Question #$2$: Option Valuation $($Binomial Option Pricing$)[20$ Points$]$

Suppose you have just purchased one share of Carpenter Technology Corporation stock $($CRS$)$ for $$71\mathrm{.}10.$ You have forecasted that in one year the stock price will either rise to $$76\mathrm{.}60$ or fall to $$65\mathrm{.}60$

Suppose further that you can either buy or sell a call option on CRS stock with a strike price of $$70.$ Assume that this is a European style contract that expires exactly in one year and that the risk$-$free interest rate is $3\mathrm{.}9\%.$

$($a$)$ Calculate the hedge ratio $(H).[5$ Points$]$

$($b$)$ Based on your answer from Part $($a$),$ fill in the following table showing that you have created a riskless portfolio. $[8$ Points$]$

$\backslash$table$[[,$Stock Price $=$$$65\mathrm{.}60,$Stock Price $=$$$76\mathrm{.}60$