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- Consider the below graph: E(R₁) E(RM) R₁ stocks M O stocks O What is the slope of the graph? If the historical return of an individual stock is lying the slope then the stock is undervalued or overvalued?Suppose stock A's return is related to the market return by: RetA=0.6*Market Return + 0.04* (Market Return)² What is the change in stock A given a change in the market return? Suppose stock B's return is related to the market return by: RetB=0.6*Market Return What is the difference in returns between A and B if the market return is 5%? What is the difference if the market return is -5%?4. Valuation of a Derivative Consider a derivative on a stock with the time to expiration T and the following payoff: 0 K₁ 0 if ST K₁. What is the present value of the derivative? Provide an analytic expression of the price using N(), the cumulative probability distribution function of a standard normal random variable.
- What are the expected returns for stocks Y and Z under the conditions shown below? A0 0.04 k1 0.07 k2 0.05 by,1 0.5 by,2 1.3 bz,1 1.2 bz,2 0.9Stocks A and B have the following data. Assuming the stock marketyls efficient and the stocks are in equilibrium, which of the following statements is CORRECT? \table[[,A,BLet Ps be the current market price of a share of common stock of Company X. Let P; be the "fundamental" value of a share of common stock of Company X. Let r be the long-run average annual compounded rate of return on common stocks, ånd b be the long-run annual compounded rate of return on corporate bonds. Finally, let ɛ be a random error term. Which of the following equations best characterizes the Efficient Markets Hypothesis? Select one: O a. Ps = Pf + r+ ɛ O b. Ps = Pf + ɛ- b O c. Ps = (Pf + ɛ) x (r – b) O d. Ps = Pf + ɛ
- Consider a financial market consisting of a bank account So(t) and a stock S₁ (t) modelled on a probability space (2, F, P) with the time indices t = 0, 1, 2, ..., T. consider a one period financial market model with T = 1, S = {w₁, W₂}, F is the collection of all events and P is a probability measure such that P({w₁}) > 0, P({₂}) > 0. Assume that So(0) = 1, S₁ (0) = d> 0 and So(1,₂)= (1+r) So(1, ₁) = S₁(1, ₁) = S₁ (1, ₂) = where 0 0 is the interest rate. Question: d₁, d₂, a) Write the payoff of the European call option with strike price K. b) Assume d = 5, r = 0.2, d₁ = 3, d₂ = 8, K = 7. Find the price of the option. c) Find the replicating strategy for the option.Consider a financial market consisting of a bank account So(t) and a stock S₁ (t) modelled on a probability space (, F, P) with the time indices t = 0, 1, 2, ..., T. Give conditions under which a market is arbitrage-free. Explain what it means to say that a market is complete. Give conditions under which an arbitrage-free market is complete.If the interest rate is approximately equal to the growth rate of dividends, the price of a stock will be close to Select one: a. infinity O b. It is impossible to tell based on the information above O c. 100000 O d. 0
- 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.Q2) Consider the below graph: E(R₁) Ans: E(RM) R₁ stocks M O stocks O What is the slope of the graph? If the historical return of an individual stock is lying the slope then the stock is undervalued or overvalued? Ans: Slope of the Graph is called= BAssume that security returns are generated by the single-index model,Ri = αi + βiRM + eiwhere Ri is the excess return for security i and RM is the market’s excess return. The risk-free rate is 2%. Suppose also that there are three securities A, B, and C, characterized by the following data: Security βi E(Ri) σ(ei) A 0.7 7 % 20 % B 0.9 9 6 C 1.1 11 15 a. If σM = 16%, calculate the variance of returns of securities A, B, and C. b. Now assume that there are an infinite number of assets with return characteristics identical to those of A, B, and C, respectively. What will be the mean and variance of excess returns for securities A, B, and C? (Enter the variance answers as a percent squared and mean as a percentage. Do not round intermediate calculations. Round your answers to the nearest whole number.)