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Unformatted text preview: 1 Diversifcation and PortFolios Economics 71a: Spring 2007 Mayo chapter 8 Malkiel, Chap 910 Lecture notes 3.2b Goals PortFolios and correlations Diversifable versus nondiversifable risk CAPM and Beta Capital asset pricing model Is the CAPM really useFul? Asset allocation Risk: Individual>PortFolio Early models Risk is based on each individual stock Modern approaches Consider how it eFFects “portFolio” oF holdings Markowitz Modern portFolio theory Diversifcation Diversifcation and PortFolios “Don ’ t put all your eggs in one basket” Buying a large set oF securities can reduce risk 2 What is the return of a portfolio? $ values in assets 1 and 2 = h1 and h1 R1 and R2 are returns of assets 1 and 2 Rp is the return of the portfolio Ending portfolio = End Starting value = Start End = h 1 (1 + R 1 ) + h 2 (1 + R 2 ) End Start = h 1 Start (1 + R 1 ) + h 2 Start (1 + R 2 ) (1 + R p ) = w 1 (1 + R 1 ) + w 2 (1 + R 2 ) In words The return of a portfolio is equal to a weighted average of the returns of each investment in the portfolio The weight is equal to the fraction of wealth in each investment Malkiel ’ s Example of Risk Reduction +50%25% Sunny Season25% +50% Rainy Season Resort Company Umbrella Company Portfolio 50/50 in Each Return = Rain : (0.5) (0.50) + (0.5)(0.25) = 12% Shine: (0.5) (0.25) + (0.5)(0.50) = 12% = 12% rain or shine No risk This is the beauty of diversiFcation Simple risk management Quirk: Need “negative” relation 3 What is going on? Asset returns have perfect “negative correlation” They move exactly opposite to each other Is this always necessary? No DiversiFcation Experiment Assume the following framework for stock returns Two parts Part that moves with market: β Part that is unique to the Frm: e Rm is the return of the market Experiment: Choose two stocks and beta ’ s Beta determines how closely the stock move with each other Combine two stocks as x and (1x) fractions Return = x R1 + (1x) R2 Example portfolio variance R j = ! j R m + e j Web Examples See multiBeta scatter plots Portfolio 2 Quick Application: A perfect hedge Security 1: y = 0.1 + b*v Security 2: x = 0.1 + b*v v is random Portfolio: (1/2) each port = 0.5(0.1+b*v) + 0.5(0.1b*v) port = 0.1 + 0.5(bb)*v = 0.1 Risk free Perfect negative correlation 4 Summary: Portfolio Theory A radically new approach to risk In the 1950 ’ s Two key points...
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