and exciting new products. He discusses how short-sale constraints might
explain the diversification discount; our firms are extreme examples of such
discounts.
One potentially confusing aspect of short sales is that the cost for those
borrowing the stock is income for those lending the stock. Thus it is not
quite accurate to say that only an irrational investor would buy an over-
priced stock. A rational investor might be willing to buy an overpriced
stock if he can derive sufficient income from lending it to short-sellers. On
the basis of this fact, one might be tempted to conclude that the situation
we observe is therefore “rational,” since rational investors are willing to
buy the subsidiaries. Along these lines, one could argue that the observed
returns for Palm, for example, are not a “real” return since the true return
should include the income from lending (reflecting the convenience yield or
dividend from securities lending) and that the “marginal” investor sets the
traded price to embody all income generated by the shares.
Such an interpretation would be a mistake. It is important to recognize
that irrationality, or at least some nonstandard phenomena causing
downward-sloping demand curves for stocks, is a crucial element to any
explanation of the facts we are studying. Consider the following example.
A firm, consisting of $100 in cash, issues 100 shares. The firm will liquidate
tomorrow, and each share will pay a liquidating dividend of $1.00. These
shares are issued and sold by auction to investor I, who buys all 100 shares
directly from the firm. Investor Imistakenly believes that the shares will
pay out $2.01 tomorrow and “wins” the auction with a bid of $2.00 per
share. It is clear in this example that investor Ihas overpaid for the shares
and that $2.00 is a “real price.”
Now suppose that two other investors, Yand Z, enter the market. In-
vestor Ybuys all 100 shares from the firm for $2.00 and lends them to Z.
Investor Zpays Ya fee of $1.00 for each share lent and sells the shares to I
for $2.00. Now in this example, Yand Zare both acting rationally. How-
ever, there is no sense in which Yand Zare the “marginal” investors that
set prices. Investors Yand Zwould be just as happy with a price of $200
per share (and a corresponding loan fee of $199). It is the willingness of in-
vestor Ito overpay that sets the price of the shares. The price of $2.00 is a
real price, and the firm should rationally respond to the mispricing by issu-
ing more shares. The fact that Yand Zare intervening actors between the
firm and the owner is irrelevant in this example.
The number of shares not lent out must equal the number of shares out-
standing; it is always true that someonehas to own the shares issued by the
firm; not all owners can lend their shares. If the firm issues 100 shares, exactly
100 shares have to be owned by someone who is not lending them out. Thus
it is not an empirical issue whether the owners of Palm lent out their shares or
not, but rather a simple identity: $2.5 billion worth of shares were owned by
investors who were not receiving any lending income from their shares.
150 LAMONT AND THALER