You have a portfolio made up of three stocks Tesla is 60 of

You have a portfolio made up of three stocks. Tesla is 60% of the portfolio, IBM is 20%, and GE is 20%. There are three possible states of the world with probability of occurrence given below. For this problem find the following 1. The expected return, the Standard Deviation, andthe Coefficent of Variation for Tesla 2. The expected return, the Standard Deviation, and the Coefficent of Variation for the portfolio .20 60 Tesla 0.05 0.01 0.04 20 IBM 0.01 0.6 0.09 GE Portfolio State of the World .30 Below Ave Avg. Above Avg 0.01 0.03 0.07 40 30 E(r) Std Deviation Coefficient of Variatiorn You must show work and use the appropriate formulas: Please put your answers in the table above

Solution

For Telsa,

Expected return= Prob. of below avg* Expected return in below avg +Prob. of avg * Expected return in avg + Prob. of above avg* Expected return in above avg

0.30*-0.05+0.40*-0.01+0.30*0.04=-0.70%

Expected Variance= Prob. of below avg*( Expected return in below avg-expected return) ^2 +Prob. of avg * (Expected return in avg -expected return) ^2+ (Prob. of above avg* (Expected return in above avg-expected return) ^2

=0.00013

Expected Std deviation= Variane^1/2=0.01145

Cof. Of variation= std deviation/expected return=0.01145/-0.007=-1.64

For Portfolio,

Expected return in below avg= +.60*-.05+.20*.01+.20*-.01=-.03

Expected return in avg =+.60*-.01+.20*.6+.20*-.03 =0.108

Expected return in above avg = =+.60*0.04+.20*.09+.20*.07=0.056

Expected return of portfolio= Prob. of below avg* Expected portfolio return in below avg +Prob. of avg * Expected portfolio return in avg + Prob. of above avg* Expected portfolio return in above avg

= 0.30*-0.03+0.40*0.108+0.30*0.056 =0.051 i.e 5.10%

Expected Variance= Prob. of below avg*( Expected portfolio return in below avg-expected return) ^2 +Prob. of avg * (Expected portfolio return in avg -expected return) ^2+ (Prob. of above avg* (Expected portfolio return in above avg-expected return) ^2

= 0.00328

Expected Std deviation= Variane^1/2=0.0572

Cof. Of variation= std deviation/expected return=0.0572/0.051=1.12