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4 Positions in equity securities: specific and generic requirements

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576



Risk Management and Shareholders’ Value in Banking



on market indices are registered based on the market value of the individual securities or

indices. Futures on an index can also be broken down into a number of positions relative

to the number of securities included in the index. Positions in options, on the other hand,

are converted into positions on the underlying equities based on their delta coefficient.



19.5 THE REQUIREMENT FOR POSITIONS IN FOREIGN

CURRENCIES

The standardized approach to computing the capital requirement on foreign exchange

risk12 is divided into three phases. The first phase is to compute, for each foreign currency

position j , the bank’s net position NP j , given by the sum of:13

– the net spot position (i.e., all asset items less all liability items, including accrued

interest, denominated in the relevant currency);

– the net forward position (i.e., all amounts to be received less all amounts to be paid

under forward foreign exchange transactions, including currency futures and the principal on currency swaps not included in the spot position);

– guarantees (and similar instruments) that are certain to be called and are likely to be

irrecoverable;

– net future income/expenses not yet accrued but already fully hedged (at the discretion

of the reporting bank);

– depending on particular accounting conventions in different countries, any other item

representing a profit or loss in foreign currencies;

– the net delta-based equivalent of the total book of foreign currency options.

The second phase involves summing the net positive (long) positions (NP + ) and the net

j

negative (short) positions (NP − ) on the different currencies, the latter taken in absolute

j

value. The larger of these two sums is called the “net open foreign exchange position”.

The capital requirement is then set equal to 8 % of this net open position:









kFX = 8 % · Max 



NP + ,

j

j



NP −

j







(19.6)



j



Let us consider the example in Table 19.6

Table 19.6 Example of net foreign currency positions

Currency

WWW.



US dollar British Japanese Swiss Australian Canadian Total

pound

yen

franc

dollar

dollar



NP j (¤ mns)



30



NP +

j



30



|NP − |

j

12



−15



25



−30



25

15



5



−3



5

30



12

60



3



48



The Basel Committee asks that the net position in gold be included among the foreign exchange positions.

The positions in basket-currencies can be considered either as positions in independent currencies or spread

among the individual currencies in the basket.

13



The Capital Requirements for Market Risks



577



The sum of the long positions is equal to 60 million euros, while the sum of the short

positions is 48 million euros. The result is:

kFX = 8 % · Max (60, 48) = 4.8

It is interesting to note that this simplified approach represents a sort of compromise

between two extreme approaches, one hardly prudent, the other highly conservative.

The first approach assumes a perfect correlation (100 %) between exchange rate changes

of the different currencies. In other words, it assumes that when the euro appreciates/depreciates, it does so to the same extent against all the foreign currencies. If this

is true, it is right to offset the long and short positions not only within the individual

currencies but also among the various currencies, computing the capital ratio as:

kmin = 8 % ·

FX



NP j + +



NP j = 8 % ·

j



NP j −



j



(19.7)



j



which in our example would give 8 %·12 = 0.96.

The second approach assumes a perfectly negative correlation (−100%) between the

exchange rates for the long and short positions. In other words, if the euro depreciates

against currencies where the bank is “long”, it simultaneously appreciates against the

currencies where the bank is “short”. In this case, both the net positive and net negative

positions are considered in determining losses, and the capital ratio must be computed as





kMax

FX







= 8% · 



NP +

j



NP −

j



+



j







(19.8)



j



which in our example would take the capital requirement to 8 %·108 = 8.64.

These are obviously two extreme hypotheses: in reality, the correlation will be neither

perfectly positive nor perfectly negative. It will therefore be reasonable to set the capital

requirement by selecting a value midway between k min and k Max ; this value coincides

precisely with the kF X seen earlier. In fact:

Max

min

kFX + kFx

= 8%

2







 max 





= 8%









NP + +

j

j



NP −

j



j



2



j



NP −

j

j



=











 + min 



NP + ,

j

j



NP −

j







j



+



2





max 



NP + +

j

j





NP + ,

j







+



NP − +

j

j







NP −  − min 

j



NP + ,

j

j







j



NP + ,

j

j



2







= 8 % · max 



NP + ,

j

j



NP −

j



 = kFX



j



Indeed, in our case, kFX = 4.8 = (0.96 + 8.64)/2.



j



NP −  

j





=









578



Risk Management and Shareholders’ Value in Banking



Lastly, we note that both the Basel Committee and the European Union directive provide

that banks whose assets in foreign currencies are negligible with respect to their total assets

can be exempted from the capital requirement on foreign exchange risk.



19.6 THE REQUIREMENT FOR COMMODITY POSITIONS

Financial intermediaries that invest in commodities such as oil, copper or silver, directly

or more often through derivative instruments,14 are exposed to a series of risks. The

most obvious is directional risk, linked to changes in the spot prices of commodities.

Forward positions and positions in derivative instruments also involve basis risk (possible

misalignments between the prices of two commodities that in the past had always had

similar price movements), interest rate risk (forward prices of commodities also depend on

interest rates) and so-called “forward gap risk”, i.e. the risk that forward prices may diverge

from their expected levels for reasons unrelated either to spot prices or interest rates.

The Basel Committee has established that the capital requirement on commodities can

be computed in two ways. Both require that, for each commodity (or group of commodities

with strongly correlated prices), the banks identify their long and short positions (spot

and forward positions, positions in derivative instruments), expressed in standard units of

measurement (barrels, gallons, grams, etc.) and valued in domestic currency at the current

spot price.

According to the simplified method, the capital requirement for each commodity is

given by 15 % of the net position (long less short positions) plus 3 % of the gross position

(long plus short positions).

According to the “maturity ladder” method, the positions assumed in each commodity

must be broken down among seven maturity bands like those seen (Table 19.2) for the

capital requirement on generic interest rate risk. Long and short positions can be offset

within each band by applying a capital requirement of 1.5 % to the offset portion. Offsetting is also possible between different bands, subject to a requirement of 0.6 %. Lastly,

the residual net balance (not offset) is subject to a capital requirement of 15 %.

Both these methods are rather rudimentary and do not permit an accurate measurement

of the risk associated with investments in commodities. Suffice it to say, in this regard,

that all commodities, regardless of their actual volatility, are subject to the same capital

ratio. For this reason, banks that operate heavily in commodities are encouraged to adopt

the internal model approach, which will be discussed in the next section.



19.7 THE USE OF INTERNAL MODELS

19.7.1 Criticism of the Basel Committee proposals

From its proposal in 1993, the standardized approach to measuring market risks was the

object of heavy criticism, especially by large banks who already developed sophisticated

models for measuring this type of risk. This criticism focused both on a few technical

features of the proposals and on the logic underlying the general framework adopted by

the Committee.

The criticism concerning the proposals’ technical features included some directed at

mechanisms regarded as overly onerous and inconsistent with the general criterion set

14

The price of gold is less volatile than that of other commodities. For this reason, positions in gold are not

treated as commodities but, as observed earlier, as foreign currency positions.



The Capital Requirements for Market Risks



579



forth by the Committee (imposition of a capital requirement that would cover potential

losses over a time period of ten days with a 95 % confidence level). In particular, the

following were regarded as excessive:

– the vertical disallowance (non-offsetting factor) of 10 % within the time bands in computing generic risk on debt securities;

– the requirement of 8 % (4 % in the case of liquid and well-diversified portfolios) for

generic risk on equity securities, which in effect was subsequently halved in the EU

directive;

– the impossibility to offset positions in different equity markets, a decision in contrast with the fact that, though not perfectly correlated, the stock markets of different

countries often tend to experience similar movements.

Also, the “delta equivalent” mechanism was regarded as rather imprudent, considering

that linear approximations prove inadequate to capture real changes in value on options,

especially when there are significant price changes.

As far as the general framework of the proposals is concerned, the main points of

criticism were the following:

– the “building blocks” approach, which required the summing of the capital requirements

computed separately for four different risk categories (debt securities, equity securities,

commodities, and foreign currencies), overestimated the risk because it failed to reflect

the imperfect correlation among the different market factors;15

– this approach also requires breaking down the risk by type of financial instrument

(equity securities, debt securities, positions in foreign currencies and commodities)

rather than by type of underlying risk;

– the standardized approach assigned little value to the internal models developed by

banks and would have forced them to compute two different measures of risk: for

risk management purposes, estimated by internal models, and for regulatory purposes,

estimated by the standardized approach.

Another more general criticism regarded the rather artificial distinction between trading

book and banking book. In fact, this distinction prevents a bank from considering its entire

interest rate risk exposure, which does not emerge only from the bonds held for trading

purposes but also from those held for investment purposes and, more generally, from the

complex of assets and liabilities in the banking book (as shown in the first part of this

volume). Consequently, a long position on interest rates in the trading portfolio might be

more than offset by a short position in the investment portfolio or by a positive duration

gap. This distinction also discouraged banks from measuring and managing financial risks

in a truly integrated manner.

19.7.2 The 1995 revised draft

Some of this criticism persuaded the Basel Committee to review its 1993 proposal and

publish a new draft in April 1995. The most significant changes included the possibility

15

Given two stochastic variables x and y, let us recall that σx+y = σx + σy is true if and only if their correlation

is 100 %. Otherwise, σx+y < σx + σy .



580



Risk Management and Shareholders’ Value in Banking



for banks to choose between the above described standardized system and an internal

model for risk measurement. To be accepted for regulatory purposes, however, the internal

models had to conform to a few minimum requirements.

This need for uniformity became relevant after a simulation exercise conducted by the

Committee: 15 banks from different countries were asked to assess the risk of a virtual

portfolio of 350 positions, providing the total VaR and that related to interest rate, foreign

exchange and equity risks (given a holding period of ten days and a 99 % confidence

level). Some of the banks provided diverging results, due primarily to differences:

– in the historical sample used to estimate volatility;

– in the risk factors used, particularly for interest rate risk (yield curves with a different

number of nodes, possibility of non-parallel shifts of the yield curve, possibility of

changes in the spreads between different curves, etc.);

– in the criterion for aggregating the different types of risk;

– in the criteria for measuring the risk of option portfolios.

This empirical evidence persuaded the Committee to require that a few minimum criteria

be followed so that internal models could be used in lieu of the standardized approach.

In particular, it established the following quantitative requirements, still in force:















VaR must be estimated daily;

the confidence level must be at least 99 %;

the holding period must be at least ten working days;

the historical sample for estimating volatility must be at least one year;

the data on volatility and correlations must be updated at least quarterly;

total VaR must be obtained by summing the VaRs for the different market factors (thus

assuming perfect correlation);

– the models must adequately reflect the different risk profiles (delta, gamma and vega)

of option contracts.

The quantitative requirements were accompanied by, and are still accompanied by, the

following qualitative criteria:

– banks must have an independent risk management unit, responsible for designing and

implementing the risk management system. This unit must perform periodic backtesting, i.e. ex post comparisons, between the estimated risk measures and the actual

changes in portfolio value;

– the risk measurement model must be supplemented by regular stress tests, aimed at

simulating potential losses in extreme market situations;

– the adequacy and functioning of the risk measurement model must be verified and

controlled regularly;

– top management must be actively involved in the risk control process and consider

that control as an essential aspect of operations, allocating sufficient resources to it;

– the internal risk measurement model must be closely integrated into the daily risk

management process and used in conjunction with the internal limits on trading and

exposure;

– the model must in any case be explicitly approved by the supervisory authorities,

which verify that it is conceptually correct, applied with integrity and historically



The Capital Requirements for Market Risks



581



accurate in forecasting losses, and that the bank has sufficient specialized personnel to

manage it.

If the internal model complies with these criteria, it can be used to determine the minimum

regulatory capital against market risks. In particular, each day the capital requirement will

be given by the average of the the previous 60 days VaRs multiplied by a safety factor

F established by the authorities, or by the VaR of the previous day, if greater.

If, as often occurs, the internal model estimates the generic market risks only, and

does not properly address the specific risks related to the individual securities and issuers,

then capital must be supplemented by the specific risk requirement (kSR ) computed by

the standardized approach. In summary, the capital requirement on market risks will be

given by:





60



kMKT









= max VaR t−1 , F ·







i=1



VaR t−i 





 + kSR



60





(19.9)



where VaR t−1 indicates the ten-day VaR for day t−1, with a 99 % confidence level, and

F represents the multiplying factor. This factor is established by the national supervisory

authorities but can in no case be less than 3. More precisely, it varies from 3 to 4 according

to the quality of the internal model. It is therefore increased in inverse proportion to the

past performance of the model, measured through backtesting.16 This provides an incentive

to improve the quality of the internal models.

19.7.3 The final amendment of January 1996

As expected, the draft of April 1995 was heavily criticized. Four objections seem particularly significant:

(1) The safety factor F , equal to at least 3, was judged arbitrary and so high as to

eliminate any form of incentive for banks to adopt the internal models’ approach;

(2) the fact that total VaR is determined as the sum of the VaRs on the individual risks

is equivalent to ignoring the benefits of diversification among positions which are

sensitive to different market factors (foreign exchange rates, interest rates, equity

prices), thus overestimating overall risk and discouraging banks from adopting portfolio diversification policies.

(3) the indication that F could be increased to above 3 was extremely vague. It was

established to be inversely proportional to the quality of the model (i.e. its ability to

forecast losses correctly), but no transparent criteria were established for measuring

this quality and thus for determining the extent of the increase.

(4) Lastly, there was criticism of a failure to recognize internal models for estimating

specific risk, due to the fact that they were regarded as concentrating solely on generic

risk.

16



See Chapter 8.



582



Risk Management and Shareholders’ Value in Banking



These objections were satisfied in the final text of the reform, approved in January

1996 (Basel Committee, 1996) in the form of an amendment to the 1988 Capital Accord.

In particular:

(1) the amendment confirmed that the safety factor F is equal to 3. This decision was

motivated by the fact that the average of daily VaRs “must be converted into a

capital requirement that offers a sufficient cushion for cumulative losses deriving

from adverse market conditions for an extended period of time”. The theoretical

limits of the internal models (normality and stability of the distributions, linearity of

the payoffs, etc.) and the fact that they overlook the intra-day risks (because they are

based on closing prices) and cannot forecast the effects of extreme shocks or liquidity

crises were cited in favor of a high safety factor.

(2) More objective, transparent criteria were established for determining whether to

increase F to over 3. It was clarified that this depends on the results of specific

backtesting to be performed quarterly, based on a comparison of actual losses to indications from internal models (the Basel Committee backtesting criteria and the ones

for determining F were presented in Chapter 8).

(3) The criticism regarding the failure to recognize the benefits of diversification was also

partially satisfied. In fact, the Committee introduced the possibility of using “empirical

correlations not only within broad risk categories but also between different risk

categories, provided that the supervisory authority is satisfied that the bank’s system

for measuring correlations is sound and implemented with integrity”. The Committee

took the opportunity to approve another amendment to make the use of internal

models more flexible and permitted the estimation of 10-day VaR using data on daily

volatility multiplied by the square root of 10.17

(4) Lastly, the amendment confirmed the inability of internal models to grasp specific risk

adequately. The Committee did not forbid their use for estimating this risk component;

however, it also imposed a lower limit on the capital requirement estimated with

internal models, which cannot be less than 50 % of the requirement computed by the

standardized approach.

Lastly, the amendment indicated the conditions to be followed when a bank possesses an

internal model acceptable to the authorities but is not yet able to apply it to the entire

range of market risks or outstanding positions, so this model is used in conjunction with

the standardized approach:

– each broad class of risks must be assessed on the basis of a single approach;

– banks cannot modify the combination of the two approaches without valid reasons;

– banks that use an internal model for a certain risk category must, in time, extend it to

include all their positions;

– banks that use internal models are not permitted to return to the standardized approach.

19.7.4 Advantages and limitations of the internal model approach

The internal model approach represents a sort of revolution in supervisory policy: for

the first time, in fact, financial institutions were allowed to determine their own capital

17



See Chapter 5.



The Capital Requirements for Market Risks



583



requirements based on risk measurements produced in-house (although subject to numerous conditions and to an explicit process of validation by the supervisory authorities).

It therefore represented a move from a detached relationship between the supervisory

authority and supervised banks towards a closer relationship based on trust, collaboration,

and the exchange of competences and information. It represented a recognition that supervisory authorities and banks, though their objectives are different, share a common interest

in the stability of the individual intermediaries and of the financial system as a whole.

However, this kind of evolution also gives rise to the risk of “regulatory capture”:

the supervisory authorities, after analyzing the banks’ models, may impose changes and

finally approve them. This means that they become less free in the future to point out limitations and errors in instruments that they themselves helped design. In this respect, their

independence might be partially “captured” by the banks, and any problems of inadequacy

in the banks’ risk management system might not be pointed out or pointed out late.

Another limitation of the internal model approach is associated with the existence of

the safety factor F equal to at least 3. This multiplying factor, as we saw, was criticized

back in 1995 as excessive. It is clear that if the internal model approach leads to capital

requirements which are higher than those contemplated by the standardized approach, the

banks would have no incentive to adopt it.

In this regard, it is interesting to mention the results of an empirical study by Saita and

Sironi (2002). Using daily yield data on seven different equity markets,18 they compared

the capital requirement computed with the standard approach and with different types

of internal models (parametric model with volatility estimated by exponential moving

averages, parametric model with volatility estimated by a GARCH model, or historical

simulations) for seven different typical portfolios valued in dollars.19 Table 19.7 reports

the results: in particular, it shows the percentage of days, in the period 1985–1999, in

which the use of an internal model would have produced a lower capital requirement than

the standardized approach.

As the Table shows, the latter generally requires less capital; however, internal models

become more advantageous as the portfolio becomes more internationally diversified. In

fact, they permit more frequent savings of capital (38.6 % of days) in the case of an

equally weighted portfolio in the seven equity markets and less frequent for a portfolio

heavily concentrated in the US market. Since the standardized approach fails to recognize

diversification among several equity markets, it is comparatively more penalizing for

well-diversified portfolios. Indeed, by adding the capital requirement on generic risk of

equity securities to the requirement on foreign exchange risk, the standardized approach

is simply more penalizing the larger the fraction of the portfolio denominated in foreign

currencies.

The internal models approach is more advantageous the more a bank’s trading portfolio

is diversified internationally. It is therefore clear why the internal models method has thus

far been adopted primarily by large international banks, with heavily diversified trading

portfolios and with branches and subsidiaries in the world’s main financial markets.

19.7.5 The pre-commitment approach

As observed by the Basel Committee, a safety factor of three is also justified by the

numerous limitations of internal models: the use of historical volatilities, the assumption

18

19



France, Germany, Japan, Italy, Switzerland, UK, USA.

The analysis only considers equity positions (and not even derivatives or short positions).



584



Risk Management and Shareholders’ Value in Banking



Table 19.7 Comparison of capital requirements – standardized approach and internal models

% of days in which the internal model

approach requires less capital than the standardized approach

Portfolio



Parametric

with EWMA



Parametric

with GARCH



Historical

simulations



Average



Equally Weighted



44.1 %



31.7 %



40.1 %



38.6 %



25 % USA, 75 % EW



41.2 %



33.9 %



44.2 %



39.7 %



25 % USA, 75 % MSCI



37.5 %



31.2 %



35.7 %



34.8 %



50 % USA, 50 % EW



30.0 %



28.1 %



35.2 %



31.1 %



MSCI



24.6 %



19.0 %



20.0 %



21.2 %



75 % USA, 25 % EW



5.9 %



1.3 %



1.3 %



2.8 %



75 % USA, 25 % MSCI



7.5 %



1.3 %



0.0 %



3.0 %



27.3 %



20.9 %



25.2 %



24.5 %



Average



Key EW = equally weighted. MSCI = weights assigned in conformity with the Morgan Stanley Capital International index. Source: Saita-Sironi (2002).



of a linear relationship between changes in risk factors and changes in the value of

financial assets, the lack of attention to the risk of liquidity crises, and the assumption of

a normal distribution for market factor returns.

In this regard, Table 19.8 shows the frequency with which weekly changes in the yields

on British, US and German 10-year treasury notes exceeded certain extreme thresholds,

expressed as volatility multiples, in the period 1989–1993. These frequencies are compared with the probabilities implicit in a normal distribution: as the table shows, the actual

frequencies are significantly higher.

Table 19.8 Weekly changes in the yields on 10-year instruments

Change (expressed

as a multiple of the

standard deviation)



Actual frequency (period 1989–93)



Probability assigned by

a normal distribution



UK



US



3



2.3 %



2.8 %



1.5 %



0.3 %



4



0.6 %



0.4 %



0.2 %



0.006 %



5



0.2 %



0.4 %



0.0 %



0.0 %



6



0.2 %



0.1 %



0.0 %



0.0 %



6.4



7.6



4.1



Maximum multiple of

the standard deviation



Germany



Source: Chew (1994).



The use of a normal distribution thus makes it difficult to employ internal models

to estimate the losses associated with “extreme” events, since that distribution depicts



The Capital Requirements for Market Risks



585



exceptionally marked changes in market factors as almost impossible (to the point that

stress testing must be used to project the impact of highly pessimistic scenarios, to which

the model would otherwise assign too low a probability).

The problem of “fat tails” can also be understood by simply noting that over the past

20 years banks have had to cope with numerous abnormal events in the equity markets (October 1987, April 2000, September 2001), foreign exchange markets (autumn

1992), and bond markets (January–February 1994), probably more than a normal distribution would have suggested. It is precisely the need to narrow this gap between

empirical data and normal distribution that justifies the safety factor imposed by the

Basel Committee.

Paul Kupiec and James O’Brien, two economists of the Federal Reserve Board of

the United States, suggested a possible alternative solution to the problem. According to

this proposal (called the “pre-commitment approach”), each bank would be required to

“declare” in advance each quarter the capital put at risk by its trading activity.20 This

amount, decided autonomously by each bank based on its internal models and certified

by the supervisory authority, would represent the capital requirement for market risks.

However, the individual banks would be subject to a penalty each time their trading losses

during the quarter exceed the amount of capital initially declared. The possible penalties

would be: (i) a fine, (ii) the imposition of a capital requirement, for the following period,

greater than that declared by the bank, (iii) the imposition of a capital increase or a

reduction of dividends.

The pre-commitment approach offers four main advantages:

• it recognizes the role of banks’ internal risk management;

• it shifts the focus from ten-day VaR to potential losses over a longer time horizon of

three months;

• it provides banks with an incentive to limit their risk taking activity to their initial

declarations;

• it stimulates the supervisory authorities to monitor the losses actually incurred by the

individual banks (expressed in market values).

Along with these advantages, however, the proposal also presents some significant

drawbacks that make its adoption quite problematic. First of all, it would allow banks to

reduce their capital requirement on market risks independently when they have difficulty

complying with it (as after they have suffered losses). Secondly, it would force banks to

increase capital (or pay a fine) precisely when their capital has been reduced by losses

greater than expected. Lastly, since the results would only be audited, and penalties

levied, every three months (or in any case at discrete time intervals), this would enable

the individual banks to accumulate new risk positions without any immediate impact on

their capital requirement.



SELECTED QUESTIONS AND EXERCISES

1. Which of the following quantitative requirements is not necessary for a bank’s internal

model on market risk to get validated by the Basel Committee for capital computation

purposes?

20



Kupiec, O’Brien (1995).



586



Risk Management and Shareholders’ Value in Banking



(A)

(B)

(C)

(D)



10-day time horizon;

3-month minimum update frequency for volatility and correlation estimates;

Measurement of VaR at least once a fortnight;

Minimum confidence level of 99 %.



2. A bank holds the following equity portfolio (L and S denote long and short positions,

respectively):

Position



Market



Type of shares



Amount

(euro m)



L



New York Stock

Exchange



Liquid and well diversified

portfolio



100



S



New York Stock

Exchange



Liquid and well diversified

portfolio, made of different stocks

than the previous one



60



L



Frankfurt Stock

Exchange



Shares of one single company

(Alpha GMBH)



40



S



Frankfurt Stock

Exchange



Liquid and well diversified

portfolio, including 3 m of stocks

by Alpha GMBH



70



WWW.



Compute the capital requirements for the bank, against generic and specific risk.

3. A bank holds 1 million euros in a BB-rated bond and is contemplating to replace it

with a bond of the same amount, but issued by an unrated company. Based on the

standardized approach, its capital requirement against market risk is going to:

(A)

(B)

(C)

(D)



increase, as the creditworthiness of the unrated bond might be below BB;

decrease, as the creditworthiness of the unrated bond might be above BB;

stay unchanged;

this depends on whether the bond is a “qualifying issue” or not.



4. Consider a bank with the following simplified structure of assets and liabilities:

Assets



Amount

(euro m)



Liabilities



Amount

(euro m)



Short-term T-Bills, coupon

6 %, T-bond, 6 % coupon,

with a life to maturity of

15 days

WWW.



100



Fixed rate bonds, coupon

4 %, life to maturity

5.2 years



300



Medium term notes, fixed

rate, coupon 2 %, life to

maturity 3 years



400



Zero coupon bonds, life to

maturity 8 years



200



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