HML_Dur] is the holding-period return
on the HML portfolio; %[DELTA]AggDur is the percentage change in aggregate ten-year-equivalent duration outstanding; %[DELTA]FV is the percentage change in the aggregate face value of U.
Eliminating the last n-1 years before selecting an observation guarantees that the n-year holding-period return
can be computed.
Using the holding-period return
formula results in the following annual rates of return.
Consequently, financial economists and investors use a wide variety of terms to describe returns in these different contexts, such as total return, holding-period return
, annualized return, simple return, compound return, arithmetic average return, geometric average return, time-weighted return, dollar-weighted return, nominal return, real (inflation-adjusted) return, risk-adjusted return, after-tax return, taxable-equivalent return, internal rate of return, and various modified internal rate of return measures.
The expectations hypothesis would suggest that this slope is due to either (1) a persistently incorrect belief that the interest rate will begin to fall about twenty years from now or (2) a decrease in the risk premium for bonds with maturities beyond twenty years, even though the uncertainty of the holding-period return
for thirty-year bonds is greater than that for twenty-year bonds.
Under this theory, if long-term rates, such as the 7-year rate, did not fall today, then the expected holding-period return
over the next four years would be higher for those who held long-term bonds than for those who held a succession of short-term bonds throughout the period.
The investor's return could be measured as the holding-period return
over the two years:
This return (and the others we report) is calculated by computing the firm's holding-period return
and subtracting from it the holding-period return
on an industry portfolio (with daily rebalancing and excluding the sample firm) based on the firm's two-digit SIC industry, as defined by CRSP.
We calculate the total holding-period return
earned by an investor purchasing the shares of a SIP by using the first available closing market price after the initial offering date.
Our measure of long-term abnormal performance is the abnormal long-term holding-period return
and is calculated as follows:
Our measure of issuing firm abnormal post-issue l ong-run stock price performance is the holding-period return
for the issuing firm minus the holding-period return
for its reference portfolio over the same period (henceforth the portfolio-adjusted return).
We define the buy-and-hold abnormal return as the difference between the holding-period returns
of the sample and matched firms as