Reading 43: Risk Management Applications of Option Strategies effective, interest, current, annual, borrow

youzizhang

 

LOS b: Determine the effective annual rate for a given interest rate outcome when a borrower (lender) manages the risk of an anticipated loan using an interest rate call (put) option.

Q1. In 30 days, a firm wishes to borrow $15 million for 90 days. The borrowing rate is LIBOR plus 250 basis points. The current LIBOR is 3.8%. The firm buys an interest-rate call that matures in 30 days with a notional principal of $15 million, 90 days in underlying, and a strike rate of 4%. The call premium is $4,000. What is the maximum effective annual rate the firm can anticipate paying?

A)   0.0687.

B)   0.0671.

C)   0.0603.

 

Q2. In 90 days, a firm wishes to borrow $10 million for 180 days. The borrowing rate is LIBOR plus 200 basis points. The current LIBOR is 4%. The firm buys an interest-rate call that matures in 90 days with a notional principal of $10 million, 180 days in underlying, and a strike rate of 4.1%. The call premium is $9,000. What is the effective annual rate of the loan if at expiration LIBOR = 4%?

A)   0.0619.

B)   0.0637.

C)   0.0787.

 

Q3. In 60 days, a bank plans to lend $10 million for 180 days. The lending rate is LIBOR plus 200 basis points. The current LIBOR is 4.5%. The bank buys an interest-rate put that matures in 60 days with a notional principal of $10 million, days in underlying of 180 days, and a strike rate of 4.3%. The put premium is $4,000. What is the effective annual rate of the loan if at expiration LIBOR = 4.1%?

A)   0.0648.

B)   0.0619.

C)   0.0640.

youzizhang

 

LOS b: Determine the effective annual rate for a given interest rate outcome when a borrower (lender) manages the risk of an anticipated loan using an interest rate call (put) option. fficeffice" />

Q1. In 30 days, a firm wishes to borrow $15 million for 90 days. The borrowing rate is LIBOR plus 250 basis points. The current LIBOR is 3.8%. The firm buys an interest-rate call that matures in 30 days with a notional principal of $15 million, 90 days in underlying, and a strike rate of 4%. The call premium is $4,000. What is the maximum effective annual rate the firm can anticipate paying?

A)   0.0687.

B)   0.0671.

C)   0.0603.

Correct answer is A)

First we compute the implied net amount to be borrowed after the cost of the call:

$ 14,995,979 = $15,000,000 ? $4,000 × (1 + (0.038 + 0.025) × (30 / 360))

The most the firm will expect to pay is the rate associated with the strike rate: 4% plus the 250 basis-point spread equals 6.5%. This gives the nominal cost of the loan:

$243,750 = $15,000,000 × 0.065 (90 / 360)

The highest effective annual rate is:

0.0687 = ($15,243,750 / $14,995,979)^(365/90) ? 1

 

Q2. In 90 days, a firm wishes to borrow $10 million for 180 days. The borrowing rate is LIBOR plus 200 basis points. The current LIBOR is 4%. The firm buys an interest-rate call that matures in 90 days with a notional principal of $10 million, 180 days in underlying, and a strike rate of 4.1%. The call premium is $9,000. What is the effective annual rate of the loan if at expiration LIBOR = 4%?

A)   0.0619.

B)   0.0637.

C)   0.0787.

Correct answer is B)       

The call option is out-of-the-money. The implied net amount to be borrowed after the cost of the call is:

$9,990,865 =$10,000,000 - $9,000 × (1 + (0.04+0.02) × (90/360))

For LIBOR = 0.04 at expiration, the dollar cost is:

$300,000 = $10,000,000 × 0.06 × (180/360)

The effective annual rate is:

0.0637 = ($10,300,000 / $9,990,865)^(365/180) - 1

 

Q3. In 60 days, a bank plans to lend $10 million for 180 days. The lending rate is LIBOR plus 200 basis points. The current LIBOR is 4.5%. The bank buys an interest-rate put that matures in 60 days with a notional principal of $10 million, days in underlying of 180 days, and a strike rate of 4.3%. The put premium is $4,000. What is the effective annual rate of the loan if at expiration LIBOR = 4.1%?

A)   0.0648.

B)   0.0619.

C)   0.0640.

Correct answer is C)

The effective amount the bank parts with or “lends” at time of the loan is:

$10,004,043 = $10,000,000 + $4,000 × (1 + (0.045 + 0.02) × (60/360))

If LIBOR at maturity equals 4.1%, the payoff of the put would be:

payoff = ($10,000,000) × [max(0, 0.043 – 0.041) × (180/360)

payoff = $10,000

The dollar interest earned is:

$305,000=$10,000,000 × (0.041 + 0.02) × (180/360), and
EAR = [($10,000,000 + $10,000 +$305,000) / ($10,004,043)]^(365/180) - 1
EAR = 0.0640 or 6.40%

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