Determination of fair value

The calculation of fair value is based on market conditions at a specific point in time and therefore may not be reflective of future fair values. The Bank has controls and processes in place to ensure that the valuation of financial instruments is appropriately determined.

The Bank discloses the classification of all financial instruments carried at fair value in a hierarchy based on the determination of fair value. The best evidence of fair value for a financial instrument is the quoted price in an active market. Fair value based on unadjusted quoted market prices for identical instruments in active markets represents a Level 1 valuation. Where possible, valuations are based on quoted prices or observable inputs obtained from active markets. Independent Price Verification (IPV) is undertaken to assess the reliability and accuracy of prices and inputs used in the determination of fair value. The IPV process is performed by price verification groups that are independent from the business. The Bank maintains a list of pricing sources that are used in the IPV process. These sources include, but are not limited to, brokers, dealers and consensus pricing services. The valuation policies relating to the IPV process require that all pricing or rate sources used be external to the Bank. On a periodic basis, an independent assessment of pricing or rate sources is performed to determine market presence or market representative levels.

Quoted prices are not always available for

over-the-counter

(OTC) transactions, as well as transactions in inactive or illiquid markets. OTC transactions are valued using internal models that maximize the use of observable inputs are used to estimate fair value. The chosen valuation technique incorporates all the factors that market participants would take into account in pricing a transaction. When a fair value is based on all significant market observable inputs, the valuation is classified as Level 2. Financial instruments traded in a less active market are valued using indicative market prices, the present value of cash-flows or other valuation techniques. Fair value estimates normally do not consider forced or liquidation sales.

Where financial instruments trade in inactive markets or when using models where observable parameters do not exist, significant management judgment is required for valuation methodologies and model inputs. Valuations that require the significant use of unobservable inputs are considered Level 3.

The specific inputs and valuation techniques used in determining the fair value of financial instruments are noted below. For Level 3 instruments, additional information is disclosed in the Level 3 sensitivity analysis on page 180.

The fair values of cash and deposits with banks, securities purchased under resale agreements and securities borrowed, customers’ liability under acceptances, obligations related to securities sold under repurchase agreements and securities lent, acceptances, and obligations related to securities sold short are assumed to approximate their carrying values, either due to their short-term nature or because they are frequently repriced to current market rates.

Consolidated Financial Statements

Trading loans

Trading loans are comprised of loans that serve as hedges to total return swaps, purchased mortgages pooled for securitization, and precious metal loans. Trading loans that serve as hedges to loan-based credit total return swaps are valued using consensus prices from Bank approved independent pricing services (Level 2). Purchased mortgages that are held prior to securitization are valued using inputs observed from the MBS market (Level 2). Precious metal loans are valued using a discounted cash flow model incorporating observable market inputs, including precious metals spot and forward prices and interest rate curves (Level 2).

Government issued or guaranteed securities

The fair values of government issued or guaranteed debt securities are primarily based on unadjusted quoted prices in active markets, where available (Level 1). Where quoted prices in active markets are not available, the fair value is determined by utilizing recent transaction prices, reliable broker quotes, or pricing services, which derive fair values using only observable valuation inputs, which are significant to the fair values (Level 2).

For securities for which quoted prices are not available, the Bank uses a discounted cash flow method, using the effective yield of a similar instrument adjusted for instrument-specific risk factors that are observable inputs such as credit spread and contracted features (Level 2).

Corporate and other debt

Corporate and other debt securities are valued using unadjusted quoted prices from independent market data providers or third-party broker quotes from an active market (Level 1). Where direct prices from active markets are not available, the valuation is performed with a yield-based valuation approach (Level 2). In some instances, interpolated yields of similar bonds are used to price securities (Level 2). The Bank uses pricing models with observable inputs from market sources such as credit spread, interest rate curves, and recovery rates (Level 2). These inputs are verified through an IPV process on a monthly basis.

For certain securities where there is no active market, no consensus market pricing and no indicative or executable independent third-party quotes, the Bank uses pricing by third-party providers or internal pricing models and cannot readily observe the significant inputs used to price such instruments (Level 3).

Mortgage-backed securities

The fair value of residential mortgage-backed securities is primarily determined using broker quotes and independent market data providers (Level 1/2). In limited circumstances, an internal price-based model may be used with the unobservable inputs that are significant to the fair value (Level 3).

Equity securities

The fair value of equity securities is based on unadjusted quoted prices in active markets, where available (Level 1). Where equity securities are less frequently traded, the most recent exchange-quoted pricing is used to determine fair value (Level 2).

For private equity securities, where quoted prices in active markets are not readily available, the fair value is determined as a multiple of the underlying earnings or percentage of underlying net asset value obtained from third-party general partner statements (Level 3).

Derivatives

Fair values of exchange-traded derivatives are based on unadjusted quoted market prices from an active market (Level 1). Fair values of

over-the-counter

(OTC) derivatives or inactive exchange-traded derivatives are determined using pricing models, which take into account observable valuation inputs such as current market and contractual prices of the underlying instruments, as well as time value and yield curve or volatility factors underlying the positions (Level 2). The determination of the fair value of derivatives includes consideration of credit risk, estimated funding costs and ongoing direct costs over the life of the instruments.

Derivative products valued using a valuation technique with market-observable inputs mainly include interest rate swaps and options, currency swaps and forward foreign exchange contracts. The most frequently applied valuation techniques include forward pricing and swap models, using present value calculations. The models incorporate various inputs including foreign exchange spot and forward rates and interest rate curves (Level 2).

Derivative products valued using a valuation technique with significant unobservable inputs are long dated contracts (interest rate swaps, currency swaps, option contracts and certain credit default swaps) and other derivative products that reference a basket of assets. These models incorporate certain significant

non-observable

inputs such as volatility and correlation (Level 3).

Loans

The estimated fair value of loans carried at amortized cost reflects changes in the general level of interest rates and creditworthiness of borrowers that have occurred since the loans were originated or purchased. The particular valuation methods used are as follows:

•

Canadian fixed rate residential mortgages are fair valued by discounting the expected future contractual cash flows, taking into account expected prepayments and using management’s best estimate of average market interest rates currently offered for mortgages with similar remaining terms (Level 3).

•

For fixed rate business and government loans, fair value is determined by discounting the expected future contractual cash flows of these loans at interest rates estimated by using the appropriate currency swap curves for the remaining term, adjusted for a credit mark of the expected losses in the portfolio (Level 3).

•

For all other fixed rate loans, fair value is determined by discounting the expected future contractual cash flows of these loans at interest rates estimated by using the appropriate currency swap curves for the remaining term (Level 3).

•

For all floating rate loans fair value is assumed to equal book value.

The fair value of loans is not adjusted for the value of any credit protection the Bank has purchased to mitigate credit risk.

Deposits

The fair values of deposits payable on demand or after notice or floating rate deposits payable on a fixed date is assumed to equal book value.

The estimated fair values of Canadian personal fixed rate deposits payable on a fixed date are fair valued by discounting the expected future contractual cash outflows, using management’s best estimate of average market interest rates currently offered for deposits with similar remaining terms (Level 2).

Deposits under the Canada Mortgage Bond (CMB) program are fair valued by discounting expected future contractual cash flows using market observable inputs (Level 2).

For all other fixed rate deposits, fair value is determined by discounting the expected future contractual cash flows of these deposits at interest rates estimated by using the appropriate currency swap curves for the remaining term (Level 2)

For structured notes containing embedded features that are bifurcated from plain vanilla notes, the fair value of the embedded derivatives is determined using option pricing models with observable inputs similar to other interest rate or equity derivative contracts (Level 2).

Certain deposits that are designated at FVTPL are structured notes. Their coupon or repayment terms can be linked to the performance of market parameters such as interest rates, equities, and foreign currencies. The fair value of these structured notes is determined using models which incorporate observable market inputs, such as interest rate curves, equity prices, equity volatility and foreign exchange rates (Level 2). Some structured notes have significant unobservable inputs to model valuation such as interest rate volatility and equity correlation (Level 3).

Obligations related to securities sold short

The fair values of these obligations are based on the fair value of the underlying securities, which can include debt or equity securities. The method used to determine fair value is based on the quoted market prices where available in an active market (Level 1 and/or Level 2).

Subordinated debentures and other liabilities

The fair values of subordinated debentures, including debentures issued by subsidiaries which are included in other liabilities, are determined by reference to quoted market prices where available or market prices for debt with similar terms and risks (Level 2). The fair values of other liabilities are determined by the discounted contractual cash flow method with appropriate currency swap curves for the remaining term (Level 2).

Fair value of financial instruments

The following table sets out the fair values of financial instruments of the Bank using the valuation methods and assumptions described above. The fair values disclosed do not include

non-financial

assets, such as property and equipment, investments in associates, precious metals, goodwill and other intangible assets.


	2021				2020
As at October 31 ($ millions)	Total fair value		Total carrying value		Total fair value		Total carrying value
Assets:
Cash and deposits with financial institutions	$	86,323	$	86,323	$	76,460	$	76,460
Trading assets		146,312		146,312		117,839		117,839
Securities purchased under resale agreements and securities borrowed		127,739		127,739		119,747		119,747
Derivative financial instruments		42,302		42,302		45,065		45,065
Investment securities – FVOCI and FVTPL		57,042		57,042		79,745		79,745
Investment securities – amortized cost		18,133		18,157		32,129		31,644
Loans		641,964		636,986		612,368		603,263
Customers’ liability under acceptances		20,404		20,404		14,228		14,228
Other financial assets		14,256		14,256		12,700		12,700
Liabilities:
Deposits		798,335		797,259		755,395		750,838
Financial instruments designated at fair value through profit or loss		22,493		22,493		18,899		18,899
Acceptances		20,441		20,441		14,305		14,305
Obligations related to securities sold short		40,954		40,954		31,902		31,902
Derivative financial instruments		42,203		42,203		42,247		42,247
Obligations related to securities sold under repurchase agreements and securities lent		123,469		123,469		137,763		137,763
Subordinated debentures		6,733		6,334		7,827		7,405
Other financial liabilities		39,802		40,254		43,776		42,660

Changes in interest rates, credit spreads and liquidity costs are the main cause of changes in the fair value of the Bank’s financial instruments resulting in a favourable or unfavourable variance compared to carrying value. For the Bank’s financial instruments carried at cost or amortized cost, the carrying value is not adjusted to reflect increases or decreases in fair value due to market fluctuations, including those due to interest rate changes. For FVOCI investment securities, derivatives and financial instruments measured at FVTPL or designated as fair value through profit or loss, the carrying value is adjusted regularly to reflect the fair value.

Fair value hierarchy

The following table outlines the fair value hierarchy of instruments carried at fair value on a recurring basis and of instruments not carried at fair value.


	2021								2020
As at October 31 ($ millions)	Level 1		Level 2		Level 3		Total		Level 1		Level 2		Level 3		Total
Instruments carried at fair value on a recurring basis:
Assets:
Precious metals (1)	$	–	$	755	$	–	$	755	$	–	$	1,181	$	–	$	1,181
Trading assets
Loans		–		8,113		–		8,113		–		8,352		–		8,352
Canadian federal government and government guaranteed debt		9,272		3,842		–		13,114		9,154		3,882		–		13,036
Canadian provincial and municipal debt		5,556		4,298		–		9,854		–		9,320		–		9,320
US treasury and other US agencies’ debt		6,760		63		–		6,823		5,182		–		–		5,182
Other foreign governments’ debt		129		9,559		–		9,688		9,230		3,415		–		12,645
Corporate and other debt		2,595		9,185		40		11,820		–		10,570		18		10,588
Equity securities		85,688		160		1		85,849		57,199		361		–		57,560
Other		–		1,051		–		1,051		1,156		–		–		1,156
	$	110,000	$	36,271	$	41	$	146,312	$	81,921	$	35,900	$	18	$	117,839
Investment securities (2)
Canadian federal government and government guaranteed debt	$	1,125	$	4,679	$	–	$	5,804	$	1,728	$	15,100	$	–	$	16,828
Canadian provincial and municipal debt		1,937		3,218		–		5,155		93		17,454		–		17,547
US treasury and other US agencies’ debt		11,462		2,175		–		13,637		11,930		1,299		–		13,229
Other foreign governments’ debt		67		26,605		17		26,689		14,101		13,798		23		27,922
Corporate and other debt		10		1,319		27		1,356		265		850		23		1,138
Equity securities		2,879		218		1,304		4,401		1,954		263		864		3,081
	$	17,480	$	38,214	$	1,348	$	57,042	$	30,071	$	48,764	$	910	$	79,745
Derivative financial instruments
Interest rate contracts	$	–	$	13,124	$	1	$	13,125	$	–	$	21,013	$	4	$	21,017
Foreign exchange and gold contracts		–		18,293		–		18,293		–		17,943		–		17,943
Equity contracts		184		3,513		21		3,718		290		2,655		3		2,948
Credit contracts		–		245		–		245		–		480		–		480
Commodity contracts		–		6,921		–		6,921		–		2,677		–		2,677
	$	184	$	42,096	$	22	$	42,302	$	290	$	44,768	$	7	$	45,065
Liabilities:
Deposits	$	–	$	175	$	–	$	175	$	–	$	73	$	–	$	73
Financial liabilities designated at fair value through profit or loss		–		22,354		139		22,493		–		18,899		–		18,899
Obligations related to securities sold short		35,487		5,467		–		40,954		25,584		6,318		–		31,902

Derivative financial instruments
Interest rate contracts		–		13,148		15		13,163		–		16,937		17		16,954
Foreign exchange and gold contracts		–		18,171		–		18,171		–		19,511		–		19,511
Equity contracts		307		4,737		6		5,050		599		2,133		2		2,734
Credit contracts		–		30		–		30		–		53		–		53
Commodity contracts		–		5,789		–		5,789		–		2,995		–		2,995
	$	307	$	41,875	$	21	$	42,203	$	599	$	41,629	$	19	$	42,247

Instruments not carried at fair value (3) :
Assets:
Investment securities – amortized cost	$	3,714	$	14,417	$	2	$	18,133	$	4,946	$	26,864	$	319	$	32,129
Loans (4)		–		–		400,565		400,565		–		–		374,767		374,767

Liabilities:
Deposits (4)		–		290,341		–		290,341		–		307,457		–		307,457
Subordinated debentures		–		6,733		–		6,733		–		7,827		–		7,827
Other liabilities		–		24,414		209		24,623		–		26,831		–		26,831

(1)	The fair value of precious metals is determined based on quoted market prices and forward spot prices, where applicable.

(2)	Excludes debt investment securities measured at amortized cost of $18,157 (October 31, 2020 - $31,644).

(3)	Represents the fair value of financial assets and liabilities where the carrying amount is not a reasonable approximation of fair value.

(4)	Represents fixed rate instruments.

Level 3 instrument fair value changes

Financial instruments categorized as Level 3 as at October 31, 2021, in the fair value hierarchy comprise certain foreign government bonds, structured corporate bonds, equity securities, complex derivatives and financial liabilities designated at fair value through profit or loss.

The following table summarizes the changes in Level 3 instruments carried at fair value for the year ended October 31, 2021.

All positive balances represent assets and negative balances represent liabilities. Consequently, positive amounts indicate purchases of assets or settlements of liabilities and negative amounts indicate sales of assets or issuances of liabilities.


	As at October 31, 2021
($ millions)	Fair value November 1 2020			Gains/(losses) recorded in income			Gains/(losses) recorded in OCI			Purchases/ Issuances			Sales/ Settlements			Transfers into/out of Level 3			Fair value October 31 2021			Change in unrealized gains/(losses) recorded in income for instruments still held (1)
Trading assets
Corporate and other debt	$	18		$	7		$	–		$	28		$	(22	)	$	9		$	40		$	1
Equity securities		–			–			–			–			(72	)		73			1			–
		18			7			–			28			(94	)		82			41			1

Investment securities
Other foreign governments’ debt		23			–			(6	)		–			–			–			17			n/a
Corporate and other debt		23			1			(4	)		7			–			–			27			1
Equity securities		864			287			51			253			(180	)		29			1,304			287
		910			288			41			260			(180	)		29			1,348			288

Derivative financial instruments – assets
Interest rate contracts		4			(1	)		–			10			(9	)		(3	)		1			(1	)
Equity contracts		3			4			–			12			–			2			21			4	(2)

Derivative financial instruments – liabilities
Interest rate contracts		(17	)		(11	)		–			(70	)		60			23			(15	)		(11	) (3)
Equity contracts		(2	)		4			–			(14	)		–			6			(6	)		4	(2)
		(12	)		(4	)		–			(62	)		51			28			1			(4	)

Financial liabilities designated at fair value through profit or loss		–			(2	)		–			(101	)		–			(36	)		(139	)		(2	)
Total	$	916		$	289		$	41		$	125		$	(223	)	$	103		$	1,251		$	283

(1)	These amounts represent the gains and losses from fair value changes of Level 3 instruments still held at the end of the period that are recorded in the Consolidated Statement of Income.

(2)

Certain unrealized gains and losses on derivative assets and liabilities are largely offset by

mark-to-market

changes on other instruments included in trading revenues in the Consolidated Statement of Income, since these instruments act as an economic hedge to certain derivative assets and liabilities.

(3)	Certain unrealized losses on interest rate derivative contracts are largely offset by mark-to-market changes on embedded derivatives on certain deposit liabilities in the Consolidated Statement of Income.

The following table summarizes the changes in Level 3 instruments carried at fair value for the year ended October 31, 2020.


	As at October 31, 2020
($ millions)	Fair value November 1 2019			Gains/(losses) recorded in income (1)		Gains/(losses) recorded in OCI		Purchases/ Issuances			Sales/ Settlements			Transfers into/out of Level 3			Fair value October 31 2020
Precious metals	$	–		$	1	$	–	$	23		$	(24	)	$	–		$	–
Trading assets		18			6		–		22			(28	)		–			18
Investment securities		920			13		7		257			(259	)		(28	)		910
Derivative financial instruments		(60	)		14		–		(21	)		32			23			(12	)

(1)	Gains or losses for items in Level 3 may be offset with losses or gains on related hedges in Level 1 or Level 2.

Significant transfers

Significant transfers can occur between the fair value hierarchy levels when additional or new information regarding valuation inputs and their refinement and observability becomes available. The Bank recognizes transfers between levels of the fair value hierarchy at the end of the reporting period during which the change has occurred.

The following significant transfers made between Levels 1 and 2 for the year ended October 31, 2021, were based on whether the fair value was determined using quoted market prices from an active market:

•

Trading assets of $10,045 million, investment securities of $3,407 million and obligations related to securities sold short of $2,550 million were transferred out of Level 2 into Level 1.

•

Trading assets of $9,972 million, investment securities of $13,522 million and obligations related to securities sold short of $2,235 million were transferred out of Level 1 into Level 2.

The following significant transfers made between Levels 2 and 3 for the year ended October 31, 2021, were based on whether the fair value was determined using significant unobservable inputs:

•

Trading equity securities of $72 million were transferred out of Level 2 into Level 3.

There were no significant transfers into and out of Level 3 for the year ended October 31, 2020.

Level 3 sensitivity analysis

The table below sets out information about significant unobservable inputs used in measuring financial instruments categorized as Level 3 in the fair value hierarchy.

Valuation technique

Significant unobservable inputs

Range of estimates for
unobservable inputs

(1)

Changes in fair value
from reasonably
possible alternatives
($ millions)

Investment securities

General Partner valuations

Private equity securities

(2)

Market comparable

per net asset value

97%

Capitalization rate

(51)/51

Derivative financial instruments

Interest rate contracts

Option pricing

Interest rate

model

volatility

37% - 66%

(10)/10

Equity contracts

Option pricing

Equity volatility

2% - 112%

model

Correlation

0% - 97%

(3)/3

Financial liabilities designated at fair value through profit or loss

Interest rate contracts

Option pricing

Interest rate

model

swaption volatility

20% - 273%

(11)/11

(1)	The range of estimates represents the actual lowest and highest level inputs used to fair value financial instruments within each financial statement category.

(2)

The valuation of private equity securities utilizes net asset values as reported by fund managers. Net asset values are not considered observable as the Bank cannot redeem these instruments at such values. The range for net asset values per unit or price per share has not been disclosed for these instruments since the valuations are not model-based.

The Bank applies judgment in determining unobservable inputs used to calculate the fair value of Level 3 instruments.

The following section discusses the significant unobservable inputs for Level 3 instruments.

General Partner (GP) Valuations per Net Asset Value

Net asset values provided by GPs represent the fair value of investments in private equity securities.

Correlation

Correlation in a credit derivative or debt instrument refers to the likelihood of a single default causing a succession of defaults. It affects the distribution of the defaults throughout the portfolio and therefore affects the valuation of instruments such as collateralized debt obligation tranches. A higher correlation may increase or decrease fair value depending on the seniority of the instrument.

Correlation becomes an input into equity derivative pricing when the relationship between price movements of two or more of the underlying assets is relevant.

Volatility

Volatility for equity derivatives is a measure of asset price fluctuation. Interest rate volatility measures variability of a security yield or interest rate. Historic volatility is often calculated as the annualized standard deviation of daily price or yield variation for a given time period. Implied volatility is such that, when input into an option pricing model, returns a value equal to the current market value of the option.