❚❤❡ s❤♦rt r❛t❡ ❞✐s❝♦♥♥❡❝t ✐♥ ❛ ♠♦♥❡t❛r② ❡❝♦♥♦♠② ▼♦r✐t③ ▲❡♥❡❧✱ ▼♦♥✐❦❛ P✐❛③③❡s✐ ❛♥❞ ▼❛rt✐♥ ❙❝❤♥❡✐❞❡r ❉❡❝❡♠❜❡r ✷✵✶✽
▼♦t✐✈❛t✐♦♥ ❙t❛♥❞❛r❞ ❊✉❧❡r ❡q✉❛t✐♦♥ ❢♦r ♥♦♠✐♥❛❧ s❤♦rt r❛t❡ � − ✶ � � � ✶ + i t ✶ E t M t + ✶ = ✶ → ( ✶ + i t ) = E t M t + ✶ ✶ + π t + ✶ ✶ + π t + ✶ r❡♣r❡s❡♥t❛t✐✈❡ ❛❣❡♥t ♠♦❞❡❧✿ M t + ✶ ❂ ▼❘❙ ◮ ■♠♣♦rt❛♥t ❡q✉❛t✐♦♥ ❢♦r ♠♦♥❡t❛r② ❡❝♦♥♦♠✐❝s ❝❡♥tr❛❧ ❜❛♥❦ ♣♦❧✐❝② r❛t❡ i t ❂ s❤♦rt r❛t❡ ✐♥ ♣r✐❝✐♥❣ ❦❡r♥❡❧ ◮ i t ❝❤❛♥❣❡s ✫ π t + ✶ st✐❝❦② → M t + ✶ ❛❞❥✉sts → r❡❛❧ ❡✛❡❝ts ◮ ❊♠♣✐r✐❝❛❧ s✉❝❝❡ss ♦❢ ❛ss❡t ♣r✐❝✐♥❣ ❡q✉❛t✐♦♥ ♠✐①❡❞ ♠♦❞❡❧s t❤❛t ✜t ✇❡❧❧ ❧♦♥❣ ♠❛t✉r✐t② ❛ss❡ts ❞♦♥✬t ♣r✐❝❡ s❤♦rt r❛t❡ ◮ → s❤♦rt r❛t❡ ❞✐s❝♦♥♥❡❝t s✉r♣r✐s✐♥❣❄ ❍♦✉s❡❤♦❧❞s ❞♦♥✬t ❤♦❧❞ s❤♦rt ❜♦♥❞s✱ ♦♥❧② ✈✐❛ ❜❛♥❦s✴▼▼❋s ◮
▼♦t✐✈❛t✐♦♥ ❙t❛♥❞❛r❞ ❊✉❧❡r ❡q✉❛t✐♦♥ ❢♦r ♥♦♠✐♥❛❧ s❤♦rt r❛t❡ � − ✶ � � � ✶ + i t ✶ E t M t + ✶ = ✶ → ( ✶ + i t ) = E t M t + ✶ ✶ + π t + ✶ ✶ + π t + ✶ r❡♣r❡s❡♥t❛t✐✈❡ ❛❣❡♥t ♠♦❞❡❧✿ M t + ✶ ❂ ▼❘❙ ◮ ■♠♣♦rt❛♥t ❡q✉❛t✐♦♥ ❢♦r ♠♦♥❡t❛r② ❡❝♦♥♦♠✐❝s ❝❡♥tr❛❧ ❜❛♥❦ ♣♦❧✐❝② r❛t❡ i t ❂ s❤♦rt r❛t❡ ✐♥ ♣r✐❝✐♥❣ ❦❡r♥❡❧ ◮ i t ❝❤❛♥❣❡s → π t + ✶ ✐s st✐❝❦② → M t + ✶ ❛❞❥✉sts → r❡❛❧ ❡✛❡❝ts ◮ ❊♠♣✐r✐❝❛❧ s✉❝❝❡ss ♦❢ ❛ss❡t ♣r✐❝✐♥❣ ❡q✉❛t✐♦♥ ♠✐①❡❞ ♠♦❞❡❧s t❤❛t ✜t ✇❡❧❧ ❧♦♥❣ ♠❛t✉r✐t② ❛ss❡ts ❞♦♥✬t ♣r✐❝❡ s❤♦rt r❛t❡ ◮ → s❤♦rt r❛t❡ ❞✐s❝♦♥♥❡❝t s✉r♣r✐s✐♥❣❄ ❍♦✉s❡❤♦❧❞s ❞♦♥✬t ❤♦❧❞ s❤♦rt ❜♦♥❞s✱ ♦♥❧② ✈✐❛ ❜❛♥❦s✴▼▼❋s ◮
❚❤✐s ♣❛♣❡r✿ ♠♦♥❡t❛r② ❛ss❡t ♣r✐❝✐♥❣ ✇✐t❤ ❜❛♥❦s ◆♦♥✲✜♥❛♥❝✐❛❧ s❡❝t♦r✿ ♣r✐❝✐♥❣ ❦❡r♥❡❧ M t + ✶ ✫ ❞❡♣♦s✐t ❞❡♠❛♥❞ ❇❛♥❦s ✐ss✉❡ ❞❡♣♦s✐ts✱ ❝❤♦♦s❡ ❛ss❡ts ✫ ❧❡✈❡r❛❣❡ ❢r✐❝t✐♦♥✿ ❛ss❡t ♠❛♥❛❣❡♠❡♥t ❝♦st❧②✱ ♠♦r❡ s♦ ✐❢ ❧❡✈❡r❛❣❡ ❤✐❣❤ ◮ ❜❛♥❦s ✈❛❧✉❡ s❤♦rt s❛❢❡ ❜♦♥❞s t♦ ❜❛❝❦ ❞❡♣♦s✐ts → ❙❤♦rt s❛❢❡ s❛❢❡ ❜♦♥❞s s❝❛r❝❡ → ♣r✐❝❡❞ ❡①❝❧✉s✐✈❡❧② ❜② ❜❛♥❦s ♦❜s❡r✈❡❞ s❤♦rt r❛t❡ ❁ s❤♦rt r❛t❡ ✐♥ M t + ✶ ✿❂ ✏s❤❛❞♦✇ r❛t❡✑ ◮ tr❛♥s♠✐ss✐♦♥ ♦❢ ♠♦♥❡t❛r② ♣♦❧✐❝② t❤r♦✉❣❤ ❜❛♥❦ ❜❛❧❛♥❝❡ s❤❡❡ts ◮ ◗✉❛♥t✐t❛t✐✈❡ ❛ss❡ss♠❡♥t ❡st✐♠❛t❡ s❤❛❞♦✇ s♣r❡❛❞ ✐♥ t❤❡ ❞❛t❛✿ ❤✐❣❤ ❛t t❤❡ ❡♥❞ ♦❢ ❜♦♦♠s ◮ ❜❛♥❦ ❊✉❧❡r ❡q♥s✳✿ ❤✐❣❤ s♣r❡❛❞ → ❧♦✇ ❧❡✈❡r❛❣❡ ✫ ❧♦✇ s❛❢❡ ❛ss❡t s❤❛r❡ ◮ ❞❛t❛✿ st❛❜❧❡ r❡❧❛t✐♦♥s❤✐♣s ❛t ❜✉s✐♥❡ss ❝②❝❧❡ ❢r❡q✉❡♥❝✐❡s ◮
❍♦✉s❡❤♦❧❞s✱ ❜❛♥❦s✱ ❛ss❡ts Reserves Banks Short safe bonds Non-financial sector Risky bonds Other assets
▲✐q✉✐❞✐t② ❜❡♥❡✜ts ❢r♦♠ ❞❡♣♦s✐ts✱ r❡s❡r✈❡s Reserves Banks Short safe bonds Non-financial sector Risky bonds Other assets
❇❛♥❦ ❝❛♣✐t❛❧ str✉❝t✉r❡✿ ❞❡❜t ✭❞❡♣♦s✐ts✮ ✈s ❡q✉✐t② Reserves Banks Short safe bonds Non-financial sector Risky bonds Other assets
❙♦♠❡ ❛ss❡ts ❤❡❧❞ ❞✐r❡❝t❧② ❜② ❤♦✉s❡❤♦❧❞s Reserves Banks Short safe bonds Non-financial sector Risky bonds Other assets
❲❤♦ ❤♦❧❞s ❜♦♥❞s❄ ❇❛♥❦s ✇❛♥t s❛❢❡ ❝♦❧❧❛t❡r❛❧ Reserves Banks Short safe bonds Non-financial sector Risky bonds Other assets
❚❤✐s ♣❛♣❡r✿ ♠♦♥❡t❛r② ❛ss❡t ♣r✐❝✐♥❣ ✇✐t❤ ❜❛♥❦s ◆♦♥✲✜♥❛♥❝✐❛❧ s❡❝t♦r✿ ♣r✐❝✐♥❣ ❦❡r♥❡❧ M t + ✶ ✫ ❞❡♣♦s✐t ❞❡♠❛♥❞ ❇❛♥❦s ✐ss✉❡ ❞❡♣♦s✐ts✱ ❝❤♦♦s❡ ❛ss❡ts ✫ ❧❡✈❡r❛❣❡ ❢r✐❝t✐♦♥✿ ❛ss❡t ♠❛♥❛❣❡♠❡♥t ❝♦st❧②✱ ♠♦r❡ s♦ ✐❢ ❧❡✈❡r❛❣❡ ❤✐❣❤ ◮ ❜❛♥❦s ✈❛❧✉❡ s❤♦rt s❛❢❡ ❜♦♥❞s t♦ ❜❛❝❦ ❞❡♣♦s✐ts → ❙❤♦rt s❛❢❡ s❛❢❡ ❜♦♥❞s s❝❛r❝❡ → ♣r✐❝❡❞ ❡①❝❧✉s✐✈❡❧② ❜② ❜❛♥❦s ♦❜s❡r✈❡❞ s❤♦rt r❛t❡ ❁ s❤♦rt r❛t❡ ✐♥ M t + ✶ ✿❂ ✏s❤❛❞♦✇ r❛t❡✑ ◮ tr❛♥s♠✐ss✐♦♥ ♦❢ ♠♦♥❡t❛r② ♣♦❧✐❝② t❤r♦✉❣❤ ❜❛♥❦ ❜❛❧❛♥❝❡ s❤❡❡ts ◮ ◗✉❛♥t✐t❛t✐✈❡ ❛ss❡ss♠❡♥t ❡st✐♠❛t❡ s❤❛❞♦✇ s♣r❡❛❞ ✐♥ t❤❡ ❞❛t❛✿ ❤✐❣❤ ❛t t❤❡ ❡♥❞ ♦❢ ❜♦♦♠s ◮ ❜❛♥❦ ❊✉❧❡r ❡q♥s✳✿ ❤✐❣❤ s♣r❡❛❞ → ❧♦✇ ❧❡✈❡r❛❣❡ ✫ ❧♦✇ s❛❢❡ ❛ss❡t s❤❛r❡ ◮ ❞❛t❛✿ st❛❜❧❡ r❡❧❛t✐♦♥s❤✐♣s ❛t ❜✉s✐♥❡ss ❝②❝❧❡ ❢r❡q✉❡♥❝✐❡s ◮
❚❤✐s ♣❛♣❡r✿ ♠♦♥❡t❛r② ❛ss❡t ♣r✐❝✐♥❣ ✇✐t❤ ❜❛♥❦s ◆♦♥✲✜♥❛♥❝✐❛❧ s❡❝t♦r✿ ♣r✐❝✐♥❣ ❦❡r♥❡❧ M t + ✶ ✫ ❞❡♣♦s✐t ❞❡♠❛♥❞ ❇❛♥❦s ✐ss✉❡ ❞❡♣♦s✐ts✱ ❝❤♦♦s❡ ❛ss❡ts ✫ ❧❡✈❡r❛❣❡ ❢r✐❝t✐♦♥✿ ❛ss❡t ♠❛♥❛❣❡♠❡♥t ❝♦st❧②✱ ♠♦r❡ s♦ ✐❢ ❧❡✈❡r❛❣❡ ❤✐❣❤ ◮ ❜❛♥❦s ✈❛❧✉❡ s❤♦rt s❛❢❡ ❜♦♥❞s t♦ ❜❛❝❦ ❞❡♣♦s✐ts → ❙❤♦rt s❛❢❡ s❛❢❡ ❜♦♥❞s s❝❛r❝❡ → ♣r✐❝❡❞ ❡①❝❧✉s✐✈❡❧② ❜② ❜❛♥❦s ♦❜s❡r✈❡❞ s❤♦rt r❛t❡ ❁ s❤♦rt r❛t❡ ✐♥ M t + ✶ ✿❂ ✏s❤❛❞♦✇ r❛t❡✑ ◮ tr❛♥s♠✐ss✐♦♥ ♦❢ ♠♦♥❡t❛r② ♣♦❧✐❝② t❤r♦✉❣❤ ❜❛♥❦ ❜❛❧❛♥❝❡ s❤❡❡ts ◮ ◗✉❛♥t✐t❛t✐✈❡ ❛ss❡ss♠❡♥t ❡st✐♠❛t❡ s❤❛❞♦✇ s♣r❡❛❞ ✐♥ t❤❡ ❞❛t❛✿ ❤✐❣❤ ❛t t❤❡ ❡♥❞ ♦❢ ❜♦♦♠s ◮ ❜❛♥❦ ❊✉❧❡r ❡q♥s✳✿ ❤✐❣❤ s♣r❡❛❞ → ❧♦✇ ❧❡✈❡r❛❣❡ ✫ ❧♦✇ s❛❢❡ ❛ss❡t s❤❛r❡ ◮ ❞❛t❛✿ st❛❜❧❡ r❡❧❛t✐♦♥s❤✐♣s ❛t ❜✉s✐♥❡ss ❝②❝❧❡ ❢r❡q✉❡♥❝✐❡s ◮
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