ř ě
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.
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•
•
•
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𝜌 = 0
𝜌 = +1 𝜌 = −1
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𝛽
0𝑎𝑛𝑑 𝛽
1)
(𝑒
𝑖𝑎𝑛𝑑 𝜀
𝑖) 𝑅
2)
22
𝑥 = 0.
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𝑅
2= 1
𝑋
𝑖𝑅
2•
•
•
•
•
•
26
𝜌
𝑥𝑦=
𝑐𝑜𝑣(𝑥,𝑦)𝜎𝑥∗ 𝜎𝑦
[
1 𝜌
1,2𝜌
1,3𝜌
2,11 𝜌
2,3𝜌
3,1𝜌
3,21
]
27
28
•
•
•
29
𝑥 < µ − 3𝜎, µ + 3𝜎 > 𝑥
〈𝑥̃
0.25− 1.5𝐼𝑄𝑅, 𝑥̃
0.25− 3𝐼𝑄𝑅〉 ∪ 〈𝑥̃
0.75+ 1.5𝐼𝑄𝑅, 𝑥̃
0.25+ 3𝐼𝑄𝑅〉
〈𝑥̃
0.25− 3𝐼𝑄𝑅, −∞〉 ∪ 〈𝑥̃
0.75+ 3𝐼𝑄𝑅, + ∞〉
30
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•
•
•
•
•
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𝑅𝑒𝑡𝑢𝑟𝑛𝑠 − 𝑅𝑖𝑠𝑘 𝐴𝑑𝑗𝑢𝑠𝑡𝑒𝑑 𝑅𝑒𝑡𝑢𝑟𝑛𝑠 = 𝑅𝑖𝑠𝑘
41
•
•
•
•
•
•
42
43
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𝑌
𝑖= 𝛽0 + 𝛽1𝑆𝑢𝑠𝑡𝑎𝑖𝑛𝑎𝑏𝑖𝑙𝑖𝑡𝑦 𝑆𝑐𝑜𝑟𝑒
𝑖+ 𝛽2𝐴𝑔𝑒
𝑖+ 𝛽3𝑙𝑜𝑔 (𝐹𝑢𝑛𝑑 𝑆𝑖𝑧𝑒 𝐸𝑈𝑅)
𝑖+ ∑𝑆𝑡𝑦𝑙𝑒 𝑆𝑖𝑧𝑒 𝐵𝑜𝑥
𝑖+ 𝜀
𝑖where:
Y
i− alternative performance metrics for fund i
Sustainability Score
i− ESG score provided by Morningstar for fund i Age
i− years since inception date measured at April 2021 for fund i
log (Fund Size EUR)
i− logarithm of mutual fund size in EUR temrs for fund i
∑Style Size Box
i− dummies of Morningstar style and size categories for fund i
β0, β1, β2 and β3 are parameters of the regression and ε
iis the error term for fund i
45
𝑌
𝑖= 𝛽0 + 𝛽1𝐸𝑛𝑣𝑖𝑟𝑜𝑛𝑚𝑒𝑛𝑡𝑎𝑙 𝑆𝑐𝑜𝑟𝑒
𝑖+ 𝛽2𝑆𝑜𝑐𝑖𝑎𝑙 𝑆𝑐𝑜𝑟𝑒
𝑖+ 𝛽3𝐺𝑜𝑣𝑒𝑟𝑛𝑎𝑛𝑐𝑒 𝑆𝑐𝑜𝑟𝑒
𝑖+ 𝛽4𝐴𝑔𝑒
𝑖+ 𝛽5𝑙𝑜𝑔 (𝐹𝑢𝑛𝑑 𝑆𝑖𝑧𝑒 𝐸𝑈𝑅)
𝑖+ ∑𝑆𝑡𝑦𝑙𝑒 𝑆𝑖𝑧𝑒 𝐵𝑜𝑥
𝑖+ 𝜀
𝑖where:
Y
i− alternative performance metrics for fund i
Environmental Score
i− Environmental score provided by Morningstar for fund i Social Score
i− Social score provided by Morningstar for fund i
Governance Score
i− Governance score provided by Morningstar for fund i Age
i− years since inception date measured at April 2021 for fund i
log (Fund Size EUR)
i− logarithm of mutual fund size in EUR temrs for fund i
∑Style Size Box
i− dummies of Morningstar style and size categories for fund i
β0, β1, β2, β3, β4 and β5 are parameters of the regression and ε
iis the error term for fund i
46
Sin Industries
i− the sum of assets invested in "sin industries" for fund i Age
i− years since inception date measured at April 2021 for fund i
log (Fund Size EUR)
i− logarithm of mutual fund size in EUR temrs for fund i
∑Style Size Box
i− dummies of Morningstar style and size categories for fund i
β0, β1, β2, and β3 are parameters of the regression and ε
iis the error term for fund i
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48
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52 )
√ √ √ √ √ √ √ √ √ √
√ √ √ √ √ √ √ √ √ √ √
√ √ √ √ √ √ √ √ √ √ √ √ √
■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■
√ ■ ; ■ =
53
■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■
√ ■ ; ■ =
√
■
√ ■ ; ■ =
54
𝐻1
𝑎𝑑𝑗𝑢𝑠𝑡𝑒𝑑55
56
57
𝐻3
𝑎𝑑𝑗𝑢𝑠𝑡𝑒𝑑58
∑
59
60
𝐻2
𝑎𝑑𝑗61
𝐻3
𝑎𝑑𝑗62
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