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- A stock is trading at $80 per share. The stock is expected to have a yearend dividend of $4 per share (D1 = $4), and it is expected to grow at some constant rate, g, throughout time. The stock’s required rate of return is 14% (assume the market is in equilibrium with the required return equal to the expected return). What is your forecast of gL?Consider a stock portfolio consisting of two units of S' and one unit of S2. Calculate the probability of delta losses over one day, if the daily log-returns (X1, X2) of the stocks are independent with X1 are S = 100, S = 50. N(0.5, 1.1), X2 N(-0.2,0.5) and the current stocks valueYou have a stock trading at $100. The stock follows a lognormal distribution: with drift of 20% and volatilty of 30%. The risk free rate is 2%. What is the risk-neutral probability for a 3- month 100 put to expire in the money? Find N(-d2). Compare the results.
- Suppose the returns on a small stock are normally distributed. The historical average return is 18 percent, and the standard deviation is 6 percent. What is the probability that your return on this stock will be no less than 12 percent in a given year? What range of returns would you expect to see 95 percent of the time? What range would you expect to see 99 percent of the time?Suppose that your estimates of the possible one-year returns from investing in the common stock of the AYZ Corporation were as follows: Probability of occurrence 0.15 0.25 0.3 0.15 0.15 Possible return -10% 5% 20% 35% 50% What are the expected return? Calculate the standard deviation?A stock is expected to earn 10.0% over the next year with a 40% probability and 3.0% otherwise. What is the standard deviation of returns based on this scenario analysis? Answer in percent, rounded to one decimal place.
- The next year's return on stock X is expected to be either -7% with probability 0.2 or 20% with probability 0.8. Find the stnadard deviation of the returns. a.12.37% b.11.10% c.12.88% d.11.69% e.10.80%Assume that the future stock price in T years is given by ST = S0 exp[(μ – 0.5σ2)T + (σ√T)ε], where the current stock price S0=105, expected return µ=0.15, volatility σ=0.80 and ϵ is a standard normal random variable. What is the price level in 6 months such that there is only a 1% chance of the actual value being higher? a. 360 b. 26 c. 105 d. 570Consider a stock currently trading at $10, with expected annual return of 15% and annual volatility of 0.2. Under our standard assumption about the evolution of stock prices, what is the probability that the price of the stock in one years time will be below $9?
- 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.You know that the prices on a stock market follow a lognormal geometric random walk. Given the following parameters: 0,15 o? = 0,04, calculate: The expected log return for 5 years The median log return for 10 years The median gross 10-year return If the stock price starts at $100, what is the expected price after 10 years?Suppose you are attempting to value a 1-year expiration option on a stock with volatility (i.e., annualized standard deviation) of σ = 0.34. What would be the appropriate values for u and d if your binomial model is set up using: 1 period of 1 year. 4 subperiods, each 3 months. 12 subperiods, each 1 month.