Shares in Springfield Nuclear Power Corp. $($SNP$)$ currently sell for $$25.$ You believe that the shares will be worth $$30$ in one year, and this implies that return you expect on these shares is $20\%($the company pays no dividends$).$

$1.$ If you invest $$10,000$ by purchasing $400$ shares, what the expected value of your holdings next year?

$2.$ Now suppose that you buy $400$ shares of SNP$,$ but you finance this purchase with $$5,000$ of your own funds and $$5,000$ that you raise by selling short $100$ shares of Nader Insurance Inc. Nader Insurance shares currently sell for $$50,$ but next year you expect them to be worth $$52.$ This implies an expected return of $4\%.$ If both shares perform as you expect, how much money will you have at the end of the year after you repurchase $100$ Nader shares at the market price and return them to your broker? What rate of return on your $$5,000$ investment does this represent?

$3.$ Suppose you buy $400$ shares of SNP and finance them as described in part b$.$ However, at the end of the year SNP share is worth $$31.$ What was the percentage increase in SNP share? What is the rate of return on your portfolio $($again$,$ after you repurchase Nader shares and return them to your broker$)?$

$4.$ Finally, assume that at the end of one year, SNP shares have fallen to $$24.$ What was the rate of return on SNP share for the year? What is the rate of return on your portfolio?

$5.$ What is the general lesson illustrated here? What is the impact of short selling on the expected return and risk of your portfolio?