Measuring gaps between hypothetical investment returns and actual investor returns

Actual investor returns from mutual funds lag behind those same funds’ hypothetical investment returns based on a fixed initial investment and reinvestment of all distributions.  This gap between actual investor returns and hypothetical investment returns arises from behaviorally driven errors in timing.  By chasing recent returns and abandoning funds at any sign of weakness, actual investors buy high and sell low.

Persistent gaps between actual investor returns and hypothetical investment returns expose a deep flaw in portfolio theory's mechanical reliance on simple mean-variance optimization.  To provide complete guidance to fiduciaries who must prudently manage investments entrusted to them, financial regulators should develop and enforce sophisticated measures of the impact of investor behavior on portfolio-wide performance.

This paper seeks to formalize the definition of the behaviorally driven investor gap and to correlate that gap to downside and upside volatility specific to each financial instrument.  This paper proceeds in three parts:

First, objectives: This paper will formally define the investor gap as the net reduction (or increase) in a publicly traded, open-ended mutual fund's internal rate of return based on net cash flows in and out of that fund, relative to the hypothetical rate of return that would have been realized by an investor who left undisturbed an initial investment in that fund and reinvested all dividends and capital gains distributions.  The resulting investor gap will be named psi, after the Greek letter representing psychology (ψυχή + λογος).

Second, data and methods: After calculating psi, this paper will correlate the magnitude of each mutual fund's investor gap to that fund's upside and downside volatility.  Using diverse but related measures of financial volatility (Sortino, omega, and kappa), this paper will compute the upper and lower partial moments of the distribution of returns for each mutual fund.  This paper will repeat its analysis for different target returns: zero, background inflation, and the broad market of publicly traded securities.  This paper will also compare cash flow-adjusted returns on mutual funds with the Chicago Board Options Exchange’s VIX index as a broad gauge of market-wide volatility.

Third, expected results:  I hypothesize that psi will correlate with downside and upside volatility specific to individual securities.  I expect to find significant gaps in investor performance attributable not only to downside fear, but also to upside greed. I further hypothesize that fund-specific gaps in investor performance will be more pronounced than the impact of overall, market-wide volatility.