年度：2017 NO： 著者：Jiro Hodoshima, Tetsuya Misawa, Yoshio Miyahara

Evaluation of performance of stocks is fundamental and
practically quite important in finance.
Normally performance of stocks is evaluated using the Sharpe ratio and information ratio
based on the first two moments of stock
returns,
showing how much excess returns stocks earned compared to the risk-free rate
and a benchmark portfolio return adjusted for their volatilities.
However, the Sharpe ratio and information ratio do not satisfy the monotonicity property.
A higher return can result in a lower Sharpe ratio.
In other words, it is possible the Sharpe ratio of $\mb$ is higher than that of $\mb$
when $\mb \geq \mb a.s.$ where $\mb$ and $\mb$ denote random variables of two financial asset
returns.
Therefore evaluation by the Sharpe ratio and information ratio is
not always appropriate for many investors.
In this paper, we present an evaluation of performance of stocks based on
a value measure using utility indifference pricing which satisfies desirable properties including monotonicity
under which a higher return always results in a higher value measure.
We compare evaluation by a value measure based on utility indifference pricing and the Sharpe ratio
using selective Japanese stock return data. The two measures are quite similar in most of the comparison results
but show different results in the two companies of Softbank and Kao
where the Sharpe ratio is higher than the value measure based on utility
indifference pricing in Softbank but the opposite is the case in Kao.
We show the evaluation by the value measure based on utility indifference pricing
is more relevant than that based on the Sharpe ratio, giving values corresponding to
those of the risk-averse value measure of the underlying performance of stock returns
rather than the first two moments of stock returns.
In particular, the evaluation by the value measure based on utility indifference pricing
depends on the entire underlying distribution of stock returns instead of the first two
moments in the Sharpe ratio so that it is not controlled by a few influential observations of stock return data.
We derive the comparison
results by assuming the underlying data of stock returns to follow discrete normal mixture
distributions.

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