(II) Consider two assets, X and Y. There are three states, i.e. N = 3, each...
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(II) Consider two assets, X and Y. There are three states, i.e. N = 3, each with probability 1/3. Asset rate of returns are as follows: X₁ = 0.09, X₂ = 0.03, X3 = -0.06 and Y₁ = 0.06, Y₂ = -0.03, Y3 = 0. (A) Calculate E(X), Vol(X), E(Y) and Vol(Y). Can we say that one asset is better than the other? (B) Calculate Cov(X, Y) and the correlation coefficient px,y. Are the returns of the two assets per- fectly correlated, positively correlated or negatively correlated? Explain also intuitively your answer. (C) Suppose you invest a fraction Wx in asset X and the rest, Wy = 1- Wx in asset Y. Calculate for the values Wx 0, WX = 1/5, Wx 2/5, Wx= 3/5, Wx 4/5 and Wx = 1 the values of E[WxX + (1 - Wx)Y] and Vol [WxX + (1 - Wx)Y] and report in a table. Then draw a graph with these values in a coordinate system with the volatility on the first axis and expected value on the second axis. Why is the graph not a straight line? = = = (II) Consider two assets, X and Y. There are three states, i.e. N = 3, each with probability 1/3. Asset rate of returns are as follows: X₁ = 0.09, X₂ = 0.03, X3 = -0.06 and Y₁ = 0.06, Y₂ = -0.03, Y3 = 0. (A) Calculate E(X), Vol(X), E(Y) and Vol(Y). Can we say that one asset is better than the other? (B) Calculate Cov(X, Y) and the correlation coefficient px,y. Are the returns of the two assets per- fectly correlated, positively correlated or negatively correlated? Explain also intuitively your answer. (C) Suppose you invest a fraction Wx in asset X and the rest, Wy = 1- Wx in asset Y. Calculate for the values Wx 0, WX = 1/5, Wx 2/5, Wx= 3/5, Wx 4/5 and Wx = 1 the values of E[WxX + (1 - Wx)Y] and Vol [WxX + (1 - Wx)Y] and report in a table. Then draw a graph with these values in a coordinate system with the volatility on the first axis and expected value on the second axis. Why is the graph not a straight line? = = =
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A To calculate the expected value E and volatility Vol for assets X and Y we use the following formulas EX xi pi VolX sqrtxi EX2 pi EY yi pi VolY sqrt... View the full answer
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