The Mathematics of Financial Modelingand Investment Management

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2-Financial Markets Page 63 Wednesday, February 4, 2004 1:15 PM


Overview of Financial Markets, Financial Assets, and Market Participants 63

transaction costs of entering into and closing the cash position as well
as round-trip transactions costs for the futures contract that do affect
the theoretical futures price. Transaction costs widen the boundaries for
the theoretical futures price.
In the strategy involving short-selling of the underlying asset, it is
assumed that the proceeds from the short sale are received and rein-
vested. In practice, for individual investors, the proceeds are not
received, and, in fact, the individual investor is required to put up mar-
gin (securities margin not futures margin) to short-sell. For institutional
investors, the asset may be borrowed, but there is a cost to borrowing.
This cost of borrowing can be incorporated into the model by reducing
the yield on the asset.
In our derivation, we assumed that only one asset is deliverable.
There are futures contracts, such as the government bond futures con-
tract in the United States and other countries, where the short has the
option of delivering one of several acceptable issues to satisfy the
futures contract. Thus, the buyer of a futures contract with this feature
does not know what the deliverable asset will be. This leads to the
notion of the “cheapest to deliver asset.” It is not difficult to value this
option granted to the short.
Finally, the underlying for some futures contracts is not a single
asset but a basket of assets, or an index. Stock index futures contracts
are an example. The problem in arbitraging these futures contracts on
an index is that it is too expensive to buy or sell every asset included in
the index. Instead, a portfolio containing a smaller number of assets
may be constructed to “track” the index. The arbitrage, however, is no
longer risk-free because there is the risk that the portfolio will not track
the index exactly. All of this leads to higher transaction costs and uncer-
tainty about the outcome of the arbitrage.

The Role of Futures in Financial Markets
Without financial futures, investors would have only one trading loca-
tion to alter portfolio positions when they get new information that is
expected to influence the value of assets—the cash market. If economic
news that is expected to impact the value of an asset adversely is
received, investors can reduce their price risk exposure to that asset. The
opposite is true if the new information is expected to impact the value
of that asset favorably: an investor would increase price-risk exposure
to that asset. There are, of course, transaction costs associated with
altering exposure to an asset—explicit costs (commissions), and hidden
or execution costs (bid-ask spreads and market impact costs).
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