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C. Statistics |
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Performance
Benchmarking for PnL
This post shares
with you, gentle reader, some thoughts and considerations regarding
‘performance’ in the context of benchmarking PnL.
This post is a
follow up to yesterday’s post, which was also on the topic of ‘performance’,
though for that post, it was in the context of system runtimes, i.e., how fast
things run in a CTRM system.
Outline
1) What Are We
Talking About? Point Of View as *Consumer* Of Commodities, e.g., Cocoa Butter
2) Natural
Short
3) Need a
‘Hedge Model’
4) Point Of
View as *Producer* Of Commodities, e.g., Natural Gas wellheads
5) Periodic
Comparisons, Reporting PnL Differences
6) CTRM System
Design Considerations
1) What Are We Talking About? Point Of
View as *Consumer* Of Commodities, e.g., Cocoa Butter
Benchmarking in
this context is comparing your actual performance, i.e., the trades you really
made and the PnL (Profit and/or Loss) that you actually incurred to some other
benchmark.
Using the
stock market example, a hedge fund that picks stocks with certain characteristics
may want to compare their performance to either the S&P 500 index or to
similar type hedge funds.
The example
we’ll give is for CTRM systems and for a *Consumer* of commodities.
We will
consider the case of a firm that makes, for example, candy bars. And they are in business now and expect to be
in business for a long time.
They buy
various commodities as raw ingredients to their factory. We’ll use Cocoa Butter in our example as one
of them.
Figuring that
they’ll need to buy a certain amount of Cocoa Butter, let’s say, monthly,
‘forever’, they may decide they want to hedge their market risk.
When it comes
to market risk, we can describe two choices:
a) They can do
no market risk hedging, at least nothing formal or organized. They can simply buy the raw materials each
month at whatever the current market price is.
And perhaps
buy physical, i.e., physical purchase trades, where they agree as of the time
they did the trade to pay a fixed price for delivery at some point in the
future. E.g., monthly
deliveries and corresponding monthly (fixed) payments for the next six months.
b)
Alternately, they can decide to do hedging with derivatives, i.e., mostly futures with maybe some swaps and options.
There are
actually some special considerations for Cocoa Butter hedging, which we’ll
mention here, though it is a bit off topic… not that that has ever stopped us
before.
Consideration 1)
While Cocoa
Butter is what is used in the factory, there are no Cocoa Butter futures. Instead, they trade Cocoa Beans. Cocoa Butter is to Cocoa Beans as Unleaded
Gas is to Crude Oil. One is refined from
the other.
So, naturally,
you would expect one MT (metric ton) of Cocoa Butter to cost more than the same
weight of Cocoa Beans. The ratio of
prices is called the ‘Butter to Bean’ ratio and has historically been around 2
to 1, plus or minus a bit. E.g., with a
ratio of 2.1, if Beans are $2000/MT, then Butter would be $4200/MT.
Point here is, you need to adjust the quantity of futures that you would
buy for hedging purposes by the ratio to be properly hedged.
Consideration 2)
For Cocoa
Beans and the ‘Softs’ in general, e.g., Sugar, Coffee, only a limited number of
futures months are actively trades. March, May, July, September and December. However, your factory might run all year,
i.e., all twelve months of the year. If
you want to hedge planned/forecasted January purchases of Cocoa Butter, you’ll
want to hedge that with the March futures contract, i.e., the closest one that
exists/is actively traded.
Consideration 3)
There is
another consideration that is not special to Cocoa Beans, but we’ll mention it
anyway in the interest of completeness.
Which is that you need to convert the physical quantity that you need to
hedge, e.g., 110 MT of the physical, to the appropriate number of futures
contracts. The contract size for Cocoa
Beans is 10 MT, so if you are trying to hedge 110 MT of Cocoa Bean equivalent need, that would mean you would buy 11 MT of the futures
contracts to hedge.
An important
note on that: At some point, you’ll need
to buy the real physical Cocoa Butter so as to run your factory. When you do, you’ll need to sell out any
futures contracts you bought as hedges.
So, ultimately, for each and every hedge you added, so as to hedge the
market risk, you’ll need to reverse at some point.
2) Natural Short
For clarify,
in this example, there is no speculation.
i.e., no trades are being done for ‘for profit’ purposes. Everything is being done to hedge existing
risk that naturally arises from having a need for the raw commodity.
Such a need is
called a ‘Natural Short’. In fact, for
CTRM system purposes, you would typically enter this into the system as if it
were a ‘trade’. i.e., if you think
you’ll need 100 MT a month for the next 2 years, you can enter that into the
system as a ‘short’ (i.e., a ‘sell physical’) trade. The 100 MT in this case is just a forecasted
amount and could go up or down. Firms
might typically revise or at least double check their forecasts about once a
month.
3) Need a ‘Hedge Model’
What we mean
by ‘hedge model’, is the official, company approved
plan for market risk hedging.
Examples might
be:
a) Hedge 100%
of your market risk, as calculated by the CTRM system, going out for 4
months. And then
nothing after that.
b) Hedge 100%
of your market risk for the next three months, then 80% of your risk for the 3
months after that, then 60% for the next three months, then 40% for months 9 to
12, then nothing after that.
Note that no
firm would, or could hedge 100% of their market risk ‘out to infinity’. For firms that decide to hedge market risk,
i.e., using derivatives, they’ll need some target end date.
Side note:
Search the internet for a case study/example of an airline that hedge too far
out into the future their fuel needs.
For a time, they did OK, relative to other airlines, when fuel prices
rose. Then they did horribly bad when
fuel prices sank and other airlines, who didn’t hedge,
where able to buy/take advantage of the cheaper fuel, and so were able to
undercut their prices.
4) Point Of View as *Producer* Of
Commodities, e.g., Natural Gas wellheads
You could flip
the signs from the example above to go from a consumer of commodities to a
producer of commodities.
For a producer
example, suppose you have/own or have leased natural gas wellheads or some
source of natural gas. Your normal
business is to sell it, which can be at the current/spot market or at some
point in the future. If you sell it at a
fixed price, e.g., monthly for the next 12 months, you have locked in your
price and effectively have no market risk on that gas.
Alternately,
you can ‘sell it’ in the derivatives market, i.e., sell futures for some months
out, so as to hedge your market risk.
Then when you actually sell the physical product, you would reverse the
futures, i.e., buy them back.
As with the
consumer example, you need some plan for how this is done, which we called a
‘hedge model’, with the main parts of the plan being how much to hedge and for
what time periods.
5) Periodic Comparisons, Reporting PnL
Differences
Now that we
have established the example and that there is some ‘company approved’ hedge
model, we’ll note that in practice, traders, meaning the people doing the
market risk hedging, will typically be given some discretion.
They can
choose to hedge more or less than the approved hedge model dictates. Or they may choose to hedge in a different
month versus what the hedge model requires.
For example, if they feel the March month is too illiquid, they may
hedge the same volume in the May month (futures contracts) instead.
Now we get to
the good part of this blog post, where we tie these things together. You have these two parts:
5.1) You have
the hedge model recommendations for hedging, i.e., we are assuming that a CTRM
system is capable of providing a report that combines all existing physical,
derivatives (e.g., futures) and forecasted usage (sometimes called ‘demand’),
as well as your hedge model, e.g., 100%/80%/60%/40% for each of the upcoming 3
month periods, and shows how many futures you need to buy/sell to comply with
the hedge model rules.
5.2) And you have the actual trades that were done.
What you want,
therefore, is to see how the real trades and traders did versus the rules-based
model. Hopefully, the traders are doing
better. Otherwise, you might feel you
are better off just getting a bunch of college interns to come in and ‘blindly’
do trades (buy/sell futures) based on whatever the model produces (in the form
of a report).
You’ll
compare, e.g., weekly or monthly, the PnL of the ‘benchmark portfolio’ of
trades, i.e., a fictitious set of trades that were imaginarily booked into the
CTRM system to match the hedge model report recommendations, to the real trades
that were entered.
Ideally, a
CTRM system would allow for multiple benchmarks, i.e., multiple hedge
models. E.g., show PnL of actual trades
versus a hedge model of 100% for 4 months, and, separately, show PnL versus the
above example of 100%/80%/60%/40%.
6) CTRM System Design Considerations
6.1) A ‘cheat’ approach to benchmarking would be for a system to
actually create ‘real’ benchmark trades into the system. i.e., book futures trades, buys and sells,
into a separate trade book/portfolio called, for example, ‘Benchmark #1’. Or have a separate ‘trade status’ to indicate
that these are benchmark trades.
For this
approach, creating PnL difference reports, i.e., between the real/actual trades
and the benchmark trades would be the easy part. Since you are effectively
comparing just two sets of trades.
6.2) A better approach would be to not have to actually book and
‘fake’ trades. Instead, the system would
calculate the PnL difference between the benchmark and the real trades by
examining the daily hedge model reports to see what they recommended and
compare that to the closing prices for each day.
The advantage
of this approach is that firms can create new ‘hedge model’ parameters and
apply them, even retroactively, since you’ll always have the real trades to
work with and the other information needed, i.e., closing prices and the hedge
reports.
Also, this
approach can be better for performance of the system, since you would not need
to include hedge model trades as part of the end-of-day process.
Introduction to
CTRM
Click on this
link for a great introduction to CTRM software: Introduction to CTRM Software