1) Assume that the market has an expected return of 12% and volatility (standard deviation) of 20%. Company X has a 50% volatility (standard deviation). The correlation between the market and Company X is 90%. The risk-free rate is 3%. What would be the expected return on Company X?

1. 23%
2. 23,25%
3. 23,50%
4. 23,75%

2)Refer to Question 1 above. Suppose that you want to take only 15% risk (standard deviation) on your investment portfolio. What would be the return you can get if you invest in only Company X and the risk-free asset?

1. 9%
2. 9,025%
3. 9,050%

1. Expected return of the market = 12%

Standard deviation of the market = 20%

Standard deviation of the Company X = 50%

Correlation between the market and the company X = 90%

Risk free rate = 3%

To calculate the expected return of company X which is calculated through CAPM we need to calculate beta.

Beta = Covariance / variance of market

Where, Covariance = Correlation * standard deviation of X * standard deviation of the market.

So, Beta = Correlation * standard deviation of X * standard deviation of the market / variance of market

= 0.9 * 0.5 * 0.2 / (0.2)^2

= 0.9 * 0.5 / 0.2

= 0.45 / 0.2

= 2.25

According to CAPM,

Expected return of company X = Risk free rate + ( Expected return of the market – Risk free rate) * Beta

= 3 + ( 12 – 3) * 2.25

= 3 + 9*2.25

= 3 + 20.25

= 23.25%

Therefore, Expected return of the Company X = 23.25% (ANSWER)

Option B is the correct answer.

2. In this question, the volatility of the Company X has changed from 50% to 15%

Expected return of the market = 12%

Standard deviation of the market = 20%

Standard deviation of the Company X = 15%

Correlation between the market and the company X = 90%

Risk free rate = 3%

To calculate the expected return of company X which is calculated through CAPM we need to calculate beta.

Beta = Covariance / variance of market

Where, Covariance = Correlation * standard deviation of X * standard deviation of the market.

So, Beta = Correlation * standard deviation of X * standard deviation of the market / variance of market

= 0.9 * 0.15 * 0.2 / (0.2)^2

= 0.9 * 0.15 / 0.2

= 0.135 / 0.2

= 0.675

According to CAPM,

Expected return of company X = Risk free rate + ( Expected return of the market – Risk free rate) * Beta

= 3 + ( 12 – 3) * 0.675

= 3 + 9*0.675

= 3 + 6.075

= 9.075%

Therefore, Expected return of the Company X = 9.075% (ANSWER)

Option D is the correct answer.

PLEASE LIKE THE ANSWER IF YOU FIND IT HELPFUL OR YOU CAN COMMENT IF YOU NEED CLARITY / EXPLANATION ON ANY POINT.