in section $22-1,$ we used a simple one$-$step model to value to amazon options each with an exercise price of $$1,830.$ We showed that the call option could be replicated by borrowing $$815\mathrm{.}51$ and investing $$998\mathrm{.}18$ in $0\mathrm{.}54545$ shares of amazon stock. The put option could be replicated by selling short $$693\mathrm{.}18$ of amazon stock and lending $$988\mathrm{.}18.$ a$.$ If the beta of Amazon stock is $1\mathrm{.}5,$ what is the beta of the call according to the one$-$step model? b$.$ What is the beta of the put? c$.$ Suppose that you were to buy one call and invest the present value of the exercise price in a bank loan. What would be the beta of your portfolio? d$.$ Suppose instead that you were to buy one share and one put option of amazon. What would be the beta of your portfolio now? e$.$ Your answers to parts $($c$)$ and $($d$)$ should be the same. Explain.