In Question 1.3, you paid €850 to purchase stock in a company on the advice of your financial advisor. Now suppose you are risk-averse and have the concave utility function \(U(W)=\sqrt{W}\), where \(W\) is wealth, and it is equally likely that the stock will not do as well. Its value will be \(850+x\) if it does well, and \(850-x\) if it does not do well. What is your risk premium if \(x=400\) and if \(x=160\) ? In comparing your two answers, what can you deduce about the relationship between the risk premium and the value of \(x\) (the variability of the prospect)?

Data From Question 1.3:-

On the advice of your financial advisor, you buy 50 shares of a company at the price of \(€ 17\) per share. She has told you that there is an \(80 \%\) probability that the stock price will increase to \(€ 25\) over the course of the next six months and a \(20 \%\) chance that the stock price will fall to \(€ 15\) per share. What is the expected value and the variance of your purchase?