CHAPTER SEVENINTRODUCTIONSlide 3Slide 4INITIAL AND TERMINAL WEALTHSlide 6Slide 7THE MARKOWITZ APPROACHSlide 9Slide 10Slide 11Slide 12Slide 13Slide 14Slide 15INDIFFERENCE CURVE ANALYSISSlide 17PORTFOLIO RETURNSlide 19Slide 20PORTFOLIO RISKSlide 22Slide 23Slide 241CHAPTER SEVENTHE PORTFOLIO SELECTION PROBLEM2INTRODUCTION•THE BASIC PROBLEM:–given uncertain outcomes, what risky securities should an investor own?3INTRODUCTION•THE BASIC PROBLEM:–The Markowitz Approach•assume an initial wealth•a specific holding period (one period)•a terminal wealth•diversify4INTRODUCTION•Initial and Terminal Wealth•recall one period rate of returnwhere rt = the one period rate of returnwb = the beginning of period wealth we= the end of period wealthbbetwwwr5INITIAL AND TERMINAL WEALTH•DETERMINING THE PORTFOLIO RATE OF RETURN–similar to calculating the return on a security–FORMULA001wwwrp6INITIAL AND TERMINAL WEALTH•DETERMINING THE PORTFOLIO RATE OF RETURNFormula:where w0 = the aggregate purchase price at time t=0 w1 = aggregate market value at time t=1001wwwrp7INITIAL AND TERMINAL WEALTH•OR USING INITIAL AND TERMINAL WEALTHwhere w0 =the initial wealth w1 =the terminal wealth 011 wrwp8THE MARKOWITZ APPROACH•MARKOWITZ PORTFOLIO RETURN–portfolio return (rp) is a random variable9THE MARKOWITZ APPROACH•MARKOWITZ PORTFOLIO RETURN–defined by the first and second moments of the distribution•expected return•standard deviation10THE MARKOWITZ APPROACH•MARKOWITZ PORTFOLIO RETURN–First Assumption:•nonsatiation: investor always prefers a higher rate of portfolio return11THE MARKOWITZ APPROACH•MARKOWITZ PORTFOLIO RETURN–Second Assumption•assume a risk-averse investor will choose a portfolio with a smaller standard deviation•in other words, these investors when given a fair bet (odds 50:50) will not take the bet12THE MARKOWITZ APPROACH•MARKOWITZ PORTFOLIO RETURN–INVESTOR UTILITY•DEFINITION: is the relative satisfaction derived by the investor from the economic activity.•It depends upon individual tastes and preferences•It assumes rationality, i.e. people will seek to maximize their utility13THE MARKOWITZ APPROACH•MARGINAL UTILITY–each investor has a unique utility-of-wealth function–incremental or marginal utility differs by individual investor14THE MARKOWITZ APPROACH•MARGINAL UTILITY–Assumes•diminishing characteristic•nonsatiation•Concave utility-of-wealth function15THE MARKOWITZ APPROACHUTILITY OF WEALTH FUNCTIONWealthUtilityUtility of Wealth16INDIFFERENCE CURVE ANALYSIS•INDIFFERENCE CURVE ANALYSIS–DEFINITION OF INDIFFERENCE CURVES:• a graphical representation of a set of various risk and expected return combinations that provide the same level of utility17INDIFFERENCE CURVE ANALYSIS•INDIFFERENCE CURVE ANALYSIS–Features of Indifference Curves:•no intersection by another curve•“further northwest” is more desirable giving greater utility•investors possess infinite numbers of indifference curves•the slope of the curve is the marginal rate of substitution which represents the nonsatiation and risk averse Markowitz assumptions18PORTFOLIO RETURN•CALCULATING PORTFOLIO RETURN–Expected returns•Markowitz Approach focuses on terminal wealth (W1), that is, the effect various portfolios have on W1•measured by expected returns and standard deviation19PORTFOLIO RETURN•CALCULATING PORTFOLIO RETURN–Expected returns:•Method One:rP = w1 - w0/ w020PORTFOLIO RETURN–Expected returns:•Method Two:where rP = the expected return of the portfolioXi = the proportion of the portfolio’s initial value invested in security iri = the expected return of security iN = the number of securities in the portfolioNtiiprXr121PORTFOLIO RISK•CALCULATING PORTFOLIO RISK–Portfolio Risk:•DEFINITION: a measure that estimates the extent to which the actual outcome is likely to diverge from the expected outcome22PORTFOLIO RISK•CALCULATING PORTFOLIO RISK–Portfolio Risk:where ij = the covariance of returns between security i and security j2/11 1 NiNjijjiPXX23PORTFOLIO RISK•CALCULATING PORTFOLIO RISK–Portfolio Risk:•COVARIANCE–DEFINITION: a measure of the relationship between two random variables–possible values:»positive: variables move together»zero: no relationship»negative: variables move in opposite directions24PORTFOLIO RISKCORRELATION COEFFICIENT–rescales covariance to a range of +1 to