Two investors, A and B, trade the stock TWTR. Each investor maximizes his expected future wealth...

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Two investors, A and B, trade the stock TWTR. Each investor maximizes his expected future wealth subject to a penalty for risk (as discussed in Chapter 5). Investor A's optimal position measured i amounts of money x4 is given by xA= (yA)-¹0-¹E(R²) Recall that yA is the risk aversion, is the risk of TWTR (i.e., variance), and E(R) is the expected excess return. The absolute risk aversion is decreasing in the investor's wealth WA such that yA = 1/WA. Further, the current dividend yield and risk free rate are zero so investor A's expected excess HA_P return is given by E (R²) = where ª > 0 is his expectation of the value of a share next year. P r (μ^-P) = ² · Finally, = var The same expressions hold for investor B with two exceptions. First, his wealth is WB and, second, his expectation is that the stock will be worthless next year (μ³ = 0) so that his expected return is E(Re) = -1 and his position is x = WB(-1). The supply of shares is given by s. a. Explain why equilibrium is characterized by the condition that XA XB P P+= =S and show that the equilibrium price without short-sale constraints is (where we assume throughout that the numerator is positive): WAμA-so WA+WB b. Is investor A long or short? What about investor B? P c. What is the equilibrium price if no investor is allowed to sell short? How does the answer compare to the equilibrium without short-sale constraints in question a.? Two investors, A and B, trade the stock TWTR. Each investor maximizes his expected future wealth subject to a penalty for risk (as discussed in Chapter 5). Investor A's optimal position measured i amounts of money x4 is given by xA= (yA)-¹0-¹E(R²) Recall that yA is the risk aversion, is the risk of TWTR (i.e., variance), and E(R) is the expected excess return. The absolute risk aversion is decreasing in the investor's wealth WA such that yA = 1/WA. Further, the current dividend yield and risk free rate are zero so investor A's expected excess HA_P return is given by E (R²) = where ª > 0 is his expectation of the value of a share next year. P r (μ^-P) = ² · Finally, = var The same expressions hold for investor B with two exceptions. First, his wealth is WB and, second, his expectation is that the stock will be worthless next year (μ³ = 0) so that his expected return is E(Re) = -1 and his position is x = WB(-1). The supply of shares is given by s. a. Explain why equilibrium is characterized by the condition that XA XB P P+= =S and show that the equilibrium price without short-sale constraints is (where we assume throughout that the numerator is positive): WAμA-so WA+WB b. Is investor A long or short? What about investor B? P c. What is the equilibrium price if no investor is allowed to sell short? How does the answer compare to the equilibrium without short-sale constraints in question a.?

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Equilibrium in the Stock Market with RiskAverse Investors a Equilibrium Condition and Price Derivati... View the full answer