Abstract
This paper extends the mathematics developed by Merton (1972) to the limiting investment opportunity set as smaller risk assets are added. Investment opportunity sets of risky assets are well-known to be described by hyperbolae in mean-standard deviation space. In practice, the asset classes in portfolios may vary from high risk common stocks to near cash assets. Low variability assets change the appearance of the investment opportunity set to the extent that a unique optimum risky asset portfolio disappears. The limiting result is similar to the investment opportunity set that arises when two assets are perfectly correlated. The location of the IOS is shown to mathematically depend upon the level of the riskless interest rate and one slope parameter. The slope parameter is estimable, using a finite number of assets, and represents a bound on market Sharpe ratios.
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Korkie, B., Turtle, H. A Note on the Analytics and Geometry of Limiting Mean—Variance Investment Opportunity Sets. Review of Quantitative Finance and Accounting 9, 289–300 (1997). https://doi.org/10.1023/A:1008235701596
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DOI: https://doi.org/10.1023/A:1008235701596