The following numbers were randomly generated from a standard normal distribution: -0.25    0.3     1.5     -1.2     -1.65     1.5 Suppose a security follows a geometric Brownian motion with volatility parameter, sigma=0.2, and interest rate r=0.01.  If the initial closing price is S0=s=50, compute six more simulated daily closing prices.   For the daily increment in time we are using 1/252 year.

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Find the standard deviation for a security that has three one-year returns of -1%,8% , and 16%, respectively .

Security A has an expected return of 12.4% with a standard deviation of 15%, and a correlation with the market of 0.85. Security B has an expected return of -0.73% with a standard deviation of 20%, and a correlation with the market of -0.67. The standard deviation of rM is 12%. a. To someone who acts in accordance with the CAPM, which security is more risky, A or B? Why? (Hint: No calculations are necessary to answer this question; it is easy.) b. What are the beta coefficients of A and B? Calculations are necessary. c. If the risk-free rate is 6%, what is the value of rM?

Assume that the risk-free rate is 7.5% and the required return on the market is 9%. What is the required rate of return on a stock with a beta of 3? Round your answer to two decimal places.

Suppose the risk free rate is 5% and the market portfolio has an expected return of 10%. Portfolio Z has a correlation coefficient with the market of 0.1 and a variance of 0.16. The market portfolio has a variance of 0.09. According to the CAPM, what is the beta of portfolio Z?

Risk-free rate is 7%, expected return on the market portfolio is 12%. Identify the correct equation for Security Market Line (SML): a. r = 5% + b(7%) b. r = 7% + b (12%) c. r = 7% + b (5%) d. r = 5% + b (12%)

Asset W has an expected return of 13.4 percent and a beta of 1.6. If the risk-free rate is 5.0 percent, complete the following table for portfolios of Asset W and a risk-free asset. (Do not round intermediate calculations and enter your expected return answers as a percent rounded to 2 decimal places, e.g., 32.16. Round your beta answers to 3 decimal places, e.g., 32.161.)   Asset W has an expected return of 13.4 percent and a beta of 1.6. If the risk-free rate is 5.0 percent, complete the following table for portfolios of Asset W and a risk-free asset. (Do not round intermediate calculations and enter your expected return answers as a percent rounded to 2 decimal places, e.g., 32.16. Round your beta answers to 3 decimal places, e.g., 32.161.)

Assume that the short-term risk-free rate is 6%, the market index S&P500 is expected to pay returns of 30% with the standard deviation equal to 40%. Asset A pays on average 10%, has a standard deviation equal to 40% and is NOT correlated with the S&P500. Asset B pays on average 16%, also has a standard deviation equal to 40% and has a correlation of 1 with the S&P500. Determine whether asset A and B are overvalued or undervalued, and explain why.  (Beta of asset i (?i) = ?i ?iM / ?M, where ?i, ?M are standard deviations of asset i and market portfolio, ?iM is the correlation between asset i and the market portfolio)

What is portfolio A's CAPM beta based on your analysis? Round off your answer to three digits after the decimal points. State your answer as a percentage point as 1.234.   Compute the Treynor measure for portfolio B. Round off your answer to three digits after the decimal point. State your answer as 1.234