where [Ret.sub.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.S.
The randomly selected return and the next n-I consecutive returns are then used to compute the compounded n-year holding-period return
. Since the n-year returns are computed from consecutive annual returns, correlation across time in the returns is preserved.
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.
The holding-period return
could be computed for each year individually.
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:
We define the buy-and-hold abnormal return as the difference between the holding-period returns
of the sample and matched firms as
Obviously, if people had perfect foresight about future short-term interest rates, holding-period returns
would necessarily be equalized through arbitrage.
The data for bonds are monthly holding-period returns
rather than daily returns in view of the fact that bonds tend to be much more thinly traded than common stocks, making their precise market value on any given day somewhat uncertain.