Introduction to Finance 1) The expected return of Security A is 10% with a standard deviation of 20%. The expected return of Security B is 15% with a standard deviation of 30%. Securities A and B have a correlation of 0.3. The market return is 12% with a standard deviation of 18% and the risk free rate is 3.5%. What is the Sharpe ratio of a portfolio if 40% of the portfolio is in Security A and the remainder in Security B? 2) The current price of Stock Y is $50. It is expected that the stock will pay 4 quarterly dividends of $0.25 each and sell for $52 in one year. The risk-free rate is 3.5%. The expected return on the market portfolio is 12% with a standard deviation of 18%. Assume the market is in equilibrium. What is the beta of Stock Y? 3) The market expected return is 8% with a standard deviation of 18%. The risk free rate is 3.5%. Security XYZ has just paid a dividend of $5 and has a current price of $80. What is the beta of Security XYZ if its dividend is expected to grow at 2% per year indefinitely? 4)The income yield and capital gain yield of a stock are 6% and 5%, respectively. The stock paid a quarterly dividend of $1.5 per share during the year. What should the stock sell for today? 5) Suppose you plan to create a portfolio with two securities: A and B. A has an expected return of 35% with a standard deviation of 22%. B has an expected return of 20% with a standard deviation of 9%. The correlation between the returns of these two securities is perfectly negative. What percentage of your investment should be in A to make the portfolio risk free? What would be the expected return on the portfolio? 6) Suppose you own a two-security portfolio. You have 54% of your money invested in Security X and the remainder in Security Y. The standard deviations of Securities X and Y are 30 percent and 25 percent. What is the correlation between the two securities if the portfolio standard.Introduction to Finance

 

1) The expected return of Security A is 10% with a standard deviation of 20%.  The expected

return of Security B is 15% with a standard deviation of 30%. Securities A and B have a

correlation of 0.3.  The market return is 12% with a standard deviation of 18% and the risk free

rate is 3.5%.  What is the Sharpe ratio of a portfolio if 40% of the portfolio is in Security A and

the remainder in Security B?  

 

2) The current price of Stock Y is $50.  It is expected that the stock will pay 4 quarterly

dividends of $0.25 each and sell for $52 in one year.  The risk-free rate is 3.5%. The expected

return on the market portfolio is 12% with a standard deviation of 18%.  Assume the market is

in equilibrium.  What is the beta of Stock Y?

 

3) The market expected return is 8% with a standard deviation of 18%.  The risk free rate is

3.5%.  Security XYZ has just paid a dividend of $5 and has a current price of $80.  What is the

beta of Security XYZ if its dividend is expected to grow at 2% per year indefinitely?

 

4)The income yield and capital gain yield of a stock are 6% and 5%, respectively.  The stock

paid a quarterly dividend of $1.5 per share during  the year. What should the stock sell for

today?

 

 5) Suppose you plan to create a portfolio with two securities: A and B. A has an expected

return of 35% with a standard deviation of 22%.  B  has an expected return of 20% with a

standard deviation of 9%.  The correlation between  the returns of these two securities is

perfectly negative.  What percentage of your investment should be in A to make the portfolio

risk free?  

What would be the expected return on the portfolio?

 

6) Suppose you own a two-security portfolio. You have 54% of your money invested in Security

X and the remainder in Security Y. The standard deviations of Securities X and Y are 30 percent

and 25 percent. What is the correlation between the two securities if the portfolio standard

deviation is 0.1414?

 

7) Stock A: expected return= 10%; standard deviation= 40%

    Stock B: expected return= 20%; standard deviation= 23%

You short sold 200 shares of A at 15 $ per share and purchased 500 shares of B at 15$ per share. The     correlation between securities is -0.32. What is the standard deviation of the portfolio?