Suppose that a security cost 41500 today. A.calculate the percentage return on t

Question

Suppose that a security cost 41500 today.
A.calculate the percentage return on the security in one year is $1000, $1500,$2000, or $2500. (note: this is the total amount returned to the investor, so you may just calculate the total return and not worry about how this is split up between current yield and capital-gains yield)

B. If each of the outcomes in part a is equally likely, calcute the expected return on the security.

C. Calculate the standard deviation of the return on the security. (again, assume that each of the outcomes in part a is equally likely.)

Explanation / Answer

I will leave all the intermediate parts in fractions because the decimals are messy
I will write the final answers as decimals.

A. Dont know exactly on this part but B and C will be right if you calculate this correctly.

for 1000 the percent return is 1000/41500 = 2/83
for 1500 it is 1500/41500 = 3/83
for 2000 it is 4/83
for 2500 it is 5/83

B. if the probability is equally likely for all outcomes and there are four outcomes then the probability for each is .25
the expected return would just be the probability of each times it percent return: so the expected return is (.25*2/83)+(.25*3/83)+(.25*4/83)+(.25*5/83) = 7/166
so the expected percent return rate is .0421686747 approx. (4.2169%)

C. The standard deviation is the the return squared times the probability minus the expected value squared squared then take the square root
so in this case it would be {.25*(2/83)^2 + .25*(3/83)^2 + .25(4/83)^2 + .25*(5/83)^2} - (7/166)^2
so the standard deviation is .00018144869

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