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Class Note for CHEE 6369 at UH


Class Note for CHEE 6369 at UH

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This 4 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at University of Houston taught by a professor in Fall. Since its upload, it has received 13 views.

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Date Created: 02/06/15
CHEMICAL ENGINEERING 6369 Risk Analysis for Chemical and Petroleum Engineers PORTFOLIOS AND DIVERSITY Simple Portfolio Concepts Why diversify Consider Risk vs Return and concept of dominance with respect to either See hypothetical E V SD points in Figures a Pure cash position Fig 1 Riskfree gt Cash 0 Ecash Expected return on cash Bank interest Scash 0 Best Investments and AssetsA A Dominated Selection a Cash y Volatility Standard W quott Investments DeVIatIon SD J and Assets w E E 3 1a a D C N a E Use MeanVariance Rule see Hertz and Thomas 1983 p 116 o For same return take investments with lower variance 0 For same variance take investments with higher return See Montgomery amp Runge pp 249250 Eqns 635 638 Intro to Portfoliosdoc Page 1 21Mar01 Portfolios and Diversity b Now assume some fraction f of value in cash balance held in investmentX or Y Then what should we do with the l f Invest Ep fEcash Einvestment Expected return of cash amp investment S13p f Scash SDinvestment 0 SDinvestment Stndd Dev of cash investment Stndd Dev of investment Best Investments and Asset A nand 5 possible with portfolios of Cash Y uand a possible with portfolios of Cash X LIJ 39 L 3 1a a D C N a E L Volatility Standard W quott Investments Devratron SD J and Assets See Fig 2 Hypothetical Ep v SDp plot Lines C X C Y Choices of X Yand f depend on returns volatility of stocks and risk averseness 0 Line btwn points represents some miX of cash stock some value of t 0 Line extension beyond X or Y represents leveraging the investment by borrowing assuming interest at the cash rate of return C c Complications arise when we hold a miX of investments Maybe stocks wells or whatever For simplicity here Assume holding 2 investments X and Y Random Variables gt 0 Ep fEX lt Ey SDp f2 SDX2 2f1 r R SDX SDy 1 D2 SDYZ 2 l f R f l correlation coefficient Intro to Portfoliosdoc Page 2 21Mar01 Portfolios and Diversity Perfect correlation R l gt SDp f SDX l f SDy Given 71 g R lt 1 EP is still weighted average but get reduction in portfolio SD 7 Uncorrelated 2 Variation in one will partly offset variation in the other and the farther R is from 1 the more this is true i Hypothetical 1 Ex By then EP EX By is known amp SDX gt SDp lt SDy Note that SDp f2 SD 2f1 t R SDX SDy 1 D2 SDyz 2 f SDX 1 0 SDy2 2f1 t 1 R SDX SDy 2 weighted average SD2 positive number V2 lt weighted average SD iiHypothetical 2 EX 5 By and SDX 5 SDy See Figs 3 and 4 Plots for R 1 for l lt R lt1 and for R 1 Point Z R 1 gt f SDy SDX SDy Best Investments and Assets A Combined investments with X amp Y perfectly positively correlated R 1 Combined investments with X amp Y imperfectly correlated 1 lt R lt 1 w E E 3 1a a D C N a E y Volatility Standard W quott Investments DeVIatIon SD J and Assets Intro to Portfoliosdoc Page 3 21Mar01 Portfolios and Diversity Best Investments and Asset Combined investments with X amp Y perfectly negatively correlated R 1 quotRisklessquot intercept 2 occurs where EZ SDY EX SDX EY I SDX SDY LIJ 39 L 3 1a a D C N a E L Volatility Standard W quott Investments DeVIatIon SD J and Assets Conclude Bene ts of diversi cation proven Extension What do we do when we hold gt2 investments Source Supplement Notes See Applied Statistics and Probability for Engineers by Montgomery amp Runge Wiley 1999 Section 67 pp 249250 Introduction to Portfolio Theory by HBS Prof Andre F Perold Harvard Business School Press Rev 9695 Risk Analysis and Its Applications by Hertz and Thomas 1983 Wiley pp 116120 Intro to Portfoliosdoc Page 4 21Mar01


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