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DH,
thanks so much for reposting this.
I'm re-reading Thomas Stridsman's
book and this post by Bob cuts straight
through to the core of what is needed to know.
cheers,
mike ball
--- DH <catapult@xxxxxxxxxxxxxxxxxx> wrote:
> There is no single "best" method to handle
> rollovers. Bob Fulks wrote a
> nice summary of the issues involved a while back.
>
> --
> Dennis
>
> -------- Original Message --------
> Subject: Re: Continuous vs Perpetual - which one is
> the best! - Part 1
> Resent-Date: Sun, 13 Jun 1999 13:10:18 -0700
> Resent-From: omega-list@xxxxxxxxxx
> Date: Sun, 13 Jun 1999 16:09:23 -0400
> From: Bob Fulks <bfulks@xxxxxxxxxxxx>
> To: "Omega List" <omega-list@xxxxxxxxxx>
>
> This topic comes up from time to time. Discussions
> always seem to generate
> a lot of strong opinions. When I started looking at
> futures a while back, I
> searched for a simple summary but was not able to
> find one so I have been
> collecting information over time.
>
> It is a fairly complicated issue so I decided to
> summarize all the factors
> that I am aware of in a long post. This will be
> "more than you ever wanted
> to know about back adjusting futures prices". If
> this is of no interest to
> you, please delete this message now.
>
> I would welcome other opinions so that I can improve
> this summary over
> time. This message already incorporates text from
> posts by several other
> people, especially Bob Brickey, mostly posted on the
> TradeLab list during a
> discussion of this topic of July 1998.
>
> I tried to post this earlier but it seems to exceed
> the size barrier of the
> list so I will post it in two parts.
>
> ------------------------------
>
> I. Introduction
>
> To backtest a trading system for trading futures
> contracts, we would like
> to have a long duration of price data on which to
> test our trading system.
> The problem is that futures contracts expire
> periodically and the data for
> each contract lasts only a few weeks or months. So
> we need some way to
> create a long series of price data from a sequence
> of contract prices. This
> post will discuss the various ways it can be done
> and explore the
> advantages and disadvantages of each method. My
> experience is with only the
> S&P futures contract so I will use it as an example
> although the same
> principles apply to any future contract.
>
> II. The Problem
>
> The issue arises because the pricing of a futures
> contract is slightly
> different than the price of the underlying commodity
> since it includes
> other factors. This difference is called the
> "premium". For the S&P Futures
> this difference includes the cost of interest and
> the dividends of the S&P
> stocks.
>
> The theoretical value is called the "fair value". It
> is the price at which
> investing in the underlying commodity has the same
> return as investing in
> the futures contract. For agricultural futures, the
> difference can include
> such things as storage costs, etc. For the S&P
> futures it is calculated as
> follows:
>
>
> Futures_Price = Cash_Price * (1 + d * (i - v)
> / 365)
>
> where:
>
> i = interest rate for fair value calculation =
> about 5% now
> v = dividend rate of the S&P cash index = about
> 1% now
> d = days_to_expiration
>
> At rollover, the days_to_expiration number jumps,
> causing the jump in the
> premium. With today's values, the jump in price is
> about 1%, or about 12
> points on the S&P futures contract. In the examples
> that follow, for
> simplicity, we will use the 12 points as the size of
> the jump at
> expiration, keeping in mind that the actual number
> does depend upon the
> level of the index, and interest and dividend rates.
>
> The interest rate term arises because with the
> futures contract, we are
> using leverage for which we are not paying interest.
> Thus, the cost of the
> interest gets built into the price of the futures
> contract.
>
> The dividend term arises because with futures, we do
> not get the dividends
> that we would have gotten if we had bought all the
> stocks in the S&P. (This
> is approximated as an average but since dividends
> occur at different times,
> an accurate simulation would include the exact
> expected dividends and when
> they were paid.)
>
> The actual price difference between the futures
> contract and the underlying
> can and does deviate from this theoretical value on
> a minute by minute
> basis. But the difference is usually very short
> lived because arbitrage
> players step in to buy one and sell the other and
> this activity keeps the
> relative prices closely tracking fair value. There
> are often fairly big
> differences in the reported daily "closing prices"
> since the futures
> markets close at a different time than the cash
> market and a lot can happen
> between the close of the two markets.
>
> Thus, we have a discontinuity in the price of the
> futures contract at the
> expiration that must be accounted for in some way
> for backtesting.
>
>
> III. Possible Methods
>
> The primary alternatives are:
>
>
> 1. Splice contracts together without price
> adjustment.
>
> This causes large price jumps at splice points. The
> price jumps cause two
> problems.
>
> a. They distort the operation of most trading
> indicators and automatic
> trading systems. For example a 14-day simple moving
> average would mix some
> of the prices from the old contract and the higher
> prices from the new
> contract giving a distorted picture of what is
> happening.
>
> b. They can cause large trading profits and
> losses to be included in
> backtest results that a trader would not have
> experienced in actual
> trading. For example, if our system was long one
> contract before the
> expiration and we sold after expiration, then the
> system would include the
> 12 point artificial jump in price for an apparent
> profit of 12 * 250 =
> $3000. If we didn't notice this, we might think our
> trading system was very
> profitable. Even worse, if we were optimizing the
> parameters of our trading
> system, some of the parameter values might cause us
> to hold the position
> through the transition and some might not, causing
> big discontinuities in
> the results and causing us to get false optimum
> parameter values.
>
> As a result of these problems, this method is
> unsuitable for most backtesting.
>
>
> 2. Close out trades at "roll over" to the new
> contract at expiration.
>
> This is what we have to do in real life at the end
> of
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