Microsoft PowerPoint - PoF.ppt
Computing returns 21 Multi-period simple returns Multi-period log returns () ∏ − = − + − − +− − − − − − + = + + + = = = = = + ...
Empirical features of returns 22 Simple and log returns cannot be distinguished in such graphs Erratic (“ white noise ”), st ...
Empirical features of returns 23 Usually returns aren’t normal distributed ! -Skewness ≠ 0 Kurtosis ≠ 3, usually kurtosis &g ...
Overview 24 Properties of portfolios Return Risk Diversification Minimum variance and efficient set Combination lines ...
Properties of portfolios: return 25 Multiple-asset portfolio xj = Dollar amount in of security J bought (or sold short) / total ...
Properties of portfolios: risk 26 We quantify risk in terms of statisti cal measures, conventionally this is done using the var ...
Properties of portfolios: risk 27 Multiple-asset portfolio ⎤ ⎥ ⎥ ⎥⎦ ⎡ ⎢ ⎢ ⎢⎣ = Σ ⎤ ⎥ ⎥ ⎥⎦ ⎡ ⎢ ⎢ ⎢⎣ = = ⋅ ⋅ ⋅ ⋅ = ∑ ∑∑== nn n n ...
Examples 28 An investor has € 1000. Hearing from an investment opportunity with an expected rate of return of 24%, she sells sh ...
Properties of portfolios: diversification 29 Diversification: strategy designed to reduce risk by spreading the portfolio acros ...
Properties of portfolios: diversification 30 Naive diversification: portfolio with n assets, each asset with weight 1/nExample ...
Minimum variance and efficient set 31 A better method for diversification Find out the portfolio weights that minimize the po ...
Minimum variance and efficient set 32 Ä Combination line Single-period random cash flows: Mean-variance portfolio theory ...
Minimum variance and efficient set 33 The case of perfect positive correlation Single-period random cash flows: Mean-variance p ...
Minimum variance and efficient set 34 The case of perfect negative correlation Single-period random cash flows: Mean-variance p ...
Minimum variance and efficient setÄ 35 Spectrum of combination lines Single-period random cash flows: Mean-variance portfolio t ...
Single-period random cash flows: Mean-variance portfolio theoryMinimum variance and efficient set 36 ...
37 Given a particular level of expected rate of return, the portfolio on the minimum variance set (“ bullet ”) has the lowest ...
Minimum variance and efficient set 38 Finding the efficient set using Lagrange - Markowitz model: compute the portfolio weights ...
Minimum variance and efficient set 39 Two Fund Separation Theorem : combinations of portfolios on the minimum variance set are ...
Minimum variance and efficient set 40 Including a risk-free asset , i.e. include an asset with zero variance and zero covarianc ...
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