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Risk and Return

Risk and Return. Managing stakeholder Relationships. Corporate social Responsibility. Agency Problem. Corporate Governance:

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Risk and Return

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  1. Risk and Return

  2. Managing stakeholder Relationships Corporate social Responsibility Agency Problem Corporate Governance: refers to the system by which corporations are managed and controlled. It encompasses the relationships among a company’s shareholders, board of directors, and senior management. These relationships provide the framework within which corporate Goal Congruence Increase in Share price+ Dividend Incentives+ perquisites • Connected Stakeholder • Customer • Supplier • Banker Management Shareholder • External Stakeholder • Government • Local communities • Pressures groups

  3. Income received on an investment plus any change in market price, usually expressed as a percent of the beginning market price of the investment. Return Dt+ (Pt – Pt - 1) R = Pt - 1

  4. What rate of return do you expect on your investment (savings) this year? What rate will you actually earn? Does it matter if it is a bank Deposit or a share of stock? Risk The variability of returns from those that are expected. chance that some unfavorable event will occur

  5. R = S ( Ri )( Pi ) R is the expected return for the asset, Riis the return for the ith possibility, Pi is the probability of that return occurring, n is the total number of possibilities. Expected Return n I = 1

  6. s = S ( Ri – R )2( Pi ) Standard Deviation, s, is a statistical measure of the variability of a distribution around its mean. It is the square root of variance. Standard Deviation (Risk Measure) n i = 1

  7. Stock BW RiPi (Ri)(Pi) (Ri- R )2(Pi) –0.15 0.10 –0.015 0.00576 –0.03 0.20 –0.006 0.00288 0.09 0.40 0.036 0.00000 0.21 0.20 0.042 0.00288 0.33 0.10 0.033 0.00576 Sum1.000.090 0.01728 Expected Return and Standard Deviation

  8. Standard Deviation (Risk Measure) n s = S ( Ri – R )2( Pi ) s = .01728 s = 0.1315 or 13.15% i=1

  9. Comparing Standard Deviations Data A Mean = 15.5 S = 3.338 11 12 13 14 15 16 17 18 19 20 21 Data B Mean = 15.5 S = 0.926 11 12 13 14 15 16 17 18 19 20 21 Data C Mean = 15.5 S = 4.567 11 12 13 14 15 16 17 18 19 20 21 • The smaller the standard deviation, the more tightly clustered the scores around mean • The larger the standard deviation, the more spread out the scores from mean

  10. Coefficient of Variation The ratio of the standard deviation of a distribution to the mean of that distribution. It is a measure of RELATIVE risk. CV = s/R CV of BW = 0.1315 / 0.09 =1.46

  11. Stock A: Average price last year = $50 Standard deviation = $5 Stock B: Average price last year = $100 Standard deviation = $5 Coefficient of Variation Both stocks have the same standard deviation but stock B is less variable relative to its price

  12. Normal Distribution

  13. Certainty equivalent > Expected value Risk Preference Certainty equivalent = Expected value Risk Indifference Certainty equivalent < Expected value Risk Aversion Most individuals are Risk Averse. Risk Attitudes

  14. Risk and Return in a Portfolio Context Portfolio A combination of two or more securities or assets.

  15. Firm specific risk that can be diversified Market level risk that can not be diversified

  16. Systematic Risk is the variability of return on stocks or portfolios associated with changes in return on the market as a whole. Unsystematic Risk is the variability of return on stocks or portfolios not explained by general market movements. It is avoidable through diversification. Total Risk = SystematicRisk + UnsystematicRisk Total Risk = Systematic Risk + Unsystematic Risk

  17. Total Risk Stems from factors that systematically affect most firms: war, inflation, recessions, and high interest rates. STD DEV OF PORTFOLIO RETURN Unsystematic risk Total Risk Systematic risk NUMBER OF SECURITIES IN THE PORTFOLIO

  18. Total Risk = Systematic Risk + Unsystematic Risk lawsuits, strikes, successful and unsuccessful marketing programs, winning or losing a major contract, and other events that are unique to a particular firm. STD DEV OF PORTFOLIO RETURN Unsystematic risk Total Risk Systematic risk NUMBER OF SECURITIES IN THE PORTFOLIO

  19. RP = S ( Wj )( Rj ) RPis the expected return for the portfolio, Wjis the weight (investment proportion) for the jth asset in the portfolio, Rj is the expected return of the jth asset, m is the total number of assets in the portfolio. Portfolio Expected Return m J = 1

  20. Portfolio Standard Deviation m m sP = S SWjWks jk J=1 K=1 Wjis the weight (investment proportion) for the jth asset in the portfolio, Wkis the weight (investment proportion) for the kth asset in the portfolio, sjkis the covariance between returns for the jth and kth assets in the portfolio.

  21. sjk = s j s k rjk What is Covariance? sjis the standard deviation of thejthasset in the portfolio, skis the standard deviation of the kth asset in the portfolio, rjkis the correlation coefficient between thejthand kth assets in the portfolio.

  22. A standardized statistical measure of the linear relationship between two variables. Its range is from –1.0 (perfect negative correlation), through 0 (no correlation), to +1.0 (perfect positive correlation). Correlation Coefficient

  23. Both portfolio returns and risk are bounded by the range set by the constituent assets when ρ=+1 Example of Portfolio Combinations and Correlation Perfect Positive Correlation – no diversification

  24. When ρ=+0.5 these portfolio combinations have lower risk – expected portfolio return is unaffected. Example of Portfolio Combinations and Correlation Positive Correlation – weak diversification potential

  25. Portfolio risk is lower than the risk of either asset A or B. Example of Portfolio Combinations and Correlation No Correlation – some diversification potential

  26. Portfolio risk for more combinations is lower than the risk of either asset Example of Portfolio Combinations and Correlation Negative Correlation – greater diversification potential

  27. Risk of the portfolio is almost eliminated at 70% invested in asset A Example of Portfolio Combinations and Correlation Perfect Negative Correlation – greatest diversification potential

  28. ? 0.5

  29. Stock CStock DPortfolio Return 9.00% 8.00% 8.64% SD 13.15% 10.65% 10.91% CV 1.46 1.33 1.26 The portfolio has the LOWEST coefficient of variation due to diversification. Portfolio Return and Risk Calculation

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