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Computing returnsƒ 20

Simple returns, discrete compounding

ƒ

Log returns, continuous compounding

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Relation between simple and log returns

1

1

1

1

−

=

−

=

−

−

−

t t

t

t

t

t

P P

P

P

P

r

1

1

ln

ln

ln

−

−

−

=

⎞ ⎟⎟ ⎠

⎛ ⎜⎜ ⎝

=

t

t

t t

t

P

P

P P

y

(

)t

t

y

t

r

y

e

r

t

+

=

⇔

−

=

1

ln

1

Single-period random cash flows: Stocks