The author discusses the main problems associated with measuring derivatives
returns and develops a framework for performance measurement. The approach
quantifies the notional market value of futures and options. This value is then
used as the basis for performance measurement using conventional techniques. For
options, the notional market value can be calculated on a full basis (involving
detailed knowledge of option positions and hedge ratios) or on a partial basis
(in which only the market prices of the options are included). The author
advocates the use of the full exposure method whenever possible.
Measuring rates of return for derivatives offers many challenges. Futures and options are
considered separately because they have very different impacts on return distributions.
Futures have a price, which is the basis for determining gains/losses on the futures
position, but the investor is not required to pay this price on opening the contract.
Rather than a market value, futures have a net realized value, which represents the
profit or loss arising from changes in price each day. For futures, one cannot measure
return as the change in market value. Instead, the author uses the notional market value
of the futures position as the basis for return calculations. The notional market value
is the equivalent amount of a physical security that would cause the same change in net
realized value for a given change in the price of the underlying security. The notional
market value of a futures contract is calculated as the futures price multiplied by a
constant value, called the “contract multiplier” (or “tick
size”). The author measures the notional stock return (the return arising from
futures plus physical assets where appropriate) as the change in notional market value
over a period of time. For accurate results, the author must include the notional income
arising from the underlying cash, even if the cash position does not exist.
Unlike futures, options do not move in a symmetrical manner in response to movements in
the underlying security index. The factor determining the relationship between changes
in the stock price and the call option is the hedge ratio (or delta). In order to
calculate the notional market value of options, the author presents two approaches: (1)
full exposure, where the full impact of the option position is recognized as a component
of notional market value, and (2) partial exposure, where only the option value is
included in the notional market value of the option position. The full exposure approach
incorporates the full impact of the option position adjusted for the hedge ratio. The
author identifies the notional stock position, which shows an equivalent price change to
the stock/option combination for a given small change in the stock price. This approach
is similar to the approach used for futures. The full exposure method is the preferred
approach and is necessary if detailed and precise valuation and performance information
is needed at the asset level.
Under the partial method, only the stock position is adjusted to show the direct options
impact. Therefore, the hedge ratio is ignored, there are no cash adjustments, and the
return calculations are far simpler. The author values the option position at the
premium and adds it to the stock position. The author advocates the use of the full
exposure method whenever possible.