Assume you are considering investing in the following four assets. Assets 1, 2 and 3 returns...

 

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Assume you are considering investing in the following four assets. Assets 1, 2 and 3 returns depend on the market condition and the return of Asset 4 depends on the amount of rainfall. Assume that there is no correlation between the amount of rainfall and the market condition. Denote by r, the rate of return of asset / in percentage points. Market | Probability | | ra ra Good 1/4 16 4 20 1/2 Average Poor 12 6 14 888 1/4 (d) Find the expected rate of return and portfolios: Portfolio W₁ W₂ W₂ 1 1/2 1/2 0 2 1/2 0 3 1/2 4 5 6 (a) Find the expected value and the standard deviation of the rate of return for each asset. (b) Find the covariance between each pair of asset (c) Let w/ be the weight of asset i, i = 1, ...., 4, in a portfolio composed of the four assets. Derive the expected rate of return and variance of the portfolio as a function of wi. OOR org 0 0 0 0 1/2 0 0 1/2 1/2 0 1/2 0 1/2 0 1/2 1/2 ONN 0 Rainfall Plentiful Average Light 1/2 Portfolio 7 Probability 1/3 1/3 1/3 8 9 10 11 TA 16 12 18 .com the following W₁ W₂ W3 1/3 1/3 1/3 0 1/3 0 1/3 1/3 1/3 0 1/3 1/3 1/4 1/4 1/4 W₁ 0 1/3 1/3 1/3 (e) Plot the original four assets and each of the portfolios in (d) in the 7-o plane. 1/4 (f) What is the r um expected rate of return that a mean-variance optimizer (à la Markowitz) investor should accept from the four-asset portfolio? Short sales are not allowed. (g) What expected rate of return would you want from the four-asset portfolio? Briefly explain the logic behind your choice. (h) Determine the portfolio that yields the return you specified in (g). Assume you are considering investing in the following four assets. Assets 1, 2 and 3 returns depend on the market condition and the return of Asset 4 depends on the amount of rainfall. Assume that there is no correlation between the amount of rainfall and the market condition. Denote by r, the rate of return of asset / in percentage points. Market | Probability | | ra ra Good 1/4 16 4 20 1/2 Average Poor 12 6 14 888 1/4 (d) Find the expected rate of return and portfolios: Portfolio W₁ W₂ W₂ 1 1/2 1/2 0 2 1/2 0 3 1/2 4 5 6 (a) Find the expected value and the standard deviation of the rate of return for each asset. (b) Find the covariance between each pair of asset (c) Let w/ be the weight of asset i, i = 1, ...., 4, in a portfolio composed of the four assets. Derive the expected rate of return and variance of the portfolio as a function of wi. OOR org 0 0 0 0 1/2 0 0 1/2 1/2 0 1/2 0 1/2 0 1/2 1/2 ONN 0 Rainfall Plentiful Average Light 1/2 Portfolio 7 Probability 1/3 1/3 1/3 8 9 10 11 TA 16 12 18 .com the following W₁ W₂ W3 1/3 1/3 1/3 0 1/3 0 1/3 1/3 1/3 0 1/3 1/3 1/4 1/4 1/4 W₁ 0 1/3 1/3 1/3 (e) Plot the original four assets and each of the portfolios in (d) in the 7-o plane. 1/4 (f) What is the r um expected rate of return that a mean-variance optimizer (à la Markowitz) investor should accept from the four-asset portfolio? Short sales are not allowed. (g) What expected rate of return would you want from the four-asset portfolio? Briefly explain the logic behind your choice. (h) Determine the portfolio that yields the return you specified in (g).

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