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Next year, the economy will be in recession with probability 0
Next year, the economy will be in recession with probability 0.3, experience normal growth with probability 0.4, or expansion with probability 0.3. There are only two stocks available to trade in this economy (stock MJ and stock OBN). The stocks annual returns in each of the states of the world are according to the following table: Stocks MJ OBN Recession 6% 15% Normal Growth 12% 5% Expansion 14% 10% a) Show whether you can rank the stocks by the criterion of first order stochastic dominance. If yes, which stock first order stochastically dominates the other? [3 marks] b) Show whether you can rank the stocks by the criterion of second order stochastic dominance. If yes, which stock second order stochastically dominates the other? [3 marks] 3 MA535/MA835 c) Calculate the expected annual return of cach stock. [2 marks] d) Calculate the annual variance and standard deviation of each stock. [4 marks) e) Calculate the covariance and correlation coefficient between the two stocks. [3 marks] 1) Assuming that the CAPM holds, calculate the composition of the market portfolio with an expected return of 10% per annum. [2 marks] g) Calculate the beta of each security, under the assumption that the risk-free rate of interest is 1% per annum. [4 marks] h) State the limitations of the CAPM. [2 marks]
Expert Solution
You have asked a question with multiple sub parts. I have addressed the first four sub parts. Please post the balance sub parts, separately. Please don't down vote just because I have answered first four sub parts.
Q - 2
Part (a)
Since neither of the two stocks is a definitive better performer in each of the states, we can't rank the stocks using first order stochastic dominance.
Part (b)
Min of MJ returns = 6%
Min of OBN returns = 5%
Expected value of MJ returns = Sum of (probability x returns) across each of the state = 0.3 x 6% + 0.4 x 12% + 0.3 x 14% = 10.80%
Expected value of OBN returns = 0.3 x 15% + 0.4 x 5% + 0.3 x 10% = 9.50%
Thus, we have:
- Expected value of MJ returns > Expected value of OBN returns
- Min of MJ returns > Min of OBN returns
Thus, based on second order stochastic dominance, MJ dominates over OBN
Part (c)
We have already calculated them in part (b) above.
Expected value of MJ returns = 10.80%
Expected value of OBN returns = 9.50%
Part (d)
Variance = Sum of [probability x (Return - expected return)2] across each of the scenario
Std dev = Variance1/2
For MJ stock:
Variance = 0.3 x (6% - 10.8%)2 + 0.4 x (12% - 10.8%)2 + 0.3 x (14% - 10.80%)2 = 0.00106
Std dev = 0.001061/2 = 3.25%
For BN stock:
Variance = 0.3 x (15% - 9.50%)2 + 0.4 x (5% - 9.50%)2 + 0.3 x (10% - 9.50%)2 = 0.00173
Std dev = 0.001731/2 = 4.15%
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