You have $$10$M to invest, and you are considering different trading strategies. Apple's stock $($AAPL$)$ is currently trading at $$24\mathrm{.}68($ask price$)$ and $$24\mathrm{.}65($bid price$),$ and you have the following information on option prices with APPL as the underlying asset and all maturing in January:

Calls $($C$)$ Puts $($P$)$

Strike $($K$)$ Bid Ask Bid Ask

$22\mathrm{.}52\mathrm{.}552\mathrm{.}60\mathrm{.}150\mathrm{.}2$

$250\mathrm{.}750\mathrm{.}80\mathrm{.}850\mathrm{.}9$

$27\mathrm{.}50\mathrm{.}10\mathrm{.}152\mathrm{.}82\mathrm{.}9$ You are debating the risks and rewards associated with the following trading strategies:

Invest the $$10$M in AAPL stock.

Use the $$10$M to buy call options with a strike of K $=$ $$25$ and, for each call bought, sell a call with a strike of K $=$ $$27\mathrm{.}50$

Use the $$10$M to buy put options with a strike of K $=$ $$25$

and, for each put bought, sell a put with a strike of K $=$ $$22\mathrm{.}50$

Let ST denote the value of AAPL at maturity.

$($a$)(*)$ Using Excel, generate the returns of the three strategies for a range of values of ST that goes from $$20$ to $$30,$ with increments of $$1.$ Remember that returns are defined as $($value of the portfolio at the final date minus cost of the portfolio at the initial date$)/($cost of the portfolio at the initial date$).$

$($Write your final answers in percentage and round to one decimal: for instance, if the answer is $3\mathrm{.}45\%$ or $3\mathrm{.}47\%,$ write $3\mathrm{.}5$ without the percentage sign; if the answer is $-3\mathrm{.}44\%$ or $-3\mathrm{.}42\%,$ write $-3\mathrm{.}4.)$

If

$,$ the return of strategy A is

$\%,$ the return of strategy B is

$\%,$ and the return of strategy C is

$\%$

If

$,$ the return of strategy A is

$\%,$ the return of strategy B is

$\%,$ and the return of strategy C is

$\%$

If

$,$ the return of strategy A is

$\%,$ the return of strategy B is

$\%,$ and the return of strategy C is

$\%$

If

$,$ the return of strategy A is

$\%,$ the return of strategy B is

$\%,$ and the return of strategy C is

$\%$

If

$,$ the return of strategy A is

$\%,$ the return of strategy B is

$\%,$ and the return of strategy C is

$\%$