A futures price is currently 41 and has a volatility of 30%. The risk-free rate is 5%. The strike price on a 9-month put is 40. A three-period binomial lattice is used. Calculate the risk-neutral probability p*.
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- The discounted returns on a portfolio are normally distributed with mean 1.2% and volatility 13%. Find the 1% 10-day expected shortfall (ES) assuming the returns are i.i.d. You are given that ϕ(Φ−1(0.01))=0.02265.Assume that the risk free rate is currently 3% and that the market retunr is currently 11%. Calculate the market risk premium Give the previous datea, calculate the required retun on asset A having a beta of 0.3 and asset B having a beta of 1.5.The risk-free rate is 4%, and the expected rate of return on the market portfolio is 9%. Calculate the required rate of return on a security with a beta of 1.21. (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.)
- Asset W has an expected return of 8.8 percent and a beta of .9O. If the risk-free rate is 2.6 percent, complete the following table for portfolios of Asset W and a risk-free asset. (Do not round intermediate calculations. Enter your expected returns as a percent rounded to 2 decimal places, e.g., 32.16, and your beta answers to 3 decimal places, e.g., 32.161.) Answer is complete and correct. Percentage of Portfolio in Asset W Portfolio Expected Portfolio Return Beta % 2.60 % 25 4.15 % 0.225 50 5.70 % 0.450 75 7.25 % 0.680 100 8.80 % 0.900 125 10.35 % 1.130 150 11.90 % 1.350 you plot the relationship between portfolio expected return and portfolio beta, what is the slope of the line that results? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) If X Answer is not complete. Slope of the lineAn investiment portfolio consists of two securities, X and Y. The weight of X is 30%. Asset X's expected return is 15% and the standard deviation is 28%. Asset Y's expected return is 23% and the standard deviation is 33%. Assume the correlation coefficient between X and Y is 0.37. A. Calcualte the expected return of the portfolio. B. Calculate the standard deviation of the portfolio return. C. Suppose now the investor decides to add some risk free assets into this portfolio. The new weights of X, Y and risk free assets are 0.21, 0.49 and 0.30. What is the standard deviation of the new portfolio?Suppose the market premium is 12%, market volatility is 20% and the risk-free rate is 6%. Suppose a security has a beta of 0.8. Using the CAPM, what is its expected return? (Round off the final answer to one decimal place. Example of writing your answer 2.5%)
- Suppose the market risk premium is 9 % and also that the standard deviation of returns on the market portfolio is 0.26 . Further assume that the correlation between the returns on ABX (Barrick Gold) stock and returns on the market portfolio is 0.62 , while the standard deviation of returns on ABX stock is 0.36 . Finally assume that the risk-free rate is 2 %. Under the CAPM, what is the expected return on ABX stock? (write this number as a decimal and not as a percentage, e.g. 0.11 not 11%. Round your answer to three decimal places. For example 1.23450 or 1.23463 will be rounded to 1.235 while 1.23448 will be rounded to 1.234)Suppose a security follows a geometric Brownian motion with interest rate r=0.01, volatility parameter, sigma=0.2, and drift parameter mu=-0.01. If the initial closing price is S0=s=50, compute six more simulated daily closing prices.For the upcoming year, the risk-free rate is 2 percent, and the expected return to the market is 7 percent, and the standard deviation of the market is 20 percent. You are also given the following covariance matrix for Securities J, K, and L. Covariance Security J Security K Security J 0.0012532 0.0010344 Security K 0.0010344 0.0023717 0.0013558 Security L 0.0019711 0.0013558 0.0048442 Also assume that you form a portfolio by putting 40 percent of your funds in Security J, O percent of your funds in Security K, and 60 percent of your funds in Security L. Based on this information, determine the required return of the resulting portfolio, based on the Capital Market Line (CML). O 3.17% O 2.94% O 3.49% O 3.34% Security L 0.0019711 O 3.64%
- Assume that K=61, St =65, t = 0.25 (i.e. time to expiry is 3 months), and the risk-free rate is 0.04. The current price of the put option is p = 4. If the price of the call option is 7.17, describe the arbitrage that would be possible, and calculate the profit that would result.If the T Bill rate is 1.1% and the market risk premium is 10.8%, what is the CAPM-implied expected return on a portfolio invested 50% in the risk-free asset and 50% in the market?Enter your answer as a percentage rounded to 2 decimal places.Consider the discrete-time binomial tree model with three periods of length 1, i.e. T = 3 and t = 0, 1, 2, 3. In each period the price can move up or down, St+1 is either uSt or dSt. Assume that the factor for moving up is u = 4/3, the factor for moving down is d = 3/4, and that the interest rate is r = 0.0. The initial stock price is So = 1. (a) Compute the price process (i.e. prices at all times and states) for a European Put option on the stock with strike price K = 1 and maturity T = 3. (x - ž) (b) Compute the price at time t = 0 of the Australian option K with ST K = 1. Note: As this option is path dependent, you will not be able to use the recursive method, nor will you be able to use the CRR formula.