Circular Letter No. 3,498, of April 8, 2011 1

CIRCULAR LETTER NO. 3,498

Clarifies the methodology used in the calculation of the standard volatility value and the multiplier for day "t", to be disclosed daily by the Central Bank of Brazil, for the purpose of calculating the portion of the Required Reference Equity (PRE) related to exposures subject to variation in fixed interest rates denominated in real (PJUR[1]).

In view of the provisions of Circular No. 3,361, of September 12, 2007, amended by Circular No. 3,498, of June 28, 2010, which establishes the procedures for calculating the portion of the Required Reference Equity (PRE) related to exposures subject to variation in fixed interest rates denominated in real (PJUR[1]), and aiming to promote greater transparency regarding the procedures adopted and ensure that the calculation can be fully replicated by interested parties, the procedures adopted for the calculation of volatility for each of the vertices Pi (σi,t), of the standard volatilities (σI,t, σII,t and σIII,t) and of the multiplier (Mpre t), to be disclosed daily by the Central Bank of Brazil, are disclosed.

Construction of the interest rate term structure

2. The calculation of the Value at Risk (VaR) resulting from exposure in certain financial instruments is carried out from the construction of the series of returns of the corresponding risk factors. The relevant risk factors for the calculation of VaR related to the risk of fixed-rate operations denominated in real are the rates associated with fixed terms previously chosen, defined as vertices of the term structure.

3. The vertices for constructing the term structure of fixed interest rates are the terms of 21, 42, 63, 126, 252, 504, 756, 1,008, 1,260 and 2,520 business days, with the last one used only in the mapping of cash flows, without effect on the volatility calculation.

4. The return on date "t" associated with the vertex Pi of term "T" is given by:
   Rt,T = [100 / (1 + (rt,T * T / 100))]^(252/T) - 1

where:
Rt,T = the annual interest rate with discrete compounding (considering 252 business days in the year) for date "t", to occur during the term of "T" business days.

5. For each business day, the rates related to the different chosen terms are calculated, which provide the generation of daily series of spot rates concerning each of the vertices. For this purpose, data related to interbank deposits (DI) and futures and swap contracts traded on BM&FBovespa S.A. - Stock, Commodities and Futures Exchange (BM&FBovespa) are used, seeking to identify the most liquid instruments in each maturity range.

However, due to variations in liquidity observed in the financial market, the Central Bank of Brazil may exclude or add new financial instruments and/or vertices from which the term structure and volatilities will be calculated for the purpose of calculating PJUR[1].

6. The term structure is obtained through the use of interest rates embedded in DI over quotes, DI futures contracts (first to third maturity) and DI swap rates x fixed rates calculated for terms of 6, 12, 24, 36, 48 and 60 months. The construction of spot rates is obtained by accumulating the implicit forward rates between the maturities of the listed financial instruments, assuming the hypothesis that the forward rate between the maturities is constant. Thus, the interest rate implicit in the prices of the mentioned financial instruments, for a term of "T" business days, is given by:

Rt,T = [ (1 + (R0/100)) * Π(j=0 to 8) (1 + (Rj,j+1/100))^(Tj/T) - 1 ] * (100/T)

for T ≤ T9

where:
R0 = DI over spot rate calculated;
R0,1 = forward rate implicit by DI and the quote of the first DI future maturity; R1,2 = forward rate implicit by the quotes of the first and second DI future maturities; R2,3 = forward rate implicit by the quotes of the second and third DI future maturities; R3,4 = forward rate implicit by the quotes of the third DI future maturity and the 6-month DI swap rate x fixed rates; R4,5 = forward rate implicit by the 6 and 12-month DI swap rates x fixed rates; R5,6 = forward rate implicit by the 12 and 24-month DI swap rates x fixed rates; R6,7 = forward rate implicit by the 24 and 36-month DI swap rates x fixed rates; R7,8 = forward rate implicit by the 36 and 48-month DI swap rates x fixed rates; R8,9 = forward rate implicit by the 48 and 60-month DI swap rates x fixed rates; and T0 to T9 = terms, in business days, of maturity of each financial instrument used, respectively, DI (1 business day), first, second and third DI future maturities, 6, 12, 24, 36, 48 and 60-month swaps.

7. For terms greater than 1,260 business days (sixty months), the hypothesis of a constant spot rate with a value equal to that calculated for the 1,260 business day vertex is assumed. This criterion may be altered if longer-term instruments present greater liquidity.

Treatment of investment funds that observe regulatory limits

8. 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 portion, duly documented, may be used, according to the following instructions:

I - the maximum exposure limits present in the fund's regulations must be used to define the percentages related to the factor or risk portion in question; and

II - the minimum exposure limits present in the regulations must be considered for the calculation of maximum exposures to risk portions that do not have upper limits.

Example for calculating the composition of investment funds that observe regulatory limits

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

Risk Portion | Allocation in Risk Portions | Origin of Percentage --- | --- | --- Fixed Interest | 50% | Maximum percentage Currency Swap | 30% | Maximum percentage Inflation Swap | 45% | 100%-(35%+20%) Interest Swap | 50% | 100%-(35%+15%) Stocks | 10% | Maximum percentage Exchange | 30% | 100%-(35%+15%+20%) Commodities | 30% | 100%-(35%+15%+20%)

Calculation of daily volatility for vertex Pi

9. For each vertex Pi, the Central Bank of Brazil builds two volatility series, each with a specific value of the parameter λ, using the following function:
   σi,t(λ) = √[ (1-λ) * Σ(k=0 to ∞) λ^k * rt-k,i^2 ]

where:
rt,i = return on day "t" related to the rate associated with the term of vertex Pi; λ (lambda parameter) = smoothing method decay factor, representing the structure of weights assigned to returns that occurred in the recent past vis-à-vis the more distant past. The parameters currently used for the construction of the volatility series are: λ1 = 0.85 and λ2 = 0.94; and σi = volatility at vertex "i".

10. The daily volatility of each vertex Pi of the term structure of interest rates is the maximum value between the volatilities of the two series, according to the following formula:
    σi,t = max{ σi,t(λ1), σi,t(λ2) }

11. The maximum value rule used allows for the rapid absorption of a shock through a smaller lambda, as well as a more cautious exit from it through a larger lambda.

Calculation of daily standard volatility for vertex Pi

12. The standard volatilities for each vertex "i" used for the calculation of VaRi,t are determined based on the application of the concept of volatility families, being determined by the maximum values of the volatilities of the vertices of the same family. Three families are considered, whose maximum volatilities are determined by the following formula:

I - σI,t = max(σ21,t, σ42,t, σ63,t);
II - σII,t = max(σ126,t, σ252,t, σ504,t); and
III - σIII,t = max(σ756,t, σ1008,t, σ1260,t).

13. On day "t", the standard volatility is defined according to the following formulas:

I - σI,t = σ21,t = σ42,t = σ63,t;
II - σII,t = σ126,t = σ252,t = σ504,t; and
III - σIII,t = σ756,t = σ1008,t = σ1260,t = σ2520,t.

14. The standard volatility σI,t is assigned to vertices 21, 42 and 63; σII,t is the standard volatility assigned to vertices 126, 252 and 504; and σIII,t is the standard volatility assigned to vertices 756, 1,008, 1,260 and 2,520. The standard volatility σIII,t is calculated based only on the volatilities of vertices 756, 1,008 and 1,260, but is also used in the determination of the standard volatility of vertex 2,520.

Standard volatility to be used in the calculation of the multiplier

15. The standard volatility σt to be used in the calculation of the multiplier is represented by the maximum value of the volatilities associated with each of the vertices "i". It is used only for the definition of the value of the multiplier Mpre t, not being used in the calculation of VaRi,t. Its calculation is given by:
    σt = max(σI,t, σII,t, σIII,t).

Calculation of the multiplier (Mpre t)

16. In order to avoid abrupt fluctuations in capital requirements during periods of low volatility, the standard volatility (maximum of the volatility of the vertices) is replaced by the average of this standard volatility over the last sixty business days. The expression for the calculation of this average is given by:
    σ̄t = (1/60) * Σ(i=0 to 59) σt-i

17. The multiplier Mpre t is a decreasing function of the average of the standard volatility over the last sixty business days. This function considers the frequency distribution of the average of the standard volatility over the last sixty business days and the desired values for the highest and lowest value of the multiplier, "M" and "m", respectively.

18. Being σpico the highest volatility observed in the series of averages of standard volatility over the last sixty business days, with a window of 252 business days, and being σP% the value related to a given percentile (P%) associated with the frequency distribution of the same series of averages of standard volatility over the last sixty business days, with a window of 252 business days, the multiplier Mpre t is given by:

Mpre t = { M + C1*(σt - σP%) if σt > σP%
{ M if σt ≤ σP%

19. The determination of constants C1 and C2 is carried out considering M(σP%) = M and M(σpico) = m, therefore:
    C1 = (M - m) / (σP% - σpico) and C2 = M - C1*σP%.

20. The table below specifies the values of the parameters currently in force for the calculation of the multiplier Mpre t:

Parameter	Specification
M	3 m
P%	0
Window for calculation of σP%	Last 252 business days Window for calculation of σpico

Calculation of parameters "ρ" and "k" for the construction of the correlation matrix between vertices

21. The correlation ρi,j between two vertices "i" and "j", used for the purpose of determining the Standard VaRt, defined in Circular No. 3,361, of 2007, is obtained according to the following formula:
    ρi,j = ρ * exp(-k * |Pi - Pj|)

where:
Pi, Pj = terms of the vertices;
ρ = base parameter for the calculation of correlations ρi,j, calculated on the penultimate business day of each month or on any other date, at the discretion of the Central Bank of Brazil, and disclosed daily; and k = correlation decay factor, calculated on the penultimate business day of each month or on any other date, at the discretion of the Central Bank of Brazil, and disclosed daily.

22. To obtain the parameters "ρ" and "k" on day "t", first the historical empirical correlations between the return series rt,i of vertices 21, 42, 63, 126, 252, 504, 756, 1,008 and 1,260 are calculated, considering a window of 252 business days.

23. Thus, the historical correlation ρHist i,j on day "t" is given by the formula:
    ρHist i,j = Σ(k=0 to 251) (rt-k,i - r̄i)(rt-k,j - r̄j) / √[ Σ(k=0 to 251) (rt-k,i - r̄i)^2 * Σ(k=0 to 251) (rt-k,j - r̄j)^2 ]

where:
rt,i = return of vertex "i" on date "t"; rt,j = return of vertex "j" on date "t"; r̄i = average of returns of vertex "i" over the last 252 days; and r̄j = average of returns of vertex "j" over the last 252 days.

24. Estimates are made using various values for "ρ" and "k", in order to find the minimum value for the sum of the squares of the differences, given by Σ(ρHist i,j - ρi,j)^2. The values of the parameters "ρ" and "k" chosen and disclosed by the Central Bank of Brazil are the two values located in the interval [0,1] that meet the condition of generating a positive definite matrix and that minimize the sum of the squares of the differences, that is:
    (ρ, k) = Arg min (ρ,k) Σ(ρHist i,j - ρi,j)^2

25. These same values of "ρ" and "k" are also used for the calculation of the correlation ρi,j of the 2,520 business day vertex with the other vertices.

Calculation of stress parameters

26. The parameters for the second part of the capital requirement formula (parameters for calculating the stressed Value at Risk – sVaRt Standard) are those disclosed by the Central Bank of Brazil for the calculation of the Standard VaRt of day "t" in which the largest sum of the Standard VaRt calculated for each financial institution was verified, from July 1, 2008, for days "t" belonging to periods of high volatility previously identified.

Example of the calculation of the capital requirement, according to Circular No. 3,361, of 2007, amended by Circular No. 3,498, of 2010.

27. In order to illustrate the calculations to be carried out by institutions for the determination of PJUR[1], the following example is presented, assuming that, at the close of June 30, 2006, Circular No. 3,361, of 2007, amended by Circular No. 3,498, of 2010, had already been in effect for more than sixty business days, and that an institution had in its portfolio the following exposures subject to variation in fixed interest rates denominated in real:

I - a swap operation, with a long position in DI on one side and a short position in fixed rate on the other, with BM&FBovespa guarantee on both sides, contracted on May 8, 2006, with a notional value of R$10,000,000.00 (ten million reais), rate of 14.89% p.a. and total term of 1,953 calendar days (1,343 business days) on the date of contracting;

II - a swap operation, with a long position in fixed rate on one side and a short position in DI on the other, without guarantee, contracted on December 19, 2005, with a notional value of R$5,000,000.00 (five million reais), rate of 15.48% p.a. and total term of 1,841 calendar days (1,264 business days) on the date of contracting;

III - a swap operation, with a long position in fixed rate on one side and a short position in DI on the other, without guarantee, contracted on December 6, 2005, with a notional value of R$2,000,000.00 (two million reais), rate of 15.69% p.a. and total term of 1,491 calendar days (1,023 business days) on the date of contracting;

IV - 2,000 National Treasury Bills (LTN), code 100000, issued on July 22, 2005 and maturing on January 1, 2008, acquired on August 15, 2005;

V - 1,000 LTN, code 100000, issued on December 17, 2005 and maturing on October 1, 2006, acquired on February 28, 2005;

VI - 10,000 LTN, code 100000, issued on October 27, 2004 and maturing on July 1, 2006, acquired on January 17, 2005; and

VII - a swap operation, with a long position in fixed rate on one side and a short position in DI on the other, without guarantee, contracted on April 17, 2006, with a notional value of R$1,000,000.00 (one million reais), rate of 16.00% p.a. and total term of 3,789 calendar days (2,607 business days) on the date of contracting.

28. The guarantee present in the instrument cited in paragraph 27, item I, does not exempt the institution from including it in the calculation of the capital requirement, since the guarantee covers only credit risk, not protecting against market risk. Regarding the calculation of the capital requirement for exposures subject to variation in fixed interest rates denominated in real, the flow considered by the instrument is an outflow of R$10,000,000.00 (ten million reais) on September 12, 2011, capitalized from May 8, 2006 until maturity on September 12, 2011, by the contracted fixed rate of 14.89% p.a. This value will be brought to present value for June 30, 2006, using the market fixed rate in force on that day for the term to occur of 1,305 business days.

29. The flow considered by the instrument mentioned in paragraph 27, item II, is an inflow of R$5,000,000.00 (five million reais) on January 3, 2011, capitalized from December 19, 2005 until maturity on January 3, 2011, by the contracted fixed rate of 15.48% p.a. This value will be brought to present value for June 30, 2006, using the market fixed rate in force on that day for the term to occur of 1,131 business days.

30. The flow considered by the instrument referred to in paragraph 27, item III, is an inflow of R$2,000,000.00 (two million reais) on January 5, 2010, capitalized from December 6, 2005 until maturity on January 5, 2010, by the contracted fixed rate of 15.69% p.a. This value will be brought to present value for June 30, 2006, using the market fixed rate in force on that day for the term to occur of 881 business days.

31. The flow considered by the instrument contained in paragraph 27, item IV, is an inflow of R$2,000,000.00 (two million reais) on January 2, 2008. This value will be brought to present value for June 30, 2006, using the market fixed rate in force on that day for the term to occur of 376 business days.

32. The flow considered by the instrument cited in paragraph 27, item V, is an inflow of R$1,000,000.00 (one million reais) on October 2, 2006. This value will be brought to present value for June 30, 2006, using the market fixed rate in force on that day for the term to occur of 65 business days.

33. The flow considered by the instrument mentioned in paragraph 27, item VI, is an inflow of R$10,000,000.00 (ten million reais) on July 3, 2006. This value will be brought to present value for June 30, 2006, using the market fixed rate in force on that day for the term to occur of one business day.

34. The flow considered by the instrument referred to in paragraph 27, item VII, is an inflow of R$1,000,000.00 (one million reais) on August 31, 2016, capitalized from April 17, 2006 until maturity on August 31, 2016, by the contracted fixed rate of 16.00% p.a. This value will be brought to present value for June 30, 2006, using the market fixed rate in force on that day for the term to occur of 2,556 business days.

Procedures for the calculation of daily values related to the calculation of the PJUR[1] portion

35. Calculation of volatility for vertex Pi and day "t", in the case of June 30, 2006:

36. The formulas used for the calculation of volatility are:

I - σi,t = √[ (1-λ) * rt,i^2 + λ * σi,t-1^2 ], having a series with λ1=0.85 and another with λ2 = 0.94; and

II - σi,t = max{ σi,t(λ1), σi,t(λ2) }, obtaining each day the maximum between the volatilities of the two aforementioned series.

Vertex Pi | Return rt,i 30/6/2006 | Daily Volatility λ1=0.85 t=29/6/2006 | Daily Volatility λ1=0.85 t=30/6/2006 ("A") | Daily Volatility λ2=0.94 t=29/6/2006 | Daily Volatility λ2=0.94 t=30/6/2006 ("B") | Maximum between "A" and "B" --- | --- | --- | --- | --- | --- | --- 1 21 | -0.0001808 | 0.0001535 | 0.0001579 | 0.0002423 | 0.0002390 | 0.0002390 2 42 | -0.0001282 | 0.0002633 | 0.0002478 | 0.0004346 | 0.0004225 | 0.0004225 3 63 | -0.0002015 | 0.0003275 | 0.0003118 | 0.0005672 | 0.0005521 | 0.0005521 4 126 | -0.0002535 | 0.0004252 | 0.0004041 | 0.0007573 | 0.0007369 | 0.0007369 5 252 | -0.0005455 | 0.0008899 | 0.0008472 | 0.0013552 | 0.0013207 | 0.0013207 6 504 | -0.0017791 | 0.0013670 | 0.0014364 | 0.0018979 | 0.0018910 | 0.0018910 7 756 | -0.0023577 | 0.0014578 | 0.0016249 | 0.0018880 | 0.0019194 | 0.0019194 8 1.008 | -0.0022259 | 0.0015225 | 0.0016473 | 0.0019585 | 0.0019756 | 0.0019756 9 1.260 | -0.0022304 | 0.0015185 | 0.0016451 | 0.0019530 | 0.0019707 | 0.0019707

37. Calculation of standard volatilities σI,t, σII,t and σIII,t, to be assigned to vertices on day "t", in the case of June 30, 2006, which are disclosed by the Central Bank of Brazil:

Vertex Pi	Standard Volatility (*)
1 21	0.000552116
2 42	0.000552116
3 63	0.000552116
4 126	0.001890952
5 252	0.001890952
6 504	0.001890952
7 756	0.001975563
8 1.008	0.001975563
9 1.260	0.001975563
10 2.520	0.001975563

(*) σI,t, σII,t and σIII,t disclosed by the Central Bank of Brazil

I - the three standard volatilities are calculated according to the following formulas:

a) σI,t = max(σ21,t, σ42,t, σ63,t); b) σII,t = max(σ126,t, σ252,t, σ504,t); and c) σIII,t = max(σ756,t, σ1008,t, σ1260,t).

II - the standard volatilities are assigned to vertices according to the following formulas:

a) σI,t = σ21,t = σ42,t = σ63,t; b) σII,t = σ126,t = σ252,t = σ504,t; and c) σIII,t = σ756,t = σ1008,t = σ1260,t = σ2520,t.

38. The formulas used for the calculation of Mpre t are:

I - Mpre t = { M + C1*(σt - σP%) if σt > σP%
{ M if σt ≤ σP%

and

Circular Letter No. 3,498, of April 8, 2011 11

II -

P pico
M m
C
σ σ
1 1
%
1
−
−
= e
%
1
2
P
C
C M
σ
= − .

Parameter Specification
M 3 m 1
P% 0
Window for calculation of
σ P%
Last 252 business days
Window for calculation of
σ pico
Last 252 business days

39. Calculation of the multiplier (
    pre Mt
    ):

M σ 30/06/06 σ P% σ pico
C1 C2 pre Mt
(*)
0,001993 0,000981 0,001993 0,003866 -0,939814 1,00

(*) Disclosed by the Central Bank of Brazil

40. The multiplier (
    pre Mt
    ) resulted in 1.00 because the average of the maximum volatility over the last sixty days, M σ 30/06/06 , resulted in the maximum value of a 252-business-day window of the series of averages of the last sixty days of maximum volatility.

41. Based on the information disclosed by the Central Bank of Brazil, institutions proceed to calculate the PJUR[1] portion. The values of the active and passive positions that make up the cash flows must be marked to market on the day for which the capital requirement portion (PJUR[1]) to be maintained by the institution on the following business day is calculated. In the case of the example, the forward structure at the close of June 30, 2006, is used to calculate the capital applicable to July 3, 2006.

42. The marked-to-market cash flows related to the fixed-rate cash flows of the financial instruments in the example are presented below:

Instrument
Term in calendar days
Term in business days
Total value at maturity (R$)
Marked to market value (R$)
Market rate considered a 1,900 1,305 -20,953,955.08 -9,939,750.02 15.49% b 1,648 1,131 10,291,911.70 5,390,414.30 15.50% c 1,285 881 3,613,939.59 2,189,655.75 15.41% d 551 376 2,000,000.00 1,625,656.12 14.90% e 94 65 1,000,000.00 965,068.89 14.78% f 3 1 10,000,000.00 9,994,393.40 15.18% g 3,715 2,556 4,643,369.51 1,077,592.40 15.49%

Circular Letter No. 3,498, of April 8, 2011 12

43. The formula used for marking to market is:

252 (1 )
100 l l T
Valor total F taxa de juros vigente

, in which:
Tl

• term to expire in business days.

44. For terms to expire between 21 and 2,520 business days, the marked-to-market cash flows are allocated to the vertices according to the following formulas:

I - Value allocated to the previous vertex l j i j l F P T × − − = ; and

II - Value allocated to the value at the subsequent vertex l j i l i F P P T P × − − = .

45. For terms to expire less than 21 business days or more than 2,520 business days, the marked-to-market cash flows are allocated to vertices 21 and 2,520, respectively, according to the following formulas:

I - Value allocated to vertex 21 l l F
T
= ×
21
; and

II - Value allocated to vertex 2,520 l l F
T
= ×
2.520
.

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

Term in business days
Marked to market value (R$) Previous vertex Subsequent vertex Value allocated to previous vertex (R$) Value allocated to subsequent vertex (R$) 1,305 -9,939,750.02 1,260 2,520 -9,584,758.95 -354,991.07 1,131 5,390,414.30 1,008 1,260 2,759,378.75 2,631,035.55 881 2,189,655.75 756 1,008 1,103,516.99 1,086,138.77 376 1,625,656.12 252 504 825,730.09 799,926.03 65 965,068.89 63 126 934,431.78 30,637.11 1 9,994,393.40 None 21 None 475,923.50 2,556 1,077,592.40 2,520 None 1,092,986.58 None

Circular Letter No. 3,498, of April 8, 2011 13

Total values allocated by vertex:

Vertex
Pi
Marked to market value (R$)
21 475,923.50
42 0.00
63 934,431.78
126 30,637.11
252 825,730.09
504 799,926.03
756 1,103,516.99
1,008 3,845,517.52
1,260 -6,953,723.39
2,520 737,995.51

47. With the standard volatilities provided in paragraph 37, the following risk values associated with the vertices (VaRi,t) are obtained:

Vertex σi,30/6/2006
Allocated MtM Value
(R$)
VaRi,30/6/2006
(R$)
21 0.000552116 475,923.50 161.34
42 0.000552116 0.00 0.00
63 0.000552116 934,431.78 950.33
126 0.001890952 30,637.11 213.43
252 0.001890952 825,730.09 11,504.68
504 0.001890952 799,926.03 22,290.31
756 0.001975563 1,103,516.99 48,188.91
1008 0.001975563 3,845,517.52 223,903.85
1,260 0.001975563 -6,953,723.39 -506,097.51
2,520 0.001975563 737,995.51 107,423.80

48. The formula used is:

10
252 , = 2.33× × i,t × i,t × i i t VMtM
P
VaR σ .

Circular Letter No. 3,498, of April 8, 2011 14

49. Assuming that the Central Bank of Brazil had disclosed, for June 30, 2006, ρ = 0.33 and k = 0.47, the following correlation matrix is obtained:

21 42 63 126 252 504 756 1,008 1,260 2,520
21 1 0.90424 0.84112 0.72470 0.60592 0.49805 0.44556 0.41455 0.39434 0.35237 42 0.90424 1 0.94597 0.84112 0.72470 0.60592 0.54057 0.49805 0.46797 0.39434 63 0.84112 0.94597 1 0.90424 0.79379 0.67500 0.60592 0.55899 0.52455 0.43357 126 0.72470 0.84112 0.90424 1 0.90424 0.79379 0.72470 0.67500 0.63670 0.52455 252 0.60592 0.72470 0.79379 0.90424 1 0.90424 0.84112 0.79379 0.75601 0.63670 504 0.49805 0.60592 0.67500 0.79379 0.90424 1 0.94597 0.90424 0.87008 0.75601 756 0.44556 0.54057 0.60592 0.72470 0.84112 0.94597 1 0.96226 0.93101 0.82399 1,008 0.41455 0.49805 0.55899 0.67500 0.79379 0.90424 0.96226 1 0.97098 0.87008 1,260 0.39434 0.46797 0.52455 0.63670 0.75601 0.87008 0.93101 0.97098 1 0.90424 2,520 0.35237 0.39434 0.43357 0.52455 0.63670 0.75601 0.82399 0.87008 0.90424 1

50. The formula used for the calculation is:

.

51. The risk value of the operations (VaRt
    Standard), considering all vertices, is R$146,004.93 (one hundred and forty-six thousand, four reais and ninety-three cents), obtained by the formula:

i t j t i j i j
Standard VaRt VaR , VaR , ,
10
1
10
1
= ∑ ∑ × × ρ
= =
.

52. The first part of the PJUR[1] formula is:

{ }
−
−

−
− ∑
Standard t i
Standard t i pre t VaR VaR M
1
60
1
1
,
60 max .

53. Assuming that the average of the VaRt
    Standard over the last sixty days had been R$189,000.00 (one hundred and eighty-nine thousand reais) and using a multiplier equal to 1 (one) calculated according to paragraph 39, the result of the first part of the capital requirement formula, calculated with the closing data of June 30, 2006, applicable to July 3, 2006, would be R$189,000.00 (one hundred and eighty-nine thousand reais).

Average of VaR over the last 60 days, on the day 30/6/2006 (R$) Multiplier ( pre Mt ) disclosed for the day 30/6/2006 Risk value of the set of operations (VaRt Standard), on 30/6/2006 (R$) 1st part of PJUR[1] due on day 3/7/2006 (R$) 189,000.00 1.00 146,004.93 189,000.00

54. Assuming that the parameters defined by the Central Bank of Brazil for the calculation of sVaRt
    Standard were in effect on June 30, 2006, the procedures for calculating the second part of the formula for calculating PJUR[1] are presented below:

Circular Letter No. 3,498, of April 8, 2011 15

I - ρ
S
= 0.18;
II - k
S
= 0.90; and
III - standard volatilities for calculating sVaRt Standard :
σI
S
= 0.001920
σII
S
= 0.006047
σIII
S
= 0.006135

55. With the standard volatilities from paragraph 54, the following stressed risk values associated with the vertices (sVaRi,t) are obtained:

Vertex σi
S Allocated MtM Value (R$) sVaRi,t (R$)
21 0.001920 475,923.50 561.06
42 0.001920 0.00 0.00
63 0.001920 934,431.78 3,304.80
126 0.006047 30,637.11 682.52
252 0.006047 825,730.09 36,790.36
504 0.006047 799,926.03 71,281.32
756 0.006135 1,103,516.99 149,647.95
1008 0.006135 3,845,517.52 695,320.88
1,260 0.006135 -6,953,723.39 -1,571,657.48
2,520 0.006135 737,995.51 333,598.59

56. The formula used is:

10
252 , = 2.33× × × i,t ×
S i t VMtM
P sVaR σ .

57. From the values ρ
    S
    = 0.18 and k S
    = 0.90, the following correlation matrix is obtained:

21 42 63 126 252 504 756 1,008 1,260 2,520
21 1 0.87051 0.76660 0.54958 0.33607 0.21124 0.18679 0.18155 0.18037 0.18000 42 0.87051 1 0.93138 0.76660 0.54958 0.33607 0.24888 0.21124 0.19445 0.18037 63 0.76660 0.93138 1 0.87051 0.68105 0.45540 0.33607 0.27014 0.23278 0.18413 126 0.54958 0.76660 0.87051 1 0.87051 0.68105 0.54958 0.45540 0.38673 0.23278 252 0.33607 0.54958 0.68105 0.87051 1 0.87051 0.76660 0.68105 0.60967 0.38673 504 0.21124 0.33607 0.45540 0.68105 0.87051 1 0.93138 0.87051 0.81592 0.60967 756 0.18679 0.24888 0.33607 0.54958 0.76660 0.93138 1 0.95329 0.91031 0.73629 1,008 0.18155 0.21124 0.27014 0.45540 0.68105 0.87051 0.95329 1 0.96459 0.81592 1,260 0.18037 0.19445 0.23278 0.38673 0.60967 0.81592 0.91031 0.96459 1 0.87051 2,520 0.18000 0.18037 0.18413 0.23278 0.38673 0.60967 0.73629 0.81592 0.87051 1

Circular Letter No. 3,498, of April 8, 2011 16

58. The formula used for the calculation is:

S k i j i j
P
S i j
×
×

− min( , ) max( , )
,
ρ ρ (1 ρ ) .

59. The risk value of the set of vertices is R$483,617.63 (four hundred and eighty-three thousand, six hundred and seventeen reais and sixty-three cents), obtained by the formula:

S i t j t i j i j
Standard t sVaR sVaR , sVaR , ,
10
1
10
1
= ∑ ∑ × × ρ
= =
.

60. Assuming that the average of the sVaRt
    Standard over the last sixty days had been R$467,000.00 (four hundred and sixty-seven thousand reais), and the incorporation factor S in effect during the period was 0.50, the result of the second part of the capital requirement formula, calculated with the closing data of June 30, 2006, applicable to July 3, 2006, would be R$241,808.81 (two hundred and forty-one thousand, eight hundred and eight reais and eighty-one cents).

Average of stressed VaRs over the last 60 days, on day 30/6/2006 (R$) Stressed risk value of the set of operations (sVaRt Standard), on 30/6/2006 (R$) Incorporation factor S, in effect on 30/6/2006 2nd part of PJUR[1] due on day 3/7/2006 (R$) 467,000.00 483,617.63 0.50 241,808.81

61. The capital requirement related to PJUR[1] is:

1st part of PJUR[1] due on day 3/7/2006
(R$)
2nd part of PJUR[1] due on day 3/7/2006
(R$)
Total Value of PJUR[1] due on day 3/7/2006
(R$)
189,000.00 241,808.81 430,808.81

62. The PJUR[1] formula is:

{ }
{ }
−
−

−
− ∑ ∑
Standard t sVaR i
Standard t i
S sVaR
Standard t
VaR i
Standard t i
VaR pre
M t
JUR P 1
,
60
60 1
1 max 1
,
60
60 1
1 max [1]
.

63. This circular letter enters into force on January 1, 2012, when Circular Letter No. 3,309, of April 15, 2008, will be revoked.

Brasília, April 8, 2011.
Department of Standards of the Financial System Sérgio Odilon dos Anjos Chief

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