*Learning outcomes: Explain the motivation to initiate a covered call or a protective put strategy. Describe principal protected notes (PPNs) and explain necessary conditions to create a PPN. Describe the use and calculate the payoffs of various spread strategies. Describe the use and explain the payoff functions of combination strategies.*

**Questions:**

26.1. Acme bank wants to offer a principal-protected note (PPN) to certain retail customers who have a conservative investment philosophy. The PPN will consist of a three-year zero-coupon bond plus a call option on a stock portfolio. The bond's principal is $10,000 and the three-year call option on the portfolio will have a strike price of $10,000, aka, at-the-money. The stock portfolio pays a 2.0% dividend yield. The risk-free rate is 4.0% per annum with continuous compounding.

If the stock portfolio's implied volatility is 13.135% then the price of the call is $1,130.80, which solves for $10.000 - $10,000*exp(-4.0%*3) = $1,130.80. Consequently, if the portfolio's implied volatility is 13.135%, this PPN is (barely) not profitable for the bank.

Under which of the following scenarios is this PPN profitable?

a. The riskfree rate increases (from 4.0%) to 5.50%

b. The term is reduced (from 3.0 years) to 30 months

c. The implied volatility increases (from 13.135%) to 20.0%

d. The portfolio's dividend yield reduces (from 2.0%) to 1.0%

26.2. A non-dividend-paying stock has a current price of $10.00 and a volatility of 25.0% per annum. The risk-free rate is 4.0% per annum with continuous compounding. Consider the following four spread trades:

- Trade #1 is a bull spread with calls. The strike prices are: K1 = $9.00, K2 = $11.00. The up-front cost is $1.00.
- Trade #2 is a bull spread with puts. The strike prices are: K1 = $9.00, K2 = $11.00. The up-front cash flow is $0.93.
- Trade #3 is a bear spread with puts. The strike prices are: K1 = $8.00, K2 = $12.00. The up-front cost is $1.84.
- Trade #4 is a bear spread with calls. The strike prices are: K1 = $8.00, K2 = $12.00. The up-front cash flow is $2.00.

**EXCEPT**which is false?

a. Trade #1 offers a maximum profit of $1.00

b. Trade #2 offers a maximum profit of $0.93

c. Trade #3 offers a maximum profit of $0.84

d. Trade #4 offers a maximum profit of $2.00

26.3. Sally wants to execute a long volatility trade with respect to a stock that is currently trading at a price of $40.00 while the risk-free rate is 5.0%. She is considering:

- An at-the-money straddle (i.e., K = $40.00) that will cost $8.40 because the stock's current implied volatility is 30.0%
- A chooser (aka, as you like it) option with a strike price, K = $40.00, that expires in nine months (0.75 years), but the holder chooses it to be either a put or call in three months (0.25 years).

**TRUE**?

a. If the cost of the long call is $4.84, then the cost of the put is $2.95

b. If the implied volatility of the put increases, then the cost of the straddle will increase

c. The chooser is more expensive because it is exotic but the straddle is merely a combination

d. Compared to this straddle, a strangle will incur a higher up-front cost, but the strangle's profit will be greater if the stock reaches $50.00 on the upside (or $30.00 on the downside) at expiration

**Answers here:**