Academic journal article Quarterly Journal of Finance and Accounting

# Aggregation and Dollar-Weighted Returns Issues

Academic journal article Quarterly Journal of Finance and Accounting

# Aggregation and Dollar-Weighted Returns Issues

## Article excerpt

Introduction

This paper reexamines the relationship between buy-and-hold or geometric mean returns (GM) and aggregate dollar-weighted returns (DWR) following the methodology used by Dichev (2007). Dichev (2007) discusses how investors' actual returns are determined by both the returns on securities and the size and timing of investors' investment flows. Dichev's (2007) study explicitly recognizes this difference and attempts to develop a new, more accurate measure of stock investors' actual historical returns by applying the concept of DWR. DWR has been extensively discussed in the literature, including Bodie, Kane and Marcus (1996), Zweig (2002) and Johnston, Hatem and Carnes (2010). When cash inflows/outflows are present, the result that DWR and GM will differ is well known. However, Dichev (2007) uses DWR in a unique way: to systematically evaluate historical stock returns in aggregate. That is, Dichev attempts to determine if the DWR and GM differ for investors in aggregate. To our knowledge, Dichev (2007) is the first paper that attempts to combine aggregation and DWR.

To address the difficulty of obtaining accurate measures of capital flows caused by their case specificity, Dichev (2007) proposes a solution using market capitalization and the total value weighted return. Using monthly data he calculates capital flows as:

Distributions = [d.sub.t] = [MV.sub.t-1] (1+[r.sub.t]) - [MV.sub.t] (1)

where MV is market capitalization and r is the return on the index. A positive distribution means capital flows from companies in the index to investors during that period. A negative distribution means capital flows from investors to the companies in the index. In the DWR calculation, the beginning market value of the index and capital inflows are given a negative sign and the ending market value of the index and capital outflows are given a positive sign.

Using this measure, Dichev concludes that DWR are systematically lower than GM. He suggests that poor timing of investor capital flows drives these results. However, in response, Keswani and Stolin (2008) demonstrate that the results are not statistically robust and that there is little evidence that the performance gap between GM and DWR is of the size reported by Dichev. However, other studies using similar methodologies have found significant differences between the GM and DWR that are in line with the findings of Dichev. Freisen and Sapp (2007) find the GM return to be 1.6% higher than the DWR on an annual basis for U.S. mutual funds. Examining U.K. mutual funds, Clare and Motson (2010) find a difference of 0.8%, and Dichev and Yu (2011) report a difference of 3.6% for hedge funds. Overall the literature suggests that in aggregate, the effects of bad investor timing have been significant.

Hayley (2014) breaks down Dichev's results into two components: a timing effect and a hindsight effect. In essence, he demonstrates that distributions and injections of funds reweight the monthly returns in the DWR calculation. Reweighting future returns is a timing effect, while reweighting past returns is a hindsight effect. Hayley derives a method to quantify and remove the hindsight effect and demonstrates that very little of the difference in returns found in Dichev's (2007) study is due to market timing.

This study focuses on the findings of Dichev (2007) and Hayley (2014). In Section 2, it is demonstrated that Dichev's results are driven principally by differences in the beginning and ending portfolio balances. This is contrary to Dichev's claim that "varying capital exposure over time is insufficient to create differences between buy-and-hold and dollar-weighted returns" (388) and Hayley's claim that dollar-weighted returns are low, and, thus, the differences (GM -DWR) are significant because aggregate investor flows reflect past returns rather than future returns.

The third section presents simulations illustrating problems with Hayley's methodology. …

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