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Abstract:
Market risk can be easily reduced through diversification due to the covariance of the assets. This reduces the overall risk, while maintaining returns, thus achieving the rationale investor's dual goal of maximum returns and minimal risk. Determining the number of assets required to reduce the risk has been long debated. Adding more assets to the portfolio reduces firm specific risk. The downside of adding additional assets is the increased associated trading costs. As a result, investors will want a limit of how many assets to include in their portfolio to gain the optimal level of reduced risk while simultaneously reducing excess trading costs. Most industry professionals estimate a number of assets ranging from 20-30 in a portfolio to reduce the market risk. We seek to test this theory by simulating various portfolios from the S&P500. From the S&P500, 100 individual random portfolios holding 10, 25, 50, 100 and 150 stocks were generated from the years from 1997 - 2016. Each of the portfolios generated returns and standard deviation of returns of the portfolio. These returns and risk metrics were then compared with the overall S&P500. We found the optimal portfolio had 25 stock positions.
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