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A project has a 0.7 chance of doubling your investment in a year and a 0.3 chance of halving your investment in a year. What is the standard deviation of the rate of return on this investment?

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Answer:

Explanation:

Given that 0.7 chance of doubling your investment in a year and a 0.3 chance of halving your investment in a year.

So the expected return is:

r =  0.7*100 + 0.3*-50%

= 70% - 15%

= 55%

  • Then the Variance formula is:

[tex]0.7*(1-0.55)^{2} + 0.3*(-0.5 -0.55)^{2}[/tex]

=0.14175+0.33075

=0.4725

=47.25%

  • The Standard Deviation is the square root of the variance.

[tex]\sqrt{0.4725}[/tex]

=0.6874

= 68.74%

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