Morningstar Magazine - April/May 2018 - 39

EXHIBIT 2

The final two ratios use different measures of
severe downside risk, and thus, we think
of them as being two related tail-risk-based
Sharpe ratios.

A Tale of Two Funds and Risk Different risk measures can have a dramatic impact
on performance rankings.

More specifically, the CVaR-based Sharpe ratio
(or simply, the CVaR ratio, also called
STARR in Rachev, Martin, and Siboulet, 2003)
measures the expected or realized average
loss conditional on the risk meeting or exceeding
a particular threshold; e.g., the worst 1st or
5th percentile.

Sequoia SEQUX

1.00

3.51

Hodges Blue Chip Equity Income HDPBX

0.72

3.08

The maximum drawdown-based Sharpe ratio, or
MDD ratio, measures the extent to which losses
are sustained. It is typically measured as the
cumulative loss from peak to trough for a period
such as three or five years. The MDD ratio is the
corresponding maximum drawdown-based Sharpe
ratio with maximum drawdown as the risk
measure. The MDD ratio was suggested by Young
(1991). It can be measured, for example, as the
average annual rate of return for three or five years
divided by the maximum drawdown for the past
three or five years.

Source: Morningstar.

Both of these tail-risk-based Sharpe ratios-the
CVaR ratio and the MDD ratio-provide a
risk-adjusted measure of return that incorporates
non-normal return characteristics. As such,
they are more relevant than the standard Sharpe
ratio when investors and asset managers care
more about downside risk, as measured by either
CVaR or maximum drawdown.
An Example on Different Rankings

Here is an example of risk rankings using two
real-world funds: Sequoia SEQUX and Hodges Blue
Chip Equity Income Retail HDPBX, which are
both U.S. equity funds. Their return distribution
statistics are summarized in the first table of
E X H I B I T 2 and computed from the five-year period
January 2011 to December 2015.
Sequoia has a higher return, a higher
volatility, and much more negative skewness
than does the Hodges Blue Chip Equity
Income fund. On the other hand, the Hodges
fund has a negative serial correlation
and a much lower maximum drawdown than
does Sequoia.

Return Summary (%)

Relative Performance Rankings (%)

Mean

Std. Dev. Skewness

Serial
MDD Correlation

Kurtosis

CVaR

-0.64

3.67

-7.73

-21.83

13.39

0.33

3.56

-5.55

-9.88

-19.02

Ranking on
MDD Ratio Sharpe Ratio

Ranking on
CVaR Ratio

Ranking on
MDD Ratio

Sharpe Ratio

CVaR Ratio

Sequoia SEQUX

0.287

0.1299

0.046

81.90

66.16

56.14

Hodges Blue Chip Equity Income HDPBX

0.234

0.1301

0.073

54.83

66.37

93.70

In the second table of EXHIB IT 2 , we rank the two
funds' performance against the U.S. equity
fund universe. The relative rank of the standard
Sharpe ratio for Sequoia is high, at the
82nd percentile. Hodges Blue Chip is lower, at the
55th percentile. The rankings on the MDD-based
Sharpe ratio are almost exactly reversed:
Sequoia is at the 56th perentile, while Hodges is at
the 94th percentile. The ranking on the CVaRbased Sharpe ratio is approximately the same for
both funds.
This example clearly illustrates that different risk
measures can have a dramatic impact on
relative performance rankings. Hodges Blue Chip
looks unattractive when compared against
the U.S. equity fund universe based on the
traditional Sharpe ratio but very attractive on the
MDD ratio. Sequoia has nearly the opposite
ranking movements.
Positive Correlation Between Volatility
and Skewness

Volatility and skewness in stocks and funds tend
to be positively correlated. In our stock and
fund universes, on a five-year rolling basis, the
average contemporaneous correlation between
volatility and skewness is positive, at 34%
for U.S. stocks (for a 50-year horizon) and 12% for
U.S. equity funds (for a 35-year horizon).
This positive correlation confirms the systematic
trade-off between volatility and skewness:
All else the same, investors like low volatility, but

unfortunately, it seems to come with a more
negative skewness, or higher crash risk. Thus, an
investment with a reasonable return and a low
standard deviation will typically look good from a
traditional Sharpe ratio perspective and less
attractive when viewed through a tail-risk-based
Sharpe ratio.
Quantify Performance Ranking Variation

Investors' preferences for different aspects of risk
should influence their choice to use the standard
Sharpe ratio or one of the tail-risk-based
Sharpe ratios, given that the measures lead to
different rankings and, thus, different implications
on performance evaluation, fund flows,
and asset allocation. Building on our two-fund
comparison above, we examine the ranking
variation distribution from a much larger sample
for both individual stocks and equity funds.
For a given five-year horizon, we rank all funds on
the realized standard Sharpe ratio. We then
separately rank all funds on the realized tail-riskbased Sharpe ratios (either CVaR ratio or MDD
ratio). We then compute the ranking difference for
each fund by subtracting the standard Sharpe ratio
ranking from the CVaR/MDD ratio ranking. For
example, if a fund is ranked at the 60th percentile
with the standard Sharpe ratio and the 50th
percentile with the CVaR ratio, the ranking
percentile change or variation of the CVaR ratio
relative to the standard Sharpe ratio will be
negative 10 percentage points (i.e., a downgrade
by 10 percentage points).

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Table of Contents for the Digital Edition of Morningstar Magazine - April/May 2018