Appendix to Subpart B - Examples of Derivative Limit Authority Calculations

Appendix to Subpart B of Part 708 - Examples of Derivative Limit Authority Calculations

Limit authority. A Federal credit union that is approved for derivatives authority under § 703.111 may use any of the products and characteristics described in § 703.102(a), subject to the following position and risk limits:

Table 1 - Authority Limits

Limit authority	Entry limits (first 12 months of transactions)	Standard limits
Fair Value Loss (See (a) below)	15% of net worth	25% of net worth.
Weighted Average Remaining Maturity Notional (WARMN) (See (b) below)	65% of net worth	100% of net worth.

(a) Calculating the fair value loss limit for compliance with this subpart. To demonstrate compliance with the fair value loss limit authority of this subpart, a Federal credit union must combine the total fair value (as defined by product group below) of all derivatives transactions. The fair value loss limit is exclusive to the derivatives positions (not net of offsetting gains and losses in the hedged item).

(1) The resulting figure, if a loss, must not exceed the Federal credit union's authorized fair value loss limit:

(i) Options - the gain or loss is the difference between the fair value and the unamortized premium at the reporting date;

(ii) Swaps - the gain or loss is the fair value at the reporting date; and

(iii) Futures - the gain or loss is the difference between the exchange closing price at the reporting date and the purchase or sales price.

(2) Example calculations for compliance with this subpart: fair value loss limit. The table below provides an example of the fair value loss limit calculations for a sample Federal credit union that has entry level authority. The sample Federal credit union has a net worth of $100 million and total assets of $1 billion; its fair value loss limit is −$15 million (15 percent of net worth).

Table 2 - Example Fair Value Loss Calculations

	Fair value gains (losses)				% of Net worth (percent)	Limit violation
	Options	Swaps	Futures	Total
Scenario A	$1,000,000	$2,000,000	$200,000	$3,200,000	3	No.
Scenario B	5,000,000	10,000,000	2,000,000	17,000,000	17	No.
Scenario C	1,000,000	(3,000,000)	250,000	(1,750,000)	(2)	No.
Scenario D	1,000,000	(20,000,000)	(2,000,000)	(21,000,000)	(21)	Yes.
Scenario E	(2,000,000)	(10,000,000)	1,000,000	(11,000,000)	(11)	No.

(b) Calculating the WARMN exposure for compliance with this subpart. The WARMN calculation adjusts the gross notional of a derivative to take into account its price sensitivity and remaining maturity. The WARMN limit is correlated to the fair value loss limit, as described in paragraph (a) of this appendix, for a 300 basis point parallel shift in interest rates. To demonstrate compliance with the WARMN limit authority of this subpart, a Federal credit union must calculate the WARMN using the following reference table, definitions, and calculation steps:

Table 3 - Summary of WARMN Calculation

Product	Step #1 gross notional	Adjustment factor (percent)	Step #2 adjusted notional	Step #3 WARM
Options (Caps)	Current notional	33	33% of current notional	Time remaining to maturity.
Options (Floors)	Current notional	33	33% of current notional	Time remaining to maturity.
Swaps	Current notional	100	100% of current notional	Time remaining to maturity.
Futures	Contract size	100	100% of contract size	Underlying contract.
			Sum = Total Adjusted Notional	Sum = Overall WARM
Step #4 WARMN = Adjusted Notional x (WARM/10)

(1) Step #1 - Calculate the gross notional of all outstanding derivative transactions.

(i) For options and swaps, all gross notional amounts must be absolute, with no netting (i.e., offsetting a pay-fixed transaction with a receive-fixed transaction). The gross notional for derivatives transactions with amortizing notional amounts is the current contracted notional amount, in accordance with the amortization schedule.

(ii) For futures, the gross notional is the underlying contract size as designated by the Chicago Mercantile Exchange (CME) product specifications (e.g., a five-year Treasury note futures contract will use $100,000 for each contract purchased or sold and reported here on a gross basis for limit purposes.)

(2) Step #2 - Convert each gross notional by its derivative adjustment factor to produce an adjusted gross notional. The derivative adjustment factor approximates the price sensitivity for each of the product groups in order to weight the notional amount by sensitivity before weighting for maturity.

(i) For cap and floor options, the derivative adjustment factor is 33 percent. For example, an interest rate cap with a $1 million notional amount has an adjusted gross notional of $330,000 ($1,000,000 × 0.33 + $330,000).

(ii) For interest rate swaps and Treasury futures, the derivative adjustment factor is 100 percent. For example, an interest rate swap with a $1 million notional amount has an adjusted gross notional of $1,000,000 ($1,000,000 × 1.00 = $1,000,000).

(iii) The total adjusted notional for all derivatives positions is the sum of (i) and (ii) above.

(3) Step #3 - Produce the weighted average remaining time to maturity (WARM) for all derivatives positions.

(i) For interest rate caps, interest rate floors, and interest rate swaps, the remaining maturity is the time left between the reporting date and the contracted maturity date, expressed in years (round up to two decimals);

(ii) For Treasury futures, the remaining maturity is the underlying deliverable Treasury note's maximum maturity (e.g., a five-year Treasury note future has a five-year remaining maturity); and

(iii) Determine the WARM using the adjusted gross notional, as set forth in subsection (2) of this section, and the remaining time to maturity as defined for each product group above in paragraphs (b)(3)(i) and (ii) of this appendix.

(4) Step #4 - Produce the WARMN by converting the WARM to a percentage and then multiplying the percentage by the total adjusted gross notional.

(i) Divide the WARM, as calculated in paragraph (b)(3) of this appendix, by ten to convert it to a percentage (e.g., 7.75 WARMN is translated to 77.5 percent); and

(ii) Multiply the WARM converted to a percentage, as described in paragraph (c)(4)(i) of this appendix, by total adjusted gross notional, described in paragraph (c)(2) of this appendix.

(5) Compare WARMN calculation to the WARNM limit for compliance. The total in step four (4) must be less than the limit in paragraph (a)(1)(ii) or (a)(2)(ii) of this appendix, as applicable.

(6) Example calculations for compliance with this subpart: WARMN. The table below provides an illustrative example of the WARMN limit calculations for a sample Federal credit union that has entry level authority. The sample Federal credit union has a net worth of $100 million and total assets of $1 billion; its notional limit authority is $65 million (65 percent of net worth).

Table 4 - Example WARMN Limit Calculation

	Options	Swaps	Futures	Total
Gross Notional (Step #1)	$100,000,000	$50,000,000	$5,000,000	$155,000,000
Adjustment Factor	33%	100%	100%
Adjusted Notional (Step #2)	$33,000,000	$50,000,000	$5,000,000	$88,000,000
Weighted Average Remaining Maturity (WARM) (Step #3)	7.00	8.50	5.00	7.74
		Weighted Average Remaining Maturity Notional (WARMN) (Step #4):		1 $68,100,000
		Notional Limit Authority (65% of net worth)		$65,000,000
		Under/(Over) Notional Limit Authority		($3,100,000)

¹ (77.4% of Step #3.)