Morningstar Magazine - June/July 2018 - 63

EXHIBIT 1

Asset Allocation of the Five Morningstar Target Risk Indexes The table also includes two 'extensions' of the index family:
Ultra Conservative and Ultra Aggressive to create a more complete risk spectrum.
Extension (%)

Morningstar Target-Risk Index Family (%)

Extension (%)

Ultra Conservative

Conservative

Moderately
Conservative

US Large-Cap Stocks*

0.00

9.00

17.00

23.00

29.50

35.00

40.53

US Mid-Cap Stocks*

0.00

3.00

6.50

11.00

14.50

16.50

19.11

US Small-Cap Stocks*

0.00

1.00

3.00

3.50

5.50

8.00

9.26

Dev Mkts ex-US Stocks

0.00

5.00

9.00

14.50

19.50

23.50

27.21

Emerging Mkt Stocks

0.00

2.00

4.50

7.00

10.00

11.00

12.74

REITs

0.00

0.00

0.00

1.00

1.00

1.00

1.16

Commodities**

0.00

0.00

0.00

0.00

0.00

0.00

0.00

Global Ex US Govt Bond

3.75

3.00

0.00

0.00

0.00

0.00

0.00

Emerging Mkt Bonds

8.75

7.00

6.00

5.00

3.00

1.00

0.00

TIPS***

6.25

5.00

4.00

2.00

0.00

0.00

0.00

LT Core Bonds

7.50

6.00

5.00

3.00

2.00

0.00

0.00

IT Core Bonds

49.38

39.50

31.50

23.50

12.00

4.00

0.00

ST Core Bonds

21.88

17.50

12.50

5.50

3.00

0.00

0.00

Cash

2.50

2.00

1.00

1.00

0.00

0.00

-10.00

Total Equity Allocation

0.00

20.00

40.00

60.00

80.00

95.00

110.00

0

1

2

3

4

5

6

Asset Class

Risk Score

Moderate

Moderately
Aggressive

Aggressive

Ultra Aggressive

Source: Morningstar.
* Rollup of value, core, and growth.
**Although commodities are not included in the Morningstar Target Risk Indexes, they are an asset class in the returns-based style analysis.
***Rollup of long-term and short-term.

Run Returns-Based Style Analysis
Sharpe (1988, 1992) developed returns-based
style analysis as a method of estimating how much
exposure a fund has to various asset classes.1
Sharpe's model is very much like a time-series
regression model.
As with a time-series regression, the risk-scoring
engine estimates the asset-class exposures
from a time series of returns on the fund or
portfolio composite and the time series of returns
on the asset-class indexes listed in E X H I BI T 1
over the past 48 months. The estimation procedure
minimizes the empirical variance of the residuals.
What makes returns-based style analysis different

from conventional regression is that it typically
imposes constraints on the asset-class exposures:
All asset-class exposures are non-negative,
and the asset-class exposures must sum to 100%.
These constraints mean that the asset-class
exposures can be interpreted as weights
on a long-only portfolio of the asset-class indexes,
which, in turn, can be interpreted as a
custom multi-asset-class benchmark for the
fund or portfolio.
How useful the results of the returns-based style
analysis are depends on how well the custom
benchmark explains the returns on the fund or

portfolio composite. This is measured by
the R-squared of the model. It is the square of the
correlation between the returns on the fund or
portfolio composite and the return on the custom
benchmark. The risk-scoring engines use the
R-squared as a diagnostic tool to determine if the
fund or portfolios' returns are driven primarily
by asset-class exposure. If the R-squared is at least
85%, the fund or portfolio passes this test.
Calculate the Risk Score and the Misfit Risk
If the results of returns-based style analysis pass
the R-squared test, the engine calculates the risk
score and misfit risk. The risk score is based
on an extended version of the target-risk indexes.

1 This discussion of returns-based style analysis is based on Kaplan (2017).

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Table of Contents for the Digital Edition of Morningstar Magazine - June/July 2018
