(I) Suppose there are two assets, Z and Y. N = 3 and the three probabilities...

  

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(I) Suppose there are two assets, Z and Y. N = 3 and the three probabilities are 1/3 for each outcome. For the first outcome, Z has a payout of $4 and Y $1. We write this as Z = 4 and Y = 1. For the second outcome, Z has a payout of $6 and Y $0, so Z2 = 6 and Y2 = 0. For the third outcome, Z has a payout of $8 and Y $-1, i.e. Z3 = 8 and Y3 = -1. You may think about the payout as the value (f.i. price + dividend) of the asset after one period, so that this is what you get from holding the asset for one period. (A) What are then the expected gross returns for each asset? (B) What is the covariance between the gross returns of the two assets? What is their correlation coefficient? (C) The price of the first asset, Z is $4, while the price of the second, Y is $0. You have $80.000 to invest. How much should you buy of each of the assets (i.e. how should you compose your portfolio), if you like high returns, but dislike risks? What would then be your return for each outcome and your expected return on your $80.000 investment? (D) Suppose the price of the second asset is instead $2, while the first still has price $4. Assume that it is not possible to go short in any of the two assets. (i) If you want zero risk, how should you invest your $80.000 and what will your expected (gross) return be? (ii) If in stead you want maximal ate Windo expected (gross) return (so not caring at all about risks), how should you invest your $80.000 and what would your expected return be? Explain for each case! to Settings to act (I) Suppose there are two assets, Z and Y. N = 3 and the three probabilities are 1/3 for each outcome. For the first outcome, Z has a payout of $4 and Y $1. We write this as Z = 4 and Y = 1. For the second outcome, Z has a payout of $6 and Y $0, so Z2 = 6 and Y2 = 0. For the third outcome, Z has a payout of $8 and Y $-1, i.e. Z3 = 8 and Y3 = -1. You may think about the payout as the value (f.i. price + dividend) of the asset after one period, so that this is what you get from holding the asset for one period. (A) What are then the expected gross returns for each asset? (B) What is the covariance between the gross returns of the two assets? What is their correlation coefficient? (C) The price of the first asset, Z is $4, while the price of the second, Y is $0. You have $80.000 to invest. How much should you buy of each of the assets (i.e. how should you compose your portfolio), if you like high returns, but dislike risks? What would then be your return for each outcome and your expected return on your $80.000 investment? (D) Suppose the price of the second asset is instead $2, while the first still has price $4. Assume that it is not possible to go short in any of the two assets. (i) If you want zero risk, how should you invest your $80.000 and what will your expected (gross) return be? (ii) If in stead you want maximal ate Windo expected (gross) return (so not caring at all about risks), how should you invest your $80.000 and what would your expected return be? Explain for each case! to Settings to act