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Indifference Curves and Risk Aversion

The method used in selecting the most desirable portfolio involves the use of indifference curves. These curves represent an investor's preferences for risk and return. It can be drawn on a two-dimensional graph, where the horizontal axis usually indicates risk as measured by variance or standard deviation and the vertical axis indicates reward as mesured by expected return. Using variance as relevant risk measure comes from Markowitz's paper and is always used in practice, although other possibilities have been considered (see [#!Rothschild:Risk!#].) This definition gives us the following properties, assuming we have a 'rational investor'1: But how are the indifference curves shaped? Generally it is assumed that investors are risk averse, which means that the investor will choose the portfolio with the smaller variance given the same return. Risk averse investors will not want to take fair gambles (where the expected payoff is zero). These two assumptions of nonsatiation and risk aversion cause indifference curves to be positively sloped and convex.
 
Figure: A high, moderately and slightly risk averse indifference curves.
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next up previous
Next: Efficient Set Up: On Portfolio Management Previous: On Portfolio Management
Magnus Bjornsson
1998-05-12