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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- A portfolio consists of two securities: a 90-day T-bill and the S&P/TSX Composite. The expected return on the T-bill is 4.5%. The expected return on the S&P/TSX Composite is 12% with a standard deviation of 20%. What is the portfolio standard deviation if the expected return for this portfolio is 15%?The prices of a certain security follow a geometric Brownian motion with parameters mu=.12 and sigma=.24. If the security's price is presently 40, what is the probability that a call option, having four months until its expiration time and with a strike price of K=42, will be exercised? (A security whose price at the time of expiration of a call option is above the strike price is said to finish in the money).The prices of a certain security follow a geometric Brownian motion with parameters mu=.12 and sigma=.24. If the security's price is presently 40, what is the probability that a call option, having four months until its expiration time and with a strike price of K=42, will be exercised? (A security whose price at the time of expiration of a call option is above the strike price is said to finish in the money.) If the interest rate is 8%, what is the risk-neutral valuation of the call option?
- For the upcoming year, the risk-free rate is 2 percent, and the expected return to the market is 7 percent. You are also given the following covariance matrix for Securities J,K, andL. \table[[Covariance,Security J,Security K,Security L],[Security J,0.0012532,0.0010344,0.0019711],[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 0 percent of your funds in Security J, 40 percent of your funds in Security K, and 60 percent of your funds in Security L. Based on this information, determine the standard deviation of the resulting portfolio. ◻ 6.47% 5.27% 4.98% 5.82% 4.77%A stock is estimated to have a covariance with the market of 0.45. For the coming period, the market expected return is 10%, the market variance is 0.60 and the market risk-premium is 5%. If the stock is currently trading at RM2.00, use to CAPM to calculate the future price of the stock at the end of the period.Suppose that the standard deviation of quarterly changes in the prices of a commodity is $0.65, the standard deviation of quarterly changes in a futures price on the commodity is $0.81, and the coefficient of correlation between the two changes is 0.8. What is the optimal hedge ratio for a three-month contract? What does it mean? Explain what is meant by basis risk when futures contracts are used for hedging.
- Use the Black-Scholes Model to find the price for a call option with the following inputs: (1) current stock price is $30, (2) strike price is $35, (3) time toexpiration is 4 months, (4) annualized risk-free rate is 5%, and (5) varianceof stock return is 0.25.Suppose you are attempting to value a 1-year expiration option on a stock with volatility (i.e., annualized standard deviation) of σ = .40. What would be the appropriate values for u and d if your binomial model is set up using:a. 1 period of 1 year.b. 4 subperiods, each 3 months.c. 12 subperiods, each 1 month.The risk premium on the market portfolio is estimated at 8 % with a standard deviation of 22 %. What is the risk premium on a portfolio invested 25 % in AELZ with a beta of 1.15 and 75 % in BAT with a beta of 1.25?
- These securities pay $0 coupons at the end of the first 6-month period and par value at maturity. What is the weighted-average portfolio yield? What is the portfolio yield (i.e., portfolio internal rate of return)?The expected rates of return for Stocks A, B, and C are.10,.15, and .20 respectively. The risk free rate is .03 and the market risk premium is .08 . If you invest$400,$200, and$200in Stocks A, B, and C respectively, what is the beta of the portfolio? Assume that the three stocks are priced in equilibrium.The market risk premium is 10% and the risk-free rate is 4%, beta of the stock is 0.75, then Expected return under the CAPM is a. 8.5 percent b. 7 percent c. 6.35 percent d. 11.5 percent