Question 8

Tess Mulroney, a veteran options investor, wishes to do some speculating and hedging with options, but isn’t sure the derivatives currently available are attractively priced. Before making any transactions, Mulroney puts her calculator to work to determine a fair price for the options.

First, Mulroney seeks to protect a large variable-rate investment. She has loaned $40 million to her nephew’s construction company. The loan is payable in one year, and the current interest rate is 7.6 percent. Based on data provided by her brokerage house, Mulroney believes interest rates will fall sharply over the next year, with a 70 percent chance of a decline to 5.9 percent and a 30 percent chance of a decline to 4.7 percent.

To protect her cash flows, Mulroney is considering the purchase of a 6.2 percent floor. Mulroney knows a banker who writes such options, but she must come to him with a price in mind.

Next on Mulroney’s list is call options on Merrill Materials stock. She has obtained the following assumptions through a subscription options service:

• The stock trades for $35 per share.

• The chance of an upward movement over the next year is 60 percent.

• The likely downward movement is 20 percent.

• At-the-money calls currently sell for $4.75.

Despite her experience, Mulroney knows she always has more to learn. So she then reviews some technical material on options that she found on the Internet. Mulroney spends the next hour reading up on sensitivity factors related to option pricing.

Later that day, Mulroney meets with Ben Glanda, her financial adviser. He has prepared some investment recommendations and advice for Mulroney.

His first suggestion addresses a series of investments Mulroney was considering. She had proposed buying a stock, buying a European put option on the stock, and writing a call option. Glanda has proposed an alternative investment that will be simpler to make.

Next Glanda attempts to convince Mulroney to start using an alternate method for valuing her options. Glanda suggests using the Black-Scholes-Merton model because of its precision and ability to consider more factors, but Mulroney prefers the binomial model because it requires fewer assumptions.

Mulroney doesn’t like the Black-Scholes Merton model for the following reasons:

• It does not work for American options.

• It does not consider volatility of interest rates.

• It does not reflect the compounding of returns.

• It does not work for assets that generate cash flows.

Part 1)

Which of Mulroney’s arguments against the Black-Scholes-Merton model is least compelling? Her statement about:

A)   American options.

B)   interest-rate volatility.

C)   compounding returns.

D)   cash flows.

Part 2)

The Black-Scholes-Merton model is designed to solve for:

A)   volatility.

B)   theta.

C)   time to maturity.

D)   option returns.

Part 3)

During the course of her review, Mulroney reads about a factor related to interest rates. The variable is negative for put options. Mulroney is reading about:

A)   rho.

B)   gamma.

C)   vega.

D)   theta.

Part 4)

Assuming the risk-free rate is 5.5 percent, call options on Merrill Materials are:

A)   $0.2083 undervalued.

B)   $0.2263 undervalued.

C)   $0.5201 overvalued.

D)   $0.0502 overvalued.

Part 5)

The value of the floor Mulroney seeks is closest to:

A)   $236,571.

B)   $228,023.

C)   $233,494.

D)   $231,029.

Part 6)

If Glanda is attempting to duplicate the effects of Mulroney’s proposed stock and option investment, he should recommend the:

A)   sale of a riskless bond.

B)   purchase of a riskless bond.

C)   purchase of a stock.

D)   sale of a stock.

Part 1)

Which of Mulroney’s arguments against the Black-Scholes-Merton model is least compelling? Her statement about:

A)   American options.

B)   interest-rate volatility.

C)   compounding returns.

D)   cash flows.

The correct answer was C)

The Black-Scholes-Merton model requires the assumption that the underlying asset has no cash flows. The assumption of a constant risk-free interest rate does not allow the model to take into account interest-rate volatility. BSM is not suited for calculating American options because they can be exercised before the maturity date. However, the model does assume compounded stock returns in its calculation of volatility.

This question tested from Session 17, Reading 64, LOS c

Part 2)

The Black-Scholes-Merton model is designed to solve for:

A)   volatility.

B)   theta.

C)   time to maturity.

D)   option returns.

The correct answer was A) volatility.

There are five inputs to the BSM model. Stock price, exercise price, risk-free rate, and time to maturity are observable. Volatility is generally found by trial and error, using the market price in the computation.

This question tested from Session 17, Reading 64, LOS c

Part 3)

During the course of her review, Mulroney reads about a factor related to interest rates. The variable is negative for put options. Mulroney is reading about:

A)   rho.

B)   gamma.

C)   vega.

D)   theta.

The correct answer was A) rho.

Rho measures the sensitivity of option prices to changes in the risk-free rate.

This question tested from Session 17, Reading 64, LOS c

Part 4)

Assuming the risk-free rate is 5.5 percent, call options on Merrill Materials are:

A)   $0.2083 undervalued.

B)   $0.2263 undervalued.

C)   $0.5201 overvalued.

D)   $0.0502 overvalued.

The correct answer was D) $0.0502 overvalued.

The chance of an upward movement is 60 percent. The likely downward movement is 20 percent, so the size of the down move is 0.8 resulting in a downward movement price of $35 × 0.8 = $28. The size of the up move is 1 / 0.8 = 1.25 for an upward movement price of $35 × 1.25 = $43.75. The payout on the option would be $43.75 − $35 = $8.75. The risk-neutral probability of an upward movement is (1 + 5.5% − 0.8) / (1.25 − 0.8) = 56.67%. To calculate the value of the call option a year from now, multiply the payout ($8.75) by the risk-neutral probability of an upward movement, for a value of $4.9583. Discount that by the risk-free rate, and the call is worth $4.6998. By that measurement, the call is $0.0502 overvalued.

This question tested from Session 17, Reading 64, LOS c

Part 5)

The value of the floor Mulroney seeks is closest to:

A)   $236,571.

B)   $228,023.

C)   $233,494.

D)   $231,029.

The correct answer was C) $233,494.

To calculate the value of the floor, we start out with the values of the two floorlets. At an interest rate of 5.9%, the floorlet would be valued as follows: [(floor rate – 1-year rate) × principal] / (1 + 1-year rate) = [(6.2% − 5.9%) × $40 million)] / (1 + 5.9%) = $113,314. Using the same formula, the second floorlet would be worth $573,066 at an interest rate of 4.7%. To calculate the value of the floor, we calculate a weighted average of the floorlet values and discount it by the current interest rate as follows: [($113,314 × 70%) + ($573,066 × 30%)] / (1 + 7.6%) = $233,494.

This question tested from Session 17, Reading 64, LOS c

Part 6)

If Glanda is attempting to duplicate the effects of Mulroney’s proposed stock and option investment, he should recommend the:

A)   sale of a riskless bond.

B)   purchase of a riskless bond.

C)   purchase of a stock.

D)   sale of a stock.

The correct answer was B) purchase of a riskless bond.

Buying a stock, buying a put option, and writing a call option creates a synthetic riskless bond.

This question tested from Session 17, Reading 64, LOS c

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