Suppose the stock price today is $$50,$ in year time the stock price goes up to $$77\mathrm{.}65$ and goes down to $$48\mathrm{.}47,$ dollar rate of return in one year is $1\mathrm{.}0513.$

i$.$ Set up a perfect hedge and compute the put option$$s value using the synthetic approach. Let the put have the same strike price K $=$$$65.$

ii$.$ What is the hedge ratio? What does it signify?