Statistics Papers

Document Type

Journal Article

Date of this Version


Publication Source

The American Statistician





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Students who are new to Statistics and its role in modern Finance have a hard time making the connection between variance and risk. To link these, we developed a classroom simulation in which groups of students roll dice that simulate the success of three investments. The simulated investments behave quite differently: one remains almost constant, another drifts slowly upward, and the third climbs to extremes or plummets. As the simulation proceeds, some groups have great success with this last investment – they become the “Warren Buffetts” of the class, accumulating far greater wealth than their classmates. For most groups, however, this last investment leads to ruin because of its volatility, the variance in its returns. The marked difference in outcomes surprises students who discover how hard it is to separate luck from skill. The simulation also demonstrates how portfolios, weighted combinations of investments, reduce the variance. Students discover that a mixture of two poor investments emerges as a surprising performer. After this experience, our students immediately associate financial volatility with variance. This lesson also introduces students to the history of the stock market in the US. We calibrated the returns on two simulated investments to mimic returns on US Treasury Bills and stocks.

Copyright/Permission Statement

This is an Accepted Manuscript of an article published by Taylor & Francis in The American Statistician on 01 Jan 2012, available online:


geometric mean, long-run return, portfolio, volatility drag



Date Posted: 27 November 2017