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Unformatted text preview: 111Learning ObjectivesTo get the most out of this chapter, spread your study time across:1. How to calculate expected returns and variancesfor a security.2. How to calculate expected returns and variances for a portfolio.3. The importance of portfolio diversification.4. The efficient frontier and importance of asset allocation.112112Diversification and Asset Allocation•Our goal in this chapter is to examine the role of diversification and asset allocation in investing.•In the early 1950s, professor Harry Markowitz was the first to examine the role and impact of diversification.•Based on his work, we will see how diversification works, and we can be sure that we have “efficiently diversified portfolios.” 113113Expected Returns•Expected return is the “weighted average” return on a risky asset, from today to some future date. The formula is:•To calculate an expected return, you must first:–Decide on the number of possible economic scenarios (states) that might occur.–Estimate how well the security will perform in each states, and–Assign a probability to each states[ ]∑=×=n1ssi,sireturnpReturnExpected114114Calculating Expected Returns115115Expected Risk Premium•Define:•Suppose riskfree investments have an 8% return. Then,–The expected risk premium on Jpod is 20%8%=12%–The expected risk premium on Starcents is 25%8%=17%rateriskfreereturnexpectedpremiumriskexpected=116116Calculating the Variance of Expected Returns•The variance of expected returns is calculated using this formula:•The standard deviation is simply the square root of the variance.VarianceσDeviationStandard==( 29[ ]∑=×==n1s2ss2returnexpectedreturnpσVariance117117Example: Calculating Expected Returns and Variances: Equal State Probabilities(1)(3)(4)(5)(6)(7)Return ifState ofStateExpectedDifference:Squared:Product:EconomyOccursReturn:(3)  (4)(5) x (5)(2) x (6)Recession0.200.250.450.20250.10125Boom0.700.250.450.20250.10125Sum:0.202500.45(1)(3)(4)(5)(6)(7)Return ifState ofStateExpectedDifference:Squared:Product:EconomyOccursReturn:(3)  (4)(5) x (5)(2) x (6)Recession0.300.200.100.01000.00500Boom0.100.200.100.01000.00500Sum:0.010000.10(2)Probability ofState of Economy0.500.501.00Sum = the Variance:Standard Deviation:Jpod:(2)1.00Sum is Variance:Standard Deviation:Probability ofState of Economy0.500.50118118Expected Returns and Variances, Starcents and Jpod119...
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 Fall '08
 phsiao
 Modern portfolio theory, Markowitz efficient frontier, jPod

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