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1.
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Definition
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The
Sharpe ratio or Sharpe index or Sharpe measure or
reward-to-variability ratio is a measure of the mean return per unit
of risk in an investment asset or a trading strategy.
This
ratio was developed by William Forsyth Sharpe in 1966. Sharpe
originally called it the "reward-to-variability" ratio in before it
began being called the Sharpe Ratio by later academics and financial
professionals. Recently, the (original) Sharpe ratio has often been
challenged with regard to its appropriateness as a fund performance
measure during evaluation periods of declining markets (Scholz
2007).
Other Resources:
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2.
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Examples, Types, or
Variations
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Suppose
the asset has an expected return of 15%. We typically do not know
the asset will have this return; suppose we assess the risk of the
asset, defined as standard deviation of the asset's excess return,
as 10%. The risk-free return is constant. Then the Sharpe ratio
(using a new definition) will be 1.5 (R
= 0.15 and σ = 0.10).
As a
guide post, one could substitute in the longer term return of the
S&P500 as 10%. The risk-free return is constant. And the average
standard deviation of the S&P500 is about ±16%. Doing the math, we
get that the average, long-term Sharpe ratio of the US market is
about 0.625. But we should note that if one were to calculate the
ratio over, for example, three-year rolling periods, then the Sharpe
ratio would vary dramatically.
Other Resources:
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Stanford University:
The Ex Ante Sharpe Ratio. Let Rf represent the
return on fund F in the forthcoming period and RB the
return on a benchmark portfolio or security.
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3.
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Formula
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Since
its revision made by the original author in 1994, it is defined as:
-
![S = \frac{E[R-R_f]}{\sigma} = \frac{E[R-R_f]}{\sqrt{Var[R-R_f]}}](http://upload.wikimedia.org/math/2/0/4/20441e432e313273990a93f74d8fe424.png) ,
where
R is the asset return,
Rf is the
return on a benchmark asset, such as the risk free rate of return,
E[R − Rf]
is the expected value of the excess of the asset return over the
benchmark return, and σ is the standard
deviation of the excess return (Sharpe 1994).
Note,
if Rf is a
constant risk free return throughout the period,
![\sqrt{Var[R-R_f]}=\sqrt{Var[R]}](http://upload.wikimedia.org/math/8/c/1/8c1422654508b9c580d78e53560fdf25.png) .
Sharpe's 1994 revision acknowledged that the risk free rate changes
with time. Prior to this revision the definition was
![S = \frac{E[R]-R_f}{\sigma}](http://upload.wikimedia.org/math/4/b/8/4b8d87f14e89201e8d5cedd3d9b34bb2.png)
assuming a constant Rf.
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4.
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Related Terms
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5.
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As
Used in the Hedge Fund World
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Generally, hedge
funds have a Sharpe Ratio of 1 or greater – sometimes significantly
greater.
Other Resources:
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Enterprise Fund
Distributors:
The Sharpe ratio, developed by Nobel Laureate William Sharpe, is
a risk-adjusted measure. The higher the ratio, the better the
risk-adjusted performance.
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6.
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Applications
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The
Sharpe ratio is used to characterize how well the return of an asset
compensates the investor for the risk taken. When comparing two
assets each with the expected return E[R] against the same benchmark
with return Rf, the asset with the higher Sharpe ratio gives more
return for the same risk. Investors are often advised to pick
investments with high Sharpe ratios.
Sharpe ratios, along with Treynor ratios and Jensen's alphas, are
often used to rank the performance of portfolio or mutual fund
managers.
Other Resources:
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EIM Group:
An investment's Sharpe ratio is its return over the risk-free
rate (such as the 90-day US Treasury Bill rate) divided by its
volatility.
More…
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SuperiorInvestor.net:
Although to “Hedge” a bet is to protect against loss by betting
a counterbalancing amount against the original bet, “Hedge in
the financial world is a transaction that reduces risk.
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7.
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Misused & Abused
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Other Resources:
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Journal of Financial Planning:
Those making
the case for hedge funds based on their Sharpe ratio also fail
to consider that there are other measures of risk that are of
concern to investors.
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8.
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Additional Sources of Information
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Books
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News
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Scholarly Papers
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Back to Terms
| HEDGE FUND RISK AND OTHER
DISCLOSURES |
Hedge funds, including fund of funds (“Hedge
Funds”), are unregistered private investment partnerships, funds or
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strategies and instruments (including securities, non-securities and
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as mutual funds, including mutual fund requirements to provide
certain periodic and standardized pricing and valuation information
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carefully note the following:
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ability, sophistication/experience and willingness to bear the
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set aside strictly for speculative purposes.
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a Hedge Fund and none is expected to develop.
- A Hedge Fund may have little or no operating history or
performance and may use hypothetical or pro forma performance
which may not reflect actual trading done by the manager or
advisor and should be reviewed carefully. Investors should not
place undue reliance on hypothetical or pro forma performance.
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over the Hedge Fund.
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generally charged at the fund as well as the sub-fund levels;
therefore fees charged investors will be higher that those charged
if the investor invested directly in the sub-fund(s).
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valuation information to investors.
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various conflicts of interest.
The above general
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to any particular Hedge Fund, is subject to the more complete and
specific disclosures contained in such Hedge Fund’s respective
offering documents. Before making any investment, an investor should
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investment in the Hedge Fund is suitable for the investor in light
of the investor’s investment objectives, financial circumstances and
tax situation.
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representation is made that any fund will or is likely to achieve
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