Using NORMDIST function in Excel, putting the value of X as -9.3, Mean as 7.6 and standard deviation as 8.6, Cumulative value as true , we get the value as 0.0247 = 2.47%
i.e the probability that the return will be less than -9.3% is 2.47%
The range corresponding to 95% probability in Normal distribution is given by
(mean - 1.96 * st. dev , mean +1.96* st. dev)
= (7.6-1.96*8.6, 7.6+1.96*8.6)
= (-9.256, 24.456)
so, 95% of the time, returns will be in the range of -9.26% to 24.46%
The range corresponding to 95% probability in Normal distribution is given by
(mean - 2.57583 * st. dev , mean +2.57583* st. dev) (To be exact)
= (7.6-2.57583*8.6, 7.6+2.57583*8.6)
= (-14.55, 29.75)
so, 99% of the time, returns will be in the range of -14.55% to 29.75%
Blume's formula is given by
Expected Return = (T - 1) / (N - 1) * Geometric average + (N - T) / (N - 1) * Arithmetic average
Where N - Past period in years
T- Future period in years
So,
Expected return for 7 years = (7-1)/(44-1) *9.7% + (44-7)/(44-1) *11.8% = 11.51%
Expected return for 12 years = (12-1)/(44-1) *9.7% + (44-12)/(44-1) *11.8% = 11.26%
Expected return for 22 years = (22-1)/(44-1) *9.7% + (44-22)/(44-1) *11.8% = 10.77%
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