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As an investor you are faced with two choices investing in a risky fund which has a return of 12% and a standard deviation of 20% and risk free asset which has a return of 6%.

1)As a risk averse investor, my objectives is to invest in a portfolio of a 15% risk.What would be the allocation between risk free and risk assets of my investment?

2)My brother is less risk averse than me, and he is trying to acheive a return of 14%. If it is possible find the weights in both risky fund and risk free as well as the level of risk that he will be faced with.

3)What is the assets allocation (budget line) equation?

4)Show in graph, the budget line, indifference curves that represent my investment and my brother's.

In 95% of the time will the actual rate be within 2 standard deviations away from the mean.

I am confused by your question on many points.

I need some clarification wrt the risky fund. Is the average rate of return 12% with a standard deviation 20% of that. So that, the return on a $100 investment will be $12 plus or minus $4.80 in 95% of the time.

Or is the standard deviation 20 points. So that the return on a $100 investment will be $12 plus or minus $40.

Im not sure what a "portfolio of 15% risk" means. Is is a portfolio with 15% of the assest invested in a risky investment, 85% in save assets?

If the brother invests everything in the risky fund, the likelyhood he will achieve a 14% rate of return or better is well under 50%. So, with the given information, I cannot predict his risky/safe investment choice, except to say that he will choose more that 15% risky assets.

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