Ch10 - Chapter 10 Portfolio Theory Road Map Part A...

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Chapter 10 Portfolio Theory Road Map Part A Introduction to Fnance. Part B Valuation of assets, given discount rates. Part C Determination of discount rates. Historic asset returns. Time value of money. Risk. Portfolio theory. Capital Asset Pricing Model (CAPM). Arbitrage Pricing Theory (APT). Part D Introduction to corporate Fnance. Main Issues Returns of Portfolios DiversiFcation Optimal Portfolio Selection and ±rontier Portfolios ±rontier Portfolios with a Risk-free Asset Individual Assets’ Contribution to Portfolio Risk
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10-2 Portfolio Theory Chapter 10 Contents 1 In t r odu c t i onandO v e r v i ew. .................. 1 0 - 3 2 R e tu rn so fP o r t f o l i o s...................... 1 0 - 4 2 . 1 P o r t f o l i oo fTw oA s s e t s....................... 1 0 - 4 2 . 2 P o r t f o l i fM u l t i p l eA s s e t s..................... 1 0 - 9 3 D i v e r s iF c a t i on . ........................ 1 0 - 1 2 4 Op t im a lP o r t f o l i oS e l e c t i on. 1 0 - 1 6 4 . 1 P o r t f o l i r o n t i e rw i t hTw s s e t s ................. 1 0 - 1 8 4 . 2 P o r t f o l i r o n t i e i t hM u l t i p l s s e t s ............... 1 0 - 2 2 5 Portfolio ±rontier with A Safe Asset . . . . . . . . . . . . . . 10-23 6 Ind i v idu a lA s s e t sandP o r t f o l i o s ................ 1 0 - 2 5 6.1 Contribution of An Asset to A Portfolio . . . . . . . . . . . . . . 10-26 6.2 Individual Asset and ±rontier Portfolios . . . . . . . . . . . . . . . 10-29 7 Summ a r y............................ 1 0 - 3 1 8 Appendix A: Solve ±rontier Portfolios . . . . . . . . . . . . . 10-32 9 App end i xB :P o r t f o l i o sAn a l y t i c s................ 1 0 - 3 5 9.1 Matrices . . . . . . . . . . . . . . ................. 1 0 - 3 5 9 . 2 ± r o n t i e rP o r t f o l i o sw i t h o u tR i s k - f r e s s e t ............. 1 0 - 3 7 9 . 3 ± r o n t i e o r t f o l i o i t hAR i s k r e s s e 1 0 - 4 4 9 . 4 P r o p e r t i e r o n t i e o r t f o l i o s................... 1 0 - 4 6 1 0 H om ew o r k ........................... 1 0 - 4 8 15.407 Lecture Notes ±all 2003 c ° Jiang Wang
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Chapter 10 Portfolio Theory 10-3 1 Introduction and Overview In order to understand risk-return trade-oF, we observe: 1. Risks in individual asset returns have two components: (a) Systematic risks—common to many assets (b) Non-systematic risks—speci±c to individual assets. 2. Systematic risks and non-systematic risks are diFerent: (a) Systematic risks are non-diversi±able (b) Non-systematic risks are diversi±able. 3. ²orming portfolios can eliminate non-systematic risks. 4. Investors hold diversi±ed portfolios instead of single assets. 5. Investors care only about portfolio risks—systematic risks. 6. Return on an asset compensates only for systematic risks. c ° Jiang Wang ²all 2003 15.407 Lecture Notes
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10-4 Portfolio Theory Chapter 10 2 Returns of Portfolios 2.1 Portfolio of Two Assets We start with two assets, 1 and 2, whose returns, { ˜ r 1 , ˜ r 2 } ,a re characterized by their mean, variance and covariances. Mean returns: Asset 12 Mean Return ¯ r 1 ¯ r 2 Variances and covariances (given by the covariance matrix): ˜ r 1 ˜ r 2 ˜ r 1 σ 2 1 σ 12 ˜ r 2 σ 21 σ 2 2 Covariance of an asset with itself is its variance: σ 11 = σ 2 1 and σ 22 = σ 2 2 .
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This note was uploaded on 01/19/2011 for the course 15 15.407 taught by Professor Wang during the Fall '03 term at MIT.

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Ch10 - Chapter 10 Portfolio Theory Road Map Part A...

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