You are corsidering an im estment in either inandual stocks or portfolio cf stoc

Question

You are corsidering an im estment in either inandual stocks or portfolio cf stocks. The two stocks You are researching Stock A and Stock B, have the following historical returns: Year 31.00 21.80 2016 2017 2018 7.10 -2.75 20.75 10.60 Calcuate the avaraqe rate of return for cach stock during tha S-yaar perlad. Do nct round intermediate calculations. Round your answers to tao dedmal places. Sloxk A: Stock A: Suppose you had held a portfoño co sisting or 50% of S ock A and S Round your ansaers to two deimal places. Negative values, it any, should be indicated by a minus sign a. b of Stock 0 what ould have been the ealized ate of return on the orti in each year? hat vid have been the average et m *n the portfolio during this eriod? D ot round interme iate calcula i s Portfolio U17 2018 Averagc rcturn Caladate th standard deviation atreturns tor each stock And tnr the parttila. Da not round intermeiata talculations. Rand your answers tn two decimal pan Portfolio Std. Daw d. Suppo se you are isk-everse in esto. AssuminU Studs A drd dre you' orly duces, wuuld you prefer w huld suck A Stock . u' ure put ulio? why? snoet , since it offers curt expected return with-Star. A rsk awanse lnvestar snauld choose risk.

Explanation / Answer

a)

Average return of stock A = ( -0.1510 + 0.31 + 0.2 - 0.0275 + 0.2075) / 5

Average return of stock A = 0.1078 or 10.78%

Average return of stock B = ( -0.097 + 0.2180 - 0.1710 + 0.483 + 0.1060) / 5

Average return of stock B = 0.1078 or 10.78%

b)

Realized return of year 2014 = 0.5*(-0.1510) + 0.5*(-0.097)

Realized return of year 2014 = -0.0755 - 0.0485

Realized return of year 2014 = -0.124 or -12.4%

Realized return of year 2015 = 0.5*(0.31) + 0.5*(0.2180)

Realized return of year 2015 = 0.155 + 0.109

Realized return of year 2015 = 0.264 or 26.4%

Realized return of year 2016 = 0.5*(0.2) + 0.5*(-0.1710)

Realized return of year 2016 = 0.1 - 0.0855

Realized return of year 2016 = 0.0145 or 1.45%

Realized return of year 2017 = 0.5*(-0.0275) + 0.5*(0.483)

Realized return of year 2017 = -0.01375 + 0.2415

Realized return of year 2017 = 0.2278 or 22.78%

Realized return of year 2018 = 0.5*(0.2075) + 0.5*(0.106)

Realized return of year 2018 = 0.10375 + 0.053

Realized return of year 2018 = 0.1568 or 15.68%

Average return = ( -0.124 + 0.264 + 0.0145 + 0.2278 + 0.1568 ) / 5

Average return = 0.1078 or 10.78%

c)

Standard deviation of Stock A = {[(-0.1510 - 0.1078)2 + ( 0.31 - 0.1078)2 + ( 0.2 - 0.1078)2 + ( - 0.0275 - 0.1078)2 + ( 0.2075 - 0.1078)2] / 5 - 1}1/2

Standard deviation of Stock A = {[ 0.066977 + 0.040885 + 0.008501 + 0.018306 + 0.00994 ] / 4}1/2

Standard deviation of Stock A = 0.1901 or 19.01%

Standard deviation of Stock B = {[(-0.097 - 0.1078)2 + ( 0.218 - 0.1078)2 + ( -0.171 - 0.1078)2 + ( 0.483 - 0.1078)2 + ( 0.106 - 0.1078)2] / 5 - 1}1/2

Standard deviation of Stock B = {[ 0.041943 + 0.012144 + 0.077729 + 0.140775 + 0.000003 ] / 4}1/2

Standard deviation of Stock B = 0.2611 or 26.11%

Standard deviation of Stock portfolio = {[(-0.124  - 0.1078)2 + ( 0.264 - 0.1078)2 + ( 0.0145 - 0.1078)2 + ( 0.2278 - 0.1078)2 + ( 0.1568 - 0.1078)2] / 5 - 1}1/2

Standard deviation of Stock portfolio = {[ 0.053731 + 0.024398 + 0.008705 + 0.0144 + 0.002401 ] / 4}1/2

Standard deviation of Stock portfolio = 0.16096 or 16.1%

d)

A risk averse investor should choose portfolio since it offers same with lowest risk.

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