Morningstar Magazine - April/May 2018 - 41

MDD ratios. On the other hand, the highestvolatility quintile experiences an upgrade by about
2 to 3 percentage points. The t-statistics
suggest that the downgrades or upgrades are
more significant in stocks than those in
equity funds.
Beyond Mean Variance

Performance measures and their relative
ranking have an impact on a wide range of
investment-related decisions. Asset returns are not
normally distributed, and investors and asset
managers typically care most about downside risk,
which renders the standard Sharpe ratio an
inadequate performance measure. Moreover,
lower-volatility stocks and equity funds tend to
have lower or negative skewness, which makes an
economically meaningful case to call for
performance measures such as tail-risk-based
Sharpe ratios. It suggests that stocks and
funds that have relatively higher rankings based
on the standard Sharpe ratio can at the same time
have relatively lower rankings based on tail-risk-

based Sharpe ratios. Therefore, investors
should look beyond mean variance to evaluate
low-volatility stocks and funds. For an individual fund, a more negative skewness coupled
with a more positive serial correlation can
significantly lower the fund's MDD ratio ranking.
Stocks or funds in the lowest-volatility
quintile are on average experiencing a ranking
downgrade of about 2 to 3 percentage points
when the standard Sharpe ratio is switched
to the tail-risk-based Sharpe ratios. On the other
hand, the highest-volatility quintile is experiencing
an upgrade of about 2 to 3 percentage points.
The ranking variation, however, can be as high as
50 percentage points for an individual fund. K
James X. Xiong, Ph.D., CFA, is head of scientific investment
research with Morningstar Investment Management.

Optimal Portfolios and Extreme Risk Management."
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Sharpe, W.F. 1966. "Mutual Fund Performance." Journal of
Business, Vol. 39, No. 1, pp. 119-138.
Sharpe, W.F. 1994. "The Sharpe Ratio." Journal of Portfolio
Management, Vol. 21, No. 1, pp. 45-58.
Sortino, F.A. and Hopelain, D. 1980. "The Pension Fund:
Investment, or Capital Budgeting Decision?" Financial
Executive Magazine, Vol. 48, pp. 21-23.
Treynor, J. 1965. "How to Rate Management of Investment
Funds." Harvard Business Review, Vol. 43, No. 1, pp. 63-75.
Young, T.W. 1991. "Calmar Ratio: A Smoother Tool." Futures,
Oct. 1, p. 40.
Note
A longer version of the paper was published in The Journal
of Portfolio Management, Winter 2018, Vol. 44, No. 3, pp.
114-125. http://jpm.iijournals.com/content/44/3/114?etoc

Thomas M. Idzorek, CFA, is chief investment officer-retirement with Morningstar Investment Management. He is a
member of the editorial board of Morningstar magazine.
References
Rachev, S., Martin, D., and Siboulet, F. 2003. "Phi-Alpha

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