Chapter 12 Some Lessons From Capital Market History income component cash received directly from investment capital gain loss change in value of assets from when one buys investment to one sells Total Dollar Return income capital gain loss Percentage Returns dividend yield capital gains yield capital gains should be included in the cash flow dividend yield dividend paid during the year price of stock at beg of year capital gains priceend pricebeg pricebeg Returns gain loss from investment Average Returns typical year actually earns GAR 1 r1 1 r2 1 rt 1 t 1 nominal averages simply averages all the numbers does not count for inflation arithmetic average return returned earned in an average year over a multiyear period what one earned in a geometric average return average compound return earned per year over a multiyear period what someone When predicting future forecasts use arithmetic average return IF one knows the exact AAR if one only knows estimates use Blume s Formula T 1 N 1 geometric average N T N 1 arithmetic average where N years of data T how many desired years average risk premiums excess return required from an investment in a risky asset over that required from a risk free asset Variability of Returns frequency distribution chart of distribution variance average squared difference between the actual return and the average return standard deviation positive square root of the variance normal distribution bell shaped frequency distribution that s defined by mean and standard deviation On average bearing risk is handsomely rewarded Capital Marketing Efficiency market values of stocks bonds can fluctuate widely from year to year efficient capital market security prices reflect available information no need to question appropriateness weak form at very least a stock s past prices are reflected no need to study past patterns semi strong form all PUBLIC info is reflected in stock price strong form all info of every kind is incorporated in stock price no such thing as inside info efficient market hypothesis actual capital markets such as the NYSE are efficient all investments in market are ZERO NPV investments Chapter 13 Return Risk And the Security Market Line Expected Returns the return on a risky asset expected in the future weighted against probability of future economy Projected Risk Premium Expected Return Risk free rate Variance Sum return deviation from expected return1 2 probability1 RDERN 2 pN Standard Deviation variance1 2 portfolio weights of a portfolio s total value that is in a particular asset ex StockN1 50 Stock2 150 Portfolio 200 Portfolios a group of assets such as stocks and bonds held by an investor Weight1 50 200 25 Weight2 150 200 75 expected portfolio returns probability of economy state portfolio weight1 p2 weight2 portfolio variance combining assets into portfolios can substantially alter the risks faced by the investor Total Return Expected Return Unexpected Return where expected return is predicted based on data unexpected return is risk associated with unknown data announcement expected part surprise announcements can affect returns if announcement is NEW INFORMATION discount means news is already been considered Systematic and Unsystematic Risk systematic risk influences a large number of assets market risk unsystematic risk affects at most a small number of assets asset specific risk Thus Total Return Expected Return Systematic risk Unsystematic Risk Diversification and Portfolio Risk standard deviation decreases as of securities increases principle of diversification spreading and investment across a of assets will eliminate some but not all risk non diversifiable risk min level of risk that cannot be eliminated simply by diversifying unsystematic risk is essentially eliminated by diversification so a portfolio with many assets has almost no unsystematic risk diversifiable risk unsystematic risk systematic risk is non diversifiable Systematic Risk and Beta systematic risk principle expected return on a risky asset depends only on that asset s systematic risk beta amount of systematic risk present in a particular risky asset relative to that in an average risky asset ex 0 50 half as risky 2 twice as risky portfolio s beta asset1 s beta weight asset2 s beta weight The Security Market Line a risk free asset has beta 0 invested in asset can exceed 100 risk to reward ratio slope the risk to reward ratio must be the same for all assets in the market security market line positively shaped straight line showing the relationship between expected return beta market risk premium slope of SML difference between the expected return on a market portfolio and the risk free rate capital asset pricing model equation of the SML showing the relationship between expected return and beta pure time value of money reward for bearing systematic risk amount of systematic risk Expected Return Risk Free Rate Return Risk Free Rate Beta If the CAPM is true then the security market line holds as well which means all assets have the same risk premium cost of capital minimum required return on a new investment Correlation and the Diversification Principle the extent of the risk reduction achieved through portfolio diversification depends on the relationship between the returns of the various assets rho p 1 two variables are perfectly positively correlated no benefit in combining the two assets into a portfolio the portfolio s standard deviation will be an exact average of the two individual standard deviations weighted by the proportion of the portfolio each represents rho p 0 there is no relationship rho p 1 two variables are perfectly negatively correlated there is significant risk reduction but degree of risk reduction is not nearly as great as negative correlation the standard deviation is significantly lower than a weighted average of the 2 individual standard deviations however most stocks are positively correlated with each other and the economy variancePORTFOLIO square root of this is standard deviation wsws s s wtwt t t 2wswt s t st where ws weight or of investment in s s Standard Deviation of s wt weight or of investment in t t Standard Deviation of t st Correlation between s and t CH 14 Cost of Capital weighted average cost of capital WACC cost of capital for the firm as a whole required return on the firm The Cost of Capital Preliminaries the cost of capital for a risk free investment the risk free rate cost of capital depends primarily on the use of funds NOT