Outline-5

Outline-5 - Ec 173AFINANCIAL MARKETS LECTURE OUTLINE...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Ec 173AFINANCIAL MARKETS LECTURE OUTLINE Foster, UCSD July 16, 2010 TOPIC 5 MODERN PORTFOLIO THEORY A. Introduction to Modern Portfolio Theory (MPT) 1. Background: a) Harry Markowitz, 1952 [Nobel, 1990]. b) The assumptions of MPT. 2. Portfolio Rates of Return: a) Consider a portfolio of one stock and one bond. b) Portfolio ex ante rate of return. b b s s p r r r + = . Proof: c) Portfolio returns and expected returns. . 3. Portfolio Risk: a) Covariance and correlation of ex ante rates of return. NOTATION -- for j { s, b } Symb ol Definition Notes P j Beginning price of stock or bond n j Number of units of asset in portfolio V j Total value of asset in portfolio V j = n j P j CF j Cash flows per unit of asset r j Ex ante rate of return on asset r j = (CF j + P j )/ P j V p Beginning portfolio price (value) V p = V s + V b j Proportion of portfolio value in asset j = V j /V p ; j = 1 b b s s p b b b s s s p b b b b b s s s s s p p p p r r V r P n r P n V P P P CF n P P P CF n V V CF r + = + = + + + = + = ) ( ) ( ) ( ) ( ) ( ) ( b b s s p p r r r or r E + = Ec 173A MPT OUTLINE p. 2 of 11 b) Portfolio risk. 4. Example: [Table 1] 5. Generalization to N assets: a) Consider a portfolio with asset classes X i , i = 1...N. b) Ex ante portfolio return r p is a linear combination of asset returns r i . c) Information problems. 6. Principles of Diversification: a) Reduce risk thru portfolio diversification. b) Example. [Table 2] c) Notes. [Fig. 1] Table 1 State of World Pr( j) r s r b j=1: Drought 0.2 0.01 0.02 j=2: Normal 0.6 0.08 0.08 j=3: Flood 0.2 0.12 0.03 (r) = 0.070 0.058 (r) = 0.042 9 0.027 1 (r s , r b ) = 0.00046 (r s , r b ) = 0.3952 Table 2 Portfolio Return Portfolio Risk = (r p ) s b (r p ) = 0 = +1 = 1 100 % 70% 50% 44 % 30% 0% 0% 30% 50% 56 % 70% 100 % 10.0 % 8.80 % 8.00 % 7.75 % 7.20 % 6.00 % 0.090 0.066 4 0.057 0.055 7 0.055 9 0.070 0.090 0.084 0.080 0.078 8 0.076 0.070 0.090 0.042 0.010 0.000 0.022 0.070 ) ( ) ( ) , ( ) , ( ) ( ) ( ) Pr( ) , ( 1 b s b s b s b s K j bj sj b s r r r r r r n Correlatio r r j r r r r riance Cova =- = = = = = + = = = i j j i j i N i i i p N i i i p N i i i p r r r r Variance Risk Portfolio r r return Expected r r return Portfolio ) , ( 2 ) ( ) ( : ) ( ) ( : ; : 1 2 2 2 1 1...
View Full Document

This note was uploaded on 10/20/2010 for the course ECON 173A taught by Professor Foster during the Fall '09 term at UCSD.

Page1 / 11

Outline-5 - Ec 173AFINANCIAL MARKETS LECTURE OUTLINE...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online