You hold a portfolio that is currently delta neutral It has a gamma of 6000 and a vega of 10 000 There are two options traded in the market Gamma Vega Delta Option A 0 5 2 0 0 6 Option B 0 8 1 2 0 5 a What does a gamma of 6 000 and a vega of 10 000 mean Gamma 6 000 Gamma measures the rate of change of an option s delta in response to a one point movement in the underlying asset s price A gamma of 6 000 means that the delta of your portfolio will decrease by 6 000 units for every one point increase in the underlying asset s price Vega 10 000 Vega measures the sensitivity of the option s price to a 1 change in the implied volatility of the underlying asset A vega of 10 000 means that for every 1 increase in implied volatility the portfolio s value is expected to decrease by 10 000 units b What would you need to do to make the portfolio both vega and delta neutral What will be the new value of gamma Long 5000 option A Short 3000 unit of portfolio asset New gamma is 3500 c What would you need to do if you had to make the original portfolio both gamma vega and delta neutral To make the portfolio both gamma and vega neutral you should buy 800 units of Option A and 7000 units of Option B Short 3980 unit of portfolio asset John is an investor who owns 100 shares of XYZ Corporation currently trading at 100 per share He is worried that the price may decline in one year but still wants to hold onto his shares At the same time he also believes that there might be significant price movements in either direction soon There are options listed below in the market Refer to the Table 1 a Design two option strategies to satisfy John s needs and outline the positions for the two strategies b Write down the profit equation for the two strategies c For the strategies designed in Part a Maximum Profit Maximum Loss Breakeven Point s d Compare the two strategies designed in Part A What are the advantages and disadvantages of each Strategy 1 Protective Put Outline of Positions Own 100 shares of XYZ Corporation at 100 each Buy 1 put option with an exercise price of 100 premium 4 9091 expiring in 1 year This strategy involves buying a put option as insurance against a decline in the stock price By owning the put John can sell his shares at the 100 strike price regardless of how low the stock price may fall Profit Equation Profit Stock Final Price 100 100 max 100 Stock Final Price 0 4 9091 100Profit Stock Final Price 100 100 max 100 Stock Final Price 0 4 9091 100 Maximum Profit Maximum Loss Unlimited as the stock price increases the profit increases Limited to the cost of the put option premium plus any depreciation in the stock to the 100 4 9091 104 9091100 4 9091 104 9091 stock price must increase by the amount of the put premium to break even strike price 490 91 Breakeven Point Strategy 2 Straddle Outline of Positions Own 100 shares of XYZ Corporation at 100 each Buy 1 call option with an exercise price of 100 premium 12 000 expiring in 1 Buy 1 put option with an exercise price of 100 premium 4 9091 expiring in 1 year year This strategy involves buying both a call and a put option at the same strike price and expiration It is designed to profit from significant movements in either direction Profit Equation Profit Stock Final Price 100 100 12 000 4 9091 100 max 100 Stock Final Price 0 max Stock Final Price 100 0 100Profit Stock Final Price 100 100 12 000 4 909 1 100 max 100 Stock Final Price 0 max Stock Final Price 100 0 100 Unlimited as the stock moves significantly in either direction Limited to the sum of the premiums of both options if the stock price remains at 100 100 12 000 4 9091 116 9091100 12 000 4 9091 116 9091 upper breakeven 100 12 000 4 9091 83 0909100 12 000 4 9091 83 0909 lower breakeven Maximum Profit Maximum Loss 1690 91 Breakeven Points Comparison of Strategies Advantages Protective Put Protects against downside risk while allowing for unlimited upside Straddle Benefits from large price movements in either direction ideal for volatile potential stocks Disadvantages does not decline Protective Put Costs the premium which can be a significant expense if the stock Straddle Requires a significant movement in the stock price to become profitable due to the high cost of premiums for both options These strategies provide John with flexibility based on his expectations of stock price movement and his risk tolerance The protective put is more defensive focusing on downside protection while the straddle is aggressive exploiting volatility for potentially higher gains