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Lecture 5 Sep 21 2011

# Lecture 5 Sep 21 2011 - FINA3104 Lecture5 (Continued...

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FINA 3104: Investment Analysis and Portfolio Management Lecture 5 – Portfolio Mathematics and Capital Allocation (Continued) Darwin Choi September 21, 2011 Recap from Last Lecture Arithmetic & Geometric Average Returns Expected vs. Realized Return & Risk Expected: , 2 , Realized: R(r), s 2 Value at Risk (VaR) Another measure of risk, works well for any distribution Riskfree Prospects & the Risk Premium Risk Preferences & Returns Utility Risk Averse, Risk Neutral, Risk Loving Utility Indifference 2

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Outline of Today’s Lecture Risk & Return for Security Portfolios Allocation Decision Levels Complete Portfolio Return & Risk The Capital Allocation Line 3 Expected Portfolio Return, E( r P ) E( r P ) = w 1 E( r 1 ) + w 2 E( r 2 ) where w 1 and w 2 are portfolio weights, or the fraction of wealth the investor puts into each security. E.g., Invest \$25 in r 1 and \$75 in r 2 : w 1 = 25/100, w 2 = 75/100 Expected Portfolio Return 4
Suppose you have \$100 to invest, which you split equally between stocks 1 & 2: w 1 = \$50/\$100 = 50% = w 2 E( r P ) = w 1 E( r 1 ) + w 2 E( r 2 ) E( r P ) = 0.50(4%) + 0.50(8%) = 6% This portfolio is expected to return 6%. Example 5 Portfolio Variance Portfolio Variance, P 2 = E[ r P – E( r P )] 2 P 2 = E[ w 1 r 1 + w 2 r 2 – E( w 1 r 1 + w 2 r 2 )] 2 = E[ w 1 r 1 – E( w 1 r 1 ) + w 2

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Lecture 5 Sep 21 2011 - FINA3104 Lecture5 (Continued...

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