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8. Fair value of financial instruments

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The fair value of a financial asset or a liability on a given date is the amount for which it could be exchanged or settled, respectively, on that date between two knowledgeable, willing parties in an arm’s length transaction under market conditions. The most objective and common reference for the fair value of a financial asset or a liability is the price that would be paid for it on an organized, transparent and deep market (“quoted price” or “market price”).

If there is no market price for a given financial asset or liability, its fair value is estimated on the basis of the price established in recent transactions involving similar instruments; or, in the absence thereof, by using mathematical measurement models that are sufficiently tried and trusted by the international financial community. The estimates used in such models take into consideration the specific features of the asset or liability to be measured and, in particular, the various types of risk associated with the asset or liability. However, the limitations inherent in the measurement models and possible inaccuracies in the assumptions and parameters required by these models may mean that the estimated fair value of an asset or liability does not coincide exactly with the price for which the asset or liability could be exchanged or settled on the date of its measurement.

The fair value of the financial derivatives included in the held for trading portfolios is assimilated to their daily quoted price if there is an active market for these financial instruments. If for any reason their quoted price cannot be established on a given date, these derivatives are measured using methods similar to those used in over-the-counter (“OTC”) markets.

The fair value of OTC derivatives (“present value” or “theoretical price”) is equal to the sum of future cash flows arising from the instrument, discounted at the measurement date; these derivatives are valued using methods recognized by international financial markets: the “net present value” (NPV) method, option price calculation models, etc.

Determining the fair value of financial instruments -

Below is a comparison of the carrying amount of the Group’s financial assets and liabilities in the accompanying consolidated balance sheets and their respective fair values:

Fair Value and Carrying Amount Notes Millions of Euros
2011 2010 2009
Carrying Amount Fair Value Carrying Amount Fair Value Carrying Amount Fair Value
ASSETS-






Cash and balances with central banks 9 30,939 30,939 19,981 19,981 16,344 16,344
Financial assets held for trading 10 70,602 70,602 63,283 63,283 69,733 69,733
Other financial assets designated at fair value through profit or loss 11 2,977 2,977 2,774 2,774 2,337 2,337
Available-for-sale financial assets 12 58,144 58,144 56,456 56,456 63,521 63,521
Loans and receivables 13 381,076 389,204 364,707 371,359 346,117 354,933
Held-to-maturity investments 14 10,955 10,190 9,946 9,189 5,437 5,493
Fair value changes of the hedges items in portfolio hedges of interes rate risk 15 146 146 40 40 - -
Hedging derivatives 15 4,552 4,552 3,563 3,563 3,595 3,595
LIABILITIES-






Financial assets held for trading 10 51,303 51,303 37,212 37,212 32,830 32,830
Other financial liabilities designated at fair value through profit or loss 11 1,825 1,825 1,607 1,607 1,367 1,367
Financial liabilities at amortized cost 23 479,904 473,886 453,164 453,504 447,936 448,537
Fair value changes of the hedged items in portfolio hedges of interest rate risk. 15 - - (2) (2) - -
Hedging derivatives 15 2,710 2,710 1,664 1,664 1,308 1,308

In the case of financial instruments whose carrying amount is not the same as their theoretical fair value, the fair value has been calculated in the following manner:

  • The fair value of “Cash and balances with central banks” has been considered equivalent to its carrying amount, because they are short-term balances.
  • The fair value of “Held-to-maturity investments” is equivalent to their quoted price in active markets.
  • The fair values of “Loans and receivables” and “Financial liabilities at amortized cost” have been estimated by discounting estimated future cash flows using the market interest rates prevailing at each year-end.
  • The “Fair value changes of the hedged items in portfolio hedges of interest-rate risk” item in the accompanying consolidated balance sheets registers the difference between the carrying amount of the hedged deposits lent, registered under "Loans and Receivables," and the fair value calculated using internal models and observable variables of market data (see Note 15).

For financial instruments whose carrying amount is equivalent to their fair value, the measurement processes used are set forth below:

  • Level 1: Measurement using market observable quoted prices for the financial instrument in question, secured from independent sources and linked to active markets. This level includes listed debt securities, listed equity instruments, some derivatives and mutual funds.
  • Level 2: Measurement that applies techniques using inputs drawn from observable market data.
  • Level 3: Measurement using techniques, where some of the inputs are not taken from market observable data. As of December 31, 2011, the affected instruments accounted for approximately 0.31% of financial assets and 0.004% of the Group’s financial liabilities. Model selection and validation was undertaken by control areas outside the market units.

The following table shows the main financial instruments carried at fair value in the accompanying consolidated balance sheets, broken down by the measurement technique used to determine their fair value:

Fair Value by Levels Notes Millions of Euros
2011 2010 2009
Level 1 Level 2 Level 3 Level 1 Level 2 Level 3 Level 1 Level 2 Level 3
ASSETS-









Financial assets held for trading 10 22,986 46,915 700 28,914 33,568 802 39,608 29,236 889
Debt securities
19,731 793 451 22,930 921 508 33,043 1,157 471
Equity instruments
2,033 97 68 5,034 92 134 5,504 94 185
Trading derivatives
1,222 46,025 182 950 32,555 160 1,060 27,985 233
Other financial assets designated at fair value through profit or loss 11 2,358 619 - 2,326 448 - 1,960 377 -
Debt securities
647 61 - 624 64 - 584 54 -
Equity instruments
1,711 558 - 1,702 384 - 1,376 323 -
Available-for-sale financial assets 12 41,286 15,249 1,067 41,500 13,789 668 49,747 12,367 818
Debt securities
37,286 15,025 602 37,024 13,352 499 44,387 12,146 538
Equity instruments
4,000 224 465 4,476 437 169 5,360 221 280
Hedging derivatives 15 289 4,263 - 265 3,298 - 302 3,293 -
LIABILITIES-









Financial liabilities held for trading 10 5,813 45,467 23 4,961 32,225 25 4,936 27,797 96
Trading derivatives
1,202 45,467 23 916 32,225 25 1,107 27,797 96
Short positions
4,611 - - 4,046 - - 3,830 - -
Other financial liabilities designated at fair value through profit or loss 11 - 1,825 - - 1,607 - - 1,367 -
Hedging derivatives 15 - 2,710 - 96 1,568 - 319 989 -

The heading “Available-for-sale-financial assets” in the accompanying consolidated balance sheets as of December 31, 2011, 2010 and 2009, additionally includes €541 million, €499 million and €589 million, respectively, accounted for at cost, as indicated in the section of this Note entitled “Financial instruments at cost”.

The following table sets forth the main measurement techniques, hypotheses and inputs used in the estimation of fair value of the financial instruments classified under Levels 2 and 3, based on the type of financial asset and liability and the corresponding balances as of December 31, 2011:

Financial Instruments Level 2 Measurement techniques Main assumptions Main inputs used 2011
Fair value (millions of euros)
• Debt securities Present-value method. Calculation of the present value of financial instruments as the current value of future cash flows (discounted at market interest rates), taking into account:
• the estimate of prepayment rates;
• the issuer credit risk; and
• current market interest rates.
• Net Asset Value (NAV) published recurrently, but not more frequently than every quarter.		 • Risk premiums.
• Observable market interest rates
 Trading portfolio
Debt
securities		 793
Equity instruments 97

Other financial assets at fair value through profit or loss
• Equity instruments Debt
securities		 61
Equity instruments 558
Available-for-sale financial assets
Debt
securities		 15,025
Equity instruments 224
Other financial liabilities designated at fair value through profit or loss 1,825
• Derivatives Analytic/semi-analytic formulae For share, currency, inflation or commodity
derivatives:
• The Black-Scholes assumptions take into account
possible convexity adjustments
For interest rate derivatives:
• Black-Scholes assumptions apply a lognormal process for forward rates and consider possible convexity adjustments.		 For share, currency, or commodity derivatives:
• Forward structure of the underlying asset.
• Volatility of options.
• Observable correlations between underlying assets.
• For interest-rate derivatives:
• The term structure of interest rates.
• Volatility of underlying asset.
For credit derivatives:
• Credit default swap (CDS) prices.
• Historical CDS volatility.		 Assets
Trading derivatives 46,025
Hedging Derivatives 4,263
For share, currency, or commodity derivatives:
• Monte Carlo simulations.		 Local volatility model: assumes a constant diffusion of the underlying asset with the volatility depending on the value of the underlying asset and the term. Liabilities
For interest-rate
derivatives:
• Black-Derman-Toy Model, Libor Market Model and SABR.
• HW 1 factor		 This model assumes that:
The forward rates in the term structure of the interest rate curve are perfectly correlated. 		Trading derivatives 45,467
For credit derivatives:
• Diffusion models.		 These models assume a constant diffusion of
default intensity. 		Hedging Derivatives 2,710
Financial Instruments Level 3 Measurement techniques Main assumptions Main unobservable inputs 2011
Fair value (millions of euros)
Debt securities • Present-value method.
• “Time default” model for financial instruments in the collateralized debt obligations (CDOs) family.		 Determining the current value of financial instruments as the current value of future cash flows (discounted at market interest rates), taking into account:
• estimate of prepayment rates;
• issuer credit risk; and
• current market interest rates.
In the case of measurement of asset-backed securities (ABSs), future prepayments are calculated on the conditional prepayment rates that the issuers themselves provide.
The “time-to-default” model is used to measure default probability. One of the main variables used is the correlation of defaults extrapolated from several index tranches (ITRA00 and CDX) with the underlying portfolio of our CDOs.		 • Prepayment rates
• Default correlation
• Credit spread (1)		 Trading portfolio
Debt
securities
 451
Equity instruments 68
Available-for-sale financial assets
Debt
securities		 602
Equity instruments • Present-value method. Net asset value (NAV) for hedge fund and for equity
instruments listed in thin or less active markets.		 • Credit spread (1)
NAV supplied by the fund manager or issuer of the securities.		 Equity instruments 465
Trading derivatives Trading derivatives for interest-rate futures and forwards:
• Present-value method.
• “Libor Market” model. 		The “Libor Market" model models the complete term
structure of the interest-rate curve, assuming
a constant elasticity of variance (CEV) lognormal process. The CEV
lognormal process is used to measure the presence of a volatility
shift. 		Correlation decay.(2) Assets
For variable income and foreign exchange options:
• Monte Carlo simulations
• Numerical integration
• Heston		 The options are measured through generally accepted valuation models, to which the observed implied volatility is added. • Vol-of-Vol (3)
• Reversion factor (4)
• Volatility Spot Correlation (5)		 Trading derivatives 182
Liabilities
• Credit baskets These models assume a constant diffusion of default
intensity.		 • Default correlation.
• Historical CDS volatility		 Trading derivatives 23
(1)Credit spread: The spread between the interest rate of a risk-free asset (e.g. Treasury securities) and the interest rate of any other security that is identical in every respect except for asset quality. Spreads are considered as Level 3 inputs when referring to illiquid securities, based on spreads of similar issuers. (2) Correlation decay: This is the factor that allows us to calculate changes in correlation between the different pairs of forward rates. (3)Vol-of-Vol: Volatility of implied volatility. This is a statistical measure of the changes of the spot volatility. (4) Reversion Factor: The speed with which volatility reverts to its natural value. (5)Volatility- Spot Correlation: A statistical measure of the linear relationship (correlation) between the spot price of a security and its volatility.

The changes in the balance of Level 3 financial assets and liabilities included in the accompanying consolidated balance sheets are as follows:

Financial Assets Level 3
Changes in the Period		 Millions of Euros
2011 2010 2009
Assets Liabilities Assets Liabilities Assets Liabilities
Balance at the beginning 1,469 25 1,707 96 3,853 84
Valuation adjustments recognized in the income statement (*) (1) (12) (123) 12 (146) 6
Valuation adjustments not recognized in the income statement - - (18) - 33 -
Acquisitions, disposals and liquidations 268 9 (334) (100) (634) (1)
Net transfers to Level 3 33 - 236 - (1,375) 7
Exchange differences (2) 1 1 17 (24) -
Exchange differences 1,767 23 1,469 25 1,707 96
(*) Profit or loss that are attributable to gains or losses relating to those assets and liabilities held at the end of the reporting period

The financial instruments transferred between the different levels of measurement in 2011 are at the following amounts in the accompanying consolidated balance sheets as of December 31, 2011:

Transfer between levels From:
To:		 Millions of Euros
Level I Level 2 Level 3
Level 2 Level 3 Level 1 Level 3 Level 1 Level2
ASSETS






Financial assets held for trading
12 - 32 16 - 36
Available-for-sale financial assets
432 23 49 39 - -
LIABILITIES-






As of December 31, 2011, the effect on the consolidated income and consolidated equity of changing the main hypotheses used for the measurement of Level 3 financial instruments for other reasonably possible models, taking the highest (most favorable hypotheses) or lowest (least favorable) value of the range deemed probable, would be as follows:

Financial Assets Level 3
Sensitivity Analysis 		Millions of Euros
Potential Impact on Consolidated Income Statement Potential Impact on Total Equity
Most Favorable Hypotheses Least Favorable Hypotheses Most Favorable Hypotheses Least Favorable Hypotheses
ASSETS



Financial assets held for trading 21 (71) - -
Available-for-sale financial assets - - 14 (87)
LIABILITIES-        
Financial liabilities held for trading 1 (1) - -
Total 22 (72) 14 (87)
Loans and financial liabilities at fair value through profit or loss -

As of December 31, 2011, 2010 and 2009, there were no loans or financial liabilities at fair value other than those recognized under the headings "Other financial assets designated at fair value through profit and loss" and "Other financial liabilities designated at fair value through profit and loss" in the accompanying consolidated balance sheets.

Financial instruments at cost -

As of December 31, 2011, 2010 and 2009, equity instruments, derivatives with these equity instruments as underlyings, and certain discretionary profit-sharing arrangements in some companies, were recognized at cost in the Group's consolidated balance sheets because their fair value could not be reliably determined, as they are not traded in organized markets and thus their unobservable inputs are significant. On the above dates, the balance of these financial instruments recognized in the portfolio of available-for-sale financial assets amounted to €541 million, €499 million and €589 million, respectively.

The table below outlines the financial assets and liabilities carried at cost that were sold in 2011, 2010 and 2009:

Sales of financial instruments at cost Millions of Euros
2011 2010 2009
Amount of Sale 19 51 73
Carrying Amount at Sale Date 8 36 64
Gains/Losses 11 15 9
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