Please show how the work is done

1. Define the following terms, using graphs or equations to illustrate your answers where feasible.

a. Risk in general; stand-alone risk; probability distribution and its relation to risk

b. Expected rate of return

c. Continuous probability distribution

d. Standard deviation, s; variance

e. Risk aversion; realized rate of return

f. Risk premium for Stock i; market risk premium, MRP

g. Capital Asset Pricing Model (CAPM)

h. Expected return on a portfolio; market portfolio

2. Security A has an expected return of 7%, a standard deviation of returns of 35%, a correlation coefficient with the market of 0.3, and a beta coefficient of 1.5. Security B has an expected return of 12%, a standard deviation of returns of 10%, a correlation with the market of 0.7, and a beta coefficient of 1.0. Which security is riskier? Why?

3. The market and Stock J have the following probability distributions: Probability rM rJ 0.3 15% 20% 0.4 9 5 0.3 18 12 a. Calculate the expected rates of return for the market and Stock J. b. Calculate the standard deviations for the market and Stock J.

4. Suppose rRF=5%, rM=10%, and rA=12%.

a. Calculate Stock A's beta.

b. If Stock A's beta were 2.0, then what would be A's new required rate of return? 2

5. Suppose you manage a $4 million fund that consists of four stocks with the following investments: Stock Investment Beta A $400,000 1.50 B 600,000 0.50 C 1,000,000 1.25 D 2,000,000 0.75 If the market's required rate of return is 14% and the risk-free rate is 6%, what is the fund's required rate of return?

6. You are considering an investment in either individual stocks or a portfolio of stocks. The two stocks you are researching, Stock A and Stock B, have the following historical returns: Year r A r B 2014 -20.00% -5.00% 2016 42.00 15.00 2017 20.00 -13.00 2018 -8.00 50.00 2019 25.00 12.00 a. Calculate the average rate of return for each stock during the 5-year period. b. Suppose you had held a portfolio consisting of 50% of Stock A and 50% of Stock B. What would have been the realized rate of return on the portfolio in each year? What would have been the average return on the portfolio during this period? c. Calculate the standard deviation of returns for each stock and for the portfolio. d. Suppose you are a risk-averse investor. Assuming Stocks A and B are your only choices, would you prefer to hold Stock A, Stock B, or the portfolio? Why?

7. You have observed the following returns over time: Year Stock X Stock Y Market 2015 14% 13% 12% 2016 19 7 10 2017 16 5 12 2018 3 1 1 2019 20 11 15 Assume that the risk-free rate is 6% and the market risk premium is 5%. a. What are the betas of Stocks X and Y? b. What are the required rates of return on Stocks X and Y? c. What is the required rate of return on a portfolio consisting of 80% of Stock X and 20% of Stock Y?