3.3. THE LAW OF ONE PRICE FOR SPOT EXCHANGE QUOTES 93
Figure 3.9:What’s shortselling?
In a shortsale you hope to be able to buy low and
sell high, but with the selling preceding the
buying, unlike in a long position. Thus, a
shortseller hopes to make money from falling
prices rather than from rising prices.
In markets with delivery a few working days
later, you can always go short for a few hours:
sell “naked” in the morning, for instance, and
then buy later within the same day so as to be
able to deliver n days later.
For longer horizons one needs more. In the
case of securities, shortselling then requires
borrowing a security for, say, a month and sellingit now; at the end of the month you then buy back
the number of securities you borrowed and
restitute them to the asset lender, including
dividends if any were paid out during that period.
For currencies, longer-term shortselling can be
done by just borrowing forex and selling it, hoping
to be able to buy back the forex (including
interest) later at a lower price. If there is a
forward market, lastly, going short is even easier:
promise to deliver on a future date at a price that
is fixed now. If prices have dropped by then, as
you hope, you'll be able to close out (buy spot)
cheaply and make money on the forward deal.asset at 1.2135 and buy a perfect substitute at 1.2133, netting 0.0002 per unit
right now and no net cash flow atT. Such transactions are called arbitrage. These
arbitrage transactions generate an excess supply of the overpriced asset and an excess
demand for the underpriced asset, moving the prices of these two assets towards
each other. In frictionless markets, this process stops only when the two prices are
identical. Note that apart from the arbitrage gain, an arbitrage transaction does
not lead to a change in the net position of the arbitrageur; that is, it yields a sure
profit without requiring any additional investment.
The second mechanism that enforces the Law of One Price is shopping around.
Here, in contrast to arbitrage, investors do intend to make particular changes in
their portfolios. Shopping around has to do with the fact that, when choosing
between different ways of making given investments, clever investors choose the
most advantageous way of doing so. Therefore, when choosing between assets with
identical cash flows, investors buy the underpriced assets rather than the more
expensive ones. Likewise, when choosing which assets to sell, investors sell the
overpriced ones rather than the ones that are relatively cheap. This demand for the
underpriced assets and supply of the overpriced ones again leads to a reduction in
the difference between the prices of these two securities.
Although the arbitrage and shopping-around mechanisms both tend to enforce
the Law of One Price, there are two differences between these mechanisms.
- First, an arbitrage transaction is a round-trip transaction. That is, you buy
and sell, thus ending up with the same position with which you started. As
arbitrage requires a two-way transaction, its influence stops as soon as the price
difference is down to thesumof the transactions costs (buying and selling).
In contrast, in shopping around one wishes to make a particular transaction,