You have 3 assets A, B, C in a world with two future states, High and Low.
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Question:
You have 3 assets A, B, C in a world with two future states, High and Low. The probability that the state High occurs is 0.5. These assets have the following net return structure:
Low High
A 0.02 0.02
B 0 0.1
C-0.2 0.2
- Compute the covariance of the returns for each pair of these assets
- Compute the correlation coefficient of the returns for each pair of these assets
- Assume that correlation of returns of assets B and C is 1. Assume that you can only buy assets (shares of both assets must be non-negative).
- Derive the formula for portfolio variance when the share of asset B is denoted by w.
- Can you construct a portfolio of assets B and C that has a variance of zero? (Hint for b and c: recall how the efficient frontier for such assets looks likes)
- How big should be the shares of both assets in your portfolio if you would like to achieve the highest possible variance?
- Assume that correlation of returns of assets B and C is -1 (e.g., B pays now 0.1 in Low and 0 in High). Assume that you can only buy assets (shares of both assets must be non-negative).
- Derive the formula for portfolio variance when the share of asset B is denoted by w.
- Can you construct a portfolio of assets B and C that has a variance of zero? (Hint for b and c: recall how the efficient frontier for such assets looks likes)
- How big should be the shares of both assets in your portfolio if you would like to achieve the highest possible variance?
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