Suppose you want to establish a bullish spread strategy. The are two call options. The first one has X1=$50 and C1=$5. The second one has X2=$42 and C2=$6. When the underlying asset price is S(t)=$45, what is the profit from the strategy? What is the maximum profit of the strategy? What is the minimum payoff of the strategy?
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- Assuming two risk-free rates for lending and borrowing in the market: r(f) and r(b). Suppose your utility function is described by U = E(r) - 0.5A xo² with A> 0, and you are combining the risk-free asset with the optimal risky asset to maximize the utility. Consider the following two situations: 1. Suppose r(b) = r(f): you form the optimal complete portfolio C1 by borrowing money at r(f) and invest y1 (i.e., y1 represents portfolio weight) in the optimal risky portfolio (P1). Your utility score under this situation is denoted as U1; II. Suppose r(b) >r(f): you form another optimal complete portfolio C2 by borrowing money at r(b) and invest y2 (1.e., y2 represents portfolio weight) in the optimal risky portfolio (P2). Your utility score under this situation is denoted as U2. For simplicity, let's assume the optimal risky portfolios under these two situations are the same (i.e., E(P1)=E(P2) and o(P1) = o(P2)). What are the relationship between y1 and y2, U1 and U2: O a. y1=y2 and U1=U2 O…Suppose stocks X and Y have equal current prices but different volatilities of returns, ax < øy; what would be more expensive: a call option on X or Y? Please discuss.What is the equation for the Security Market Line? Define each term. If an asset has a beta of 2.0, what type of return should it realize compared to the market portfolio?
- We believe that the single factor model can predict any individual asset’s realized rate of return well. Both Portfolio A and Portfolio B are well-diversified: ri = E(ri) + βiF + Ei, where E(ei) = 0 and Cov(F, i) = 0 A B β 1.2 0.8 E(r) 0.1 0.08 (1) What is the rate of return of the risk-free asset? (2) What is the expected rate of return of the well-diversified portfolio C with βC = 1.6, which also exists in the market? (3) A fund constructs a well-diversified portfolio D. Studies show that βD = 0.6. The expected rate of return of D is 0.06. Is there an arbitrage opportunity? If so, construct a trading strategy to earn profits with no risk. If not, why?Suppose the solid line represents the capital market line that results from a CAPM equilibrium and the dotted curves represent indifference curves for a given individual. Which of the following is correct if point M corresponds to the market portfolio? Group of answer choices The individual optimally holds only the market portfolio, M. The individual optimally holds portfolio B which can be partially characterized by a long position in the riskless asset. The individual optimally holds portfolio B which can be partially characterized by a short position in the riskless security The individual optimally holds portfolio A which can be partially characterized by a long position in the riskless security. None of the above.Consider the model of Black and Scholes. Consider the cash=or-nothing put option V (T) = 1{S(T)<= K} It pays out one unit of cash if the spot is below the strike at maturity. Evaluate the price of the option.
- . Write out the equation for the Capital Market Line(CML), and draw it on the graph. Interpret theplotted CML. Now add a set of indifference curvesand illustrate how an investor’s optimal portfoliois some combination of the risky portfolio and therisk-free asset. What is the composition of the riskyportfolio?An investor is considering two possible investment alternatives, Portfolio A and Portfolio B. The expected returns for each are shown in the table below under two different market conditions, along with the investors prediction for the probability of each market condition. The investor's prediction for the probability of each market condition. The investor's utility function can be represented as U(w) - square root (w). If the investor maximises their expected utility, which alternative would they choose? Portfolio A Portfolio B Bull Market Bear Market Portfolio A 16% Portfolio B 4% Probability 0.75 3% 2% 0.25According to the Black-Scholes formula, what will be the hedge ratio (delta) of a put option for a very small exercise price?
- True or False. and briefly explain. a. Under the Capital Asset Pricing Model (CAPM), if a stock has a zero beta, then it must be identical to the riskfree asset. b. For Value at Risk (VaR) to be useful, the returns have to be normally distributed. c.If the borrowing rate is higher than the lending rate, a particular risk-averse investor can achieve a maximized utility score of UC* by choosing optimally. Now if the borrowing rate is equal to the lending rate, this investor must be able to achieve a utility score higher than UC*Consider an economy with a (net) risk-free return r1 = 0:1 and a market portfolio with normally distributed return, with ErM = 0:2 and 2M = 0:02. Suppose investor A has CARA preferences, with risk aversion coe¢ cient equal to 1 and an endowment of 10. a) Write down the maximization problem for the investor. b) Determine the amount invested in the risky portfolio and in the risk-free asset. c) Suppose another investor (B) has a coe¢ cient of absolute risk aversion equal to 2 (and the same endowment 10). Compute his optimal portfolio and compare it to that of investor A. Explain the di§erent results for investors A and B. d) Finally, consider Investor C with mean-variance preferences Ec V ar(c) (and endowment 10). Compute his optimal portfolio and compare it to that of investors A and B (as obtained in questions b and c). Compare your result with those obtained for investors A and B.Evaluate the following statement: If CAPM (Capital Asset Pricing Model) holds, the expected return from a lottery must be equal to the risk-free rate.