Interest Rate Derivative Case Analysis

February 7

Interest Rate Derivatives

2014 Submitted by, Anadi Kaistha Nabin Basha Naveen Kumar Sanoop S Sreenandan Nambiar P

Exercise 1 ACME Manufacturing has two choices, either raise debt by • 3-year Fixed Rate Note, Cost @7% for ACME • 3 year Floating Rate Note, Cost@ (one year LIBOR, 3.7% +2 % spread) The company prefers to have a Fixed Rate Liability; however looking at the above scenarios, the fixed rate cost of Debt is 7% which is greater than the Floating rate Liability which at current level of Libor is 5.7%. So it would be prudent to go for Floating rate Liability which is lower than fixed rate and subsequently take Derivative contracts for exchanging floating rate liability into a fixed rate liability. The Derivative contracts available from National Trust are Swaps, FRAs, Cap and Floor. The Fixed rate cost calculation is as under for each Derivative Contract

Solution:

Given Details 1 yr LIBOR (%) Loan Amount ($ mn) 3 yr US T-bill rate(%) Duration (yrs) 2 yr US T-bill rate (%) 3 yr US T-bill rate (%) Floating Case Additional (%)

3.7 100 4.5 3 4.1 4.5 1 yr LIBOR + 2% 2

Acme’s Initial Position: Type Fixed Floating

Condition 3 yr US T-bill rate + 250 basis 1 yr LIBOR + 2%

Actual Rate

Net Payment ($ mn)

Final Loan Cost to ACME (%)

7.0

21

7.0

5.7

NA

NA

Comments: In case company goes for a Fixed rate of interest payment than Acme’s total interest cost will be 7% (amount $ 21 million) and in case of floating rate of interest Acme’s total cost would be 5.7% for the first year and thereafter as per the prevailing LIBOR for the concerned period at that point in time.

National Trust offers:

Offer 1 - SWAP Case-1 - SWAP Fixed pay Floating rec

3 yr US t rate+ 30 bps 1 yr LIBOR

4.8 3.7

20.4 Pay (4.8-3.7= 1.1% of 100 mn) i.e 3.3 m n 11.1

6.8

If ACME enters into a SWAP contract with National Trust • It would pay a fixed rate of 4.5%+0.3%=4.8% to the National Trust. • It would receive a one year LIBOR floating rate from National Trust.

•

ACME has to pay 2% spread to meet the liability of Floating rate note

Total cost to ACME is 4.8%+2%= 6.8%. Comments: In case of first offer of SWAP if company goes for conversion of floating rate to fixed rate than company’s total cost of loan would be 6.8% (amount $ 20.4 million), because in this set up Acme has to pay 4.8% as fixed payment plus 2% spread. The LIBOR cost prevailing in the market for the respective periods would be netted off by the receipt of LIBOR payment from the counterparty. As the average rate for 3 years boils down to 6.8%, company might think it as an alternative to option of fixed interest pay of 7%.

Offer 2 - FRA 2 instruments required, one for year 2 (12X24) and another for year 3 (24X36). Instrument 1: Characteristics of the instrument: • • •

(12x24) i.e. the contract will expire in 12 months and due date is 24 months FRA reference rate: 5% p.a. (given) Underlying rate: 1 year LIBOR

Scenario-(a): Assume if 1 year LIBOR exceeds from 5% to 6% p.a. 1 year LIBOR stands at 6% p.a. In this case, the company would receive differential payoff of 1% discounted at 1 year LIBOR. Payoff = ((1 year LIBOR)-(FRA reference rate)*(Period of underlying LIBOR in months/12))/(1+((1 year LIBOR)*)*(Period of underlying LIBOR in months/12)) = ((0.06-0.05)*12/12)/(1+(0.06*12/12)) =0.01/1.06 =0.00943396 Net payoff to be received by the company = 0.00943396*100,000,000=943,396

Scenario-(b): In case if LIBOR goes down, 1 year LIBOR reduces from 5% to 4% p.a.

Assumption is that 1 year LIBOR stands at 4% p.a. In this case, the company would pay differential payoff of 1% discounted at 1 year LIBOR. Payoff = ((0.04-0.05)*12/12)/(1+(0.04*12/12)) =-0.01/1.04 =-0.00961538 Net payoff to be paid by the company = 0.00961538*100,000,000=961,538 Instrument 2: Characteristics of the instrument: • • •

(24x36) i.e. the contract will expire in 24 months and due date is 36 months FRA reference rate: 6% p.a. (given) Underlying rate: 1 year LIBOR

Scenario-(a): Considering 1 year LIBOR exceeds from 6% to 7% p.a. Assumption is that 1 year LIBOR stands at 7% p.a. In this case, the company would receive differential payoff of 1% discounted at 1 year LIBOR. Payoff = ((0.07-0.06)*12/12)/(1+(0.07*12/12)) =0.01/1.07 =0.00934579 Net payoff to be received by the company = 0.00934579*100,000,000=934,579 Scenario-(b): In case if LIBOR goes down, 1 year LIBOR reduces from 6% to 5% p.a. Assumption is that 1 year LIBOR stands at 5% p.a. In this case, the company would pay differential payoff of 1% discounted at 1 year LIBOR. Payoff = ((0.05-0.06)*12/12)/(1+(0.05*12/12)) =-0.01/1.05 =-0.00952380 Net payoff to be paid by the company = 0.00952380*100,000,000=952,380 Using data-table function in excel, we have plotted a graph between total payoff ($) and 1 year LIBOR and the same is shown as under: The total cost was calculated considering interest payments in 1st year, 2nd year and 3rd year along with FRA payoffs at different LIBOR rates.

Offer 3 - Caps

Strike Rate 4.00% 4.80% 5.00% 6.00%

Comments:

Premium 2.23% 0.70% 0.49% 0.08%

Payoff from cap 2.00% 1.20% 1.00% 0.00%

Commitment

Total Commitment(incl cap premium)

8.000% 8.000% 8.000% 8.000%

8.230% 7.500% 7.490% 8.080%

The cap is a Derivative that ACME can buy to limit the upside risk of paying more cost, as its liability is linked to a Floating LIBOR. The company would not be able to fix the interest burden rate using the CAP option. The Strike price with 5% is the least cost Scenario. Also in all the cases the interest cost crosses the threshold limit of 7% of which company has an option as an alternative. Hence it’s unlikely that company would enter into CAPS option.

Offer 4 - Floors Buy Floor: It would be a strategy for those interested in hedging against downside interest rate risk. In this case however, company is not an investor, hence is not worried about the downside interest rate risk. So, it would not buy floor.

Sell Floor: Even if company sell floor all it gets is the premium on the option. However, it faces two risks; 1) payment to counterparty if interest rates fall below the strike price and 2) upward interest rate risk. In both the above scenarios, company does not achieve the set target of fixed rate payment and that too below 7%. Hence in would not indulge in either of the strategies.

Offer5: (combination of offer 3 & 4) Collar combination

Strike Rate for cap Strike Rate for floor Cap Premium Floor Premium Payoff from Cap Payoff from Floor Net payoff Commitment 1 4.00% 4.00% 2.23% 0.18% 0.00% 1.00% -1.00% 5.000% 2 4.00% 4.80% 2.23% 0.70% 0.00% 1.80% -1.80% 5.000% 3 4.00% 5.00% 2.23% 0.90% 0.00% 2.00% -2.00% 5.000% 4 4.00% 6.00% 2.23% 3.22% 0.00% 3.00% -3.00% 5.000% 5 4.80% 4.00% 0.70% 0.18% 0.00% 1.00% -1.00% 5.000% 6 4.80% 4.80% 0.70% 0.70% 0.00% 1.80% -1.80% 5.000% 7 4.80% 5.00% 0.70% 0.90% 0.00% 2.00% -2.00% 5.000% 8 4.80% 6.00% 0.70% 3.22% 0.00% 3.00% -3.00% 5.000% 9 5.00% 4.00% 0.49% 0.18% 0.00% 1.00% -1.00% 5.000% 10 5.00% 4.80% 0.49% 0.70% 0.00% 1.80% -1.80% 5.000% 11 5.00% 5.00% 0.49% 0.90% 0.00% 2.00% -2.00% 5.000% 12 5.00% 6.00% 0.49% 3.22% 0.00% 3.00% -3.00% 5.000% 13 6.00% 4.00% 0.08% 0.18% 0.00% 1.00% -1.00% 5.000% 14 6.00% 4.80% 0.08% 0.70% 0.00% 1.80% -1.80% 5.000% 15 6.00% 5.00% 0.08% 0.90% 0.00% 2.00% -2.00% 5.000% 16 6.00% 6.00% 0.08% 3.22% 0.00% 3.00% -3.00% 5.000%

Total Commitment(incl premium) 8.050% 8.330% 8.330% 7.010% 6.520% 6.800% 6.800% 5.480% 6.310% 6.590% 6.590% 5.270% 5.900% 6.180% 6.180% 4.860%

From the above table it is evident that using collars as a strategy the company can fix the interest rate obligation. Also it is apparent from the table that the cost would be minimal in case of collar 4, with the strike price of 6%. The interest cost would come to 4.86% (including the spread payment of 2%).

Exercise 2

For Easy Money Trading Company following Strategies could be likely course of action to earn arbitrage from the given quotes by the National Trust.

Strategy 1 Strategy 1

SELL

SWAP

Fixed 4.8%

BUY

Collar 3

Fixed 5%

Notional Principal

10,00,000 ($)

Year 1, 2 & 3

Received Fixed

Pay floating part

SELL SWAP LIBOR Rate

BUY CAP@5

Received Fixed

%

Payoff

Cash inflow ($) Cash outflow ($)

SELL FLOOR@5

Premium

Payoff

(%)

Cash inflow ($)

Guaranteed

Guaranteed

Return

Return

Premium Net Cash inflow Net Cash inflow (% )

($)

(% )

0

48,000

4,900

0.49

-41,000

0.9

2,100

0.21%

1

48,000

14,900

0.49

-31,000

0.9

2,100

0.21%

2

48,000

24,900

0.49

-21,000

0.9

2,100

0.21%

3

48,000

34,900

0.49

-11,000

0.9

2,100

0.21%

4

48,000

44,900

0.49

-1,000

0.9

2,100

0.21%

5

48,000

54,900

0.49

9,000

0.9

2,100

0.21%

6

48,000

54,900

0.49

9,000

0.9

2,100

0.21%

7

48,000

54,900

0.49

9,000

0.9

2,100

0.21%

8

48,000

54,900

0.49

9,000

0.9

2,100

0.21%

9

48,000

54,900

0.49

9,000

0.9

2,100

0.21%

10

48,000

54,900

0.49

9,000

0.9

2,100

0.21%

Strategy 2 Strategy 2

SELL BUY

Notional Principal

Year 1, 2 & 3

SWAP Collar 4 10,00,000 ($)

Received Fixed SELL SWAP Received Fixed Cash inflow ($)

LIBOR Rate % 0 1 2 3 4 5 6 7 8 9 10

Strategy 3

Fixed 4.8% Fixed 6%

48,000 48,000 48,000 48,000 48,000 48,000 48,000 48,000 48,000 48,000 48,000

Pay floating part Guaranteed Guaranteed BUY CAP@6 SELL FLOOR@6 Return Return Payoff Premium Payoff Premium Net Cash inflow Net Cash inflow Cash outflow ($) % Cash inflow ($) % ($) (% ) 800 10,800 20,800 30,800 40,800 50,800 60,800 60,800 60,800 60,800 60,800

0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08

-27,800 -17,800 -7,800 2,200 12,200 22,200 32,200 32,200 32,200 32,200 32,200

3.22 3.22 3.22 3.22 3.22 3.22 3.22 3.22 3.22 3.22 3.22

19,400 19,400 19,400 19,400 19,400 19,400 19,400 19,400 19,400 19,400 19,400

1.94% 1.94% 1.94% 1.94% 1.94% 1.94% 1.94% 1.94% 1.94% 1.94% 1.94%

Strategy 3

Notional Principal

Invest

Treasury 2yrs

Received fixed - 4.1 %

SELL

FRA (24x36)

Fixed 6%

BUY

Collar 4

Fixed 6%

10,00,000 ($)

Year 1

Received Fixed

Pay floating part

Invest in T-US(2) LIBOR Rate %

BUY CAP@6

Received Fixed

Payoff

Cash inflow ($)

Cash outflow ($)

Guaranteed SELL FLOOR@6

Premium %

Guaranteed

Return

Return

Payoff

Premium

Net Cash inflow

Net Cash inflow

Cash inflow ($)

%

($)

(% )

0

41,000

800

0.08

-27,800

3.22

12,400

1.24%

1

41,000

10,800

0.08

-17,800

3.22

12,400

1.24%

2

41,000

20,800

0.08

-7,800

3.22

12,400

1.24%

3

41,000

30,800

0.08

2,200

3.22

12,400

1.24%

4

41,000

40,800

0.08

12,200

3.22

12,400

1.24%

5

41,000

50,800

0.08

22,200

3.22

12,400

1.24%

6

41,000

60,800

0.08

32,200

3.22

12,400

1.24%

7

41,000

60,800

0.08

32,200

3.22

12,400

1.24%

8

41,000

60,800

0.08

32,200

3.22

12,400

1.24%

9

41,000

60,800

0.08

32,200

3.22

12,400

1.24%

10

41,000

60,800

0.08

32,200

3.22

12,400

Year 2

Received Fixed

Pay floating part

Invest in T-US(2) LIBOR Rate %

BUY CAP@6

Received Fixed

Payoff

Cash inflow ($)

Cash outflow ($)

Guaranteed SELL FLOOR@6

Premium %

1.24%

Guaranteed

Return

Return

Payoff

Premium

Net Cash inflow

Net Cash inflow

Cash inflow ($)

%

($)

(% )

0

41,000

800

0.08

-27,800

3.22

12,400

1.24%

1

41,000

10,800

0.08

-17,800

3.22

12,400

1.24%

2

41,000

20,800

0.08

-7,800

3.22

12,400

1.24%

3

41,000

30,800

0.08

2,200

3.22

12,400

1.24%

4

41,000

40,800

0.08

12,200

3.22

12,400

1.24%

5

41,000

50,800

0.08

22,200

3.22

12,400

1.24%

6

41,000

60,800

0.08

32,200

3.22

12,400

1.24%

7

41,000

60,800

0.08

32,200

3.22

12,400

1.24%

8

41,000

60,800

0.08

32,200

3.22

12,400

1.24%

9

41,000

60,800

0.08

32,200

3.22

12,400

1.24%

10

41,000

60,800

0.08

32,200

3.22

12,400

Year 3

Received Fixed

Pay floating part

SELL FRA LIBOR Rate %

BUY CAP@6

Received Fixed

Payoff

Cash inflow ($)

Cash outflow ($)

Guaranteed SELL FLOOR@6

Premium %

1.24%

Guaranteed

Return

Return

Payoff

Premium

Net Cash inflow

Net Cash inflow

Cash inflow ($)

%

($)

(% )

0

60,000

800

0.08

-27,800

3.22

31,400

3.14%

1

60,000

10,800

0.08

-17,800

3.22

31,400

3.14%

2

60,000

20,800

0.08

-7,800

3.22

31,400

3.14%

3

60,000

30,800

0.08

2,200

3.22

31,400

3.14%

4

60,000

40,800

0.08

12,200

3.22

31,400

3.14%

5

60,000

50,800

0.08

22,200

3.22

31,400

3.14%

6

60,000

60,800

0.08

32,200

3.22

31,400

3.14%

7

60,000

60,800

0.08

32,200

3.22

31,400

3.14%

8

60,000

60,800

0.08

32,200

3.22

31,400

3.14%

9

60,000

60,800

0.08

32,200

3.22

31,400

3.14%

10

60,000

60,800

0.08

32,200

3.22

31,400

3.14%

Strategy 4

Strategy 4

Invest BUY

Notional Principal

Year 1,2 & 3

Treasury 3yrs Collar 4

Received fixed - 4.5 % Fixed 6%

10,00,000 ($)

Received Fixed Pay floating part Guaranteed Guaranteed Invest in T-US(3) BUY CAP@6 SELL FLOOR@6 Return Return Received Fixed Payoff Premium Payoff Premium Net Cash inflow Net Cash inflow Cash inflow ($) Cash outflow ($) % Cash inflow ($) % ($) (% )

LIBOR Rate % 0 1 2 3 4 5 6 7 8 9 10

45,000 45,000 45,000 45,000 45,000 45,000 45,000 45,000 45,000 45,000 45,000

800 10,800 20,800 30,800 40,800 50,800 60,800 60,800 60,800 60,800 60,800

0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08

-27,800 -17,800 -7,800 2,200 12,200 22,200 32,200 32,200 32,200 32,200 32,200

3.22 3.22 3.22 3.22 3.22 3.22 3.22 3.22 3.22 3.22 3.22

16,400 16,400 16,400 16,400 16,400 16,400 16,400 16,400 16,400 16,400 16,400

1.64% 1.64% 1.64% 1.64% 1.64% 1.64% 1.64% 1.64% 1.64% 1.64% 1.64%

In the above mentioned strategies the company would be able to make sure shot profit. When LIBOR is expected to lie below 2.4%, then Easy Money trading should enter into a Cap and simultaneously enter into opposite into FRA, Floor, Collar or SWAP to gain. When LIBOR is expected to lie between 2.4% to 5.8%, then Easy Money trading should enter into either collar or floor contract. Simultaneously it should enter into opposite position FRA, Cap or SWAP to gain. When LIBOR is expected to lie above 5.8%., then Easy Money trading should buy a collar and simultaneously it should enter into opposite position either into FRA, Cap, SWAP or Floor