6. Portfolio Theory (15 pts) Expected Return Standard Deviation Variance Coeffic

ID: 2806882 • Letter: 6

Question

6. Portfolio Theory (15 pts) Expected Return Standard Deviation Variance Coefficient of Variation (CV) Twitter 12% 17% 0.0289 1.42 Facebook 10% I 5% 0.0225 1.50 Risk-free Asset 2% 0 0 0 Covariance Matrix Twitter 0.0289 0.0102 Facebook 0.0102 0.0225 Twitter Facebook Calculation the expected return and variance for the portfolio with 40% of your money invested in Twitter and 60% i) of your money invested in Facebook. Round the variance to 4 decimal laces. Exp. Return- Variance- ii) Calculation the expected return and variance for the portfolio with 30% of your money invested in the risk-free asset and 70% of decimal places your money invested in Twitter. Round the variance to 4 Exp. Return- Variance- iii) Which risky investment is associated with the least amount of absolute risk? Circle the correct answer Facebook Twitter iv) Which risky investment is associated with the least amount of relative risk? Circle the correct answer Facebook Twitter

Explanation / Answer

6) i) Expected Return of the portfolio = Weight of Twitter* Expected Return of Twitter + Weight of Facebook * Expected return of Facebook

Weight of Twitter= 40%

Weight of Facebook = 60%

Expected Return of Twitter = 12%

Expected Return of Facebook = 10%

Expected Return of the portfolio = 0.4*12 + 0.6*10 = 10.8%

Variance of the portfolio = (Weight of Twitter) ^2* (Variance of Twitter) ^2 + (Weight of Facebook) ^2* (Variance of Facebook) ^2 + 2* covariance of (Twitter, Facebook)*(Weight of Twitter) * (Weight of Facebook)

Weight of Twitter= 40%

Weight of Facebook = 60%

Variance of Facebook = 0.0225

Variance of Twitter = 0.0289

Covariance (Facebook, Twitter) = 0.0102

Variance of the portfolio = (0.4) ^2*0.0289 + (0.6) ^2*(0.0225) + 2*0.4*0.6*0.0102 = 0.01762 = 1.76%

ii) Expected Return of the portfolio with 30% in risk free asset and 70% in twitter

Weight of Twitter* Expected Return of Twitter + Weight of Risk Free Asset * Expected return of Risk Free Asset

Weight of Twitter= 70%

Weight of Risk Free Asset = 30%

Expected Return of Twitter = 12%

Expected Return of Risk Free Asset = 2%

Expected Return of the portfolio = 12*0.7 + 2*0.3 = 9%

Variance of the portfolio = (Weight of Twitter) ^2* (Variance of Twitter) ^2 + (Weight of Risk Free Asset) ^2* (Variance of Risk Free Asset) ^2 + 2* covariance of (Twitter, Risk Free Asset)*(Weight of Twitter) * (Weight of Risk Free Asset)

Weight of Twitter= 70%

Weight of Risk Free Asset = 30%

Variance of Risk Free Asset = 0

Variance of Twitter = 0.0289

Covariance (Risk Free Asset, Twitter) = 0 (Co-Variance of Risk Free Asset and Risky Asset is Zero)

Variance of the portfolio = (0.7) ^2*0.0289 + (0.3) ^2*(0) + 2*0.7*0.3*0= 0.0142 = 1.42%

iii) Investment which is associated with least of amount of absolute risk is “Twitter”. The reason is obviously the metric of Standard Deviation or Variance which is higher in both cases for “Twitter” over “Facebook”.

iv) Investment which is associated with least of amount of relative risk is “Facebook”. The reason is obviously the metric of Coefficient of Variation as it is a standardized relative measure which measures the dispersion of variation of one stock over the other. Hence “Face book’s” dispersion is more wider than Twitter and thus it is relatively least risky.

Portfolio

Expected Return

Variance

Facebook & Twitter

10.80%

1.76%

Twitter & Risk Free Asset

1.42%