CFA Institute CFA-Level-II Exam Questions

Stan Loper is unfamiliar with the Black-Scholes-Merton (BSM) option pricing model and plans to use a two-period binomial model to value some call options. The stock of Arbor Industries pays no dividends and currently trades for $45. The up-move factor for the stock is 1.15, and the risk-free rate is 4%. He is considering buying two-period European style options on Arbor Industries with a strike price of S40. The delta of these options over the first period is 0.83.

Loper is curious about the effect of time on the value of the calls in the binomial model, so he also calculates the value of a one-period European style call option with a strike price of 40.

Loper is also interested in using the BSM model to price European and American call and put options. He is concerned, however, whether the assumptions necessary to derive the model are realistic. The assumptions he is particularly concerned about are:

* The volatility of the option value is known and constant.

* Stock prices are lognormally distributed.

* The continuous risk-free rate is known and constant.

Loper would also like to value options on Rapid Repair, Inc., common stock, but Rapid pays dividends, so Loper is uncertain what the effect will be on the value of the options. Loper uses the two-period model to value long positions in the Rapid Repair call and put options without accounting for the fact that Rapid Repair pays common dividends.

The value of the one-period European style call option is closest to:

Michelle Norris, CFA, manages assets for individual investors in the United States as well as in other countries. Norris limits the scope of her practice to equity securities traded on U .S . stock exchanges. Her partner, John Witkowski, handles any requests for international securities. Recently, one of Norris's wealthiest clients suffered a substantial decline in the value of his international portfolio. Worried that his U .S . allocation might suffer the same fate, he has asked Norris to implement a hedge on his portfolio. Norris has agreed to her client's request and is currently in the process of evaluating several futures contracts. Her primary interest is in a futures contract on a broad equity index that will expire 240 days from today. The closing price as of yesterday, January 17, for the equity index was 1,050. The expected dividends from the index yield 2% (continuously compounded annual rate). The effective annual risk-free rate is 4.0811%, and the term structure is flat. Norris decides that this equity index futures contract is the appropriate hedge for her client's portfolio and enters into the contract.

Upon entering into the contract, Norris makes the following comment to her client:

"You should note that since we have taken a short position in the futures contract, the price we will receive for selling the equity index in 240 days will be reduced by the convenience yield associated with having a long position in the underlying asset. If there were no cash flows associated with the underlying asset, the price would be higher. Additionally, you should note that if we had entered into a forward contract with the same terms, the contract price would most likely have been lower but we would have increased the credit risk exposure of the portfolio."

Sixty days after entering into the futures contract, the equity index reached a level of 1,015. The futures contract that Norris purchased is now trading on the Chicago Mercantile Exchange for a price of 1,035. Interest rates have not changed. After performing some calculations, Norris calls her client to let him know of an arbitrage opportunity related to his futures position. Over the phone, Norris makes the following comments to her client:

"We have an excellent opportunity to earn a riskless profit by engaging in arbitrage using the equity index, risk-free assets, and futures contracts. My recommended strategy is as follows: We should sell the equity index short, buy the futures contract, and pay any dividends occurring over the life of the contract. By pursuing this strategy, we can generate profits for your portfolio without incurring any risk."

Sixty days after the inception of the futures contract on the equity index, Norris has suggested an arbitrage strategy. Evaluate the appropriateness of the strategy. The strategy is:

Charles Mabry manages a portfolio of equity investments heavily concentrated in the biotech industry. He just returned from an annual meeting among leading biotech analysts in San Francisco. Mabry and other industry experts agree that the latest industry volatility is a result of questionable product safety testing methodologies. While no firms in the industry have escaped the public attention brought on by the questionable safety testing, one company in particular is expected to receive further attention---Biological Instruments Corporation (BIC), one of several long biotech positions in Mabry's portfolio. Several regulatory agencies as well as public interest groups have heavily criticized the rigor of BIC's product safety testing.

In an effort to manage the risk associated with BIC, Mabry has decided to allocate a portion of his portfolio to options on BIC's common stock. After surveying the derivatives market, Mabry has identified the following European options on BIC common stock:

Mabry wants to hedge the large BIC equity position in his portfolio, which closed yesterday (June 1) at $42 per share. Since Mabry is relatively inexperienced with utilizing derivatives in his portfolios, Mabry enlists the help of an analyst from another firm, James Grimell.

Mabry and Grimell arrange a meeting in Boston where Mabry discusses his expectations regarding the future returns of BIC's equity. Mabry expects BIC equity to make a recovery from the intense market scrutiny but wants to provide his portfolio with a hedge in case BIC has a negative surprise. Grimell makes the following suggestion:

"If you want to avoid selling the BIC position and are willing to earn only the risk-free rate of return, you should sell calls and buy puts on BIC stock with the same market premium. Alternatively, you could buy put options to manage the risk of your portfolio. I recommend waiting until the vega on the options rises, making them less attractive and cheaper to purchase."

If the premium on Put D on November 1 is $3.18, which of the following has most likely occurred?

Rock Torrey, an analyst for International Retailers Incorporated (IRI), has been asked to evaluate the firm's swap transactions in general, as well as a 2-year fixed for fixed currency swap involving the U .S . dollar and the Mexican peso in particular. The dollar is Torrey's domestic currency, and the exchange rate as of June 1,2009, was $0.0893 per peso. The swap calls for annua! payments and exchange of notional principal at the beginning and end of the swap term and has a notional principal of $100 million. The counterparty to the swap is GHS Bank, a large full-service bank in Mexico.

The current term structure of interest rates for both countries is given in the following table:

Torrey believes the swap will help his firm effectively mitigate its foreign currency exposure in Mexico, which sterns mainly from shopping centers in high-end resorts located along the eastern coastline. Having made this conclusion, Torrey begins writing his report for the management of IRI. In addition to the terms of the swap, Torrey includes the following information in the report:

* Implicit in the currency swap under consideration is a swap spread of 75 basis points over 2-year U .S . Treasury securities. This represents a 10 basis point narrowing of the spread as compared to this time last year. Thus, we can assume that the credit risk of the global credit market has decreased. Unfortunately, the decline provides no insight into the credit risk of the individual currency swap with GHS Bank, which could have increased.

* In order to decrease the counterparty default risk on the currency swap, we will need to utilize credit derivatives between the beginning and midpoint of the swap's life when this particular risk is at its highest. This is a significantly different strategy than we normally use with interest rate swaps. For interest rate swaps, counterparty default risk peaks at the middle of the swap's life, at which point we utilize credit derivative CQuntermeasures to offset the risk.

* Because currency swaps almost always include netting agreements and interest rate swaps can be structured to include mark-to-market agreements, we can significantly reduce the credit risk of these swap instruments by negotiating swap contracts that include these respective features. When negotiating these features is not possible, credit risk can be reduced by using off-market swaps that do not require an initial payment from IRI.

Six months have passed (180 days) since Torrey issued his report to IRI's management team, and the current exchange rate is now $0,085 per peso. The new term structure of interest rates is as follows:

Determine whether the excerpt from Torrey's report regarding the timing of peak credit risk is correct with regard to currency swaps and interest rate swaps.

Michelle Norris, CFA, manages assets for individual investors in the United States as well as in other countries. Norris limits the scope of her practice to equity securities traded on U .S . stock exchanges. Her partner, John Witkowski, handles any requests for international securities. Recently, one of Norris's wealthiest clients suffered a substantial decline in the value of his international portfolio. Worried that his U .S . allocation might suffer the same fate, he has asked Norris to implement a hedge on his portfolio. Norris has agreed to her client's request and is currently in the process of evaluating several futures contracts. Her primary interest is in a futures contract on a broad equity index that will expire 240 days from today. The closing price as of yesterday, January 17, for the equity index was 1,050. The expected dividends from the index yield 2% (continuously compounded annual rate). The effective annual risk-free rate is 4.0811%, and the term structure is flat. Norris decides that this equity index futures contract is the appropriate hedge for her client's portfolio and enters into the contract.

Upon entering into the contract, Norris makes the following comment to her client:

"You should note that since we have taken a short position in the futures contract, the price we will receive for selling the equity index in 240 days will be reduced by the convenience yield associated with having a long position in the underlying asset. If there were no cash flows associated with the underlying asset, the price would be higher. Additionally, you should note that if we had entered into a forward contract with the same terms, the contract price would most likely have been lower but we would have increased the credit risk exposure of the portfolio."

Sixty days after entering into the futures contract, the equity index reached a level of 1,015. The futures contract that Norris purchased is now trading on the Chicago Mercantile Exchange for a price of 1,035. Interest rates have not changed. After performing some calculations, Norris calls her client to let him know of an arbitrage opportunity related to his futures position. Over the phone, Norris makes the following comments to her client:

"We have an excellent opportunity to earn a riskless profit by engaging in arbitrage using the equity index, risk-free assets, and futures contracts. My recommended strategy is as follows: We should sell the equity index short, buy the futures contract, and pay any dividends occurring over the life of the contract. By pursuing this strategy, we can generate profits for your portfolio without incurring any risk."

Determine the price of the futures contract on the equity index as of the inception date, January 18.