091010_Portfolio theory

# 091010_Portfolio theory - Portfolio theory Risk and return...

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Portfolio theory

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Risk and return z Investors generally require a premium for bearing additional risk z What is the measure of risk? z What should be the compensation for each additional unit of risk? z Do different investors require different compensations for additional unit of risk? (Preferences)
Risk and return characteristics: single security z The actual return of a security is uncertain => instead we use expected returns as a measure of profitability z Returns and their probabilities are unknown => could use historical returns as proxies z The standard deviation is a measure of the risk of a security ( ) n n R p R p R p R E + + + = ... 2 2 1 1 () () ( ) () ( ) () 2 2 2 2 2 1 1 ... n n n R E R p R E R p R E R p + + + = σ

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Probability distribution: historical returns z A typical distribution of historical returns: normal distribution
Empirical evidence: normal distribution 0 200 400 600 800 1000 1200 1400 1600 -0,12 -0,08 -0,04 0,00 0,04 0,08 0,12 0,16 0,20 Chevron Corp. historical returns pdf 0 200 400 600 800 1000 1200 1400 -0,16 -0,11 -0,06 -0,01 0,04 0,09 0,14 0,19 Microsoft Corp. historical returns pdf E(R Chevron ) = 0,04% St. dev. = 1,5% E(R Microsoft ) = 0,1% St. dev. = 2,2%

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z Portfolio – is a collection of different assets held by a given investor z Suppose you have \$1000 and you purchase a number of assets: \$500: stocks of Gazprom
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091010_Portfolio theory - Portfolio theory Risk and return...

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