$(13$ points$)$ Jonathan's family has just settled a lawsuit with the Hawkins National Laboratory for its role in some nefarious activities that negatively affected his family. For his efforts in helping the family, Jonathan receives $$10,000.$ Jonathan is an aspiring photographer and plans to use the money to attend NYU in a couple years. He knows NYC is more expensive than Indiana and considers investing his money in some mutual funds.

a$)$ Jonathan has been perusing the internet and has decided to invest in one of the two following funds. He can alfo invest in a money market mutual fund that returns $1\%.$

$\backslash$table$[[$Fund$,$Ticker,Expected Return $(\%),$Standard Deviation $(\%)],[$Castle Byers,CB$,19,32],[$MKUltra$,$MKU,$25,40]]$

If Jonathan can only invest in a combination of the money market mutual fund and one of the two funds, which fund should he choose?

b$)$ After doing some more planning, Jonathan believes that while it would be awesome to have some more money when he moves to NYC$,$ he needs to have at least $$8,500,$ so he can't really afford to lose more than $$1,500.$ If he can tolerate a risk of $15\%$ on his investment from part $($a$),$ how much money should Jonathan invest in the fund from part $($a$)?$

c$)$ How much money should Jonathan invest in the money market mutual fund?

d$)$ If Jonathan invests the amounts you suggest, what is the expected return of his portfolio?

e$)$ Jonathan's brother, Will, is hanging around listening to The Clash and observing Jonathan's analysis. Will suggests that since funds CB and MKU have different investment strategies, their returns probably don't tend to move around together so that Jonathan might be better off investing in a combination of both funds and the money market mutual fund. Will estimates that the correlation is about $0\mathrm{.}2$ for returns on CB and MKU. What are the expected return and standard deviation of a portfolio that invests $50\%$ in CB and $50\%$ in MKU?

f$)$ Briefly explain whether Jonathan is better off investing in a combination of the money market mutual fund and the $50-50$ portfolio from part $($e$)$ compared to his decision in part $($a$)?$