Lottery tickets are risk-free ???

In business school we were taught a formula that can be used to determine the expected return on an asset.  It is called the Capital Asset Pricing Model (“CAPM”) and the equation is as follows:

Ra = Rf + βa(Rm – Rf)

where Ra is the expected return on the asset; Rf is the risk-free rate (i.e. 30-year government bond); Rm is the expected return of the market (i.e. S&P 500); and βa is the correlation of the asset’s return to the market’s return.

The beta (βa) of an asset is usually positive, indicating that when the overall market performs well, the asset also performs well; and when the overall market performs poorly, the asset also performs poorly.  Some industries possess negative betas, such as precious metals.  In this case, when the overall market performs well, the asset does poorly; and when the market goes down, the asset does well.

Yesterday I bought a lottery ticket just for fun.  I got to thinking that the beta of that lottery ticket is zero.  There is absolutely no correlation between my return on that lottery ticket and the return on the overall market.  According to the CAPM equation, my expected return on the lottery ticket should thus be the risk-free rate (which these days is trending close to 3%).  Obviously it is not, and thus the CAPM equation shows its limitations.

Securities that exhibit a zero or low beta are treasury bonds and staple stocks such as Clorox, Anheuser-Busch and Philip Morris.


One Response to “Lottery tickets are risk-free ???”

  1. Jim Says:

    HAHAHA! I like this! I shall take it to my Corporate Finance class next week!


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