In their examination of the aggregate DE in the LDB dataset, the following sections will use the PGR and PLR ratios introduced in Odean (1998), with two important differences. Odean’s method only counted paper gains and losses on days when the investor sold at least one other position in their portfolio. Here, all days during the holding period of a position on which it is not sold will be counted.8 The criteria for a position representing either a
paper gain or a loss are the same: it is a paper gain if the daily low price is above the purchase price, and a paper loss if the daily high price is below the purchase price. Hence there will be days during the holding period where the position is neither a paper gain nor loss, and it will not contribute to any of the DE components i.e. PGR or PLR.
There are arguments on both sides for which method best reflects the con- ditions under which investors were making their decisions at the time. On a day when an investor sells a position, it is reasonable to assume they also checked the current price of their other positions. Hence the presence of a sale on that day provides the strongest signal that they considered selling a position but decided not to. However, there are also likely to be days when an investor checks the price of stocks they hold but takes no action. These days would not be counted when using Odean’s method, but would by the method used here.
It is not clear which total will best reflect the number of days when an investor was aware of the price of a stock they held and chose not to sell. During the 1990s, the time in which the LDB data was collected, stock prices were available in print, by telephone, on TV channels and later, via the Internet9. So investors who wanted to know the current status of their
8To be precise, ’all days’ means U.S. business days i.e. days on which it was possible
to trade stocks.
9The majority of actual trading in this dataset was conducted via telephone, but with
positions would easily have been able to do so. Counting all days during the holding period also follows the general principle in statistics of using as much information as possible in any analysis that is being done.
The second difference is that, unlike in Odean’s method, sales of a position that occur when an investor holds no other positions at the time will be included in the counts of realized gains and losses. An investor holding only one position is a common occurrence in this dataset, and making this change doubles the number of sales that are recorded in total (from ∼315,000 to
∼630,000). These two changes bring the method more in line with more recent survival analysis approaches using PH regression models, such as in Feng and Seasholes (2005) and Barber and Odean (2011). The connection with survival analysis methods will be discussed in section 1.8. In these models the units of analysis are the holding periods of stock positions. The holding period of a position is the number of days from the date of purchase until the position is sold, hence recording paper gains and losses on all days during the holding period of a position makes a count based method more comparable to results from a PH regression model.
Together these changes greatly increase the number of investors and stocks that contribute to the aggregate DE components. An investor or stock contributes to the aggregate DE when positions held by the investor, or in the stock, add to at least one of the four DE components i.e. realized gains/losses or paper gains/losses. Under Odean’s original scheme, 28,450 investors make a contribution to the aggregate DE, compared to 62,473 investors in the modified scheme. Amongst stocks, 2,299 make a contribution in the original scheme and 9,812 do after the modification.
For a disposition effect score, the ratio of PGR and PLR will be used
DE = PGR
PLR (1.3)
If this ratio is greater than 1 then there is a disposition effect i.e. investors take a greater proportion of their opportunities to sell for a gain than for a loss.
To compare the original Odean scheme with the modified version, this score can be computed for all stocks traded in the dataset. In both cases, for it to be possible to compute a score a stock must have at least one realised loss, otherwise PLR, the denominator of the score, would be zero.10 This restriction means it is possible to compute both scores for only 2,031 stocks. For this set of stocks, the Pearson correlation between the two scores is 0.62 and there is agreement in 75% of cases as to whether there is a DE (score > 1) or not.