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portfolios_overhead - Portfolio Selection 1 PORTFOLIO...

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Unformatted text preview: Portfolio Selection 1 PORTFOLIO SELECTION Trading off expected return and risk • How should we invest our wealth? Two principles: – we want to maximize expected return – we want to minimize risk = variance Portfolio Selection 2 • goals somewhat at odds • riskier assets generally have higher expected return • investors demand a reward for bearing risk – called risk premium • there are optimal compromises between expected return and risk Portfolio Selection 3 • In this chapter – maximize expected return with upper bound on the risk – or minimize risk with lower bound on expected return. Portfolio Selection 4 Key concept: reduction of risk by diversification • Diversification was not always considered favorably in the past Portfolio Selection 5 The investment philosophy of Keynes John Maynard Keynes wrote: ... the management of stock exchange investment of any kind is a low pursuit ... from which it is a good thing for most members of society to be free I am in favor of having as large a unit as market conditions will allow ... to suppose that safety-first consists in having a small gamble in a large number of different [companies] where I have no information to reach a good judgement, as compared with a substantial stake in a company where ones’s information is adequate, strikes me as a travesty of investment policy Portfolio Selection 6 • Keynes is advocating stock picking or “fundamental analysis.” • semi-strong version of the EMH ⇒ fundamental analysis does not lead to profit • Keynes lived before the EMH – what Keynes would think about diversification now? • modern portfolio theory takes different view Portfolio Selection 7 • this is not to say that Keynes was wrong, but – Keynes was investing on a long time horizon – portfolio managers are judged on short-term successe – finding bargains is probably more difficult now Portfolio Selection 8 One risky asset and one risk-free asset Start with a simple example: • one risky asset, which could be a portfolio, e.g., a mutual fund – expected return is .15 – standard deviation of the return is .25 • one risk-free asset, e.g., a 30-day T-bill – expected value of the return is .06 – standard deviation of the return is 0 by definition of “risk-free.” Portfolio Selection 9 Problem: construct an investment portfolio • a fraction w of our wealth is invested in the risky asset • the remaining fraction 1- w is invested in the risk-free asset • then the expected return is E ( R ) = w ( . 15) + (1- w )( . 06) = . 06 + . 09 w . • the variance of the return is σ 2 R = w 2 ( . 25) 2 + (1- w ) 2 (0) 2 = w 2 ( . 25) 2 . and the standard deviation of the return is σ R = . 25 w ....
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This note was uploaded on 04/06/2008 for the course ORIE 473 taught by Professor Anderson during the Spring '07 term at Cornell.

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portfolios_overhead - Portfolio Selection 1 PORTFOLIO...

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