A trader uses delta hedging strategy to hedge a portfolio of short positions in call option on Apple Computer stocks. The trader sells $50$ call option contracts $(1$ contract controls $100$ shares$)$ on Apple stock. The option price is $$5,$ the stock price is $$230,$ and the option$$s delta is $0\mathrm{.}9.$

a$.$ Does the trade short or long the stock to create a delta$-$neutral position? Blank $1($Sample answer: long; or short$)$

b$.$ How many shares does the trader need to create a delta$-$neutral position? Blank $2($Sample answer: $3000$ shares$)$

Suppose the next day, the stock price decreases to $$220$ and the call option delta changes to $0\mathrm{.}72.$ please answer questios c and d:

c$.$ Does the trader long additional shares or short additional shares to hold the delta neutral position? Blank $3($Sample answer: long; or short$)$

d$.$ How many additional shares does the trader need to create a delta$-$neutral position? Blank $4($Sample answer: $20$ shares$)$