#### Nicole Seaman

##### Director of FRM Operations
Staff member
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. In regard to each trade's maximum profit, each of the following statements is true 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). With respect to this choice (straddle versus chooser), which of the following statements is 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