Question

1. An investor makes decisions based on the utility function U(w) = w - 6w^2, where w is the investor's wealth in millions of rand (Rm). (a) Demonstrate that the investor has both increasing absolute and relative risk aversion. [3 marks] The investor has R50,000 to invest over a 1-year period and has no other wealth. They have three options: i. Invest in a risk-free account. There will be no change in the value of the investment over 1 year. ii. Invest in an asset that will give a 60% return over 1 year with probability 0.2, a 20% return with probability 0.7 and a -40% return with probability 0.1. iii. Invest in an asset that will give a 30% return with probability 0.5 and a 20% return with probability 0.5. The investor makes no allowance for discounting when making investment decisions. The investor must invest the whole R50,000 in a single option. (b) Determine which option the investor should choose to maximise their expected utility at the end of the year. [6 marks] (c) Comment on why the investor could not use U(w) to choose from the above options if their initial wealth was R65,000. [3 marks] [Total: 12 marks]

          1. An investor makes decisions based on the utility function U(w) = w - 6w^2, where w is the investor's wealth in millions of rand (Rm).
(a) Demonstrate that the investor has both increasing absolute and relative risk aversion.
[3 marks]

The investor has R50,000 to invest over a 1-year period and has no other wealth. They have three options:
i. Invest in a risk-free account. There will be no change in the value of the investment over 1 year.
ii. Invest in an asset that will give a 60% return over 1 year with probability 0.2, a 20% return with probability 0.7 and a -40% return with probability 0.1.
iii. Invest in an asset that will give a 30% return with probability 0.5 and a 20% return with probability 0.5.
The investor makes no allowance for discounting when making investment decisions. The investor must invest the whole R50,000 in a single option.
(b) Determine which option the investor should choose to maximise their expected utility at the end of the year.
[6 marks]
(c) Comment on why the investor could not use U(w) to choose from the above options if their initial wealth was R65,000.
[3 marks]
[Total: 12 marks]

1. An investor makes decisions based on the utility function U(w) = w - 6w^2, where w is the investor's wealth in millions of rand (Rm).
(a) Demonstrate that the investor has both increasing absolute and relative risk aversion.
[3 marks]

The investor has R50,000 to invest over a 1-year period and has no other wealth. They have three options:
i. Invest in a risk-free account. There will be no change in the value of the investment over 1 year.
ii. Invest in an asset that will give a 60% return over 1 year with probability 0.2, a 20% return with probability 0.7 and a -40% return with probability 0.1.
iii. Invest in an asset that will give a 30% return with probability 0.5 and a 20% return with probability 0.5.
The investor makes no allowance for discounting when making investment decisions. The investor must invest the whole R50,000 in a single option.
(b) Determine which option the investor should choose to maximise their expected utility at the end of the year.
[6 marks]
(c) Comment on why the investor could not use U(w) to choose from the above options if their initial wealth was R65,000.
[3 marks]
[Total: 12 marks]

Added by Temeeka D.

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