Microsoft PowerPoint - PoF.ppt

Minimum variance and efficient setƒ 41 One Fund Theorem: there is a single risky portfolio F such that any efficient portfolio c ...

Minimum variance and efficient setƒ 42 Finding the efficient set using Lagrange - Tobin model: compute the portfolio weights tha ...

Overviewƒ 43 Decisions under uncertainty / Decision criteria ƒ Utility functions ƒ 3 (possible) categories ƒ Degree of risk aver ...

Decisions under uncertainty / Decision criteriaƒ 44 Expected value criterion ƒ St. Petersburg Paradox (Daniel Bernoulli , 1738): ...

Decisions under uncertainty / Decision criteriaƒ 45 Daniel Bernoulli's solution involved two ideas that have since revolutionize ...

Decisions under uncertainty / Decision criteriaƒ 46 With only a handful of exceptions, Bernoulli's expected utility hypothesis w ...

Utility functions: 3 (possible) categoriesƒ 47 Strict risk aversion and (weak) risk aversion ƒ Risk neutral ƒ Strict risk loving ...

ƒ 48 (Strict) risk aversion ƒ u’ > 0, (u’’ < 0) u’’ ≤ 0 ... “(strictly) diminishing marginal utility“ ƒ ... “Jensen’s (str ...

Utility functions: degree of risk aversionƒ 49 u is unique up to a strictly increasi ng affine transformation (, i.e. u can be r ...

Some utility functionsƒ 50 Power utility ƒ Quadratic utility (special case of power utility: for N = -1 ) ƒ Negative exponential ...

Expected utility and expected value criterionƒ 51 Obviously the expected value criterion can be reconciled with the expected uti ...

Expected utility and mean-variance criterionƒ 52 The mean-variance criterion used in the Markowitz model can be reconciled with ...

Overviewƒ 53 Assumptions ƒ Capital market line (CML) ƒ Security market line (SML) ƒ Critique ƒ Performance measurement ƒ Additio ...

Assumptionsƒ 54 The CAPM was simultaneously and independently discovered by W. Sharpe (1964), J. Lintner ( 1965), and J. Mossin ...

CMLƒ 55 From the one-fund separation theorem we know that all investors choose portfolios which are a combination of the tangenc ...

CMLƒ 56 The tangency portfolio is the same for all investors Ä tangency portfolio = summation of all assets = “market portfolio” ...

CMLƒ 57 In equilibrium returns of the assets have to adjust such that the market portfolio is efficient! How does this happen? ƒ ...

SMLƒ 58 Theorem: If the market is efficient then there exists a perfect linear relation between the beta factors for stocks and ...

SMLƒ 59 Proof: ƒ Consider the following portfolio 2 2 2 2 ) (^1) ( ) (^1) ( ) 2 (^1) ( M iM i M i r r r σ α σ α α σ α σ α α α α ...

SML 60 ƒ The curve generated by asset i and M ca nnot cross the capital market line, i.p. the curve at α =0 has to be tangent to ...