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Dollar-weighted Returns for Equity Investors

Posted in Big Ideas, Individual Investing

A reader interested in the gap between time-weighted equity returns and actual dollar-weighted returns experienced by investors flagged critiques of prior studies described in:

“Returns for Investors (Rather Than Markets)”: “…the actual aggregate (timing) experience of equity investors is inferior to passive buy-and-hold stock market returns. An active approach of buying after pronounced capital outflows from the market and selling after pronounced capital inflows to the market is likely to be successful.”

“Actual Return Experience of Hedge Fund Investors”: …actual hedge fund investor return/risk experience, due to the timing of entries and exits, is much worse than that indicated by the continuously measured returns and volatilities of the funds themselves.”

The critiques of these findings are a January 2008 paper entitled “Dollar-Weighted Returns to Stock Investors: A New Look at the Evidence” by Aneel Keswani and David Stolin, and a November 2010 paper entitled “Historical Returns: Hindsight Bias in Dollar-Weighted Returns” by Simon Hayley. Using the same data considered in the first study above, along with some additional data, the authors of these critiques argue that:

In “Dollar-Weighted Returns to Stock Investors: A New Look at the Evidence”, the authors investigate the robustness of the conclusions described in the first summary above. Using the original samples for NYSE/AMEX during 1926-2002, NASDAQ during 1973-2002 and 19 country stock market indexes during 1973-2004, extensions of these samples to include more recent data and an alternative sample for UK stocks during 1975-2003, they find that:

  • The highly non-linear nature of dollar-weighted returns makes them very sensitive to aggregation both across markets and across subperiods.
  • Investor dollar-weighted experience for the 1926-2002 NYSE/AMEX sample, while underperforming buy-and-hold during the first third, actually outperforms during the last two-thirds. The average underperformance for the three subperiods is only 0.4% per year, much smaller than calculated in the prior study. The average dollar-weighted underperformance¬† across 673 overlapping 25-year intervals during 1926-2006 is also 0.4% per year, with standard deviation 0.7%.
  • For the NASDAQ sample, extending the sample period from 1973-2002 to 1973-2006 cuts the dollar-weighted underperformance relative to buy-and-hold nearly in half.
  • For the international sample, extending the sample period through July 2007 essentially eliminates the dollar-weighted underperformance relative to buy-and-hold.
  • For the newly tested UK sample, dollar-weighted investor experience actually beats buy-and-hold.

In summary, evidence from this additional testing indicates that the originally reported conclusion of underperformance associated with investor mistiming (dollar-weighted) is unreliable and misleading.

In “Historical Returns: Hindsight Bias in Dollar-Weighted Returns”, the author argues that there is hindsight bias in the original research stemming from an incorrect assumption that investors never permanently extract cash from equity investments (for example, they always reinvest dividends). The author then examines the implications of such bias. Using the original data sets for NYSE/AMEX during 1926-2002 and NASDAQ during 1973-2002, with four-year extensions of both through 2006, he finds that:

  • Only the correlation of cash distributions (e.g., dividends) with future returns affects expected terminal wealth. The correlation with past returns, as used in the original study, instead introduces a hindsight bias by retrospectively altering the weight given to those past returns. This “quit-while-ahead” bias that comes from assuming that investors reinvest all distributions is similar to that encountered when calculating the yield to maturity on bonds assuming reinvestment of premiums and is also responsible for the superior returns claimed for dollar-cost averaging.
  • About 0.95% of the previously found 1.26% per year dollar-weighted underperformance relative to buy-and-hold in the original NYSE/AMEX sample derives from this hindsight bias. Extending the sample through 2006 makes little difference.
  • For the The 1973-2002 NASDAQ sample,¬† only about 1.0% of the previously found 5.37% per year dollar-weighted underperformance relative to buy-and-hold derives from this hindsight bias. The main contributor is terrible investor timing during the dotcom boom. However, extending the sample through 2006 cuts the impact of poor timing by more than half.

In summary, evidence from this arguably more realistic alternative set of assumptions indicates that bad investor timing has actually had only modest impact on investor returns for U.S. equities overall.

Note that many analyses of investment performance across financial markets assume immediate (and frictionless) reinvestment of cash distributions, and results may well be sensitive to this assumption. As argued in the preceding critique, many investors retain dividends as cash rather than reinvest them. Moreover, as argued in the study described in “One Up on the Fed Model?”, investors in aggregate cannot fully reinvest all dividends because the market does not issue enough new shares to absorb all cash distributed.

It does seem plausible that investor mistiming concentrates in extreme period such as the dotcom boom/bust.

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