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22a_CAPM_Mean_Variance - John Geanakoplos The Capital Asset...

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John Geanakoplos The Capital Asset Pricing Model from a Mean Variance Perspective 1 Finance Answers Questions Like 1) For individuals: how to choose a portfolio, which stocks to pick. For the indi- vidual, the answer to “which portfolio?” might depend upon a) Wealth b) Risk Aversion c) Age [In the US, a broker is required by law to pay attention to these factors and not make inappropriate investments for you.] d) Stream of income e) Knowledge 2) How to judge a portfolio manager? Expected returns? Expected return given risk? risk measured by standard deviation? 3) Economy: What is a f rm’s fundamental value? Can prices vary from funda- mental values if people are rational? Do f rm managers choose investments properly? for the f rm? for the economy? Do “experts” make more money investing in stocks? Should rational agents speculate on the basis of private information. 4) Purposes of the stock market/ f nancial system a) Way of transferring ownership and control. b) Allow transfers of wealth across time. c) Transfer of risk i) Invest securities to transfer wealth across states of nature ii) Invent a mechanism to ensure people keep promises. d) Allows speculation: gambling, knowledge transmission. Perhaps a good way of stating the investor’s problem is that she must quantify ignorance. The future is uncertain and we must price that uncertainty. In general we must price not only our own ignorance, but other people’s, our ignorance about other’s ignorance and so on. 1
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2 A Mean-Variance Framework for Understanding Fi- nance Markowitz pioneered an approach to f nancial analysis that quanti f ed risk in a port- folio, and gave very concrete advice about which risky assets a single investor should hold. This work was extended by Tobin into a theory of the economy and equilib- rium, in which a large number of investors interact. The work was further extended by Sharpe and Lintner, who derived a remarkable theorem about how risky assets must be priced in equilibrium. The equilibrium model developed by Tobin, Sharpe, and Lintner is called the capital asset pricing model (CAPM). Their theory shows that if agents really respond to risk as Markowitz argued they should, then one can price every asset even when there is not full spanning. Markowitz, Tobin, and Sharpe all won Nobel Prizes for their work (Lintner died before he had a chance to receive his Prize). Markowitz and Tobin were members of the Cowles Foundation, and Sharpe was a Stanford Business School professor. 2.1 Portfolio Analysis and Risk Markowitz posited that every “reasonable” investor should prefer a portfolio with a higher expected payout and lower variance (no matter what the third or fourth moments might be). Innocuous as that assumption seems, he derived remarkable conclusions about the optimal portfolio any ”reasonable” investor should hold.
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22a_CAPM_Mean_Variance - John Geanakoplos The Capital Asset...

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