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At 8:14 PM -0800 3/28/02, Lance Fisher wrote:
>Originally, my thinking was - "Why does the risk-less rate of return
>need to be included in the calculation? Why can't we simply assume the
>risk-less rate to be a constant at any given time and, for the sake of
>simplicity, just exclude it from the calculation?"
<snip>
>...Thus the Sharpe Ratio provides the correct answer (a strategy using Y
>is preferred to one using X), while the "return information ratio"
>provides the wrong one."
This is important because the return numbers you are working with are
so small. With returns in the 30% to 50% range the error is pretty
small.
>
>This brings me to a few questions.
>
>- Should the Discount Rate or the Investment Rate be used to calculate
>Sharpe Ratio? I would assume Investment Rate, but will everyone else
>assume the same?
The usual assumption is to use the rate you would receive if you
didn't invest but left the money sitting in an account. This is
typically the T-Bill rate or the interest rate on a money-market
fund. (In some countries, the risk-free rate is much higher.)
>- Pardon my ignorance, but am I correct in assuming that the above
>posted 91 Day T-Bill rate is annualized (I can't believe the risk free
>rate is 1.854% every 3 months)?
It is annualized. It has the same value on the daily rate table...
>- Does anyone know any other reliable websites to find the current,
>correct, 91 Day T-Bill rate?
The history of the monthly rate can be found at: <http://www.stls.frb.org/fred/data/irates/tb3ms>
The history of the daily rate can be found at:
http://www.stls.frb.org/fred/data/wkly/dtb3
>- Has anyone coded a correct Sharpe Ratio calculation in EL that allows
>Risk-Free Rate to be included as an input? Would you be
>willing to share?
My new SharpeMeasure indicator (which is currently in "beta test"
with a few friends) allows for a separate data series in which you
can put the interest rate series.
>(I'm assuming that since Omega couldn't get it right in their $2000+
>program...
I figured out how TradeStation was doing the calculation some time
ago and posted an explanation and some derogatory comments. Very soon
thereafter, I was contacted my a manager at Rina Systems, the company
who wrote the code for TradeStation. We discussed the errors and the
way it should be calculated and he was very responsive. He said that
they would make the change in the software they sell and offered me a
free use of the software for a while for pointing out the error. But
he said he had no idea if or when the corrections would ever make it
into TradeStation since that was in the hands of Omega. I was
surprised at how responsive they were. It was good to see that there
are companies in this business who care about the accuracy of their
products...
>...there must be some significant pitfalls to calculating this
>correctly).
It is complicated if you want to do it accurately. I have many pages
of posts I have written on the topic if you would like to see them.
The key is how you calculate the periodic returns. The Reader's
Digest version:
If you are trading a fixed account size, as when you withdraw profits
to live on, then the perfect equity curve would be linearly
increasing vs. time and the monthly return is:
Return = (Equity_now - Equity_month_ago) / Account_size;
If you are scale-trading, as in fixed-fractional bet-sizing or
reinvesting your profits each month, the ideal equity curve is
exponentially increasing vs. time and the monthly return is:
Return = LN(Equity_now / Equity_month_ago);
For an ideal equity curve, the standard deviation of returns should
be zero resulting in an infinite Sharpe Ratio.
These are the simple cases. It gets more complicated if you trade a
fixed account size but hold a position for several months. You are
basically reinvesting profits at the end of each month until you sell
the position then you withdraw all profits.
If you are trading stocks or mutual funds, you then need to subtract
the risk-free rate you could have gotten by leaving the money in the
money market fund since you are forgoing the interest you could have
received.
If you are trading futures, you DO NOT subtract the risk free rate
since you are NOT investing your money. You are simply signing a
contract to deliver something in the future. The deposit in your
brokerage account is just a "security deposit" to protect the broker
against losses. You can even collect interest on the deposit.
Technically, buying one SP contract (BigPointValue = $250) at a price
today of about 1150 is exactly the same as:
> Borrowing 1150 * $250 = $287,500 at some interest rate
> Prepaying the interest until contract expiration date
> Buying 250 "shares" of the SPX and collecting the dividends
on the shares.
so the price of the futures contract includes the interest and
dividends in the "fair value" calculation.
Back to your original point, whether or not you include the risk-free
rate is a small error. For the OddBall system, for example, I show a
33% annualized return with about a 15% annualized standard deviation.
So whether or not you bother to subtract the 2% from the 33% is not
all that important.
Bob Fulks
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