CHAPTER 9 – TRADING STRATEGIES INVOLVING OPTIONS
I. Short concept question
9.1. What position in call options is equivalent to a protective put?
9.2. When is it appropriate for an investor to purchase a butterfly spread?
9.3. What is the difference between a strangle and a straddle?
II. Practice questions
9.1. A share of stock with recent price is $20. A call option with a strike price of $25 costs $3. Construct a
table showing how profit varies with stock price for the covered call strategy. Draw a diagram showing the
variation of the profit and loss with the terminal stock price for the strategy.
9.2 Assume you originally opened 100 short shares of ATT at $50, but it is currently trading at $70, then
selling a $60-strike put for a $1 credit against the short shares. Construct a table showing how profit varies
with stock price for the protective put strategy. Draw a diagram showing the variation of the profit and loss
with the terminal stock price for the strategy.
9.3. Call options on a stock are available with strike prices of $15, $17.5, and $20, and expiration dates in 3
months. Their prices are $4, $2, and $0.5, respectively. Explain how the options can be used to create a
butterfly spread. Construct a table showing how profit varies with stock price for the butterfly spread. Draw
a diagram showing the variation of the profit and loss with the terminal stock price for the strategy.
9.4. A call option with a strike price of $50 costs $2. A put option with a strike price of $45 costs $3. Construct
a table that shows the profit from a strangle. For what range of stock prices would the strangle lead to a
maximum loss? Breakeven? Draw a diagram showing the variation of the profit and loss with the terminal
stock price for the strategy.
9.5. A call with a strike price of $60 costs $6. A put with the same strike price and expiration date costs $4.
Construct a table that shows the profit from a straddle. For what range of stock prices would the straddle lead
to a maximum loss? Breakeven? Draw a diagram showing the variation of the profit and loss with the terminal
stock price for the strategy.
9.6. Suppose that put options on a stock with strike prices $30 and $35 cost $4 and $7, respectively. How
can the options be used to create (a) a bull spread and (b) a bear spread? Construct tables that show the profit
for both spreads. For what range of stock prices would each strategy to a maximum loss? Maximum profit?
Breakeven? Draw a diagram showing the variation of the profit and loss with the terminal stock price for the
strategy.
CHAPTER 11 – VALUE AT RISK
11.1. Consider a portfolio of options on a single asset. Suppose that the value of the asset is $10, and the
daily volatility of the asset is 2%. Estimate the 1-day 95% VaR for the portfolio assuming normally.
11.2. Suppose a risk manager wants to calculate the value at risk using the parametric method for a one-day
time horizon. The weight of the first asset is 40%, and the weight of the second asset is 60%. The standard
deviation is 4% for the first and 7% for the second asset. The correlation coefficient between the two is 25%.
The z-score is -1.645. The portfolio value is $50 million.
11.3. Consider a position consisting of a $100,000 investment in asset A and a $100,000 investment in asset
B. Assume that the daily volatilities of both assets are 1% and that the coefficient of correlation between
their returns is 0.3. Estimate the 5-day 99% VaR for the portfolio assuming normally.
11.4. Consider a portfolio of 10 k€ which is invested in equal parts in two instruments: First, treasury bonds
with an annual return of 6% and second, a stock which has a 20% chance of losing half its value and an 80%
chance of increasing value by a quarter. Estimate the 1-year 99% VaR for the portfolio assuming normally.
