1. a. Citigroup believes that market volatility will be 20 percent annually for the next 3 years. 3-year at-the-money put options on the market index sell at an implied volatility of 18 percent. What position in puts and shares can Citigroup establish to speculate on its volatility belief without taking a bullish or bearish position on the market? 3-year at- the-money options have N(dj) =.6. b. If the value of the stock index increases, should Citigroup buy or sell shares to maintain its hedged position? C. If the market index moves by a large amount, will Citigroup suffer a loss, or enjoy a profit, despite its presumed market-neutral position? d. Is the theta of Citigroup's position positive or negative? 1. a. Citigroup believes that market volatility will be 20 percent annually for the next 3 years. 3-year at-the-money put options on the market index sell at an implied volatility of 18 percent. What position in puts and shares can Citigroup establish to speculate on its volatility belief without taking a bullish or bearish position on the market? 3-year at- the-money options have N(dj) =.6. b. If the value of the stock index increases, should Citigroup buy or sell shares to maintain its hedged position? C. If the market index moves by a large amount, will Citigroup suffer a loss, or enjoy a profit, despite its presumed market-neutral position? d. Is the theta of Citigroup's position positive or negative