On the Individual Expectations of Non-Average Investors

An “average investor” is an investor who has “average risk aversion”, “average expectations” on the market returns and should invest in the “market portfolio” (this is, according to the Capital Asset Pricing Model, the best possible portfolio for such an investor). He is compared with a “non-average investor”. This—in our setting—is an investor who has the same “average risk aversion” but invests in other investment strategies, for example options. Such a “non-average investor” must consequently have expectations on the market return that are different from the average: the “non-average expectations”. In this paper we give an explicit formula for the “non-average expectations” in an arbitrary N-step model and for the extended concept in a BlackScholes model, in the path-independent case and in the path-dependent case. Further we explicitly classify all the investment strategies for which the resulting “non-average expectations” show this mean aversion property. Various examples are given in the paper. These investigations were part of more general investigations initiated by an investment company carrying out certain subtle option trading strategies.