Given I have 3 index values at time $t = 0, 1 , 2$, how would I go about calculating the daily continuously compounded return?
Time: $ 0, 1, 2$
Index Values: $4000, 4086, 4114$
Any help would be much appreciated. Thanks.
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Sign up to join this communityGiven I have 3 index values at time $t = 0, 1 , 2$, how would I go about calculating the daily continuously compounded return?
Time: $ 0, 1, 2$
Index Values: $4000, 4086, 4114$
Any help would be much appreciated. Thanks.
In continuous compounding, a nominal (or an index value) in time $t$ is given by formula
$$ N_t = N_0\mathrm{e}^{rt}, $$
where $r$ is return (or interest) rate per annum.
Based on the equation above, the $r$ can be calculated as
$$ r = \frac{1}{t}\ln\frac{N_t}{N_0}. $$
So, for $t = 1$ we have the annualized return: $$ r_{t=1} = \frac{1}{1}\ln\frac{4086}{4000} = 2.1272\, \%. $$
And for $t = 2$ we have the annualized return:
$$
r_{t=2} = \frac{1}{2}\ln\frac{4114}{4000} = 1.4051\, \%.
$$