holding Period Return P 0 = Beginning price P 1 = Ending price D 1 = Dividend during period one 1

21 5-21 Rates of Return: Single Period Example Ending Price = 110 Beginning Price = 100 Dividend = 4 HPR = ( )/ (100) = 14%

22 Expected Return and Standard Deviation 5-22 Expected (or mean) returns E( r) p( s) r( s) s p(s) = probability of a state r(s) = return if a state occurs s = state

23 5-23 Scenario Returns: Example State Prob. of State r in State Excellent Good Poor Crash E(r) = (0.25)(0.31) + (0.45)(0.14) + (0.25)( ) + (0.05)(-0.52) = = 9.76% (think of a probability-weighted avg) NOTE: use decimals instead of percentages to be safe

24 5-24 Variance and Standard Deviation Variance (VAR): 2 2 s p( s) r( s) E( r) Standard Deviation (STD): STD 2

25 5-25 Scenario VAR and STD Example VAR calculation: σ 2 = 0.25( ) ( ) ( ) ( ) 2 = = Example STD calculation:

26 5-26 Time Series Analysis of Past Rates of Return n s n s s r n s r s p r E 1 1 ) ( 1 ) ( ) ( ) ( The Arithmetic Average of historical rate of return as an estimator of the expected rate of return

27 5-27 Geometric Average Return TV n ( 1 r )(1 r2 )...(1 r 1 n ) TV = Terminal Value of the Investment Solve for a rate g that, if compounded n times, gives you the same TV TV n 1 g g 1/ n 1 TV g = geometric average rate of return

28 Geometric Variance and Standard Deviation Formulas Recall the definition of variance s p( s) r( s) E( r) Estimated Variance = expected value of squared deviations (from the mean) ˆ 2 1 n n s1 2 rs r

29 Geometric Variance and Standard Deviation Formulas Using the estimated r avg instead of the real E(r) introduces a bias: 5-29 we already used the n observations to estimate r avg we really have only (n-1) independent observations correct by multiplying by n/(n-1) When eliminating the bias, Variance and Standard Deviation become*: ˆ 1 n 1 n j1 2 rs r * More at

30 The Reward-to-Volatility (Sharpe) 5-30 Ratio Sharpe Ratio for Portfolios: Risk Premium SD of Excess Returns

31 5-31 The Normal Distribution Investment management math is easier when returns are normal Standard deviation is a good measure of risk when returns are symmetric If security returns are symmetric, portfolio returns will be, too Assuming Normality, future scenarios can be estimated using just mean and standard deviation

32 5-32 Figure 5.4 The Normal Distribution

33 5-33 Normality and Risk Measures What if excess returns are not normally distributed? Standard deviation is no longer a complete measure of risk Sharpe ratio is not a complete measure of portfolio performance Need to consider skew and kurtosis

34 5-34 Skew and Kurtosis skew average R 3 ˆ R 3 kurtosis average R R this equals 3 for a Normal distribution 4 4 ˆ 3

35 Figure 5.5A Normal and Skewed Distributions 5-35

36 Figure 5.5B Normal and Fat-Tailed Distributions (mean = 0.1, SD =0.2) 5-36

CHAPTER 5. Introduction to Risk, Return, and the Historical Record INVESTMENTS BODIE, KANE, MARCUS. McGraw-Hill/Irwin

CHAPTER 5. Introduction to Risk, Return, and the Historical Record INVESTMENTS BODIE, KANE, MARCUS. McGraw-Hill/Irwin CHAPTER 5 Introduction to Risk, Return, and the Historical Record McGraw-Hill/Irwin Copyright 2011 by The McGraw-Hill Companies, Inc. All rights reserved. 5-2 Interest Rate Determinants Supply Households

More information

CHAPTER 5. Introduction to Risk, Return, and the Historical Record INVESTMENTS BODIE, KANE, MARCUS

CHAPTER 5. Introduction to Risk, Return, and the Historical Record INVESTMENTS BODIE, KANE, MARCUS CHAPTER 5 Introduction to Risk, Return, and the Historical Record INVESTMENTS BODIE, KANE, MARCUS McGraw-Hill/Irwin Copyright 2011 by The McGraw-Hill Companies, Inc. All rights reserved. 5-2 Supply Interest

More information

Risk and Return: Past and Prologue

Risk and Return: Past and Prologue Chapter 5 Risk and Return: Past and Prologue Bodie, Kane, and Marcus Essentials of Investments Tenth Edition What is in Chapter 5 5.1 Rates of Return HPR, arithmetic, geometric, dollar-weighted, APR, EAR

More information

Risk and Return: Past and Prologue

Risk and Return: Past and Prologue Chapter 5 Risk and Return: Past and Prologue Bodie, Kane, and Marcus Essentials of Investments Tenth Edition 5.1 Rates of Return Holding-Period Return (HPR) Rate of return over given investment period

More information

Rationale Reference Nattawut Jenwittayaroje, Ph.D., CFA Expected Return and Standard Deviation Example: Ending Price =

Rationale Reference Nattawut Jenwittayaroje, Ph.D., CFA Expected Return and Standard Deviation Example: Ending Price = Rationale Lecture 4: Learning about return and risk from the historical record Reference: Investments, Bodie, Kane, and Marcus, and Investment Analysis and Behavior, Nofsinger and Hirschey Nattawut Jenwittayaroje,

More information

Rationale. Learning about return and risk from the historical record and beta estimation. T Bills and Inflation

Rationale. Learning about return and risk from the historical record and beta estimation. T Bills and Inflation Learning about return and risk from the historical record and beta estimation Reference: Investments, Bodie, Kane, and Marcus, and Investment Analysis and Behavior, Nofsinger and Hirschey Nattawut Jenwittayaroje,

More information

Chapter 3 How Securities are Traded (Cont d) Copyright 2010 by The McGraw-Hill Companies, Inc. All rights reserved.

Chapter 3 How Securities are Traded (Cont d) Copyright 2010 by The McGraw-Hill Companies, Inc. All rights reserved. Chapter 3 How Securities are Traded (Cont d) McGraw-Hill/Irwin Copyright 2010 by The McGraw-Hill Companies, Inc. All rights reserved. Margin Trading Magnifies Profits and Losses 3-2 Short Sales Purpose

More information

1 A Brief History of. Chapter. Risk and Return. Dollar Returns. PercentReturn. Learning Objectives. A Brief History of Risk and Return

1 A Brief History of. Chapter. Risk and Return. Dollar Returns. PercentReturn. Learning Objectives. A Brief History of Risk and Return Chapter Learning Objectives To become a wise investor (maybe even one with too much money), you need to know: 1 A Brief History of Risk and Return How to calculate the return on an investment using different

More information

INTRODUCTION TO PORTFOLIO ANALYSIS. Dimensions of Portfolio Performance

INTRODUCTION TO PORTFOLIO ANALYSIS. Dimensions of Portfolio Performance INTRODUCTION TO PORTFOLIO ANALYSIS Dimensions of Portfolio Performance Interpretation of Portfolio Returns Portfolio Return Analysis Conclusions About Past Performance Predictions About Future Performance

More information

Financial Econometrics Jeffrey R. Russell. Midterm 2014 Suggested Solutions. TA: B. B. Deng

Financial Econometrics Jeffrey R. Russell. Midterm 2014 Suggested Solutions. TA: B. B. Deng Financial Econometrics Jeffrey R. Russell Midterm 2014 Suggested Solutions TA: B. B. Deng Unless otherwise stated, e t is iid N(0,s 2 ) 1. (12 points) Consider the three series y1, y2, y3, and y4. Match

More information

University of Colorado at Boulder Leeds School of Business Dr. Roberto Caccia

University of Colorado at Boulder Leeds School of Business Dr. Roberto Caccia Applied Derivatives Risk Management Value at Risk Risk Management, ok but what s risk? risk is the pain of being wrong Market Risk: Risk of loss due to a change in market price Counterparty Risk: Risk

More information

Monetary Economics Measuring Asset Returns. Gerald P. Dwyer Fall 2015

Monetary Economics Measuring Asset Returns. Gerald P. Dwyer Fall 2015 Monetary Economics Measuring Asset Returns Gerald P. Dwyer Fall 2015 WSJ Readings Readings this lecture, Cuthbertson Ch. 9 Readings next lecture, Cuthbertson, Chs. 10 13 Measuring Asset Returns Outline

More information

Financial Econometrics

Financial Econometrics Financial Econometrics Introduction to Financial Econometrics Gerald P. Dwyer Trinity College, Dublin January 2016 Outline 1 Set Notation Notation for returns 2 Summary statistics for distribution of data

More information

Financial Econometrics Jeffrey R. Russell Midterm 2014

Financial Econometrics Jeffrey R. Russell Midterm 2014 Name: Financial Econometrics Jeffrey R. Russell Midterm 2014 You have 2 hours to complete the exam. Use can use a calculator and one side of an 8.5x11 cheat sheet. Try to fit all your work in the space

More information

An investment s return is your reward for investing. An investment s risk is the uncertainty of what will happen with your investment dollar.

An investment s return is your reward for investing. An investment s risk is the uncertainty of what will happen with your investment dollar. Chapter 7 An investment s return is your reward for investing. An investment s risk is the uncertainty of what will happen with your investment dollar. The relationship between risk and return is a tradeoff.

More information

Chapter. Diversification and Risky Asset Allocation. McGraw-Hill/Irwin. Copyright 2008 by The McGraw-Hill Companies, Inc. All rights reserved.

Chapter. Diversification and Risky Asset Allocation. McGraw-Hill/Irwin. Copyright 2008 by The McGraw-Hill Companies, Inc. All rights reserved. Chapter Diversification and Risky Asset Allocation McGraw-Hill/Irwin Copyright 008 by The McGraw-Hill Companies, Inc. All rights reserved. Diversification Intuitively, we all know that if you hold many

More information

Lecture 4. Risk and Return: Lessons from Market History

Lecture 4. Risk and Return: Lessons from Market History Lecture 4 Risk and Return: Lessons from Market History Outline 1 Returns 2 Holding-Period Returns 3 Return Statistics 4 Average Stock Returns and Risk-Free Returns 5 Risk Statistics 6 More on Average Returns

More information

Fin 3710 Investment Analysis Professor Rui Yao CHAPTER 5: RISK AND RETURN

Fin 3710 Investment Analysis Professor Rui Yao CHAPTER 5: RISK AND RETURN HW 3 Fin 3710 Investment Analysis Professor Rui Yao CHAPTER 5: RISK AND RETURN 1. V(12/31/2004) = V(1/1/1998) (1 + r g ) 7 = 100,000 (1.05) 7 = $140,710.04 5. a. The holding period returns for the three

More information

Principles of Finance Risk and Return. Instructor: Xiaomeng Lu

Principles of Finance Risk and Return. Instructor: Xiaomeng Lu Principles of Finance Risk and Return Instructor: Xiaomeng Lu 1 Course Outline Course Introduction Time Value of Money DCF Valuation Security Analysis: Bond, Stock Capital Budgeting (Fundamentals) Portfolio

More information

Chapter 12. Some Lessons from Capital Market History. Dongguk University, Prof. Sun-Joong Yoon

Chapter 12. Some Lessons from Capital Market History. Dongguk University, Prof. Sun-Joong Yoon Chapter 12. Some Lessons from Capital Market History Dongguk University, Prof. Sun-Joong Yoon Outline Returns The Historical Record Average Returns: The First Lesson The Variability of Returns: The Second

More information

I. Return Calculations (20 pts, 4 points each)

I. Return Calculations (20 pts, 4 points each) University of Washington Winter 015 Department of Economics Eric Zivot Econ 44 Midterm Exam Solutions This is a closed book and closed note exam. However, you are allowed one page of notes (8.5 by 11 or

More information

For 9.220, Term 1, 2002/03 02_Lecture12.ppt Student Version. What is risk? An overview of market performance Measuring performance

For 9.220, Term 1, 2002/03 02_Lecture12.ppt Student Version. What is risk? An overview of market performance Measuring performance Risk and Return Introduction For 9.220, erm, 2002/03 02_Lecture2.ppt Student Version Outline Introduction What is risk? performance Measuring performance Return and risk measures Summary and Conclusions

More information

CHAPTER 5: LEARNING ABOUT RETURN AND RISK FROM THE HISTORICAL RECORD

CHAPTER 5: LEARNING ABOUT RETURN AND RISK FROM THE HISTORICAL RECORD CHAPTER 5: LEARNING ABOUT RETURN AND RISK FROM THE HISTORICAL RECORD PROBLEM SETS 1. The Fisher equation predicts that the nominal rate will equal the equilibrium real rate plus the expected inflation

More information

Statistics for Business and Economics

Statistics for Business and Economics Statistics for Business and Economics Chapter 7 Estimation: Single Population Copyright 010 Pearson Education, Inc. Publishing as Prentice Hall Ch. 7-1 Confidence Intervals Contents of this chapter: Confidence

More information

CHAPTER 9 SOME LESSONS FROM CAPITAL MARKET HISTORY

CHAPTER 9 SOME LESSONS FROM CAPITAL MARKET HISTORY CHAPTER 9 SOME LESSONS FROM CAPITAL MARKET HISTORY Answers to Concepts Review and Critical Thinking Questions 1. They all wish they had! Since they didn t, it must have been the case that the stellar performance

More information

Manager Comparison Report June 28, Report Created on: July 25, 2013

Manager Comparison Report June 28, Report Created on: July 25, 2013 Manager Comparison Report June 28, 213 Report Created on: July 25, 213 Page 1 of 14 Performance Evaluation Manager Performance Growth of $1 Cumulative Performance & Monthly s 3748 3578 348 3238 368 2898

More information

Chen-wei Chiu ECON 424 Eric Zivot July 17, Lab 4. Part I Descriptive Statistics. I. Univariate Graphical Analysis 1. Separate & Same Graph

Chen-wei Chiu ECON 424 Eric Zivot July 17, Lab 4. Part I Descriptive Statistics. I. Univariate Graphical Analysis 1. Separate & Same Graph Chen-wei Chiu ECON 424 Eric Zivot July 17, 2014 Part I Descriptive Statistics I. Univariate Graphical Analysis 1. Separate & Same Graph Lab 4 Time Series Plot Bar Graph The plots show that the returns

More information

Discrete Probability Distribution

Discrete Probability Distribution 1 Discrete Probability Distribution Key Definitions Discrete Random Variable: Has a countable number of values. This means that each data point is distinct and separate. Continuous Random Variable: Has

More information

Chapter. Return, Risk, and the Security Market Line. McGraw-Hill/Irwin. Copyright 2008 by The McGraw-Hill Companies, Inc. All rights reserved.

Chapter. Return, Risk, and the Security Market Line. McGraw-Hill/Irwin. Copyright 2008 by The McGraw-Hill Companies, Inc. All rights reserved. Chapter Return, Risk, and the Security Market Line McGraw-Hill/Irwin Copyright 2008 by The McGraw-Hill Companies, Inc. All rights reserved. Return, Risk, and the Security Market Line Our goal in this chapter

More information

CHAPTER 14. Bond Prices and Yields INVESTMENTS BODIE, KANE, MARCUS. Copyright 2011 by The McGraw-Hill Companies, Inc. All rights reserved.

CHAPTER 14. Bond Prices and Yields INVESTMENTS BODIE, KANE, MARCUS. Copyright 2011 by The McGraw-Hill Companies, Inc. All rights reserved. CHAPTER 14 Bond Prices and Yields McGraw-Hill/Irwin Copyright 2011 by The McGraw-Hill Companies, Inc. All rights reserved. 14-2 Bond Characteristics Bonds are debt. Issuers are borrowers and holders are

More information

Oklahoma State University Spears School of Business. Risk & Return

Oklahoma State University Spears School of Business. Risk & Return Oklahoma State University Spears School of Business Risk & Return Slide 2 Returns Dollar Returns the sum of the cash received and the change in value of the asset, in dollars. Dividends Ending market value

More information

FV N = PV (1+ r) N. FV N = PVe rs * N 2011 ELAN GUIDES 3. The Future Value of a Single Cash Flow. The Present Value of a Single Cash Flow

FV N = PV (1+ r) N. FV N = PVe rs * N 2011 ELAN GUIDES 3. The Future Value of a Single Cash Flow. The Present Value of a Single Cash Flow QUANTITATIVE METHODS The Future Value of a Single Cash Flow FV N = PV (1+ r) N The Present Value of a Single Cash Flow PV = FV (1+ r) N PV Annuity Due = PVOrdinary Annuity (1 + r) FV Annuity Due = FVOrdinary

More information

Full file at

Full file at KEY POINTS Most students taking this course will have had a prior course in basic corporate finance. Most also will have had at least one accounting class. Consequently, a good proportion of the material

More information

Valuing Stock Options: The Black-Scholes-Merton Model. Chapter 13

Valuing Stock Options: The Black-Scholes-Merton Model. Chapter 13 Valuing Stock Options: The Black-Scholes-Merton Model Chapter 13 1 The Black-Scholes-Merton Random Walk Assumption l Consider a stock whose price is S l In a short period of time of length t the return

More information

Chapter 11. Return and Risk: The Capital Asset Pricing Model (CAPM) Copyright 2013 by The McGraw-Hill Companies, Inc. All rights reserved.

Chapter 11. Return and Risk: The Capital Asset Pricing Model (CAPM) Copyright 2013 by The McGraw-Hill Companies, Inc. All rights reserved. Chapter 11 Return and Risk: The Capital Asset Pricing Model (CAPM) McGraw-Hill/Irwin Copyright 2013 by The McGraw-Hill Companies, Inc. All rights reserved. 11-0 Know how to calculate expected returns Know

More information

Population Mean GOALS. Characteristics of the Mean. EXAMPLE Population Mean. Parameter Versus Statistics. Describing Data: Numerical Measures

Population Mean GOALS. Characteristics of the Mean. EXAMPLE Population Mean. Parameter Versus Statistics. Describing Data: Numerical Measures GOALS Describing Data: Numerical Measures Chapter 3 McGraw-Hill/Irwin Copyright 010 by The McGraw-Hill Companies, Inc. All rights reserved. 3-1. Calculate the arithmetic mean, weighted mean, median, mode,

More information

Principles of Corporate Finance

Principles of Corporate Finance Principles of Corporate Finance Professor James J. Barkocy Time is money really McGraw-Hill/Irwin Copyright 2015 by The McGraw-Hill Companies, Inc. All rights reserved. Time Value of Money Money has a

More information

Dr. Maddah ENMG 625 Financial Eng g II 10/16/06

Dr. Maddah ENMG 625 Financial Eng g II 10/16/06 Dr. Maddah ENMG 65 Financial Eng g II 10/16/06 Chapter 11 Models of Asset Dynamics () Random Walk A random process, z, is an additive process defined over times t 0, t 1,, t k, t k+1,, such that z( t )

More information

Ch. 8 Risk and Rates of Return. Return, Risk and Capital Market. Investment returns

Ch. 8 Risk and Rates of Return. Return, Risk and Capital Market. Investment returns Ch. 8 Risk and Rates of Return Topics Measuring Return Measuring Risk Risk & Diversification CAPM Return, Risk and Capital Market Managers must estimate current and future opportunity rates of return for

More information

Day 3 Simple vs Compound Interest.notebook April 07, Simple Interest is money paid or earned on the. The Principal is the

Day 3 Simple vs Compound Interest.notebook April 07, Simple Interest is money paid or earned on the. The Principal is the LT: I can calculate simple and compound interest. p.11 What is Simple Interest? What is Principal? Simple Interest is money paid or earned on the. The Principal is the What is the Simple Interest Formula?

More information

Chapter 1 A Brief History of Risk and Return

Chapter 1 A Brief History of Risk and Return Chapter 1 A Brief History of Risk and Return Concept Questions 1. For both risk and return, increasing order is b, c, a, d. On average, the higher the risk of an investment, the higher is its expected

More information

Continuous Probability Distributions

Continuous Probability Distributions Continuous Probability Distributions Chapter 7 McGraw-Hill/Irwin Copyright 2010 by The McGraw-Hill Companies, Inc. All rights reserved. GOALS 1. Understand the difference between discrete and continuous

More information

CHAPTER 15. The Term Structure of Interest Rates INVESTMENTS BODIE, KANE, MARCUS

CHAPTER 15. The Term Structure of Interest Rates INVESTMENTS BODIE, KANE, MARCUS CHAPTER 15 The Term Structure of Interest Rates McGraw-Hill/Irwin Copyright 2011 by The McGraw-Hill Companies, Inc. All rights reserved. 15-2 Overview of Term Structure The yield curve is a graph that

More information

Introduction to Computational Finance and Financial Econometrics Return Calculations

Introduction to Computational Finance and Financial Econometrics Return Calculations You can t see this text! Introduction to Computational Finance and Financial Econometrics Return Calculations Eric Zivot Spring 2015 Eric Zivot (Copyright 2015) Return Calculations 1 / 56 Outline 1 The

More information

Chapter 10: Capital Markets and the Pricing of Risk

Chapter 10: Capital Markets and the Pricing of Risk Chapter 0: Capital Markets and the Pricing of Risk- Chapter 0: Capital Markets and the Pricing of Risk Big Picture: ) To value a project, we need an interest rate to calculate present values ) The interest

More information

Statistics & Flood Frequency Chapter 3. Dr. Philip B. Bedient

Statistics & Flood Frequency Chapter 3. Dr. Philip B. Bedient Statistics & Flood Frequency Chapter 3 Dr. Philip B. Bedient Predicting FLOODS Flood Frequency Analysis n Statistical Methods to evaluate probability exceeding a particular outcome - P (X >20,000 cfs)

More information

BUSM 411: Derivatives and Fixed Income

BUSM 411: Derivatives and Fixed Income BUSM 411: Derivatives and Fixed Income 3. Uncertainty and Risk Uncertainty and risk lie at the core of everything we do in finance. In order to make intelligent investment and hedging decisions, we need

More information

Economics 483. Midterm Exam. 1. Consider the following monthly data for Microsoft stock over the period December 1995 through December 1996:

Economics 483. Midterm Exam. 1. Consider the following monthly data for Microsoft stock over the period December 1995 through December 1996: University of Washington Summer Department of Economics Eric Zivot Economics 3 Midterm Exam This is a closed book and closed note exam. However, you are allowed one page of handwritten notes. Answer all

More information

Title: Introduction to Risk, Return and the Opportunity Cost of Capital Speaker: Rebecca Stull Created by: Gene Lai. online.wsu.

Title: Introduction to Risk, Return and the Opportunity Cost of Capital Speaker: Rebecca Stull Created by: Gene Lai. online.wsu. Title: Introduction to Risk, Return and the Opportunity Cost of Capital Speaker: Rebecca Stull Created by: Gene Lai online.wsu.edu MODULE 8 INTRODUCTION TO RISK AND RETURN, AND THE OPPORTUNITY COST OF

More information

Investment Companies Pool funds of individual investors and invest in a wide range of securities or other assets. pooling of assets Mutual Funds and Other Investment Companies Provide several functions

More information

Mathematics for Economists

Mathematics for Economists Department of Economics Mathematics for Economists Chapter 4 Mathematics of Finance Econ 506 Dr. Mohammad Zainal 4 Mathematics of Finance Compound Interest Annuities Amortization and Sinking Funds Arithmetic

More information

The Multistep Binomial Model

The Multistep Binomial Model Lecture 10 The Multistep Binomial Model Reminder: Mid Term Test Friday 9th March - 12pm Examples Sheet 1 4 (not qu 3 or qu 5 on sheet 4) Lectures 1-9 10.1 A Discrete Model for Stock Price Reminder: The

More information

Risk Reduction Potential

Risk Reduction Potential Risk Reduction Potential Research Paper 006 February, 015 015 Northstar Risk Corp. All rights reserved. info@northstarrisk.com Risk Reduction Potential In this paper we introduce the concept of risk reduction

More information

SOLUTIONS. Solution. The liabilities are deterministic and their value in one year will be $ = $3.542 billion dollars.

SOLUTIONS. Solution. The liabilities are deterministic and their value in one year will be $ = $3.542 billion dollars. Illinois State University, Mathematics 483, Fall 2014 Test No. 1, Tuesday, September 23, 2014 SOLUTIONS 1. You are the investment actuary for a life insurance company. Your company s assets are invested

More information

Assignment 3 Solutions

Assignment 3 Solutions ssignment 3 Solutions Timothy Vis January 30, 2006 3-1-6 P 900, r 10%, t 9 months, I?. Given I P rt, we have I (900)(0.10)( 9 12 ) 67.50 3-1-8 I 40, P 400, t 4 years, r?. Given I P rt, we have 40 (400)r(4),

More information

CHAPTER 15. The Term Structure of Interest Rates INVESTMENTS BODIE, KANE, MARCUS

CHAPTER 15. The Term Structure of Interest Rates INVESTMENTS BODIE, KANE, MARCUS CHAPTER 15 The Term Structure of Interest Rates INVESTMENTS BODIE, KANE, MARCUS McGraw-Hill/Irwin Copyright 2011 by The McGraw-Hill Companies, Inc. All rights reserved. INVESTMENTS BODIE, KANE, MARCUS

More information

3. Time value of money. We will review some tools for discounting cash flows.

3. Time value of money. We will review some tools for discounting cash flows. 1 3. Time value of money We will review some tools for discounting cash flows. Simple interest 2 With simple interest, the amount earned each period is always the same: i = rp o where i = interest earned

More information

Appendix S: Content Portfolios and Diversification

Appendix S: Content Portfolios and Diversification Appendix S: Content Portfolios and Diversification 1188 The expected return on a portfolio is a weighted average of the expected return on the individual id assets; but estimating the risk, or standard

More information

Midterm Exam. b. What are the continuously compounded returns for the two stocks?

Midterm Exam. b. What are the continuously compounded returns for the two stocks? University of Washington Fall 004 Department of Economics Eric Zivot Economics 483 Midterm Exam This is a closed book and closed note exam. However, you are allowed one page of notes (double-sided). Answer

More information

Section 8.3 Compound Interest

Section 8.3 Compound Interest Section 8.3 Compound Interest Objectives 1. Use the compound interest formulas. 2. Calculate present value. 3. Understand and compute effective annual yield. 4/24/2013 Section 8.3 1 Compound interest is

More information

David Tenenbaum GEOG 090 UNC-CH Spring 2005

David Tenenbaum GEOG 090 UNC-CH Spring 2005 Simple Descriptive Statistics Review and Examples You will likely make use of all three measures of central tendency (mode, median, and mean), as well as some key measures of dispersion (standard deviation,

More information

Calculating VaR. There are several approaches for calculating the Value at Risk figure. The most popular are the

Calculating VaR. There are several approaches for calculating the Value at Risk figure. The most popular are the VaR Pro and Contra Pro: Easy to calculate and to understand. It is a common language of communication within the organizations as well as outside (e.g. regulators, auditors, shareholders). It is not really

More information

Finance 100: Corporate Finance

Finance 100: Corporate Finance Finance 100: Corporate Finance Professor Michael R. Roberts Quiz 2 October 31, 2007 Name: Section: Question Maximum Student Score 1 30 2 40 3 30 Total 100 Instructions: Please read each question carefully

More information

Introduction to Computational Finance and Financial Econometrics Introduction to Portfolio Theory

Introduction to Computational Finance and Financial Econometrics Introduction to Portfolio Theory You can t see this text! Introduction to Computational Finance and Financial Econometrics Introduction to Portfolio Theory Eric Zivot Spring 2015 Eric Zivot (Copyright 2015) Introduction to Portfolio Theory

More information

Risk-neutral Binomial Option Valuation

Risk-neutral Binomial Option Valuation Risk-neutral Binomial Option Valuation Main idea is that the option price now equals the expected value of the option price in the future, discounted back to the present at the risk free rate. Assumes

More information

FINA 695 Assignment 1 Simon Foucher

FINA 695 Assignment 1 Simon Foucher Answer the following questions. Show your work. Due in the class on March 29. (postponed 1 week) You are expected to do the assignment on your own. Please do not take help from others. 1. (a) The current

More information

Random Walks vs Random Variables. The Random Walk Model. Simple rate of return to an asset is: Simple rate of return

Random Walks vs Random Variables. The Random Walk Model. Simple rate of return to an asset is: Simple rate of return The Random Walk Model Assume the logarithm of 'with dividend' price, ln P(t), changes by random amounts through time: ln P(t) = ln P(t-1) + µ + ε(it) (1) where: P(t) is the sum of the price plus dividend

More information

Business Statistics 41000: Probability 3

Business Statistics 41000: Probability 3 Business Statistics 41000: Probability 3 Drew D. Creal University of Chicago, Booth School of Business February 7 and 8, 2014 1 Class information Drew D. Creal Email: dcreal@chicagobooth.edu Office: 404

More information

Week 2 Quantitative Analysis of Financial Markets Hypothesis Testing and Confidence Intervals

Week 2 Quantitative Analysis of Financial Markets Hypothesis Testing and Confidence Intervals Week 2 Quantitative Analysis of Financial Markets Hypothesis Testing and Confidence Intervals Christopher Ting http://www.mysmu.edu/faculty/christophert/ Christopher Ting : christopherting@smu.edu.sg :

More information

3. Time value of money

3. Time value of money 1 Simple interest 2 3. Time value of money With simple interest, the amount earned each period is always the same: i = rp o We will review some tools for discounting cash flows. where i = interest earned

More information

Notes: Review of Future & Present Value, Some Statistics & Calculating Security Returns

Notes: Review of Future & Present Value, Some Statistics & Calculating Security Returns Notes: Review of Future & Present Value, Some Statistics & Calculating Security Returns I. Future Values How much is money today worth in the future? This is the future value (FV) of money today. a) Simple

More information

Chapter 4. Investment Return and Risk

Chapter 4. Investment Return and Risk Chapter 4 Investment Return and Risk Return The reward for investing. Most returns are not guaranteed. E(r) is important factor in selection. Total Return consists of Current Income Appreciation 4-2 Importance

More information

INVESTMENTS Class 2: Securities, Random Walk on Wall Street

INVESTMENTS Class 2: Securities, Random Walk on Wall Street 15.433 INVESTMENTS Class 2: Securities, Random Walk on Wall Street Reto R. Gallati MIT Sloan School of Management Spring 2003 February 5th 2003 Outline Probability Theory A brief review of probability

More information

Financial Econometrics: Problem Set # 3 Solutions

Financial Econometrics: Problem Set # 3 Solutions Financial Econometrics: Problem Set # 3 Solutions N Vera Chau The University of Chicago: Booth February 9, 219 1 a. You can generate the returns using the exact same strategy as given in problem 2 below.

More information

The Theory of Interest

The Theory of Interest The Theory of Interest An Undergraduate Introduction to Financial Mathematics J. Robert Buchanan 2010 Simple Interest (1 of 2) Definition Interest is money paid by a bank or other financial institution

More information

The Normal Distribution & Descriptive Statistics. Kin 304W Week 2: Jan 15, 2012

The Normal Distribution & Descriptive Statistics. Kin 304W Week 2: Jan 15, 2012 The Normal Distribution & Descriptive Statistics Kin 304W Week 2: Jan 15, 2012 1 Questionnaire Results I received 71 completed questionnaires. Thank you! Are you nervous about scientific writing? You re

More information

Where Vami 0 = 1000 and Where R N = Return for period N. Vami N = ( 1 + R N ) Vami N-1. Where R I = Return for period I. Average Return = ( S R I ) N

Where Vami 0 = 1000 and Where R N = Return for period N. Vami N = ( 1 + R N ) Vami N-1. Where R I = Return for period I. Average Return = ( S R I ) N The following section provides a brief description of each statistic used in PerTrac and gives the formula used to calculate each. PerTrac computes annualized statistics based on monthly data, unless Quarterly

More information

OPTIMAL RISKY PORTFOLIOS- ASSET ALLOCATIONS. BKM Ch 7

OPTIMAL RISKY PORTFOLIOS- ASSET ALLOCATIONS. BKM Ch 7 OPTIMAL RISKY PORTFOLIOS- ASSET ALLOCATIONS BKM Ch 7 ASSET ALLOCATION Idea from bank account to diversified portfolio Discussion principles are the same for any number of stocks A. bonds and stocks B.

More information

Part 1: Review of Hedge Funds

Part 1: Review of Hedge Funds Part 1: Review of Hedge Funds and structured products Luis A. Seco Sigma Analysis & Management University of Toronto RiskLab Luis Seco. Not to be distributed without permission. A hedge fund example Luis

More information

LECTURE 1. EQUITY Ownership Not a promise to pay Downside/Upside Bottom of Waterfall

LECTURE 1. EQUITY Ownership Not a promise to pay Downside/Upside Bottom of Waterfall LECTURE 1 FIN 3710 REVIEW Risk/Economy DEFINITIONS: Value Creation (Cost < Result) Investment Return Vs Risk - Analysis Managing / Hedging Real Assets Vs Financial Assets (Land/Building Vs Stock/Bonds)

More information

Course MFE/3F Practice Exam 2 Solutions

Course MFE/3F Practice Exam 2 Solutions Course MFE/3F Practice Exam Solutions The chapter references below refer to the chapters of the ActuarialBrew.com Study Manual. Solution 1 A Chapter 16, Black-Scholes Equation The expressions for the value

More information

Portfolio models - Podgorica

Portfolio models - Podgorica Outline Holding period return Suppose you invest in a stock-index fund over the next period (e.g. 1 year). The current price is 100$ per share. At the end of the period you receive a dividend of 5$; the

More information

BOND ANALYTICS. Aditya Vyas IDFC Ltd.

BOND ANALYTICS. Aditya Vyas IDFC Ltd. BOND ANALYTICS Aditya Vyas IDFC Ltd. Bond Valuation-Basics The basic components of valuing any asset are: An estimate of the future cash flow stream from owning the asset The required rate of return for

More information

Slides for Risk Management

Slides for Risk Management Slides for Risk Management Introduction to the modeling of assets Groll Seminar für Finanzökonometrie Prof. Mittnik, PhD Groll (Seminar für Finanzökonometrie) Slides for Risk Management Prof. Mittnik,

More information

KARACHI UNIVERSITY BUSINESS SCHOOL UNIVERSITY OF KARACHI BS (BBA) VI

KARACHI UNIVERSITY BUSINESS SCHOOL UNIVERSITY OF KARACHI BS (BBA) VI 88 P a g e B S ( B B A ) S y l l a b u s KARACHI UNIVERSITY BUSINESS SCHOOL UNIVERSITY OF KARACHI BS (BBA) VI Course Title : STATISTICS Course Number : BA(BS) 532 Credit Hours : 03 Course 1. Statistical

More information

Economics 424/Applied Mathematics 540. Final Exam Solutions

Economics 424/Applied Mathematics 540. Final Exam Solutions University of Washington Summer 01 Department of Economics Eric Zivot Economics 44/Applied Mathematics 540 Final Exam Solutions I. Matrix Algebra and Portfolio Math (30 points, 5 points each) Let R i denote

More information

CHAPTER 8. Personal Finance. Copyright 2015, 2011, 2007 Pearson Education, Inc. Section 8.4, Slide 1

CHAPTER 8. Personal Finance. Copyright 2015, 2011, 2007 Pearson Education, Inc. Section 8.4, Slide 1 CHAPTER 8 Personal Finance Copyright 2015, 2011, 2007 Pearson Education, Inc. Section 8.4, Slide 1 8.4 Compound Interest Copyright 2015, 2011, 2007 Pearson Education, Inc. Section 8.4, Slide 2 Objectives

More information

FNCE 4030 Fall 2012 Roberto Caccia, Ph.D. Midterm_2a (2-Nov-2012) Your name:

FNCE 4030 Fall 2012 Roberto Caccia, Ph.D. Midterm_2a (2-Nov-2012) Your name: Answer the questions in the space below. Written answers require no more than few compact sentences to show you understood and master the concept. Show your work to receive partial credit. Points are as

More information

2018 CFA Exam Prep. IFT High-Yield Notes. Quantitative Methods (Sample) Level I. Table of Contents

2018 CFA Exam Prep. IFT High-Yield Notes. Quantitative Methods (Sample) Level I. Table of Contents 2018 CFA Exam Prep IFT High-Yield Notes Quantitative Methods (Sample) Level I This document should be read in conjunction with the corresponding readings in the 2018 Level I CFA Program curriculum. Some

More information

Point Estimation. Stat 4570/5570 Material from Devore s book (Ed 8), and Cengage

Point Estimation. Stat 4570/5570 Material from Devore s book (Ed 8), and Cengage 6 Point Estimation Stat 4570/5570 Material from Devore s book (Ed 8), and Cengage Point Estimation Statistical inference: directed toward conclusions about one or more parameters. We will use the generic

More information

AN INTRODUCTION TO RISK AND RETURN. Chapter 7

AN INTRODUCTION TO RISK AND RETURN. Chapter 7 1 AN INTRODUCTION TO RISK AND RETURN Chapter 7 Learning Objectives 2 1. Calculate realized and expected rates of return and risk. 2. Describe the historical pattern of financial market returns. 3. Compute

More information

Copyright 2011 Pearson Education, Inc. Publishing as Addison-Wesley.

Copyright 2011 Pearson Education, Inc. Publishing as Addison-Wesley. Appendix: Statistics in Action Part I Financial Time Series 1. These data show the effects of stock splits. If you investigate further, you ll find that most of these splits (such as in May 1970) are 3-for-1

More information

Practice Problems on Term Structure

Practice Problems on Term Structure Practice Problems on Term Structure 1- The yield curve and expectations hypothesis (30 points) Assume that the policy of the Fed is given by the Taylor rule that we studied in class, that is i t = 1.5

More information

Financial Time Series and Their Characteristics

Financial Time Series and Their Characteristics Financial Time Series and Their Characteristics Egon Zakrajšek Division of Monetary Affairs Federal Reserve Board Summer School in Financial Mathematics Faculty of Mathematics & Physics University of Ljubljana

More information

Queens College, CUNY, Department of Computer Science Computational Finance CSCI 365 / 765 Fall 2017 Instructor: Dr. Sateesh Mane.

Queens College, CUNY, Department of Computer Science Computational Finance CSCI 365 / 765 Fall 2017 Instructor: Dr. Sateesh Mane. Queens College, CUNY, Department of Computer Science Computational Finance CSCI 365 / 765 Fall 217 Instructor: Dr. Sateesh Mane c Sateesh R. Mane 217 13 Lecture 13 November 15, 217 Derivation of the Black-Scholes-Merton

More information

Lesson Exponential Models & Logarithms

Lesson Exponential Models & Logarithms SACWAY STUDENT HANDOUT SACWAY BRAINSTORMING ALGEBRA & STATISTICS STUDENT NAME DATE INTRODUCTION Compound Interest When you invest money in a fixed- rate interest earning account, you receive interest at

More information

Two Hours. Mathematical formula books and statistical tables are to be provided THE UNIVERSITY OF MANCHESTER. 22 January :00 16:00

Two Hours. Mathematical formula books and statistical tables are to be provided THE UNIVERSITY OF MANCHESTER. 22 January :00 16:00 Two Hours MATH38191 Mathematical formula books and statistical tables are to be provided THE UNIVERSITY OF MANCHESTER STATISTICAL MODELLING IN FINANCE 22 January 2015 14:00 16:00 Answer ALL TWO questions

More information

CHAPTER 10 SOME LESSONS FROM CAPITAL MARKET HISTORY

CHAPTER 10 SOME LESSONS FROM CAPITAL MARKET HISTORY CHAPTER 10 SOME LESSONS FROM CAPITAL MARKET HISTORY Answers to Concepts Review and Critical Thinking Questions 3. No, stocks are riskier. Some investors are highly risk averse, and the extra possible return

More information

PREMIUM VERSION PREVIEW

PREMIUM VERSION PREVIEW FINANCIAL MATHS PREMIUM VERSION PREVIEW WWW.MATHSPOINTS.IE/SIGN-UP/ 205 LCHL Paper Question 6 (a) (i) Donagh is arranging a loan and is examining two different repayment options. Bank A will charge him

More information

Solutions to Practice Questions (Diversification)

Solutions to Practice Questions (Diversification) Simon School of Business University of Rochester FIN 402 Capital Budgeting & Corporate Objectives Prof. Ron Kaniel Solutions to Practice Questions (Diversification) 1. These practice questions are a suplement

More information