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Risk and Return

Risk and Return. Professor XXXXX Course Name / Number. 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). Introduction To Risk & Return.

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Risk and Return

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  1. Risk and Return Professor XXXXX Course Name / Number

  2. 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) Introduction To Risk & Return Valuing Risky Assets - Fundamental to Financial Management Trade-off Between Risk and Expected Return

  3. Real Returns on U.S. Investments, 1900 - 2000 Source: Triumph of the Optimists: 101 Years of Global Investment Returns, by Elroy Dimson, Paul Marsh, and Mike Staunton, Princeton University Press, 2002 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 Real Return Approximately Equal to Nominal Return Minus Inflation Rate

  4. The Equity Risk Premium, 1900-2000

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

  7. An example.... • Year Return • -10% • +12% • +15% • + 8% AAR = 6.25% GAR = 5.78% Arithmetic Versus Geometric Average Returns 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. An example.…Immucell Corp. Monthly Returns for Jan 2000 – Dec 2002 Average Return = 0.838% 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

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

  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. Company Average (mean) monthly return, % Standard deviation of monthly return, % WIRELESS TELECOM GROUP INC 2.03 29.16 REINSURANCE GROUP OF AMERICA INC 0.68 12.31 IMMUCELL CORP 0.83 20.98 Monthly Average Return and Volatility For Three Stocks • Use Monthly Returns for Period January 2000 – December 2002 Use The Average Returns as Estimates of Expected Returns on Each Stock

  12. 50% WIRELESS + 50% REINSURANCE 50% WIRELESS + 50% IMMUCELL Average Return and Volatility For Portfolios 0.025 0.020 100% WIRELESS TELECOM GROUP 0.015 Portfolio Expected Return 0.010 0.005 100% IMMUCELL CORP 100% REINSURANCE GROUP OF AMERICA 0.000 0.000 0.050 0.100 0.150 0.200 0.250 0.300 0.350 Portfolio Standard Deviation How Do Portfolios of These Stocks Perform?

  13. Average Return and Volatility For Portfolios • 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?

  14. 50% Wireless + 50% Immucell • 50% Wireless + 50% Reinsurance Expected Return For Portfolio 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. 50% WIRELESS – 50% REINSURANCE Average Return and Volatility For Portfolios 0.025 0.020 WIRELESS TELECOM GROUP 0.015 Portfolio Expected Return 50% WIRELESS – 50% IMMUCELL 0.010 0.005 REINSURANCE GROUP OF AMERICA IMMUCELL CORP 0.000 0.000 0.050 0.100 0.150 0.200 0.250 0.300 0.350 Portfolio Standard Deviation Wireless and Immucell Correlation: 0.80 Wireless and Reinsurance Group: -0.66

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

  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?

  20. Asset Asset 1 1 2 2 3 3 4 4 5 5 1 1 2 2 3 3 4 4 5 5 Variance of Individual Assets Account Only for 1/25th of the Portfolio Variance The Covariance Terms Determine To A Large Extent The Variance Of The Portfolio Variance – Covariance Matrix

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

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

  24. Diversifiable Risk Portfolio Risk, kp Total risk Nondiversifiable Risk 1 5 10 15 20 25 Number of Securities (Assets) in Portfolio The Impact Of Additional Assets On The Risk Of A Portfolio

  25. Risk and Return 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

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