# Stock Price Estimate

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Consider a security with stock prices:

60 with probability one eighth i.e 1/8

70 with probability two eights i.e. 2/8

S(1) =

80 with probability three eights i.e. 3/8

100 with probability two eights i.e. 2/8

T = 0 is current period

T = 1 after 1 year

E(S(1)) should be expected value of the stock after 1 year.

Return = [E((S1)) - S(0)] / S(0)

The question is:

Compute the current price S(0) of the stock for which the standard deviation of return would be 15%.

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##### Solution Summary

We estimate the future price of a stock as well as the uncertainty of this estimate based on its expected future performance.

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We have

E(S(1)) = 1/8(60) + 2/8(70) + 3/8(80) + 2/8(100)

= 1/8(60 + 2*70 + 3*80 + 2*100)

= 1/8(640)

= 80.

We also have

E(S(1)^2) = 1/8(60^2) + ...

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