http://clevelandfed.org/research/workpaper
Best available copy
NOTES
The one-eighth pricing convention applies to stocks priced $1.00 or
higher. The minimum recorded price movement allowed for stocks priced
between $0.50 and $1.00 is l∕16th of a dollar. The minimum price change
for stocks priced under $0.50 is l∕32nd of a dollar.
2. The minimum spread for stocks priced between $0.50 and $1.00 is $0.0625,
while for stocks priced under $0.50 the minimum spread is $0.03125.
3. This assumes that the risk-free rate of return, Rft, is measured with-
out error. The failure of this assumption should only affect estimates
of a, from regressions on equation (3).
4. The recorded-price errors may also have nonzero means if the returns are
calculated over holding periods subject to flow-supply or flow-demand
pressures (that is, E(Λmt> / 0 and E(Λpt> ½ 0).
5. Note the bias in the estimate of β can be positive because the positive
correlation between E(Λmt) and E(Λpt) violates the classical
condition Cov(Λmt ,Λpt) = 0∙ If all of the classical conditions
hold, then the bias in the β estimate would be negative.
6. Lakonishok and Smidt C181 and Thomson C291 discuss why it may be optimal
for investors to exercise tax-timing options at the end of the tax year.
7. The use of the weekly Treasury bill rate as the daily risk-free rate of
return assumes that the weekly term structure of interest rates is flat.
8. We use size and price deciles for the MV and PR portfolios in an attempt
to replicate the experiments of previous papers in this area (see [15],
[22], and [23])- Size and price quintiles are used for the SIZE, PRICE,
and MVPR portfolios to ensure adequate diversification of these port-
folios and because Chow tests fail to reject the pooling restriction for
adjacent MV (PR) deciles.
9. If an investor sells a stock for a capital gain and receives payment for
the stock in a different tax year from that of the sale, the investor has
the option to declare the sale an installment sale. This gives the
investor the option (which expires on April 15 of the year the payment is
received) of realizing the gain in the tax year the sale was made or
deferring the gain one additional year. Because trades are not settled
for five days, stocks sold for capital gains during the last five trading
days of the year qualify for treatment as installment sales. See Thomson
[29] for a more thorough discussion of the installment-sale option and
its implications for tax-gain selling at the end of the calendar year.
The Tax Reform Act of 1986 removes this option for sales of stocks and
bonds on organized exchanges.
10. Because the intercept term, a, is a projection of the regression line
onto the Y-axis, a shift in a may simply reflect a shift in the market
model β. This implies that if TOY-related slope seasonality is present
then one must be very careful in interpreting the TOY-related shifts in
intercept terms from regressions on the market model found by Keim [15]
and Rei nganum [22].