STOCHASTIC

20 THE REVIEW OF ECONOMICS AND STATISTICS
chase (hi > 0), the return will be simply hit.
For reasons which will be clear immediately however,
we write this in the form:
(4a) kti = h (ft -r*) + |fc| r*.
Now suppose that \ht | is invested in a short
sale (hi < o), this gross investment being equal
to the price received for the stock. (The price
received must be deposited in escrow, and in
addition, an amount equal to margin requirements
on the current price of the stock sold must
be remitted or loaned to the actual owner of the
securities borrowed to effect the short sale.)
In computing the return on a short sale, we
know that the short seller must pay to the
person who lends him the stock any dividends
which accrue while the stock is sold short (and
hence borrowed), and his capital gain (or loss)
is the negative of any price appreciation during
this period. In addition, the short seller will
receive interest at the riskless rate r* on the
sales price placed in escrow, and he may or may
not also receive interest at the same rate on his
cash remittance to the lender of the stock. To
facilitate the formal analysis, we assume that
both interest components are always received by the
short seller, and that margin requirements are
ioo%. In this case, the short seller's return per
dollar of his gross investment will be (2r*— r