An investor buys a put and a call on a stock. Currently the stock is trading at $50 and the volatility of stock is 25%. The strike price of the both the put and call is $50. The options expire in 3 months and the risk free rate is 1%.

N(0.0825)= 0.532875

N(-0.0825)= 0.467125

N(-0.0175)= 0.493019

N(0.0175)= 0.506981

N(0.1825)= 0.572405

N(0.1825)= 0.427595

N(-0.0425)= 0.48305

N(0.0425)= 0.51695

N(-0.1425)= 0.443343

N(0.1425)= 0.556657

N(0.0575)= 0.522927

N(-0.0575)= 0.477073

N(0.3963)= 0.654045

N(-0.3963)= 0.345955

N(0.2963)= 0.616486

N(-0.2963)= 0.383514

N(0.4963)= 0.690147

N(-0.4963)= 0.309853

N(0.2713) 0.606907

N(-0.2713)= 0.393093

N(0.1713) 0.567993

N(-0.1713)= 0.432007

N(0.3713) 0.64478

N(-0.3713)= 0.35522

a. What is the delta of the portfolio?

b. What is the gain or loss on the portfolio is the stock price increases by $2?

c. Is delta hedging sufficient to hedge the portfolio in (a)? Explain your answer