Presentation is loading. Please wait.

Presentation is loading. Please wait.

Risk and Return Riccardo Colacito.

Published by Modified over 9 years ago

Similar presentations

Presentation on theme: "Risk and Return Riccardo Colacito."— Presentation transcript:

1 Risk and Return Riccardo Colacito

2 Roadmap Rates of Return Summary Statistics of rates of return
Holding Period Return Arithmetic and Geometric Averages Annual Percentage Rate and Effective Annual Rate Summary Statistics of rates of return Probability Distribution Expected Return Variance, Covariance and Standard Deviation Other properties Historical record of Bills, Bonds, and Stocks Risk premia from ? Inflation and Real Rates of Return Foundations of Financial Markets

3 Holding Period Return Foundations of Financial Markets

4 Rates of Return: Single Period Example
Ending Price = 24 Beginning Price = 20 Dividend = 1 HPR = ( )/ ( 20) = 25% Foundations of Financial Markets

5 Roadmap Rates of Return Summary Statistics of rates of return
Holding Period Return Arithmetic and Geometric Averages Annual Percentage Rate and Effective Annual Rate Summary Statistics of rates of return Probability Distribution Expected Return Variance, Covariance and Standard Deviation Other properties Historical record of Bills, Bonds, and Stocks Risk premia from ? Inflation and Real Rates of Return Foundations of Financial Markets

6 Returns Using Arithmetic and Geometric Averaging
Time 1 2 3 4 HPR .1 .25 -.20 Arithmetic ra = (r1 + r rn) / n ra = ( ) / 4 = .10 or 10% Geometric rg = [(1+r1) (1+r2) .... (1+rn)]1/n - 1 rg = [(1.1) (1.25) (.8) (1.25)]1/4 - 1 = (1.5150) 1/4 -1 = = 8.29% Foundations of Financial Markets

7 Roadmap Rates of Return Summary Statistics of rates of return
Holding Period Return Arithmetic and Geometric Averages Annual Percentage Rate and Effective Annual Rate Summary Statistics of rates of return Probability Distribution Expected Return Variance and Standard Deviation Other properties Historical record of Bills, Bonds, and Stocks Risk premia from ? Inflation and Real Rates of Return Foundations of Financial Markets

8 Quoting Conventions Annual Percentage Rate
APR = (periods in year) X (rate for period) Effective Annual Rate EAR = ( 1+ rate for period)Periods per yr – 1 Example: monthly return of 1% APR = 1% X 12 = 12% EAR = (1.01) = 12.68% Foundations of Financial Markets

9 Roadmap Rates of Return Summary Statistics of rates of return
Holding Period Return Arithmetic and Geometric Averages Annual Percentage Rate and Effective Annual Rate Summary Statistics of rates of return Probability Distribution Expected Return Variance, Covariance and Standard Deviation Other properties Historical record of Bills, Bonds, and Stocks Risk premia from ? Inflation and Real Rates of Return Foundations of Financial Markets

10 Probability distribution
Definition: list of possible outcomes with associated probabilities Example: State Outcome Prob 1 -2 .1 2 -1 .2 3 .4 4 5 Foundations of Financial Markets

11 Probability distribution: figure
Foundations of Financial Markets

12 Normal distribution Foundations of Financial Markets

13 Notation Let p(i) denote the probability with which state i occurs
Outcome Prob 1 -2 .1 2 -1 .2 3 .4 4 5 Let p(i) denote the probability with which state i occurs Then p(1)=0.1 p(2)=0.2 p(3)=0.4 p(4)=0.2 p(5)=0.1 Foundations of Financial Markets

14 Roadmap Rates of Return Summary Statistics of rates of return
Holding Period Return Arithmetic and Geometric Averages Annual Percentage Rate and Effective Annual Rate Summary Statistics of rates of return Probability Distribution Expected Return Variance, Covariance and Standard Deviation Other properties Historical record of Bills, Bonds, and Stocks Risk premia from ? Inflation and Real Rates of Return Foundations of Financial Markets

15 S Expected Return E ( r ) = p s Definition:
p(s) = probability of a state r(s) = return if a state occurs 1 to s states E ( r ) = p s S Foundations of Financial Markets

16 E(r) = (.1)(-2) + (.2)(-1) + (.4)(0) + (.2)(1) + (.1)(2) = 0
Numerical Example State Prob Return 1 .1 -2 2 .2 -1 3 .4 4 5 E(r) = (.1)(-2) + (.2)(-1) + (.4)(0) + (.2)(1) + (.1)(2) = 0 Foundations of Financial Markets

17 Roadmap Rates of Return Summary Statistics of rates of return
Holding Period Return Arithmetic and Geometric Averages Annual Percentage Rate and Effective Annual Rate Summary Statistics of rates of return Probability Distribution Expected Return Variance, Covariance and Standard Deviation Other properties Historical record of Bills, Bonds, and Stocks Risk premia from ? Inflation and Real Rates of Return Foundations of Financial Markets

18 Why do we need the variance?
Two variables with the same mean. What do we know about their dispersion? Foundations of Financial Markets

19 Measuring Variance or Dispersion of Returns
Standard deviation = variance1/2 Variance = S s p ( ) [ r - E )] 2 Why do we take squared deviations? Foundations of Financial Markets

20 Numerical example State Prob Return 1 .1 -2 2 .2 -1 3 .4 4 5
4 5 Var = .1 (-2-0) (-1-0) (0-0) (1-0) (2-0)2 = 1.2 Std dev= (1.2)1/2 = 1.095 Foundations of Financial Markets

21 One important property of variance and standard deviation
Let w be a constant Var(wxr) = w2 x Var(r) Similarly Std Dev(wxr) = w x Std Dev(r) Foundations of Financial Markets

22 Covariance: Preliminaries
The extent at which two assets tend to move together Can be positive or negative Correlation Same idea of covariance, but bounded between -1 and 1 Foundations of Financial Markets

23 Covariance: definition
Foundations of Financial Markets

24 Correlation: definition
Foundations of Financial Markets

25 Correlation (cont’d) Foundations of Financial Markets

26 Other properties - Foundations of Financial Markets

27 Correlation=-1 r1 r2 probability 1 5 .2 2 4 3
Foundations of Financial Markets

28 Correlation=+1 r1 r2 probability 1 .2 2 3 4 5
Foundations of Financial Markets

29 Correlation=0 r1 r2 probability 2 .2 4 3
Foundations of Financial Markets

30 Roadmap Rates of Return Summary Statistics of rates of return
Holding Period Return Arithmetic and Geometric Averages Annual Percentage Rate and Effective Annual Rate Summary Statistics of rates of return Probability Distribution Expected Return Variance, Covariance and Standard Deviation Other properties Historical record of Bills, Bonds, and Stocks Risk premia from ? Inflation and Real Rates of Return Foundations of Financial Markets

31 Characteristics of Probability Distributions
1) Mean: most likely value 2) Variance or standard deviation 3) Skewness * If a distribution is approximately normal, the distribution is described by characteristics 1 and 2 Foundations of Financial Markets

32 Skewed Distribution: Large Negative Returns Possible
Median Negative Positive r Foundations of Financial Markets

33 Skewed Distribution: Large Positive Returns Possible
Median Negative r Positive Foundations of Financial Markets

34 Roadmap Rates of Return Summary Statistics of rates of return
Holding Period Return Arithmetic and Geometric Averages Annual Percentage Rate and Effective Annual Rate Summary Statistics of rates of return Probability Distribution Expected Return Variance, Covariance and Standard Deviation Other properties Historical record of Bills, Bonds, and Stocks Risk premia from ? Inflation and Real Rates of Return Foundations of Financial Markets

35 Risk premium An expected return in excess of that of a risk free rate
Example The expected return on the S&P500 is 9% The return on a 1-month T-bill is 3% The risk premium is 6% (9%-3%) Foundations of Financial Markets

36 Annual Holding Period Returns From Table 5.3 of Text
Geom. Arith. Stan. Series Mean% Mean% Dev.% World Stk US Lg Stk US Sm Stk Wor Bonds LT Treas T-Bills Inflation Foundations of Financial Markets

37 Risk Premia Arith. Stan. Series Mean% Dev.% World Stk 7.37 18.69
US Lg Stk US Sm Stk Wor Bonds LT Treas Foundations of Financial Markets

38 Figure 5.1 Frequency Distributions of Holding Period Returns
Foundations of Financial Markets

39 Figure 5.2 Rates of Return on Stocks, Bonds and Bills
Foundations of Financial Markets

40 Roadmap Rates of Return Summary Statistics of rates of return
Holding Period Return Arithmetic and Geometric Averages Annual Percentage Rate and Effective Annual Rate Summary Statistics of rates of return Probability Distribution Expected Return Variance, Covariance and Standard Deviation Other properties Historical record of Bills, Bonds, and Stocks Risk premia from ? Inflation and Real Rates of Return Foundations of Financial Markets

41 Real vs. Nominal Rates Notation: Exact relationship
R=nominal return i =inflation rate r =real return Exact relationship Approximate relationship Example R = 9%, i = 6%: what is r? Foundations of Financial Markets

42 Figure 5.4 Interest, Inflation and Real Rates of Return
Foundations of Financial Markets

Download ppt "Risk and Return Riccardo Colacito."

Similar presentations

Holding Period Return.

Holding Period Return.
Introduction The relationship between risk and return is fundamental to finance theory You can invest very safely in a bank or in Treasury bills. Why.

Introduction The relationship between risk and return is fundamental to finance theory You can invest very safely in a bank or in Treasury bills. Why.
Risk, Return, and the Historical Record

Risk, Return, and the Historical Record
1 Risk, Returns, and Risk Aversion Return and Risk Measures Real versus Nominal Rates EAR versus APR Holding Period Returns Excess Return and Risk Premium.

1 Risk, Returns, and Risk Aversion Return and Risk Measures Real versus Nominal Rates EAR versus APR Holding Period Returns Excess Return and Risk Premium.
Risk and Return – Introduction Chapter 9 For 9.220,

Risk and Return – Introduction Chapter 9 For 9.220,
History of Interest Rates and Risk Premiums Chapter 5.

History of Interest Rates and Risk Premiums Chapter 5.
Risk and Return: Past and Prologue CHAPTER 5. McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. Holding Period Return.

Risk and Return: Past and Prologue CHAPTER 5. McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. Holding Period Return.
McGraw-Hill/Irwin © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved. Risk and Return: Past and Prologue CHAPTER 5.

McGraw-Hill/Irwin © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved. Risk and Return: Past and Prologue CHAPTER 5.
Chapter McGraw-Hill/Irwin Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights reserved. 1 A Brief History of Risk and Return.

Chapter McGraw-Hill/Irwin Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights reserved. 1 A Brief History of Risk and Return.
Risk and Return: Past and Prologue

Risk and Return: Past and Prologue
1 Fin 2802, Spring 10 - Tang Chapter 5: Risk and Return Fina2802: Investments and Portfolio Analysis Spring, 2010 Dragon Tang Lecture 8 Risk and Return:

1 Fin 2802, Spring 10 - Tang Chapter 5: Risk and Return Fina2802: Investments and Portfolio Analysis Spring, 2010 Dragon Tang Lecture 8 Risk and Return:
Chapter 5 Risk and Return: Past and Prologue. Measuring Ex-Post (Past) Returns One period investment: regardless of the length of the period. Must be.

Chapter 5 Risk and Return: Past and Prologue. Measuring Ex-Post (Past) Returns One period investment: regardless of the length of the period. Must be.
Financial Analysis, Planning and Forecasting Theory and Application By Alice C. Lee San Francisco State University John C. Lee J.P. Morgan Chase Cheng.

Financial Analysis, Planning and Forecasting Theory and Application By Alice C. Lee San Francisco State University John C. Lee J.P. Morgan Chase Cheng.
Capital Market Theory Return & Risk Calculations, Risk Premiums, and Historical Averages.

Capital Market Theory Return & Risk Calculations, Risk Premiums, and Historical Averages.
Jacoby, Stangeland and Wajeeh, 20001 uDollar Return = Dollar Dividend + Change in Market Value uPercentage Return = Dollar Return / Beginning Market Value.

Jacoby, Stangeland and Wajeeh, uDollar Return = Dollar Dividend + Change in Market Value uPercentage Return = Dollar Return / Beginning Market Value.
Learning about Return and Risk from The Historical Record

Learning about Return and Risk from The Historical Record
Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 1 Chapter 6.

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 1 Chapter 6.
Risk and Return – Introduction For 9.220, Term 1, 2002/03 02_Lecture12.ppt Student Version.

Risk and Return – Introduction For 9.220, Term 1, 2002/03 02_Lecture12.ppt Student Version.
Fall-02 Investments Zvi Wiener tel: 02-588-3049 History of Interest Rates and.

Fall-02 Investments Zvi Wiener tel: History of Interest Rates and.
McGraw-Hill/Irwin Copyright © 2013 by The McGraw-Hill Companies, Inc. All rights reserved. Risk and Return: Past and Prologue 5 Bodie, Kane, and Marcus.

McGraw-Hill/Irwin Copyright © 2013 by The McGraw-Hill Companies, Inc. All rights reserved. Risk and Return: Past and Prologue 5 Bodie, Kane, and Marcus.

Similar presentations

Ads by Google