$($Computing the standard deviation for an individual$$ investment$)$James Fromholtz is considering whether to invest in a newly formed investment fund. The$$ fund's investment objective is to acquire home mortgage securities at what it hopes will be bargain prices. The fund sponsor has suggested to James that the$$ fund's performance will hinge on how the national economy performs in the coming year. $$ Specifically, he suggested the following possible$$ outcomes:$$LOADING$....$

a$.$Based on these potential$$ outcomes, what is your estimate of the expected rate of return from this investment$$ opportunity?

b$.$Calculate the standard deviation in the anticipated returns found in part a$.$

c$.$Would you be interested in making such an$$ investment? Note that you lose all your money in one year if the economy collapses into the worst state or you double your money if the economy enters into a rapid expansion.

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Part $1$

a$.$The expected rate of return from this investment opportunity is

$$

enter your response here$\%.($Round to two decimal$$ places$)$

The expected rate of return from this investment opportunity is$($Round to two decimal places$)$

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Data table

State of Economy

Probability

Fund Returns

Rapid expansion and recovery

$15\%$

$100\%$

Modest growth

$35\%$

$40\%$

Continued recession

$35\%$

$20\%$

Falls into depression

$15\%$

negative $100\%$