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■♥t❡r♥❛t✐♦♥❛❧ ❘❡s❡❛r❝❤ ❚r❛✐♥✐♥❣ ●r♦✉♣ ■●❉❑ ▼✉♥✐❝❤ ✕ ●r❛③ ❖♥ ▼✉❧t✐❧❡✈❡❧ ❇❡st ▲✐♥❡❛r ❯♥❜✐❛s❡❞ ❊st✐♠❛t♦rs ❉❛♥✐❡❧ ❙❝❤❛❞❡♥✱ ❊❧✐s❛❜❡t❤ ❯❧❧♠❛♥♥ ❲♦r❦s❤♦♣ ✏❖♣t✐♠✐③❛t✐♦♥ ❛♥❞ ■♥✈❡rs✐♦♥ ✉♥❞❡r ❯♥❝❡rt❛✐♥t②✑ ❘■❈❆▼ ▲✐♥③ ❊❧✐s❛❜❡t❤ ❯❧❧♠❛♥♥ ❖♥ ▼✉❧t✐❧❡✈❡❧ ❇❡st ▲✐♥❡❛r ❯♥❜✐❛s❡❞ ❊st✐♠❛t♦rs ✶✶ ◆♦✈❡♠❜❡r ✷✵✶✾ ✶

■♥t❡r♥❛t✐♦♥❛❧ ❘❡s❡❛r❝❤ ❚r❛✐♥✐♥❣ ●r♦✉♣ ■●❉❑ ▼✉♥✐❝❤ ✕ ●r❛③ ❖✉t❧✐♥❡ ■ ▲✐♥❡❛r ♠♦❞❡❧s✱ ❜❡st ❧✐♥❡❛r ✉♥❜✐❛s❡❞ ❡st✐♠❛t♦rs ✭❇▲❯❊s✮ ■ ❱❛r✐❛♥❝❡ ❜♦✉♥❞✱ ♠♦♥♦♠✐❛❧ ❡①❛♠♣❧❡ ■ ❙❛♠♣❧❡ ❛❧❧♦❝❛t✐♦♥✱ P❉❊ ❡①❛♠♣❧❡ ■ ❆s②♠♣t♦t✐❝ ❛♥❛❧②s✐s ♦❢ ♠✉❧t✐❧❡✈❡❧ ❇▲❯❊s ❊❧✐s❛❜❡t❤ ❯❧❧♠❛♥♥ ❖♥ ▼✉❧t✐❧❡✈❡❧ ❇❡st ▲✐♥❡❛r ❯♥❜✐❛s❡❞ ❊st✐♠❛t♦rs ✶✶ ◆♦✈❡♠❜❡r ✷✵✶✾ ✷

■♥t❡r♥❛t✐♦♥❛❧ ❘❡s❡❛r❝❤ ❚r❛✐♥✐♥❣ ●r♦✉♣ ■●❉❑ ▼✉♥✐❝❤ ✕ ●r❛③ ▼♦t✐✈❛t✐♦♥ ✭✶✴✸✮ ■ ●♦❛❧✿ ❊st✐♠❛t❡ ❡①♣❡❝t❡❞ ✈❛❧✉❡ ❊ [ ❩ ] ♦❢ s❝❛❧❛r ✈❛❧✉❡❞ r❛♥❞♦♠ ✈❛r✐❛❜❧❡ ❩ ■ ❈❛♥ ❣❡♥❡r❛t❡ s❛♠♣❧❡s ♦❢ ❛♣♣r♦①✐♠❛t✐♦♥s ❩ ❵ ✙ ❩ ✱ ❵ = ✶ ❀ ✿ ✿ ✿ ❀ ▲ ■ ❊①♣❡❝t❛t✐♦♥s ✖ = ( ✖ ✶ ❀ ✿ ✿ ✿ ❀ ✖ ▲ ) ❃ ✷ ❘ ▲ ❦ ❀❵ = ✶ ✷ ❘ ▲ ✂ ▲ ■ ❈♦✈❛r✐❛♥❝❡ ▼❛tr✐① ❈ = (Cov( ❩ ❦ ❀ ❩ ❵ )) ▲ ❊❧✐s❛❜❡t❤ ❯❧❧♠❛♥♥ ❖♥ ▼✉❧t✐❧❡✈❡❧ ❇❡st ▲✐♥❡❛r ❯♥❜✐❛s❡❞ ❊st✐♠❛t♦rs ✶✶ ◆♦✈❡♠❜❡r ✷✵✶✾ ✸

■♥t❡r♥❛t✐♦♥❛❧ ❘❡s❡❛r❝❤ ❚r❛✐♥✐♥❣ ●r♦✉♣ ■●❉❑ ▼✉♥✐❝❤ ✕ ●r❛③ ▼♦t✐✈❛t✐♦♥ ✭✷✴✸✮ ■ ▼❛♥② ❧✐♥❡❛r✱ ✉♥❜✐❛s❡❞ ❡st✐♠❛t♦rs ❢♦r ✖ ▲ = ❊ [ ❩ ▲ ] ✙ ❊ [ ❩ ] ■ ▼♦♥t❡ ❈❛r❧♦ ♠ ▲ � = ✶ ✖ ▼❈ � ❩ ▲ ( ✦ ✐ ) ▲ ♠ ▲ ✐ = ✶ ■ ▼✉❧t✐❧❡✈❡❧ ▼♦♥t❡ ❈❛r❧♦ ✭●✐❧❡s ✷✵✵✽✮ ▲ ♠ ❵ � � ✶ ✖ ▼▲▼❈ ( ❩ ❵ ( ✦ ❵ ✐ ) � ❩ ❵ � ✶ ( ✦ ❵ � = ✐ )) ▲ ♠ ❵ ❵ = ✶ ✐ = ✶ ■ ▼✉❧t✐✜❞❡❧✐t② ▼♦♥t❡ ❈❛r❧♦ ✭P❡❤❡rst♦r❢❡r ❡t ❛❧✳ ✷✵✶✻✮ ■ ❆♣♣r♦①✐♠❛t❡ ❈♦♥tr♦❧ ❱❛r✐❛t❡s ✭●♦r♦❞❡ts❦② ❡t ❛❧✳ ✷✵✶✽✮ ■ ❆r❡ t❤❡s❡ ❡st✐♠❛t♦rs ♦♣t✐♠❛❧❄ � ✦ ♠✐♥✐♠❛❧ ✈❛r✐❛♥❝❡ ❊❧✐s❛❜❡t❤ ❯❧❧♠❛♥♥ ❖♥ ▼✉❧t✐❧❡✈❡❧ ❇❡st ▲✐♥❡❛r ❯♥❜✐❛s❡❞ ❊st✐♠❛t♦rs ✶✶ ◆♦✈❡♠❜❡r ✷✵✶✾ ✹

■♥t❡r♥❛t✐♦♥❛❧ ❘❡s❡❛r❝❤ ❚r❛✐♥✐♥❣ ●r♦✉♣ ■●❉❑ ▼✉♥✐❝❤ ✕ ●r❛③ ▼♦t✐✈❛t✐♦♥ ✭✸✴✸✮ ■ ▲✐♥❡❛r ❝♦♠❜✐♥❛t✐♦♥ ♦❢ ▼♦♥t❡ ❈❛r❧♦ ❡st✐♠❛t♦rs✿ ❑ ♠ ❦ � � � ✶ ☞ ❦ ❩ ❵ ( ✦ ❦ ✖ ▲ = � ✐ ) ❵ ♠ ❦ ❦ = ✶ ✐ = ✶ ❵ ✷ ❙ ❦ ■ ❯♥❜✐❛s❡❞♥❡ss ✭r♦✇ s✉♠ ❝♦♥str❛✐♥t✮✿ � ❑ ❦ = ✶ ☞ ❦ ❵ = ✍ ❵❀ ▲ 1.00 1.00 1.00 1.00 -1.00 -1.00 2.00 -1.00 1.00 -1.00 0.25 -0.50 0.25 1.00 -1.00 -1.00 1.00 -1.00 1.00 1.00 -1.00 -3.00 3.00 1.00 -1.00 2.00 -2.00 ❊❧✐s❛❜❡t❤ ❯❧❧♠❛♥♥ ❖♥ ▼✉❧t✐❧❡✈❡❧ ❇❡st ▲✐♥❡❛r ❯♥❜✐❛s❡❞ ❊st✐♠❛t♦rs ✶✶ ◆♦✈❡♠❜❡r ✷✵✶✾ ✺

■♥t❡r♥❛t✐♦♥❛❧ ❘❡s❡❛r❝❤ ❚r❛✐♥✐♥❣ ●r♦✉♣ ■●❉❑ ▼✉♥✐❝❤ ✕ ●r❛③ ❊①❛♠♣❧❡ ✭✶✴✸✮ ■ ▼✉❧t✐❧❡✈❡❧ ▼♦♥t❡ ❈❛r❧♦ ✇✐t❤ ✐♥❞❡♣❡♥❞❡♥t ✐♥♣✉ts ✦ ✷ ✶ ❀ ✦ ✷ ✷ ❀ ✦ ✶ ✶ � ✷ = ✶ ✖ ▼▲▼❈ ( ❩ ✷ ( ✦ ✷ ✐ ) � ❩ ✶ ( ✦ ✷ ✐ )) + ❩ ✶ ( ✦ ✶ � ✶ ) ✷ ✷ ✐ = ✶ ✙ ( ✖ ✷ � ✖ ✶ ) + ✖ ✶ ■ ❚✇♦ s❛♠♣❧❡s t♦ ❡st✐♠❛t❡ ✖ ✷ � ✖ ✶ ❛♥❞ ♦♥❡ s❛♠♣❧❡ t♦ ❡st✐♠❛t❡ ✖ ✶ ■ ❘❡❛rr❛♥❣❡✿ � � = ✶ ✖ ▼▲▼❈ ( ❩ ✷ ( ✦ ✷ ✶ ) � ❩ ✶ ( ✦ ✷ ✶ )) + ( ❩ ✷ ( ✦ ✷ ✷ ) � ❩ ✶ ( ✦ ✷ + ❩ ✶ ( ✦ ✶ � ✷ ) ✶ ) ✷ ✷ = ✶ ✶ ) � ✶ ✷ ( ❩ ✷ ( ✦ ✷ ✶ ) + ❩ ✷ ( ✦ ✷ ✷ )) + ❩ ✶ ( ✦ ✶ ✷ ( ❩ ✶ ( ✦ ✷ ✶ ) + ❩ ✶ ( ✦ ✷ ✷ )) ■ ❚❤r❡❡ s❛♠♣❧❡s ♦❢ ❩ ✶ ❛♥❞ t✇♦ s❛♠♣❧❡s ♦❢ ❩ ✷ ❊❧✐s❛❜❡t❤ ❯❧❧♠❛♥♥ ❖♥ ▼✉❧t✐❧❡✈❡❧ ❇❡st ▲✐♥❡❛r ❯♥❜✐❛s❡❞ ❊st✐♠❛t♦rs ✶✶ ◆♦✈❡♠❜❡r ✷✵✶✾ ✻

■♥t❡r♥❛t✐♦♥❛❧ ❘❡s❡❛r❝❤ ❚r❛✐♥✐♥❣ ●r♦✉♣ ■●❉❑ ▼✉♥✐❝❤ ✕ ●r❛③ ❊①❛♠♣❧❡ ✭✷✴✸✮ ■ ❑❡② ✐❞❡❛✿ tr❡❛t ♠♦❞❡❧ ❡✈❛❧✉❛t✐♦♥s ❛s ♦❜s❡r✈❛t✐♦♥s ♦❢ ✉♥❦♥♦✇♥ ✧tr✉t❤✧ ❊ [ ❩ ] ■ ❊①❛♠♣❧❡✿ ✜✈❡ ✭❝♦rr❡❧❛t❡❞✮ ♦❜s❡r✈❛t✐♦♥s ♦❢ ❩ ✶ ❛♥❞ ❩ ✷ ■ ❘❡❢♦r♠✉❧❛t✐♦♥ ❛s ❧✐♥❡❛r ♠♦❞❡❧ ✿         ❩ ✶ ( ✦ ✷ ❩ ✶ ( ✦ ✷ ✶ ) ✖ ✶ ✶ ) � ✖ ✶ ✶ ✵           ❩ ✷ ( ✦ ✷ ❩ ✷ ( ✦ ✷ � ✖ ✶ � ✑ ✷ ( ✦ ✷ ✶ ) ✖ ✷ ✶ ) � ✖ ✷ ✵ ✶ ✶ )                   ❩ ✶ ( ✦ ✷ ❩ ✶ ( ✦ ✷ ✑ ✷ ( ✦ ✷ ✷ ) = ✖ ✶ + ✷ ) � ✖ ✶ = ✶ ✵ + ✷ )         ✖ ✷         ❩ ✷ ( ✦ ✷ ❩ ✷ ( ✦ ✷ ✑ ✶ ( ✦ ✶ ✷ ) ✖ ✷ ✷ ) � ✖ ✷ ✵ ✶ ✶ ) ❩ ✶ ( ✦ ✶ ✶ ) ✖ ✶ ❩ ✶ ( ✦ ✶ ✶ ) � ✖ ✶ ✶ ✵ ■ ❖❜s❡r✈❛t✐♦♥ ✈❡❝t♦r ❨ ✱ ❉❡s✐❣♥ ♠❛tr✐① ❍ ✱ ♣❛r❛♠❡t❡r ✖ ✱ ♠❡❛♥ ③❡r♦ ♥♦✐s❡ ✧ ❨ = ❍ ✖ + ✧ ❊❧✐s❛❜❡t❤ ❯❧❧♠❛♥♥ ❖♥ ▼✉❧t✐❧❡✈❡❧ ❇❡st ▲✐♥❡❛r ❯♥❜✐❛s❡❞ ❊st✐♠❛t♦rs ✶✶ ◆♦✈❡♠❜❡r ✷✵✶✾ ✼

■♥t❡r♥❛t✐♦♥❛❧ ❘❡s❡❛r❝❤ ❚r❛✐♥✐♥❣ ●r♦✉♣ ■●❉❑ ▼✉♥✐❝❤ ✕ ●r❛③ ❊①❛♠♣❧❡ ✭✸✴✸✮ ■ ▼♦❞❡❧ ❣r♦✉♣s ❙ ✶ = ❢ ✶ ❣ ❛♥❞ ❙ ✷ = ❢ ✶ ❀ ✷ ❣ ✇✐t❤ ❙ ✶ ❀ ❙ ✷ ✒ ❢ ✶ ❀ ✷ ❣ ✱ ▲ = ✷ ■ ♠ ✶ = ✶✱ ♠ ✷ = ✷ � � � � � � � � � � ❩ ✶ = ❘ ✶ = ✖ + ✑ ✶ ❀ ❩ ✶ = ✖ ✶ + ❩ ✶ � ✖ ✶ = ✶ ✵ ✶ ✵ � ❩ ✶ � � ✖ ✶ � � ❩ ✶ � ✖ ✶ � � ✶ � � ✶ � ✵ ✵ ❩ ✷ = ❘ ✷ = ✖ + ✑ ✷ ❀ = + = ❩ ✷ ✖ ✷ ❩ ✷ � ✖ ✷ ✵ ✶ ✵ ✶         ❩ ✶ ( ✦ ✷ ❩ ✶ ( ✦ ✷ ✶ ) ✖ ✶ ✶ ) � ✖ ✶ ✶ ✵           ❩ ✷ ( ✦ ✷ ❩ ✷ ( ✦ ✷ � ✖ ✶ � ✑ ✷ ( ✦ ✷ ✶ ) ✖ ✷ ✶ ) � ✖ ✷ ✵ ✶ ✶ )                   ❩ ✶ ( ✦ ✷ ✷ ) ❩ ✶ ( ✦ ✷ ✷ ) � ✖ ✶ ✑ ✷ ( ✦ ✷ ✷ ) = ✖ ✶ + = ✶ ✵ +         ✖ ✷         ❩ ✷ ( ✦ ✷ ✷ ) ✖ ✷ ❩ ✷ ( ✦ ✷ ✷ ) � ✖ ✷ ✵ ✶ ✑ ✶ ( ✦ ✶ ✶ ) ❩ ✶ ( ✦ ✶ ✶ ) ✖ ✶ ❩ ✶ ( ✦ ✶ ✶ ) � ✖ ✶ ✶ ✵ ❊❧✐s❛❜❡t❤ ❯❧❧♠❛♥♥ ❖♥ ▼✉❧t✐❧❡✈❡❧ ❇❡st ▲✐♥❡❛r ❯♥❜✐❛s❡❞ ❊st✐♠❛t♦rs ✶✶ ◆♦✈❡♠❜❡r ✷✵✶✾ ✽