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Hello,
The latest postings on the Sharpe Ratio got me thinking about a question
I've had for awhile on this issue.
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?"
After Googling for "William F. Sharpe", I found his website.
www.wsharpe.com
Which led me to this...
"For example, consider the choice of a strategy involving cash and one
of two funds, X and Y. X has an expected return of 5% and a standard
deviation of 10%. Y has an expected return of 8% and a standard
deviation of 20%. The risk-less rate of interest is 3%. According to the
ratio of expected return to standard deviation, X (5/10, or 0.50) is
superior to Y (8/20, or 0.40). According to the Sharpe Ratios using
excess return, X (2/10, or 0.20) is inferior to Y (5/20, or 0.25)...
...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."
So, having been freshly convinced of the value of incorporating the
risk-free rate into the calculation, I went on a search to find out just
what the risk-free rate is at this very minute. The 90 day T-Bill rate
is apparently the preferred measure for risk free rate in this context,
so I attempted to find out what this rate is right now. My search
yielded slightly different answers from website to website.
The one I would place most faith in is...
www.publicdebt.treas.gov/servlet/OFBills
Which said...
91 Day T-Bill (Issued 3/28/02) - Discount Rate%: 1.820. Investment
Rate%: 1.854.
Sorry for the length of this post, but based on the variability of the
"risk-free rate" information that I found, I can't help but be skeptical
of any claim of a particular Sharpe Ratio for any given system if the
assumed "risk-free rate" is not provided along with the performance
result.
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?
- 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)?
- Does anyone know any other reliable websites to find the current,
correct, 91 Day T-Bill rate?
- Has anyone coded a correct Sharpe Ratio calculation in EL that allows
Risk-Free Rate to be included as an input? (I'm assuming that since
Omega couldn't get it right in their $2000+ program there must be some
significant pitfalls to calculating this correctly). Would you be
willing to share?
Thanks in advance for any replies.
-Lance
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