The Term Structure of the Risk- Return Tradeoff

Size: px
Start display at page:

Download "The Term Structure of the Risk- Return Tradeoff"

Transcription

1 The Term Structure of the Risk- Return Tradeoff Luis M. Viceira Harvard Business School Netspar Opening Conference Tilburg University Tilburg, March 2005 New Research on Asset Allocation Portfolio choice is the original subject of modern finance. Massive revival of interest in recent years. New research is summarized in my recent work with John Y. Campbell: Strategic Asset Allocation: Portfolio Choice for Long-Term Investors, Oxford University Press, The Term Structure of the Risk-Return Tradeoff, Financial Analysts Journal,

2 Risk-Return Tradeoff: Traditional View Return expectations are constant over time. The variance of each asset return and its covariance with other asset returns are proportional to holding horizon: k 1 k 1 ( ) ( t+ k) t+ ( t+ ) k (1) (1) 2 t r = t r i = t r i = k σ r i= 0 i= 0 Var Var Var Thus annualized variances and covariances (risk per period) are independent of time horizon: There is a single number (σ r ) that summarizes risk for all holding periods. In this framework there is no distinction between short-term investors and long-term investors. Risk-Return Tradeoff: Traditional View Aggressive Investor Stocks Moderate Investor Best Mix of Stocks and Bonds Bonds Conservative Investor Cash The optimal portfolio is the same at all horizons 2

3 Time Variation In Investment Opportunities Recent research in empirical finance has challenged the traditional view of the risk-return tradeoff. In particular, it has documented that: 1. Real interest rates and expected inflation change over time: Future real interest rates are uncertain. 2. Expected returns (or risk premia) on equities, long-term bonds and other asset classes are also time varying: P/E ratios, D/P ratios, short term interest rates, yield spreads, forecast future stock and bond returns. 3. Changes in real interest rates, expected inflation, and risk premia are highly persistent. How should investors choose their portfolios if investment opportunities are time varying? Return Dynamics First-order vector autoregressive model, or VAR(1): ( ) z =Φ +Φ z + v, v N 0, Σ t t t+ 1 t+ 1 v The vector z t of variables includes short-term real interest rate (r 1,t+1 ), excess returns on stocks, bonds and any other asset under consideration (xr t+1 ), state variables, or return forecasting variables (s t+1 ). 3

4 Return Dynamics Traditional view sets Ф 1 = 0: k 1 ( ) ( xrt+ k) Var ( xrt+ ) 1 1 Var k k 2 t = t i = σ xr k i= 0 Modern view allows Ф 1 0: 2 ( ) xr =Φ +Φ xr + v, v N 0, σ t t t+ 1 t+ 1 xr ( ) k 1 ( xrt k) + Var ( xrt+ ) 1 1 Var k k 2 t t i = σ xr k i= 0 Implications Investors will have a different return expectation each period, based on the current levels of the variables that forecast future returns: Tactical asset allocation. Not all of the unconditional volatility of asset returns should count as risk, because part of it is driven by predictable time-variation in returns. Risk (conditional variances and correlations of asset returns) may be significantly different across investment horizons: There is a term structure of the risk return tradeoff. 4

5 Figure 1. Annualized Percent Standard Deviations of Real Returns Implied by Quarterly VAR(1) Estimates (1952.Q Q4) 18.00% Equities 16.00% Annualized Standard Deviation (%) 14.00% 12.00% 10.00% 8.00% 6.00% 4.00% 5-Year Bond Bond Held to Maturity K 2.00% T-Bill 0.00% Horizon K (Years) Aggressive Investor Stocks Moderate Investor Best Mix of Stocks and Bonds Bonds Conservative Investor Cash The optimal portfolio may change across investment horizons 5

6 Horizon Effects on Stock Market Risk Annualized Percent Standard Deviation of Real Returns on US Stocks (1952.Q Q4) 18.00% Equities 16.00% Annualized Standard Deviation (% ) 14.00% 12.00% 10.00% 8.00% 6.00% 4.00% 2.00% 0.00% Horizon K (Years) Horizon Effects on Stock Market Risk Empirically, there seem to be gradual predictable variations in stock returns: Low dividend yields and high price-earnings ratios mean high stock returns today but they forecast poor future stock returns. This is known as mean-reversion. 6

7 S&P 500 Price / 10-Year Average of Earnings P/ E in 06/ 04 = Average P/E = Year To get back to mean P/E, prices must fall by 40%, or earnings must grow 62% (which will take 10 years at 5% annual growth). Data Source: Robert Shiller (http://www.econ.yale.edu/~shiller/) Stocks Are NOT Riskless in the Long Run Annualized Percent Standard Deviation of Real Returns on US Stocks (1952.Q Q4) 18.00% Equities 16.00% Annualized Standard Deviation (%) 14.00% 12.00% 10.00% 8.00% 6.00% 4.00% 2.00% 0.00% Horizon K (Years) Mean-reversion reduces the risk of stocks for long-term investors, but this does NOT mean that long-term investors can ignore stock market risk altogether: Long term stock return volatility is 8%, not 0%! 7

8 Horizon Effects on Bond Return Volatility Figure 1. Annualized Percent Standard Deviations of Real Returns Implied by Quarterly VAR(1) Estimates (1952.Q Q4) 18.00% Equities 16.00% Annualized Standard Deviation (%) 14.00% 12.00% 10.00% 8.00% 6.00% 4.00% 5-Year Bond Bond Held to Maturity K 2.00% T-Bill 0.00% Horizon K (Years) Horizon Effects on Bond Return Volatility There are two offsetting forces affecting the volatility of bond returns: A steepening of the yield curve is good news for both current and future bond excess returns. Rising nominal short rates are bad news for bond returns today, but good news for future bond excess returns. The effect of the nominal short rate slightly dominates the volatility of bond returns at long horizons. 8

9 Figure 1. Annualized Percent Standard Deviations of Real Returns Implied by Quarterly VAR(1) Estimates (1952.Q Q4) 18.00% Equities 16.00% Annualized Standard Deviation (%) 14.00% 12.00% 10.00% 8.00% 6.00% 4.00% 5-Year Bond Bond Held to Maturity K 2.00% T-Bill 0.00% Horizon K (Years) Horizon Effects on the Volatility of Real Interest Rates and Expected Inflation Changes in expected inflation are highly persistent, and tend to amplify the volatility of real returns on long-term bonds held to maturity: Inflation risk makes holding long-term nominal bonds to maturity a risky investment. Changes in real interest rates are also highly persistent, and tend to amplify the volatility of the real return on short-term bonds when they are reinvested over long horizons: Real interest rate risk makes cash risky for long-term investors. Long-term inflation-indexed bonds are the true riskless asset for long-term investors. 9

10 Real returns on stocks and bonds are positively correlated at all horizons. Figure 2. Correlations of Real Returns Implied by Quarterly VAR(1) Estimates (1952.Q Q4) 70.0% 60.0% 50.0% 40.0% Correlation (%) 30.0% 20.0% 10.0% Stocks - 5-Year Bond 0.0% Bond held to Maturity K - Stocks -10.0% Horizon K (Years) Horizon Effects on the Bond-Stock Return Correlation At short and intermediate horizons, changes in nominal short-term rates explain the stock-fixed maturity bond correlation: When nominal short term rates rise, bond returns fall at once. Stock returns also fall, but it takes time for interest rate changes to have their full effect on stock prices. For bonds held to maturity, the stock-bond correlation reflects the negative of the stock-inflation correlation: Negative or highly negative at short and intermediate horizons. But positive at long horizons: Stocks hedge inflation risk, but only at long horizons. 10

11 Mean-Variance Allocations Across Investment Horizons We can explore the effect of return predictability on asset allocation by looking at mean-variance allocations of investors with different investment horizons. A mean-variance efficient portfolio is a combination of any two portfolios in the mean-variance frontier. We look at the changes in the composition of the global minimum variance portfolio, and the tangency portfolio with respect to a riskless rate which we keep constant across investment horizons. Figure 4. Composition of Global Minimum Variance Portfolio 120.0% 100.0% 80.0% T-bills Stocks 5-year Bond Portfolio Weight (%) 60.0% 40.0% 20.0% 0.0% -20.0% 1 Quarter 5 Years 10 Years 25 Years 50 Years 100 Years Horizon 11

12 Tangency Portfolio When Risk-Free Rate Is Equal to Mean Real T-Bill Rate Horizon 1 year 10 years 25 years 100 years (4 quarters) (40 quarters) (100 quarters) (400 quarters) Risk free rate 1.518% 1.518% 1.518% 1.518% Sharpe ratio Portfolio weights Stocks 47.40% % 71.76% 67.10% 5-year bond 52.60% % 28.24% 32.90% Sum % % % % Conclusions The volatility and correlation structure of asset returns can change dramatically across investment horizons. These patterns have important implications for portfolio allocations among cash (or T-bills), stocks and long-term bonds. Real interest rate risk (or reinvestment risk) tilts the composition of minimum variance portfolios at long horizons towards long-term bonds, and away from T-bills. The large positive correlation of bond and stock returns at intermediate horizons, and the declining volatility of stock returns at long horizons bias the composition of tangency portfolios toward stocks and away from long-term bonds at long horizons. 12

13 Pitfalls of Mean-Variance Allocations Across Investment Horizons Mean-variance analysis is only valid for buy-and-hold investors who make a one-time asset allocation decision, and are interested only in the assets available for spending at the end of a particular horizon. In practice, most investors can rebalance their portfolios frequently, and have recurrent spending needs which they must finance (fully or partially) of their financial portfolios. It is therefore tempting to conclude that the term structure of the risk-return tradeoff is irrelevant to long-term investors who can rebalance. Strategic Asset Allocation (SAA) This conclusion is not correct in general: Long-term, risk averse investors still want to protect their portfolios from unexpected, adverse shifts in investment opportunities. These investors accomplish this by holding intertemporal hedging portfolios in addition to short-term, mean-variance portfolios. Strategic portfolios are qualitatively similar to long-horizon mean-variance portfolios. 13

14 Pitfalls of Asset Allocation Models The dynamic properties of stock and bond returns are extremely difficult to estimate accurately. Asset allocation recommendations under any asset allocation paradigm (traditional and non-traditional) are very sensitive to how any model of asset returns characterizes future movements in stock and bond returns. Investors should be aware of this uncertainty, and should trim back extreme positions in stocks and bonds that may be suggested by a particular model. 14

The Term Structure of the Risk-Return Tradeoff

The Term Structure of the Risk-Return Tradeoff The Term Structure of the Risk-Return Tradeoff John Y. Campbell and Luis M. Viceira 1 Recent research in empirical finance has documented that expected excess returns on bonds and stocks, real interest

More information

Review for Exam 2. Instructions: Please read carefully

Review for Exam 2. Instructions: Please read carefully Review for Exam Instructions: Please read carefully The exam will have 1 multiple choice questions and 5 work problems. Questions in the multiple choice section will be either concept or calculation questions.

More information

Capital Allocation Between The Risky And The Risk- Free Asset. Chapter 7

Capital 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 information

Lesson 5. Risky assets

Lesson 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 information

Holding Period Return. Return, Risk, and Risk Aversion. Percentage Return or Dollar Return? An Example. Percentage Return or Dollar Return? 10% or 10?

Holding 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 information

Instructor s Manual Chapter 12 Page 144

Instructor s Manual Chapter 12 Page 144 Chapter 12 1. Suppose that your 58-year-old father works for the Ruffy Stuffed Toy Company and has contributed regularly to his company-matched savings plan for the past 15 years. Ruffy contributes $0.50

More information

Long-Horizon Mean-Variance Analysis: A User Guide

Long-Horizon Mean-Variance Analysis: A User Guide Long-Horizon Mean-Variance Analysis: A User Guide John Y. Campbell, and Luis M. Viceira This draft: September 2004 Campbell: Department of Economics, Littauer Center 23, Harvard University, Cambridge MA

More information

RISKS IN MUTUAL FUND INVESTMENTS

RISKS IN MUTUAL FUND INVESTMENTS RISKS IN MUTUAL FUND INVESTMENTS Classification of Investors Investors can be classified based on their Risk Tolerance Levels : Low Risk Tolerance Moderate Risk Tolerance High Risk Tolerance Fund Classification

More information

Introduction The U.S. retirement system has experienced a substantial transformation in recent years.

<A>Introduction<A> The U.S. retirement system has experienced a substantial transformation in recent years. Chapter 5 Life-Cycle Funds Luis M. Viceira I am grateful to the Division of Research of the Harvard Business School for generous financial support. I am grateful to John Campbell, Jim Poterba, Annamaria

More information

Equity Risk Premiums: Looking backwards and forwards

Equity Risk Premiums: Looking backwards and forwards Equity Risk Premiums: Looking backwards and forwards Aswath Damodaran Aswath Damodaran 1 What is the Equity Risk Premium? Intuitively, the equity risk premium measures what investors demand over and above

More information

NPH Fixed Income Research Update. Bob Downing, CFA. NPH Senior Investment & Due Diligence Analyst

NPH Fixed Income Research Update. Bob Downing, CFA. NPH Senior Investment & Due Diligence Analyst White Paper: NPH Fixed Income Research Update Authored By: Bob Downing, CFA NPH Senior Investment & Due Diligence Analyst National Planning Holdings, Inc. Due Diligence Department National Planning Holdings,

More information

Models of Risk and Return

Models 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 information

15.401 Finance Theory

15.401 Finance Theory Finance Theory MIT Sloan MBA Program Andrew W. Lo Harris & Harris Group Professor, MIT Sloan School Lecture 13 14 14: : Risk Analytics and Critical Concepts Motivation Measuring Risk and Reward Mean-Variance

More information

Review for Exam 2. Instructions: Please read carefully

Review 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 information

Keeping it Simple: White Paper. Lifestyle Funds: A Streamlined Approach

Keeping it Simple: White Paper. Lifestyle Funds: A Streamlined Approach Keeping it Simple: Lifestyle Funds for Retirement Planning Retirement investors who suspect that things are more complicated than they used to be can take heart from the findings of a new study by American

More information

Portfolio Management for institutional investors

Portfolio Management for institutional investors Portfolio Management for institutional investors June, 2010 Bogdan Bilaus, CFA CFA Romania Summary Portfolio management - definitions; The process; Investment Policy Statement IPS; Strategic Asset Allocation

More information

Risk Parity Portfolios:

Risk Parity Portfolios: SEPTEMBER 2005 Risk Parity Portfolios: Efficient Portfolios Through True Diversification Edward Qian, Ph.D., CFA Chief Investment Officer and Head of Research, Macro Strategies PanAgora Asset Management

More information

FRBSF ECONOMIC LETTER

FRBSF ECONOMIC LETTER FRBSF ECONOMIC LETTER 213-23 August 19, 213 The Price of Stock and Bond Risk in Recoveries BY SIMON KWAN Investor aversion to risk varies over the course of the economic cycle. In the current recovery,

More information

SAMPLE MID-TERM QUESTIONS

SAMPLE 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 information

Estimating Risk free Rates. Aswath Damodaran. Stern School of Business. 44 West Fourth Street. New York, NY 10012. Adamodar@stern.nyu.

Estimating Risk free Rates. Aswath Damodaran. Stern School of Business. 44 West Fourth Street. New York, NY 10012. Adamodar@stern.nyu. Estimating Risk free Rates Aswath Damodaran Stern School of Business 44 West Fourth Street New York, NY 10012 Adamodar@stern.nyu.edu Estimating Risk free Rates Models of risk and return in finance start

More information

CHAPTER 9: THE CAPITAL ASSET PRICING MODEL

CHAPTER 9: THE CAPITAL ASSET PRICING MODEL CHAPTER 9: THE CAPITAL ASSET PRICING MODEL PROBLEM SETS 1. E(r P ) = r f + β P [E(r M ) r f ] 18 = 6 + β P(14 6) β P = 12/8 = 1.5 2. If the security s correlation coefficient with the market portfolio

More information

Glossary of Investment Terms

Glossary of Investment Terms online report consulting group Glossary of Investment Terms glossary of terms actively managed investment Relies on the expertise of a portfolio manager to choose the investment s holdings in an attempt

More information

The CAPM (Capital Asset Pricing Model) NPV Dependent on Discount Rate Schedule

The CAPM (Capital Asset Pricing Model) NPV Dependent on Discount Rate Schedule The CAPM (Capital Asset Pricing Model) Massachusetts Institute of Technology CAPM Slide 1 of NPV Dependent on Discount Rate Schedule Discussed NPV and time value of money Choice of discount rate influences

More information

Investment Portfolio Management and Effective Asset Allocation for Institutional and Private Banking Clients

Investment Portfolio Management and Effective Asset Allocation for Institutional and Private Banking Clients Investment Portfolio Management and Effective Asset Allocation for Institutional and Private Banking Clients www.mce-ama.com/2396 Senior Managers Days 4 www.mce-ama.com 1 WHY attend this programme? This

More information

NorthCoast Investment Advisory Team 203.532.7000 info@northcoastam.com

NorthCoast Investment Advisory Team 203.532.7000 info@northcoastam.com NorthCoast Investment Advisory Team 203.532.7000 info@northcoastam.com NORTHCOAST ASSET MANAGEMENT An established leader in the field of tactical investment management, specializing in quantitative research

More information

Effective downside risk management

Effective downside risk management Effective downside risk management Aymeric Forest, Fund Manager, Multi-Asset Investments November 2012 Since 2008, the desire to avoid significant portfolio losses has, more than ever, been at the front

More information

Portfolio advice for a multifactor world

Portfolio advice for a multifactor world Portfolio advice for a multifactor world John H. Cochrane Introduction and summary A companion article in this issue, New facts in finance, summarizes the revolution in how financial economists view the

More information

The number of mutual funds has grown dramatically in recent

The number of mutual funds has grown dramatically in recent Risk-Adjusted Performance of Mutual Funds Katerina Simons Economist, Federal Reserve Bank of Boston. The author is grateful to Richard Kopcke and Peter Fortune for helpful comments and to Jay Seideman

More information

1 Capital Allocation Between a Risky Portfolio and a Risk-Free Asset

1 Capital Allocation Between a Risky Portfolio and a Risk-Free Asset Department of Economics Financial Economics University of California, Berkeley Economics 136 November 9, 2003 Fall 2006 Economics 136: Financial Economics Section Notes for Week 11 1 Capital Allocation

More information

Price-Earnings Ratios: Growth and Discount Rates

Price-Earnings Ratios: Growth and Discount Rates Price-Earnings Ratios: Growth and Discount Rates Andrew Ang Columbia University and NBER Xiaoyan Zhang Purdue University This Version: 20 May 2011 We thank Geert Bekaert, Sigbjørn Berg, and Tørres Trovik

More information

Distinction Between Interest Rates and Returns

Distinction Between Interest Rates and Returns Distinction Between Interest Rates and Returns Rate of Return RET = C + P t+1 P t =i c + g P t C where: i c = = current yield P t g = P t+1 P t P t = capital gain Key Facts about Relationship Between Interest

More information

1. a. (iv) b. (ii) [6.75/(1.34) = 10.2] c. (i) Writing a call entails unlimited potential losses as the stock price rises.

1. a. (iv) b. (ii) [6.75/(1.34) = 10.2] c. (i) Writing a call entails unlimited potential losses as the stock price rises. 1. Solutions to PS 1: 1. a. (iv) b. (ii) [6.75/(1.34) = 10.2] c. (i) Writing a call entails unlimited potential losses as the stock price rises. 7. The bill has a maturity of one-half year, and an annualized

More information

Professionally Managed Portfolios of Exchange-Traded Funds

Professionally Managed Portfolios of Exchange-Traded Funds ETF Portfolio Partners C o n f i d e n t i a l I n v e s t m e n t Q u e s t i o n n a i r e Professionally Managed Portfolios of Exchange-Traded Funds P a r t I : I n v e s t o r P r o f i l e Account

More information

Despite more than half a century of research on forecasting stock market returns,

Despite more than half a century of research on forecasting stock market returns, Rosenberg Institute of Global Finance GLOBAL FINANCE BRIEF To predict the equity market, consult economic theory Davide Pettenuzzo, Assistant Professor of Economics March 2014 Despite more than half a

More information

CHAPTER 7: OPTIMAL RISKY PORTFOLIOS

CHAPTER 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 information

Lecture 1: Asset Allocation

Lecture 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 information

Key Concepts and Skills

Key Concepts and Skills Chapter 10 Some Lessons from Capital Market History Key Concepts and Skills Know how to calculate the return on an investment Understand the historical returns on various types of investments Understand

More information

Mean Variance Analysis

Mean Variance Analysis Mean Variance Analysis Karl B. Diether Fisher College of Business Karl B. Diether (Fisher College of Business) Mean Variance Analysis 1 / 36 A Portfolio of Three Risky Assets Not a two risky asset world

More information

Wel Dlp Portfolio And Risk Management

Wel Dlp Portfolio And Risk Management 1. In case of perfect diversification, the systematic risk is nil. Wel Dlp Portfolio And Risk Management 2. The objectives of investors while putting money in various avenues are:- (a) Safety (b) Capital

More information

Invest in Direct Energy

Invest in Direct Energy Invest in Direct Energy (Forthcoming Journal of Investing) Peng Chen Joseph Pinsky February 2002 225 North Michigan Avenue, Suite 700, Chicago, IL 6060-7676! (32) 66-620 Peng Chen is Vice President, Direct

More information

ANALYSIS AND MANAGEMENT

ANALYSIS AND MANAGEMENT ANALYSIS AND MANAGEMENT T H 1RD CANADIAN EDITION W. SEAN CLEARY Queen's University CHARLES P. JONES North Carolina State University JOHN WILEY & SONS CANADA, LTD. CONTENTS PART ONE Background CHAPTER 1

More information

CFA Examination PORTFOLIO MANAGEMENT Page 1 of 6

CFA Examination PORTFOLIO MANAGEMENT Page 1 of 6 PORTFOLIO MANAGEMENT A. INTRODUCTION RETURN AS A RANDOM VARIABLE E(R) = the return around which the probability distribution is centered: the expected value or mean of the probability distribution of possible

More information

Porter, White & Company

Porter, White & Company Porter, White & Company Optimizing the Fixed Income Component of a Portfolio White Paper, September 2009, Number IM 17.2 In the White Paper, Comparison of Fixed Income Fund Performance, we show that a

More information

How Many Days Equal A Year? Non-trivial on the Mean-Variance Model

How Many Days Equal A Year? Non-trivial on the Mean-Variance Model How Many Days Equal A Year? Non-trivial on the Mean-Variance Model George L. Ye, Dr. Sobey School of Business Saint Mary s University Halifax, Nova Scotia, Canada Christine Panasian, Dr. Sobey School of

More information

Market Efficiency and Behavioral Finance. Chapter 12

Market Efficiency and Behavioral Finance. Chapter 12 Market Efficiency and Behavioral Finance Chapter 12 Market Efficiency if stock prices reflect firm performance, should we be able to predict them? if prices were to be predictable, that would create the

More information

31 Week 10. Portfolio theory detailed notes

31 Week 10. Portfolio theory detailed notes 3 Week 0. Portfolio theory detailed notes. We ve learned a lot of new facts. How do these facts affect portfolios? (a) D/P and related predictability. Should you market-time buy more when DP is high, less

More information

Solution: The optimal position for an investor with a coefficient of risk aversion A = 5 in the risky asset is y*:

Solution: 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 information

Futures Price d,f $ 0.65 = (1.05) (1.04)

Futures Price d,f $ 0.65 = (1.05) (1.04) 24 e. Currency Futures In a currency futures contract, you enter into a contract to buy a foreign currency at a price fixed today. To see how spot and futures currency prices are related, note that holding

More information

Introduction to Risk, Return and the Historical Record

Introduction to Risk, Return and the Historical Record Introduction to Risk, Return and the Historical Record Rates of return Investors pay attention to the rate at which their fund have grown during the period The holding period returns (HDR) measure the

More information

Chapter 13 Composition of the Market Portfolio 1. Capital markets in Flatland exhibit trade in four securities, the stocks X, Y and Z,

Chapter 13 Composition of the Market Portfolio 1. Capital markets in Flatland exhibit trade in four securities, the stocks X, Y and Z, Chapter 13 Composition of the arket Portfolio 1. Capital markets in Flatland exhibit trade in four securities, the stocks X, Y and Z, and a riskless government security. Evaluated at current prices in

More information

A Review of Cross Sectional Regression for Financial Data You should already know this material from previous study

A Review of Cross Sectional Regression for Financial Data You should already know this material from previous study A Review of Cross Sectional Regression for Financial Data You should already know this material from previous study But I will offer a review, with a focus on issues which arise in finance 1 TYPES OF FINANCIAL

More information

Lecture 1: Asset pricing and the equity premium puzzle

Lecture 1: Asset pricing and the equity premium puzzle Lecture 1: Asset pricing and the equity premium puzzle Simon Gilchrist Boston Univerity and NBER EC 745 Fall, 2013 Overview Some basic facts. Study the asset pricing implications of household portfolio

More information

GUIDE To INVESTING At Intrinsic our approach to investment advice is based on clearly understanding your financial situation, your goals, and how

GUIDE To INVESTING At Intrinsic our approach to investment advice is based on clearly understanding your financial situation, your goals, and how GUIDE To INVESTING At Intrinsic our approach to investment advice is based on clearly understanding your financial situation, your goals, and how much risk you are prepared to take with your money. 2 GUIDE

More information

Basic Investment Education

Basic Investment Education Disclaimer: The information provided below is for information purposes only - it is not investment advice. If you have any questions about your own personal financial situation, you should consult with

More information

Black-Litterman Return Forecasts in. Tom Idzorek and Jill Adrogue Zephyr Associates, Inc. September 9, 2003

Black-Litterman Return Forecasts in. Tom Idzorek and Jill Adrogue Zephyr Associates, Inc. September 9, 2003 Black-Litterman Return Forecasts in Tom Idzorek and Jill Adrogue Zephyr Associates, Inc. September 9, 2003 Using Black-Litterman Return Forecasts for Asset Allocation Results in Diversified Portfolios

More information

Bond Investing in a Rising Rate Environment

Bond Investing in a Rising Rate Environment September 3 W H I T E PA P E R Bond Investing in a Rising Rate Environment Contents Yields Past, Present and Future Allocation and Mandate Revisited Benchmark Comparisons Investment Options to Consider

More information

PERSPECTIVES. Reasonable Expectations for the Long-Run U.S.Equity Risk Premium. Roger G. Clarke, Ph.D and Harindra de Silva, Ph.D.

PERSPECTIVES. Reasonable Expectations for the Long-Run U.S.Equity Risk Premium. Roger G. Clarke, Ph.D and Harindra de Silva, Ph.D. Risk Management PERSPECTIVES April 2003 Reasonable Expectations for the Long-Run U.S.Equity Risk Premium Expectations for the long-run equity risk premium play an important role in asset allocation decisions

More information

These charts identify short term trends in benchmark relative performance and risk.

These charts identify short term trends in benchmark relative performance and risk. The Government Pension Global The Government Pension was established on 1 st January 6. The Government Pension comprises: The Government Pension Global (previously the Government Petroleum, established

More information

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 return. 2.

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 return. 2. For both risk and return, increasing order is b, c, a, d. On average, higher risk of an investment, higher is its expected return. 2. Since price didn t change, capital gains yield was zero. If total return

More information

Pension Fund Investments: Stocks or Bonds?

Pension Fund Investments: Stocks or Bonds? Pension Fund Investments: Stocks or Bonds? Frank de Jong University of Amsterdam and CEPR May 7, 2003 Very preliminary! Please do not quote. Abstract: This paper reviews the investment policy of collective

More information

RESP Investment Strategies

RESP Investment Strategies RESP Investment Strategies Registered Education Savings Plans (RESP): Must Try Harder Graham Westmacott CFA Portfolio Manager PWL CAPITAL INC. Waterloo, Ontario August 2014 This report was written by Graham

More information

Financial-Institutions Management

Financial-Institutions Management Solutions 3 Chapter 11: Credit Risk Loan Pricing and Terms 9. County Bank offers one-year loans with a stated rate of 9 percent but requires a compensating balance of 10 percent. What is the true cost

More information

Behind the Scenes Constructing the Amerivest Opportunistic Portfolios

Behind the Scenes Constructing the Amerivest Opportunistic Portfolios Behind the Scenes Constructing the Amerivest Opportunistic Portfolios Powered by Morningstar Associates The Amerivest Opportunistic Portfolios are constructed to be tactical and more active in their investment

More information

This paper is not to be removed from the Examination Halls

This paper is not to be removed from the Examination Halls ~~FN3023 ZA d0 This paper is not to be removed from the Examination Halls UNIVERSITY OF LONDON FN3023 ZA BSc degrees and Diplomas for Graduates in Economics, Management, Finance and the Social Sciences,

More information

The Power of Zero + The Power of the Word

The Power of Zero + The Power of the Word Epoch Investment Partners, Inc. May 29, 2014 The Power of Zero + The Power of the Word william w. priest, ceo, co-cio & portfolio manager david n. pearl, executive vice president, co-cio & portfolio manager

More information

fi360 Asset Allocation Optimizer: Risk-Return Estimates*

fi360 Asset Allocation Optimizer: Risk-Return Estimates* fi360 Asset Allocation Optimizer: Risk-Return Estimates* Prepared for fi360 by: Richard Michaud, Robert Michaud, Daniel Balter New Frontier Advisors LLC Boston, MA 02110 February 2015 * 2015 New Frontier

More information

STRATEGIC AND TACTICAL ASSET ALLOCATION LAIRD NORTON WEALTH MANAGEMENT INVESTMENT PROCESS

STRATEGIC AND TACTICAL ASSET ALLOCATION LAIRD NORTON WEALTH MANAGEMENT INVESTMENT PROCESS LAIRD NORTON WEALTH MANAGEMENT INVESTMENT PROCESS INTRODUCTION STRATEGIC AND TACTICAL LNWM INVESTMENT PROCESS In building investment plans for our clients, we start with the decisions that impact our clients

More information

Mutual Fund Investing Exam Study Guide

Mutual Fund Investing Exam Study Guide Mutual Fund Investing Exam Study Guide This document contains the questions that will be included in the final exam, in the order that they will be asked. When you have studied the course materials, reviewed

More information

CHAPTER 10. Capital Markets and the Pricing of Risk. Chapter Synopsis

CHAPTER 10. Capital Markets and the Pricing of Risk. Chapter Synopsis CHAPE 0 Capital Markets and the Pricing of isk Chapter Synopsis 0. A First Look at isk and eturn Historically there has been a large difference in the returns and variability from investing in different

More information

In recent years government-issued inflation-indexed bonds have become. Understanding Inflation-Indexed Bond Markets

In recent years government-issued inflation-indexed bonds have become. Understanding Inflation-Indexed Bond Markets JOHN Y. CAMPBELL Harvard University ROBERT J. SHILLER Yale University LUIS M. VICEIRA Harvard University Understanding Inflation-Indexed Bond Markets ABSTRACT This paper explores the history of inflation-indexed

More information

The Equity Premium in India

The 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 information

READING 14: LIFETIME FINANCIAL ADVICE: HUMAN CAPITAL, ASSET ALLOCATION, AND INSURANCE

READING 14: LIFETIME FINANCIAL ADVICE: HUMAN CAPITAL, ASSET ALLOCATION, AND INSURANCE READING 14: LIFETIME FINANCIAL ADVICE: HUMAN CAPITAL, ASSET ALLOCATION, AND INSURANCE Introduction (optional) The education and skills that we build over this first stage of our lives not only determine

More information

Equity Market Risk Premium Research Summary. 12 April 2016

Equity Market Risk Premium Research Summary. 12 April 2016 Equity Market Risk Premium Research Summary 12 April 2016 Introduction welcome If you are reading this, it is likely that you are in regular contact with KPMG on the topic of valuations. The goal of this

More information

The Role of Alternative Investments in a Diversified Investment Portfolio

The Role of Alternative Investments in a Diversified Investment Portfolio The Role of Alternative Investments in a Diversified Investment Portfolio By Baird Private Wealth Management Introduction Traditional Investments Domestic Equity International Equity Taxable Fixed Income

More information

WORKING PAPER CENTRAL BANK OF ICELAND. A Variance Decomposition of Index-Linked Bond Returns. No. 57. By Francis Breedon

WORKING PAPER CENTRAL BANK OF ICELAND. A Variance Decomposition of Index-Linked Bond Returns. No. 57. By Francis Breedon WORKING PAPER CENTRAL BANK OF ICELAND No. 57 A Variance Decomposition of Index-Linked Bond Returns By Francis Breedon January 2012 Central Bank of Iceland Working Papers are published by the Economics

More information

2016 TEN-YEAR CAPITAL MARKET ASSUMPTIONS

2016 TEN-YEAR CAPITAL MARKET ASSUMPTIONS 2016 TEN-YEAR CAPITAL MARKET ASSUMPTIONS TABLE OF CONTENTS 2016 vs. 2015 Assumptions 2 Summary & Highlights 2 Creating Arithmetic Returns 3 Creating Geometric Returns 3 Detailed Assumptions Appendix PENSION

More information

Alternative Investing

Alternative Investing Alternative Investing An important piece of the puzzle Improve diversification Manage portfolio risk Target absolute returns Innovation is our capital. Make it yours. Manage Risk and Enhance Performance

More information

The Tangent or Efficient Portfolio

The 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 information

MLC MasterKey Unit Trust Product Disclosure Statement (PDS)

MLC MasterKey Unit Trust Product Disclosure Statement (PDS) MLC MasterKey Unit Trust Product Disclosure Statement (PDS) Preparation date 1 July 2014 Issued by MLC Investments Limited (MLC) ABN 30 002 641 661 AFSL 230705 This information is general and doesn t take

More information

Obligation-based Asset Allocation for Public Pension Plans

Obligation-based Asset Allocation for Public Pension Plans Obligation-based Asset Allocation for Public Pension Plans Market Commentary July 2015 PUBLIC PENSION PLANS HAVE a single objective to provide income for a secure retirement for their members. Once the

More information

Modified dividend payout ratio =

Modified dividend payout ratio = 15 Modifying the model to include stock buybacks In recent years, firms in the United States have increasingly turned to stock buybacks as a way of returning cash to stockholders. Figure 13.3 presents

More information

The Response of Stock Prices to Permanent and Temporary Shocks to Dividends. Author: Bong-Soo Lee Presenter: Omar Salomon

The Response of Stock Prices to Permanent and Temporary Shocks to Dividends. Author: Bong-Soo Lee Presenter: Omar Salomon The Response of Stock Prices to Permanent and Temporary Shocks to Dividends Author: Bong-Soo Lee Presenter: Omar Salomon AGENDA 1 2 3 4 5 Abstract Introduction Model Development Empirical Results Conclusions

More information

SEI Income Portfolio. Investment Policy Statement

SEI Income Portfolio. Investment Policy Statement SEI Income Portfolio Investment Policy Statement INTRODUCTION An Investment Management Program will determine the right mix of investments for your personal situation in order to meet your long-term investment

More information

2013 Investment Seminar Colloque sur les investissements 2013

2013 Investment Seminar Colloque sur les investissements 2013 2013 Investment Seminar Colloque sur les investissements 2013 Session/Séance: Volatility Management Speaker(s)/Conférencier(s): Nicolas Papageorgiou Associate Professor, HEC Montréal Derivatives Consultant,

More information

Crestmont Research. Grantham and Brightman Call Gross an Optimist!

Crestmont Research. Grantham and Brightman Call Gross an Optimist! Crestmont Research Game Changer: Market Beware Slower Economic Growth By Ed Easterling April 5, 2013 Copyright 2013, Crestmont Research (www.crestmontresearch.com) The headline across the financial press

More information

Global Currency Hedging

Global Currency Hedging Global Currency Hedging John Y. Campbell Harvard University Arrowstreet Capital, L.P. May 16, 2010 Global Currency Hedging Joint work with Karine Serfaty-de Medeiros of OC&C Strategy Consultants and Luis

More information

April 27, 2016. Dear Client:

April 27, 2016. Dear Client: Dear Client: 565 Fifth Avenue Suite 2101 New York, NY 10017 212 557 2445 Fax 212 557 4898 3001 Tamiami Trail North Suite 206 Naples, FL 34103 239 261 3555 Fax 239 261 5512 www.dghm.com Our January letter

More information

Certified Personal Financial Advisor (CPFA) for Examination

Certified Personal Financial Advisor (CPFA) for Examination NATIONAL INSTITUTE OF SECURITIES MARKETS Certified Personal Financial Advisor (CPFA) for Examination Test Objectives 1. Concept of Financial Planning 1.1 Understand what financial planning constitutes

More information

Dynamic Asset Allocation Using Stochastic Programming and Stochastic Dynamic Programming Techniques

Dynamic Asset Allocation Using Stochastic Programming and Stochastic Dynamic Programming Techniques Dynamic Asset Allocation Using Stochastic Programming and Stochastic Dynamic Programming Techniques Gerd Infanger Stanford University Winter 2011/2012 MS&E348/Infanger 1 Outline Motivation Background and

More information

Chapter 5 Risk and Return ANSWERS TO SELECTED END-OF-CHAPTER QUESTIONS

Chapter 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 information

fi360 Asset Allocation Optimizer: Risk-Return Estimates*

fi360 Asset Allocation Optimizer: Risk-Return Estimates* fi360 Asset Allocation Optimizer: Risk-Return Estimates* Prepared for fi360 by: Richard Michaud, Robert Michaud, Vitaliy Ryabinin New Frontier Advisors LLC Boston, MA 02110 February 2016 * 2016 New Frontier

More information

Rate of Return. Reading: Veronesi, Chapter 7. Investment over a Holding Period

Rate 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 information

Referred to as the statement of financial position provides a snap shot of a company s assets, liabilities and equity at a particular point in time.

Referred to as the statement of financial position provides a snap shot of a company s assets, liabilities and equity at a particular point in time. Glossary Aggressive investor Balance sheet Bear market Typically has a higher risk appetite. They are prepared or can afford to risk much more and for this they stand to reap the big rewards. Referred

More information

Forecast Confidence Level and Portfolio Optimization

Forecast Confidence Level and Portfolio Optimization and Portfolio Optimization by Richard O. Michaud and Robert O. Michaud New Frontier Advisors Newsletter July 2004 Abstract This report focuses on the role and importance of the uncertainty in forecast

More information

Models of Asset Pricing The implications for asset allocation

Models of Asset Pricing The implications for asset allocation Models of Asset Pricing The implications for asset allocation 2004 Finance & Investment Conference 28 June 2004 Tim Giles CHARLES RIVER ASSOCIATES Vice President CRA London CRA 2004 Agenda New orthodoxy

More information

FIN 432 Investment Analysis and Management Review Notes for Midterm Exam

FIN 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 information

www.optionseducation.org OIC Options on ETFs

www.optionseducation.org OIC Options on ETFs www.optionseducation.org Options on ETFs 1 The Options Industry Council For the sake of simplicity, the examples that follow do not take into consideration commissions and other transaction fees, tax considerations,

More information

2015 TEN-YEAR CAPITAL MARKET ASSUMPTIONS

2015 TEN-YEAR CAPITAL MARKET ASSUMPTIONS 2015 TEN-YEAR CAPITAL MARKET ASSUMPTIONS TABLE OF CONTENTS 2015 vs. 2014 Assumptions 2 Summary & Highlights 2 Creating Arithmetic Returns 3 Creating Geometric Returns 3 Detailed Assumptions Appendix PENSION

More information

Investment Philosophies: Introduction

Investment Philosophies: Introduction Investment Philosophies: Introduction Aswath Damodaran www.damodaran.com Aswath Damodaran! 1! What is an investment philosophy? What is it? An investment philosophy is a coherent way of thinking about

More information

How to Design Target-Date Funds?

How to Design Target-Date Funds? Benjamin Bruder Research & Development Lyxor Asset Management, Paris benjamin.bruder@lyxor.com Thierry Roncalli Research & Development Lyxor Asset Management, Paris thierry.roncalli@lyxor.com September

More information