Morningstar - Q3 2021 - 66

Strategies
EXHIBIT 2
Example of the Calculation of the Morningstar Portfolio Risk Score for a Fund
Expected Return
7%
110% Equity
Base Risk Score 49.28
Morningstar Portfolio Risk Score
40% Equity
22.5% Equity
92.5% Equity
77.5% Equity
60% Equity
Fund
Asset Allocation
3
2
0.0% Equity (Cash)
0%
3
Standard Deviation
Source: Morningstar.
Emerging-Markets Fund
EXHIBIT 3
Morningstar Portfolio Risk Scores for Funds and Portfolios
U.S. High-Yield Bond Fund
Fund
U.S. Large-Cap Growth Fund
U.S. Large-Cap Value Fund
U.S.
Short-Term
Bond Fund
Conservative
Portfolio
Moderately
Conservative
Portfolio
Foreign Large-Cap Growth Fund
Emerging-Markets FundMorningstar Portfolio Risk Score
40
U.S. Short-Term Bond Fund
U.S. Intermediate-Term Bond Fund
U.S. High-Yield Bond Fund
Weighted Average of Fund Scores
Morningstar Portfolio Risk Score
Diversification Benefit
Source: Morningstar
66
Morningstar Q3 2021
˜ = F RF
W
RW
˜ + H RH
˜
W
-
W
L RL
˜
U.S. Intermediate-Term
Bond Fund
Moderate
Portfolio
114.04
100.30
104.54
141.33
8.99
20.32
59.88
Foreign Large-Cap Growth Fund
10%
Conservative
Portfolio
Moderately
Aggressive
Portfolio
80
15%
0%
0%
30%
45%
0%
38.29
27.47
10.82
Morningstar
Portfolio
Risk Score
Moderately
Conservative
Portfolio
Aggressive
Portfolio
15%
18%
Moderate
Portfolio
12% 120
0%
15%
40%
0%
57.18
46.99
10.20
22%
22%
16%
4%
0%
30%
6%
75.63
68.20
7.44
Moderately
Aggressive
Portfolio
U.S. Large-Cap Value Fund
U.S. Large-Cap Growth Fund
29%
26%
18%
6%
0%
11%
10%
88.68
84.28
4.40
40
Aggressive
Portfolio
20
160
32%
29%
19%
8%
0%
0%
12%
96.75
93.97
2.78
Calculating the Morningstar Portfolio Risk Score
The Morningstar Portfolio Risk Score takes
unsystematic risk into account by leveraging the
base asset mix to the point where the leveraged
asset mix has the same total risk of the fund
or portfolio in question. The equity allocation of
the leveraged asset mix is the Morningstar
Portfolio Risk Score.
i =1 xPi = 1, xPi ≥ 0
k =1 wk Rkt
ˆ
RPt = ∑ m
Pt
i =1 xPj Rjt
R = + + ut
RˆPt
The total risk of the fund or portfolio is:
P V P
S =
P =
RS =P
B
Let
S + u
2
2
A
RPt = ∑ NP
∑ m
6
9
12
15
18
Alignment Score
60
1
Morningstar
Target Allocation
Index Continuum
5
4
We can illustrate how the base risk score is
determined graphically using a risk/return chart.
While expected returns are not used in the
calculation of the base risk score, I assign them to
the asset classes so I can plot the Morningstar
Target Allocation Index continuum (see EXHIBIT 2 ).
The point below the continuum labeled " Asset
Allocation " shows the systematic risk and
expected return of the estimated asset mix (from
the returns-based style analysis and ) of the
fund or portfolio in question. The equity allocation
of the asset mix represented by the point on
the index continuum directly above the Asset
Allocation point determines the base risk
score. I call the asset mix at this point the " Base
Asset Mix. "
RPt = ∑ m
i =1 xPj Rjt
A
+ et
6
(the right extension). As we shall see, this
makes the range of the base risk score 0 to 110.
Consecutive pairs of asset mixes from the
extended index family can be blended to form a
continuum of asset mixes, with equity allocation
from 0% to 110%. If the systematic risk of the
fund or portfolio matches the standard deviation of
an asset mix along the continuum, the equity
allocation of the blended pair of asset mixes
is the base risk score. If systematic risk is greater
than the standard deviation of right extension,
the base risk score is 110.
denote the standard deviation of the base
asset mix. If the base risk score is less than
110, this will equal the systematic risk of the fund
or portfolio. But if the base risk score is 110,
this is the standard deviation of the rightmost
point on the Morningstar Target Allocation Index
continuum, that is, the right extension.
P RSP
B
2
AS =P
A RSP
P
2
LEVERAGE LINE

Morningstar - Q3 2021

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