Open Answer Question 2

You have been observing the stock price of TruPharma, which is currently worth $140 per share. You expect the return of TruPharma to be 12%, while the expected return on the market is 9%; TruPharma has a beta of 1.2 with respect to the market.

TruPharma is a pharmaceutical company racing to create_a vaccine against a novel disease. You are not sure of whether TruPharma will be the first company to find a vaccine and what will be the vaccine's efficacy. But they have promised to make an announcement in 1 month in which they will announce the success rates of their trials and the forecasted date for the vaccine's release. You are not sure whether they will be successful, but you expect that on the day of the announcement there will be a large price movement. If their trials seem to be successful, you expect the stock price will jump up, but if the trials seem unsuccessful you expect the price to experience a large drop (i.e. you expect the stock price to have a high volatility in the next month). After some analysis of the stock price volatility of TruPharma in prior announcement days and observing the price volatility of other pharmaceutical companies that made similar announcements, you conclude that in the next month the price of TruPharma will experience a 30% volatility (continuously compounded).

You would like to profit from this price movement. At first you try to assess whether it is more likely that the price will go up or down. You analyze TruPharma's track record, and you believe that it is likely that they will succeed in making the vaccine. You observe the following options trading in the market and decide that buying an at-the-money call option with 1 month to maturity and $140 strike price would give you the best chances of profiting from the expected price move. The current price of the options is $4. Before buying, though, you would like to assess whether this option is fairly priced and what risks it entails.

(a) (5 points) Given a continuously compounded risk free rate of 2%, use Black-Sholes to determine a fair price for the option.

(b) (5 points) Is the price the same or different to the market price? If it is different, what must be the price volatility that the average investor expects TruPharma will have in the next month?

(c) (5 points) If you are confident with your expectation about TruPharma's volatility, do you think this option is a good deal?

Provide a brief comment to explain your assessment.

Before proceeding to buy the option, you would like to assess the riskiness and return potential of this investment.

(d) (5 points) Compute the leverage ratio, expected return, alpha, beta, and volatility of the call option investment.

Given the riskiness of the strategy and your uncertainty of the direction of the price move you are not sure of whether you would like to go ahead with this investment. But then you remember that you can combine different options to construct option strategies that might be more beneficial for your situation. Since you believe that there is some likelihood that the price will experience a large drop, you decide to also consider a put option with the same strike and time to maturity as the call option you are considering purchasing. That put option is currently trading at $3.7.

(e) (5 points) According to Black and Sholes and given your expectations, what should be the price of that put?

(f) (5 points) What would the payoff and profit of your strategy be if you were to both buy the put and the call options (you can either represent it in a payoff diagram or express it by using equations)?

(g) (5 points) Do you think this is a good strategy given your expectations? Briefly explain why.

You are sure though that there will be a large price change in either direction, so that you would like to use cheaper options than the at-the-money ones that you are currently considering. For that reason, you consider the following alternative strategy: buy a call option with strike price $160 and buy a put option with strike price $120, both having 1 month to maturity.

(h) (5 points) According to Black-Sholes, based on the expected volatility of the average investor, what should be the price of these options?

BONUS QUESTIONS

(i) (5 bonus points) What would be the payoff and profit of this new strategy (you can either represent it in a payoff diagram or express it by using equations)?

(j) (5 bonus points) Briefly comment on the differences between this strategy and the previous one. What is the key trade-off you would be considering when choosing between the two?