Prices and Dividends for Investments A and B for the last 5 years are provided i

Question

Prices and Dividends for Investments A and B for the last 5 years are provided in the following:

a. Calculate the arithmetic average return for Investment A during this 5 year period.

b. Calculate the arithmetic average return for Investment B during this 5 year period.

c. Calculate the standard deviation of returns for Investment A during this 5 year period.

d. Calculate the standard deviation of returns for Investment B during this 5 year period.

e. If the returns of Investment A are normally distributed and the recent history (2012 to 2016) represents future expected return and expected risk, what is the chance of losing money next year Investment A?

f. If the returns of Investment B are normally distributed and the recent history (2012 to 2016) represents future expected return and expected risk, what is the chance of losing money next year Investment B?

Please show Work

Year Price A Dividend A Price B Dividend B 2012 80 0 150 0 2013 84 1 135 2 2014 75 2 130 3 2015 71 3 174 4 2016 90 4 165 5

Explanation / Answer

Hi,
I can help you with top four questions.

Part a and b:

Please understand that rate of return on any investment = (Dividend/Price)*100

Aithmatic average return for investment = (Rate of return in 2012 + rate of return in 2013 + rate of return in 2014 + rate of return in 2015 + rate of return in 2016)/Number of years

Therefore, Rate of return for Investment A in 2012 = Dividend for investment A in 2012/Price of A in 2012 = (0/80)*100 = 0%

Similiarly, Rate of return for Investment A in 2013 = Dividend for investment A in 2013/Price of A in 2013 = (1/84)*100 = 1.19%

See the below table for return on other periods:

Arithmetic average return for investment A = (0.00% + 1.19% + 2.67% + 4.23% + 4.44%)/5 = 2.50%

Similiarly, Rates of return for Investment B will be:

Arithmetic average return for investment B = (0.00% + 1.48% + 2.31% + 2.30% + 3.03%)/5 = 1.82%

Part c and d:

Standard deviation of rate of return = [1/n * (ri - rave)2]½

where:
ri = actual rate of return
rave = average rate of return
n = number of time periods, please note this will be 4 in our case as we 5 years in our data which will involve 4 periods.

Standard deviation calculation of A will be as follows:

Difference of return from average return

(ri - rave), where rave is 2.5% as calculated in part a

Square of difference from average return

(ri - rave)2

Standard deviation for Investment A = (0.1475/4)^(1/2) = 0.018

Standard deviation calculation of B will be as follows:

Difference of return from average return

(ri - rave), where rave is 1.82% as calculated in part a

Square of difference from average return

(ri - rave)2

Standard deviation for Investment B = (0.0536/4)^(1/2) = 0.1157

Year Price of A Dividend on A Rate of return on A 2012 80 0 =(0/80)*100 = 0% 2013 84 1 =(1/84)*100 = 1.19% 2014 75 2 =(2/75)*100 = 2.67% 2015 71 3 =(3/71)*100 = 4.23% 2016 90 4 =(4/90)*100 = 4.44%

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