Bonus Question $(10$ points$)$ Do not attempt this problem until you are finished with the rest of the exam. This problem is very time consuming relative to the number of points you can receive.

At the end of the summer, you have managed to save up some money from your internship at the banana stand. With a little capital $($there$\text{'}$s always money in the banana stand$)$ and the tools you have acquired from FIN $3503,$ you decide to start investing. You are browsing the ETF listings on Yahoo! Finance. You believe the combination of instant diversification, low cost, and flexibility makes ETFs one of the most useful innovations and attractive pieces of financial engineering to date. ETFs simplify index and sector investing, which is important given your busy schedule next year.

In your research, you see that the ETF Pharmaceutical HOLDRs $($PPH$)$ is trading at a bid price of $$43\mathrm{.}17$ and an ask price of $$43\mathrm{.}19.$ You observe the following data on holdings and the top of the order book for these assets:

$\backslash$table$[[,,,$Bid,Ask$],[$Company$,$Symbol,$\%$ Assets,Price,Size,Price,Size$],[$Pharmaceutical HOLDRs,PPH$,$n$/$a$,43\mathrm{.}17,2,100,43\mathrm{.}19,2,000],[$Johnson & Johnson,JNJ$,45,65\mathrm{.}74,1,350,65\mathrm{.}75,1,400],[$Pfizer$,$ Inc.,PFE,$40,20\mathrm{.}40,7,030,20\mathrm{.}43,700],[$Merck & Co$.,$MRK$,15,36\mathrm{.}58,1,400,36\mathrm{.}60,1,700]]$

Show that there is an arbitrage opportunity. Detail how you can exploit it$.$ Quantify your profit per share and your maximum profit before impacting prices. $($Assume no other transaction costs.$)$