Teaching the Concept of Investment Risk through Spreadsheet Monte Carlo Simulations

INTRODUCTIONThe concept of investment risk is a fundamental concept in finance. Students in undergraduate finance courses learn that investment risk can be quantified as the standard deviation of returns on an investment, and that there is a risk-reward tradeoff in which investments with higher returns are expected to have a correspondingly higher level of risk, in the form of higher standard deviation of returns. Those concepts are not necessarily difficult to understand. What is difficult, however, is to gain a concrete understanding of how those concepts affect investment outcomes in practice. For example, the canonical view is that higher-risk investments are more appropriate for investors who will be holding the investment for the long term, as holding for the long term can mitigate the effect of risk on investment performance. But how long exactly is "long term? " How does the variability of returns of an investment affect investment outcomes over time? How much does holding for the long term really mitigate the effects of return variability? This paper introduces a classroom activity designed to introduce students to a tool, Monte Carlo simulation, which can help them answer such questions. With Monte Carlo simulation students can build a model that allows them to observe the range of potential outcomes from an investment held for a given time period or a range of time periods, and even to estimate probabilities for given outcomes or ranges of outcomes. Using a Monte Carlo model, a prospective investor can choose an investment strategy based on the estimated probability of achieving outcomes of interest, rather than based on expected return and variability of return for a single time period.The activity is delivered as an in-class hands-on lab activity in which students analyze an investor's investment decision through a series of quantitative models, each providing the investor with more insight than the previous one. The base scenario for the lab is the decision of an investor who is planning to invest $1,000 at the beginning of each year over a 20-year time period. The investor is trying to choose between a small-cap index fund and a large-cap index fund. The investor's top priority is to have at least $30,000 in the account at the end of the 20-year investment period. Beyond that, she simply wants to maximize her wealth. At the beginning of the lab activity students are presented with historical yearly return data (1928 to 2012) for large-cap stocks, represented by the S&P 500 index, and small-cap stocks, represented by the set of stocks in the lowest quintile for market equity. Then the students are guided through the construction, interpretation, and evaluation of a series of quantitative models that could be employed to help the investor make a decision on her investment strategy. Following is a brief description of four models that may be included in the exercise:* Model 1: Use an Excel formula to calculate the value in the account after 20 years, assuming the average return for each year of the investment period. * Model 2: Use Excel to model the investment growth over the entire 20-year period, assuming the average return for each year of the investment period. * Model 3: Use Excel to build a Monte Carlo simulation based on a model of the investment growth over the entire 20-year period, modeling each year's return as a random draw from a normal distribution with known mean and standard deviation (based on the mean and standard deviation calculated from the historical data). * Model 4: Use Excel to build a Monte Carlo simulation based on a model of the investment growth over the entire 20-year period, drawing returns from random 20-year periods in the historical data.BENEFITS TO STUDENTSThe lab activity can benefit students in several ways. First, it helps students gain a better understanding of how variability in periodic investment returns can affect investment outcomes over time. …