Risk and Return Professor XXXXX Course Name / Number

2 Introduction To Risk & Return Valuing Risky Assets - Fundamental to Financial Management Three-Step Procedure for Valuing a Risky Asset Determine The Asset’s Expected Cash Flows Choose Discount Rate That Reflects Asset’s Risk Calculate Present Value (PV cash inflows - PV outflows) Trade-off Between Risk and Expected Return

3 Real Returns on U.S. Investments, Real Return Approximately Equal to Nominal Return Minus Inflation Rate Difference Between Average Return of Stocks and Bills = 7.7% Difference Between Average Return of Bonds and Bills = 1.1% Risk Premium - The Difference In Returns Between Investments Having Different Risks Source: Triumph of the Optimists: 101 Years of Global Investment Returns, by Elroy Dimson, Paul Marsh, and Mike Staunton, Princeton University Press, 2002

4 The Equity Risk Premium, Country Arithmetic mean (%) Geometric mean (%) Standard deviation (%) Australia Canada France Germany Italy Japan Netherlands Switzerland United Kingdom United States

5 Risk Aversion Risk Neutral Investors Seek the Highest Return Without Regard to Risk Risk Seeking Investors Have a Taste for Risk and Will Take Risk Even If They Cannot Expect a Reward for Doing So (Las Vegas) Risk Averse Investors Do Not Like Risk and Must Be Compensated For Taking It Historical Returns on Financial Assets Are Consistent with a Population of Risk-Averse Investors

6 Financial Return An example.... Investor Bought Utilyco for $60/share Dividend = $6/share Sold for $66/share Return - The Total Gain or Loss Experienced on an Investment Over a Given Period of Time.

7 Arithmetic Versus Geometric Average Returns AAR = 6.25% GAR = 5.78% An example.... Year Return % % % % Arithmetic Average is Generally Bigger Than Geometric Average The Difference Between Arithmetic Returns and Geometric Returns Gets Bigger the More Volatile the Returns Are

8 Risk Of A Single Asset How Do We Measure Risk? One Approach –Volatility of Asset’s Returns –Variance (  2 ) - The Expected Value of Squared Deviations From The Mean –Units of Variance (%-squared) - Hard to Interpret, So Calculate Standard Deviation, Square Root of  2 An example.…Immucell Corp. Monthly Returns for Jan 2000 – Dec 2002 Average Return = 0.838%

9 Historical vs. Expected Returns Decisions Must Be Based On Expected Returns There Are Many Ways to Estimate Expected Returns Assume That Expected Return Going Forward Equals the Average Return in the Past Simple Way to Estimate Expected Return

10 Expected Return For A Portfolio Most Investors Hold Multiple Asset Portfolios Key Insight of Portfolio Theory: Asset Return Adds Linearly, But Risk Is (Almost Always) Reduced in a Portfolio

11 Monthly Average Return and Volatility For Three Stocks IMMUCELL CORP REINSURANCE GROUP OF AMERICA INC WIRELESS TELECOM GROUP INC Standard deviation of monthly return, % Average (mean) monthly return, % Company Use The Average Returns as Estimates of Expected Returns on Each Stock Use Monthly Returns for Period January 2000 – December 2002

12 Average Return and Volatility For Portfolios Portfolio Standard Deviation Portfolio Expected Return How Do Portfolios of These Stocks Perform? 100% REINSURANCE GROUP OF AMERICA 100% IMMUCELL CORP 100% WIRELESS TELECOM GROUP 50% WIRELESS + 50% REINSURANCE 50% WIRELESS + 50% IMMUCELL

13 50% Wireless + 50% Immucell Risk Increases With Expected Return 50% Wireless + 50% Reinsurance Risk Decreases at First, Then Increases as Expected Return Rises Why Do Portfolios of Different Stocks Behave Differently? Average Return and Volatility For Portfolios

14 Expected Return For Portfolio 50% Wireless + 50% Immucell50% Wireless + 50% Reinsurance Expected Return of Portfolio Is The Average Of Expected Returns Of The Two Stocks

15 Two-Asset Portfolio Standard Deviation Correlation Between Stocks Influences Portfolio Volatility What is Correlation Between Wireless and Immucell? 0.80 What is Correlation Between Wireless and Reinsurance Group? -0.66

16 Correlation of Reinsurance Group, Immucell, and Wireless Wireless and Immucell Move Together; Wireless and Reinsurance Move in Opposite Directions When Stocks Move Together, Combining Them Doesn’t Reduce Risk Much

17 Average Return and Volatility For Portfolios Portfolio Standard Deviation Portfolio Expected Return % WIRELESS – 50% IMMUCELL REINSURANCE GROUP OF AMERICA IMMUCELL CORP WIRELESS TELECOM GROUP 50% WIRELESS – 50% REINSURANCE Wireless and Immucell Correlation: 0.80 Wireless and Reinsurance Group: -0.66

18 Correlation Coefficients And Risk Reduction For Two-Asset Portfolios 10% 15% 20% 25% 0%5%10%15%20%25% Standard Deviation of Portfolio Returns Expected Return on the Portfolio  is <  <1.0  is -1.0

19 Portfolios of More Than Two Assets Five-Asset Portfolio Expected Return of Portfolio Is Still The Average Of Expected Returns Of The Two Stocks How Is The Variance of Portfolio Influenced By Number Of Assets in Portfolio?

Asset The Covariance Terms Determine To A Large Extent The Variance Of The Portfolio Asset Variance of Individual Assets Account Only for 1/25 th of the Portfolio Variance Variance – Covariance Matrix

21 What Is a Stock’s Beta? Beta Is a Measure of Systematic Risk What If Beta > 1 or Beta <1? The Stock Moves More Than 1% on Average When the Market Moves 1% (Beta > 1) The Stock Moves Less Than 1% on Average When the Market Moves 1% (Beta < 1) What If Beta = 1? The Stock Moves 1% on Average When the Market Moves 1% An “Average” Level of Risk

22 Diversifiable And Non-Diversifiable Risk As Number of Assets Increases, Diversification Reduces the Importance of a Stock’s Own Variance –Diversifiable risk, unsystematic risk Only an Asset’s Covariance With All Other Assets Contributes Measurably to Overall Portfolio Return Variance –Non-diversifiable risk, systematic risk

23 How Risky Is an Individual Asset? First Approach – Asset’s Variance or Standard Deviation What Really Matters Is Systematic Risk….How an Asset Covaries With Everything Else Use Asset’s Beta

24 The Impact Of Additional Assets On The Risk Of A Portfolio Number of Securities (Assets) in Portfolio Portfolio Risk,  k p Nondiversifiable Risk Diversifiable Risk Total risk

Valuing Risky Assets Should Take Into Account Expected Return and Risk Most Investors – Risk Averse – Demand Compensation For Bearing Risk Risk Can Be Defined In Many Ways Market Should Reward Only Systematic Risk Risk and Return