Circular Letter No. 3499 — Clarifies the methodology used in calculating the Patrimônio de Referência Exigido (PRE) components for exposures subject to variation in foreign currency coupon rates (PJUR[2]), price index coupon rates (PJUR[3]), and interest rate coupon rates (PJUR[4])

Circular Letter No. 3,499, of April 8, 2011.

CIRCULAR LETTER NO. 3,499

Clarifies the methodology used in calculating the components of the Required Reference Equity (PRE) related to exposures subject to the variation of foreign currency coupon rates (PJUR[2]), price index coupon rates (PJUR[3]), and interest rate coupon rates (PJUR[4]).

In view of the provisions of Circular Letters No. 3,362, 3,363, and 3,364, all dated September 12, 2007, amended by Circular Letter No. 3,498, of June 28, 2010, which establish the procedures for calculating the components of the Required Reference Equity (PRE) related to exposures subject to the variation of foreign currency coupon rates (PJUR[2]), price index coupon rates (PJUR[3]), and interest rate coupon rates (PJUR[4]), and aiming to provide greater clarity in the calculation of said components, examples of the use of the methodology adopted in the aforementioned regulations are presented, based on the maturity ladder concepts presented in the document International Convergence of Capital Measurement and Capital Standards: A Revised Framework - Comprehensive Version, published by the Basel Committee on Banking Supervision in June 2006.

Separation by risk factors

2. In the calculation of the PJUR[2], PJUR[3], and PJUR[4] components, exposures subject to the following variations must be calculated separately:
   I - for the PJUR[2] component, of coupon rates of the United States dollar, euro, Swiss franc, yen, and British pound sterling; II - for the PJUR[3] component, of coupon rates of the Broad Consumer Price Index (IPCA) and the General Market Price Index (IGP-M); and III - for the PJUR[4] component, of coupon rates of the Reference Rate (TR), Long-Term Interest Rate (TJLP), and Basic Financial Rate (TBF).

3. In the calculation of each of the components, exposures whose values are less than 5% of the total, in each component, including, if applicable, exposures to variations in the rates of the aforementioned coupons, may be calculated jointly as subject to the variation of a single coupon rate.

4. Exposures subject to the variation of coupon rates may only be calculated jointly after marking to market their cash flows, according to the coupon rate of their respective risk factor.

5. For the calculation of the PJUR[2], PJUR[3], and PJUR[4] components, the sum of the exposures arising from long positions and the absolute value of the exposures related to short positions must be considered, as exemplified below:

Coupon	Long Exposure (C)	Short Exposure (V)	C + abs (V)	Exp. currency/Total exposure
Dollar	200	50	250	15.72%
Euro	100	150	250	15.72%
Swiss Franc	100	50	150	9.43%
Yen	200	80	280	17.61%
British Pound	90	70	160	10.06%
Other currency 1	70	90	160	10.06%
Other currency 2	50	60	110	6.92%
Other currency 3	70	30	100	6.29%
Other currency 4	60	70	130	8.18%
Total exposure	940	650	1590	100.00%

Mapping of cash flows to vertices

6. The vertices for the purpose of constructing the term structure are the tenors of 1, 21, 42, 63, 126, 252, 504, 756, 1,008, 1,260, and 2,520 business days. Cash flows must be marked to market and mapped to the following vertices (Pi), according to the number of remaining business days until their maturity date (Ti):
   I - P1, corresponding to 1 business day;
   II - P2, corresponding to 21 business days;
   III - P3, corresponding to 42 business days;
   IV - P4, corresponding to 63 business days;
   V - P5, corresponding to 126 business days;
   VI - P6, corresponding to 252 business days;
   VII - P7, corresponding to 504 business days;
   VIII - P8, corresponding to 756 business days; IX - P9, corresponding to 1,008 business days; X - P10, corresponding to 1,260 business days; and XI - P11, corresponding to 2,520 business days.

7. Cash flows with a tenor equal to Pi must be allocated to the corresponding vertices Pi. Cash flows with a tenor greater than 2,520 business days must be allocated to vertex P11, in the proportion corresponding to Ti/2,520 of their marked-to-market value.

8. The remaining cash flows, whose tenors fall between two vertices, must be allocated to the preceding (Pi) and subsequent (Pj) vertices, in the following proportion:
   I - the fraction (Pj - Ti) / (Pj - Pi) of the marked-to-market value of the cash flow must be allocated to the vertex with tenor Pi; and II - the fraction (Ti - Pi) / (Pj - Pi) of the marked-to-market value of the cash flow must be allocated to the vertex with tenor Pj.

Treatment of investment funds that observe regulatory limits

9. In the case of impossibility of calculating the proportional composition of exposures related to investment fund shares, the exposure limits established in the fund's regulations applicable to each risk component, duly documented, may be used according to the following instructions:
   I - the maximum exposure limits must be used to define the percentages related to the risk factor or component in question; II - the minimum exposure limits must be considered for the calculation of maximum exposures to risk components that do not have upper limits; III - for components where the risk factor(s) is/are unknown, the allocation must be made at the 2,520 business day vertex, together with other exposures that do not receive separate treatment; and IV - for components where the risk factor(s) is/are known, the calculation must be made in the specific factor(s) at the 2,520 business day vertex.

Example of calculation of investment fund composition according to regulatory limits

Risk Component	Minimum Percentage in Regulation	Maximum Percentage in Regulation
Fixed Interest	35%	50%
Currency Coupon	-	30%
Inflation Coupon	15%	-
Interest Coupon	20%	-
Stocks	-	10%
Exchange	-	-
Commodities	-	-

Risk Component	Allocation to Risk Components	Origin of Percentage
Fixed Interest	50%	maximum percentage
Currency Coupon	30%	maximum percentage
Inflation Coupon	45%	100%-(35%+20%)
Interest Coupon	50%	100%-(35%+15%)
Stocks	10%	maximum percentage
Exchange	30%	100%-(35%+15%+20%)
Commodities	30%	100%-(35%+15%+20%)

Formula

10. After mapping the cash flows of financial instruments to their respective vertices, the calculation of the daily value of the PJUR[2], PJUR[3], and PJUR[4] components must be performed using a formula that uses the same methodology for all components, differing only by the value of the multiplier factor Mext, to be disclosed by the Central Bank of Brazil.

The formula for calculating PJUR[2] is:

$$ PJUR[2] = M_{ext} imes left( sum_{i=1}^{11} EL_i + sum_{i=1}^{11} DV_i + sum_{j=1}^{3} DHZ_j + sum_{k=1}^{m_1} DHE_k ight) $$

in which:
Mext = multiplier factor for exposure subject to the variation of foreign currency coupon rates; m1 = number of foreign currencies in which there is exposure subject to the variation of foreign currency coupon rates; ELi = net exposure at vertex "i" and in foreign currency "k"; DVi = vertical mismatch at vertex "i" and in foreign currency "k"; DHZj = horizontal mismatch in foreign currency "k" within maturity zone "j"; and DHE = horizontal mismatch in foreign currency "k" between maturity zones.

Example of capital requirement calculation

11. In order to illustrate the calculations to be performed by institutions to determine the PJUR[2] component, due to the provisions of Circular Letter No. 3,362, of 2007, amended by Circular Letter No. 3,498, of 2010, the following example is presented, assuming that, at the close of business on June 30, 2005, this circular was already in effect and an institution had the following instruments in its portfolio adjusted by the variation in the Brazilian real quotation of the United States dollar, subject to the variation of the currency coupon:
    I - a swap operation, with a long position in Interbank Deposit (DI) on one leg and a short position in dollars on the other, with BM&F (Bolsa de Mercadorias e Futuros) guarantee on both legs, contracted on March 23, 2005, with a notional value of R$1,000,000.00, a currency coupon of 2.32% p.a. and a total tenor of 240 calendar days; II - a swap operation, with a long position in DI on one leg and a short position in dollars on the other, without BM&F guarantee on both legs, contracted on July 1, 2000, with a notional value of R$2,000,000.00, a currency coupon of 3.72% p.a. and a total tenor of 1,930 calendar days; III - 500 National Treasury Notes, Series D (NTN-D), code 780199, issued on July 1, 2000 and maturing on July 16, 2008, acquired on February 12, 2005; IV - a currency coupon futures contract (DDI), sold, traded on BM&F, maturing on September 1, 2005, traded on May 13, 2005; and V - a periodic adjustment currency swap contract (SCC) traded on BM&F, series F805, maturing on January 2, 2008, purchased on June 21, 2005.

12. The guarantee associated with the instrument cited in paragraph 11, item I, does not exempt the institution from including it in the capital requirement calculation, since the guarantee covers only credit risk, not protecting against market risk. In the calculation of the PJUR[2] component, the flow originated by the aforementioned instrument is an outflow of R$1,000,000.00 on November 18, 2005, updated by the variation of the PTAX800, from the Central Bank Information System (Sisbacen), between March 22, 2005 and June 29, 2005, and capitalized from March 23, 2005 until maturity on November 18, 2005, by the fixed rate of 2.32% p.a. This value will be brought to present value for June 30, 2005, using the market currency coupon in force on that day for the remaining tenor of 141 calendar days.

13. In the calculation of the PJUR[2] component, the flow originated by the instrument mentioned in paragraph 11, item II, is an outflow of R$2,000,000.00 on October 13, 2005, updated by the variation of PTAX800 between June 30, 2000 and June 29, 2005, and capitalized from July 1, 2000 until maturity on October 13, 2005, by the fixed rate of 3.72% p.a. This value will be brought to present value for June 30, 2005, using the market currency coupon rates in force on that day for the remaining tenor of 105 calendar days.

14. The instrument mentioned in paragraph 11, item III, is a bond that, on June 30, 2005, still had the right to seven semi-annual interest payments, respectively on July 16, 2005, January 16, 2006, July 16, 2006, January 16, 2007, July 16, 2007, January 16, 2008 and July 16, 2008, and of the principal at maturity, on July 16, 2008. Therefore, the originated flows are seven interest inflows of R$30,000.00 (12% ÷ 2 × 500 × R$1,000.00) and one inflow of R$500,000.00 (500 x R$1,000.00), coinciding with the latter with the inflow related to the last interest payment, updated by the currency variation occurred between June 30, 2000 and June 29, 2005. These values will be brought to present value for June 30, 2005, using the market currency coupon rates in force on that day for the remaining tenors of each of the flows.

15. The positioning of the instrument cited in paragraph 11, item IV, is long in currency variation plus currency coupon and short in DI. Therefore, the flow is represented by an inflow of US$50,000.00 on September 1, 2005, converted to reais by the PTAX800 of June 29, 2005. This is the value that must be marked to market for June 30, 2005, using the market currency coupon rate in force on that day for the remaining tenor of 63 calendar days.

16. The positioning of the instrument mentioned in paragraph 11, item V, is long in DI and short in currency variation plus currency coupon. Therefore, the flow is represented by an outflow of US$50,000.00 on January 2, 2008, converted to reais by the PTAX800 of June 29, 2005. This is the value that must be marked to market for June 30, 2005, using the market currency coupon rate in force on that day for the remaining tenor of 916 calendar days.

17. The values of assets and liabilities that make up the cash flows must be marked to market using the term structure of the currency coupon representative of the rates in force in the market on the day for which the respective PRE component is calculated, in the case of the example, the term structure at the close of June 30, 2005. The methodology for calculating the rates used to mark to market positions subject to the risk in question must be established based on consistent and verifiable criteria, which take into account independence in data collection regarding the rates practiced in trading desks.

18. For marking to market of cash flows, considering that the market currency coupon is on a 360-day linear basis, each flow is obtained through the following formula:

$$ F_i = \frac{\text{Total value at maturity updated by currency variation}}{1 + \text{current currency coupon} \times \frac{T}{360}} $$

19. Based on this formula, the marked-to-market cash flows of the instruments are presented below:

Instrument	Tenor in calendar days	Tenor in business days	Marked-to-market value (R$)
a	141	97	-865,814.74
b	105	73	-1,360,241.11
c	16	11	38,795.26
c	200	138	37,889.18
c	381	261	37,004.26
c	565	387	36,140.00
c	746	511	35,295.93
c	930	637	34,471.58
c	1,112	761	594,774.39
d	63	45	116,031.22
e	916	627	-104,668.53

Allocation of flows to vertices

20. For remaining tenors between 1 and 2,520 business days, the marked-to-market flows are allocated to the vertices according to the following formulas:

I - Value allocated to the preceding vertex = $F_l \times \frac{P_j - T_i}{P_j - P_i}$; and II - Value allocated to the subsequent vertex = $F_l \times \frac{T_i - P_i}{P_j - P_i}$.

21. For remaining tenors greater than 2,520 business days, the marked-to-market flows are allocated to the 2,520 vertex, according to the following formula:

Value allocated to the 2,520 vertex = $F_l \times \frac{T_i}{2,520}$.

22. Thus, the marked-to-market cash flows of the exemplified instruments are allocated to the vertices according to the table below:

Instrument	Tenor in business days	Marked-to-market value (R$)	Preceding vertex	Subsequent vertex	Value allocated to preceding vertex (R$)	Value allocated to subsequent vertex (R$)
a	97	-865,814.74	63	126	-398,549.64	-467,265.10
b	73	-1,359,276.99	63	126	-1,143,518.74	-215,758.25
c	11	38,795.26	1	21	19,397.63	19,397.63
c	138	37,889.18	126	252	34,280.68	3,608.49
c	261	37,004.26	252	504	35,682.68	1,321.58
c	387	36,140.00	252	504	16,779.29	19,360.72
c	511	35,295.93	504	756	34,315.49	980.44
c	637	34,471.58	504	756	16,278.24	18,193.33
c	761	594,774.39	756	1,008	582,973.31	11,801.08
d	45	116,031.22	42	63	99,455.33	16,575.89
e	627	-104,668.53	504	756	-53,580.32	-51,088.21

23. The total values allocated per vertex, in reais, are:

Vertex	Total Long Exposures (R$)	Total Short Exposures (R$)
1	19,397.63
21	19,397.63
42	99,455.33
63	16,575.89	-1,542,068.38
126	34,280.68	-683,023.35
252	56,070.46
504	71,276.03	-53,580.32
756	602,147.08	-51,088.21
1,008	11,801.08
1,260	-	-
2,520	-	-

Net exposure

24. Initially, exposures must be weighted by their respective Yi factors. The value of the net exposure at vertex "i" (ELi) is the net value of the long and short exposures weighted at each vertex. Assuming that, at the close of business on June 30, 2005, Circular Letter No. 3,498, of 2010, was already in effect:

Vertices	Factor Yj	Weighted Long Exposures (R$)	Weighted Short Exposures (R$)	Net Exposure (ELi) (R$)
1	0.00%	0.00
2	0.50%	96.99	0.00	96.99
3	0.70%	696.19	0.00	696.19
4	0.80%	132.61	-12,336.55	-12,203.94
5	1.20%	411.37	-8,196.28	-7,784.91
6	2.00%	1,121.41	0.00	1,121.41
7	4.00%	2,851.04	-2,143.21	707.83
8	6.00%	36,128.82	-3,065.29	33,063.53
9	8.00%	944.09	0.00	944.09
10	10.00%	0.00
11	18.00%	0.00
Total		16,641.18

25. The first term of the PJUR[2] component formula is calculated as the absolute value of the sum of the net exposures (ELi). In the example, it corresponds, therefore, to:

$$ \sum_{i=1}^{11} EL_i = \text{R$}16,641.18 $$

Vertical mismatch

26. The value of the vertical mismatch DVi corresponds to 10% of the smaller value between the absolute value of the sum of weighted long exposures and the absolute value of the sum of weighted short exposures for each vertex Pi. For example, for vertex 2, the smaller value is 0.0; for vertex 3, the smaller value is 0.0; and, for vertex 4, the smaller value is R$132.61.

Vertices	Factor Yj	Weighted Long Exposures (R$) (A)	Weighted Short Exposures (R$) (B)	Min (	A	,	B	) (R$)	DVi (R$)
1	0.00%	0.00
2	0.50%	96.99	0.00
3	0.70%	696.19	0.00
4	0.80%	132.61	-12,336.55	132.61	13.26
5	1.20%	411.37	-8,196.28	411.37	41.14
6	2.00%	1,121.41	0.00
7	4.00%	2,851.04	-2,143.21	2,143.21	214.32
8	6.00%	36,128.82	-3,065.29	3,065.29	306.53
9	8.00%	944.09	0.00
10	10.00%	0.00
11	18.00%	0.00
Total					575.25

27. The value of the second term of the PJUR[2] component formula is, therefore:

$$ \sum_{i=1}^{11} DV_i = \text{R$}575.25 $$

Maturity zones

28. The eleven vertices of the term structure used here are grouped into three maturity zones, each associated with a factor Wj:
    I - Zone 1: comprises vertices P1 to P5, with W1 = 40%; II - Zone 2: comprises vertices P6 to P8, with W2 = 30%; and III - Zone 3: comprises vertices P9 to P11, with W3 = 30%.

Horizontal mismatches

29. The value of the horizontal mismatch within each zone, DHZj, corresponds to the smaller value between the sum of positive ELi and the sum of the absolute values of negative ELi of the vertices belonging to that zone, multiplied by the corresponding factor Wj.

Zone	Vertices	Factor Wj	Sum of Positive ELi (R$)	Sum of Negative ELi (R$)	DHZj (R$)
1	1 to 5	40.00%	793.18	-19,988.85	317.27
2	6 to 8	30.00%	34,892.77	0.00	0.00
3	9 to 11	30.00%	944.09	0.00	0.00
Total					317.27

30. Thus, we have that DHZ1 = R$793.18 x 40% = R$317.27, DHZ2 = 0.00 x 30% = 0.00 and DHZ3 = 0.00 x 30% = 0.00. The value of the third term of the PJUR[2] component is equivalent to:

$$ \sum_{j=1}^{3} DHZ_j = \text{R$}317.27 $$

31. Finally, the value of the horizontal mismatch between maturity zones, DHE, corresponds to the sum of the following values, where the value of total exposures in each zone corresponds to the sum of the net exposures ELi of each vertex Pi belonging to the respective zone:
    I - 40% of the smaller absolute value between the total exposures of Zone 1 and Zone 2, if these have opposite total exposures; II - 40% of the smaller absolute value between the total exposures of Zone 2 and Zone 3, if these have opposite total exposures; and III - 100% of the smaller absolute value between the total exposures of Zone 1 and Zone 3, if these have opposite total exposures.

32. As the values of the total exposures of zones 1, 2, and 3 are, respectively, R$19,195.68, R$34,892.77, and R$944.09, the results I, II, and III above will correspond, respectively, to the values R$7,678.27, R$0.00, and R$944.09. Thus, the last term of the PJUR[2] component formula is:

Zone (R$)	Total Exposure of Zone (R$)
1	-19,195.68
2	34,892.77
3	944.09

Between Zones	Factor	DHE (R$)
1 and 2	40%	7,678.27
2 and 3	40%	0.00
1 and 3	100%	944.09
Total		8,622.36

DHE = R$8,622.36.

33. The sum of the four terms, therefore, corresponds to R$26,156.06. The value of the PJUR[2] component, in turn, will be defined by the product of this value by the respective multiplier Mext.

Calculation of the "M" factor for the PJUR[2], PJUR[3], and PJUR[4] components

34. The use of the multiplier factor M, provided for in each of the PJUR[2], PJUR[3], and PJUR[4] components, aims to maintain prudential standards adequate to the Brazilian market, as well as the more conservative profile of the standardized models, compared to internal models, for the calculation of capital requirements.

35. To define the values disclosed in art. 2 of Circular Letter No. 3,388, of June 4, 2008, amended by Circular Letter No. 3,498, of 2010, an attempt was made to converge the capital value required by the maturity ladder methodology with the capital value calculated through volatility-based methodologies, both in normal market conditions and in extreme conditions.

36. Thus, using the monthly exposures by risk factor of all financial institutions for the months between July 2008 and March 2010, the capital requirement was calculated through the maturity ladder methodology with the adaptations presented here. For each of the aforementioned monthly exposures by risk factor, the stressed Value at Risk (VaR) was calculated, with a one-tailed confidence level of 99% and assuming ten business days for position settlement. Using the United States dollar currency coupon curve, for the PJUR[2] component, the IPCA coupon, for the PJUR[3] component, and the TR coupon, for the PJUR[4] component, the following parameters were obtained:

I - for PJUR[2]:
a) vertex volatilities:
σ21 0.025832
σ42 0.013665
σ63 0.009784
σ126 0.005971
σ252 0.003861
σ504 0.002797
σ756 0.002380
σ1008 0.002082
σ1260 0.002001
σ2520 0.001949

b) correlation matrix:

	21	42	63	126	252	504	756	1008	1260	2520
21	1.000000	0.990848	0.968204	0.861541	0.721252	0.563671	0.477103	0.370543	0.336437	0.185103
42	0.990848	1.000000	0.991583	0.912164	0.778996	0.620574	0.530423	0.418984	0.379326	0.205200
63	0.968204	0.991583	1.000000	0.952187	0.834020	0.681279	0.590822	0.476256	0.432668	0.232617
126	0.861541	0.912164	0.952187	1.000000	0.945876	0.821404	0.734887	0.620657	0.569069	0.304014
252	0.721252	0.778996	0.834020	0.945876	1.000000	0.933475	0.858070	0.757175	0.704207	0.393904
504	0.563671	0.620574	0.681279	0.821404	0.933475	1.000000	0.950758	0.858705	0.800105	0.452497
756	0.477103	0.530423	0.590822	0.734887	0.858070	0.950758	1.000000	0.931877	0.875621	0.492818
1008	0.370543	0.418984	0.476256	0.620657	0.757175	0.858705	0.931877	1.000000	0.968211	0.558256
1260	0.336437	0.379326	0.432668	0.569069	0.704207	0.800105	0.875621	0.968211	1.000000	0.574019
2520	0.185103	0.205200	0.232617	0.304014	0.393904	0.452497	0.492818	0.558256	0.574019	1.000000

II - for PJUR[3]:
a) vertex volatilities:
σ21 0.015002
σ42 0.007124
σ63 0.004597
σ126 0.002754
σ252 0.001854
σ504 0.001486
σ756 0.001497
σ1008 0.001576
σ1260 0.001534
σ2520 0.001832

Circular Letter No. 3,499, of April 8, 2011.

b) correlation matrix:

	21	42	63	126	252	504	756	1008	1260	2520
21	1,000000	0,622238	0,510530	0,468817	0,275168	0,233079	0,159310	0,077288	0,105810	0,030324
42	0,622238	1,000000	0,670477	0,656100	0,314901	0,233866	0,157405	0,087523	0,086323	0,063677
63	0,510530	0,670477	1,000000	0,652005	0,340022	0,205044	0,129322	0,077714	0,105146	0,051963
126	0,468817	0,656100	0,652005	1,000000	0,429918	0,366895	0,277584	0,204392	0,217230	0,176342
252	0,275168	0,314901	0,340022	0,429918	1,000000	0,623059	0,422034	0,307971	0,310611	0,267844
504	0,233079	0,233866	0,205044	0,366895	0,623059	1,000000	0,838719	0,721608	0,693940	0,585409
756	0,159310	0,157405	0,129322	0,277584	0,422034	0,838719	1,000000	0,887162	0,843845	0,691423
1008	0,077288	0,087523	0,077714	0,204392	0,307971	0,721608	0,887162	1,000000	0,915789	0,706108
1260	0,105810	0,086323	0,105146	0,217230	0,310611	0,693940	0,843845	0,915789	1,000000	0,811894
2520	0,030324	0,063677	0,051963	0,176342	0,267844	0,585409	0,691423	0,706108	0,811894	1,000000

III - for PJUR[4]:

a) vertex volatilities:

σ21 0,000803
σ42 0,000798
σ63 0,000800
σ126 0,000813
σ252 0,000901
σ504 0,001015
σ756 0,001077
σ1008 0,001109
σ1260 0,001138
σ2520 0,001230

b) correlation matrix:

	21	42	63	126	252	504	756	1008	1260	2520
21	1,000000	0,989845	0,982079	0,947863	0,845931	0,756040	0,711008	0,672733	0,636119	0,506439
42	0,989845	1,000000	0,991592	0,963182	0,872163	0,784615	0,739216	0,699211	0,662978	0,532973
63	0,982079	0,991592	1,000000	0,976544	0,897552	0,815316	0,772109	0,732547	0,697019	0,571078
126	0,947863	0,963182	0,976544	1,000000	0,956771	0,892393	0,845885	0,807130	0,774570	0,660080
252	0,845931	0,872163	0,897552	0,956771	1,000000	0,968600	0,927813	0,896716	0,872176	0,786873
504	0,756040	0,784615	0,815316	0,892393	0,968600	1,000000	0,979899	0,962703	0,945002	0,884137
756	0,711008	0,739216	0,772109	0,845885	0,927813	0,979899	1,000000	0,990239	0,978866	0,927529
1008	0,672733	0,699211	0,732547	0,807130	0,896716	0,962703	0,990239	1,000000	0,990726	0,950425
1260	0,636119	0,662978	0,697019	0,774570	0,872176	0,945002	0,978866	0,990726	1,000000	0,966132
2520	0,506439	0,532973	0,571078	0,660080	0,786873	0,884137	0,927529	0,950425	0,966132	1,000000

Circular Letter No. 3,499, of April 8, 2011.

37. An individual multiplier was obtained for each of the mentioned exposures, calculated in a manner to equate the estimated capital requirement, still without multiplier, to three times the stressed VaR value.

38. The average of the individual multipliers weighted by their respective stressed VaR values was then determined, with a maximum weighting of 10% for each financial institution in a given month – except for the PJUR[4] portion, where the maximum weighting was 20%, given the smaller number of institutions with exposure. The resulting weighted multiplier (M) was multiplied by the average proportion between (VaR + stressed VaR) and stressed VaR, determined in studies by the Central Bank of Brazil. The proportions used were: 1.5 for the PJUR[2] portion; 1.667 for the PJUR[3] portion; and 1.7 for the PJUR[4] portion. The final multiplier therefore leads to a capital level compatible with the value of three times (VaR + stressed VaR), in consonance with the provisions in the document “Revisions to the Basel II Market Risk Framework”, published in July 2009 by the Basel Committee.

39. The Central Bank of Brazil maintains permanent monitoring of the volatilities of the interest rate curves mentioned herein and will promote any alterations in the multiplier values, as well as in the methodology used for their derivation, when necessary.

40. This Circular Letter enters into force on January 1, 2012, when Circular Letter No. 3,310, of April 15, 2008, shall be revoked.

Brasília, April 8, 2011.
Department of Standards of the Financial System Sergio Odilon dos Anjos Head

This text does not replace the published version in the DOU and in Sisbacen.