Note 17: Fair Value of Financial Instruments and Trading-Related Revenue

We record trading assets and liabilities, derivatives, certain equity and debt securities and securities sold but not yet purchased at fair value, and other non-trading assets and liabilities at amortized cost less allowances or write-downs for impairment. The fair values presented in this note are based upon the amounts estimated for individual assets and liabilities and do not include an estimate of the fair value of any of the legal entities or underlying operations that comprise our business. For certain portfolios of financial instruments where we manage exposures to similar and offsetting risks, fair value is determined on the basis of our net exposure to that risk.

Fair value represents the amount that would be received to sell an asset or paid to transfer a liability in an orderly transaction between willing market participants at the measurement date. The fair value amounts disclosed represent point-in-time estimates that may change in subsequent reporting periods due to changes in market conditions or other factors. Some financial instruments are not typically exchangeable or exchanged and therefore it is difficult to determine their fair value. Where there is no quoted market price, we determine fair value using management’s best estimates based on a range of valuation techniques and assumptions; since these involve uncertainties, the fair values may not be realized in an actual sale or immediate settlement of the asset or liability.

Governance Over the Determination of Fair Value

Senior executive oversight of our valuation processes is provided through various valuation and risk committees. In order to ensure that all financial instruments carried at fair value are reasonably measured for risk management and financial reporting purposes, we have established governance structures and controls, such as model validation and approval, independent price verification (“IPV”) and profit or loss attribution analysis (“PAA”), consistent with industry practice. These controls are applied independently of the relevant operating groups.

We establish and regularly update valuation methodologies for each financial instrument that is required to be measured at fair value. The application of valuation models for products or portfolios is subject to independent approval to ensure only validated models are used. The impact of known limitations of models and data inputs is also monitored on an ongoing basis. IPV is a process that regularly and independently verifies the accuracy and appropriateness of market prices or model inputs used in the valuation of financial instruments. This process assesses fair values using a variety of different approaches to verify and validate the valuations. PAA is a daily process used by management to identify and explain changes in fair value positions across all operating lines of business within BMO Capital Markets. This process works in concert with other processes to ensure that the fair values being reported are reasonable and appropriate.

Securities

For traded securities, quoted market value is considered to be fair value. Quoted market value is based on bid or ask prices, depending on which is the most appropriate to measure fair value. Securities for which no active market exists are valued using all reasonably available market information. Our fair value methodologies are described below.

Government Securities

The fair value of government issued or guaranteed debt securities in active markets is determined by reference to recent transaction prices, broker quotes or third-party vendor prices. The fair value of securities that are not traded in an active market is modelled using implied yields derived from the prices of similar actively traded government securities and observable spreads. Market inputs to the model include coupon, maturity and duration.

Mortgage-Backed Securities and Collateralized Mortgage Obligations

The fair value of mortgage-backed securities and collateralized mortgage obligations is determined using independent prices obtained from third-party vendor prices, broker quotes and relevant market indices, as applicable. If such prices are not available, fair value is determined using cash flow models that make maximum use of observable market inputs or benchmark prices for similar instruments. Valuation assumptions for mortgage-backed securities and collateralized mortgage obligations include discount rates, expected prepayments, credit spreads and recoveries.

Corporate Debt Securities

The fair value of corporate debt securities is determined using prices observed in the most recent transactions. When observable price quotations are not available, fair value is determined based on discounted cash flow models using discounting curves and spreads obtained from independent dealers, brokers and multi-contributor pricing sources.

Corporate Equity Securities

The fair value of equity securities is based on quoted prices in active markets, where available. Where quoted prices in active markets are not readily available, fair value is determined using either quoted market prices for similar securities or using valuation techniques, which include discounted cash flow analysis and earnings multiples.

Privately Issued Securities

Privately issued debt and equity securities are valued using prices observed in recent market transactions, where available. Otherwise, fair value is derived from valuation models using a market or income approach. These models consider various factors, including projected cash flows, earnings, revenue and other third-party evidence, as available. The fair value of limited partnership investments is based upon net asset values published by third-party fund managers.

Prices from brokers and multi-contributor pricing sources are corroborated as part of our independent review process, which may include using valuation techniques or obtaining consensus or composite prices from other pricing services. We validate the estimates of fair value by independently obtaining multiple quotes for external market prices and input values. We review the approach taken by third-party vendors to ensure that the vendor employs a valuation model which maximizes the use of observable inputs such as benchmark yields, bid-ask spreads, underlying collateral, weighted-average terms to maturity and prepayment rate assumptions. Fair value estimates from internal valuation techniques are verified, where possible, by reference to prices obtained from third-party vendors.

Loans

In determining the fair value of our fixed rate performing loans, we discount the remaining contractual cash flows, adjusted for estimated prepayment, at market interest rates currently offered for loans with similar terms and risks. For floating rate performing loans, changes in interest rates have minimal impact on fair value since interest rates are repriced or reset frequently. On that basis, fair value is assumed to be equal to carrying value.

Derivative Instruments

A number of valuation techniques are employed to estimate fair value, including discounted cash flow analysis, the Black-Scholes model, Monte Carlo simulation and other accepted market models. These independently validated models incorporate current market data for interest rates, currency exchange rates, equity and commodity prices and indices, credit spreads, recovery rates, corresponding market volatility levels, spot prices, correlation levels and other market-based pricing factors. Option implied volatilities, an input into many valuation models, are either obtained directly from market sources or calculated from market prices. Multi-contributor pricing sources are used wherever possible.

In determining the fair value of complex and customized derivatives, we consider all reasonably available information, including dealer and broker quotations, multi-contributor pricing sources and any relevant observable market inputs. Our model calculates fair value based on inputs specific to the type of contract, which may include stock prices, correlation for multiple assets, interest rates, foreign exchange rates, yield curves and volatilities.

We calculate a credit valuation adjustment (“CVA”) to recognize the risk that any given derivative counterparty may not ultimately be able to fulfill its obligations. The CVA is derived from market-observed credit spreads or proxy credit spreads and our assessment of the net counterparty credit risk exposure, taking into account credit mitigants such as collateral, master netting agreements and novation to central counterparties. We also calculate a funding valuation adjustment (“FVA”) to recognize the implicit funding costs associated with over-the-counter derivative positions. The FVA is determined by reference to market funding spreads.

Deposits

In determining the fair value of our deposits, we incorporate the following assumptions:

•

For fixed rate, fixed maturity deposits, we discount the remaining contractual cash flows for these deposits, adjusted for expected redemptions, at market interest rates currently offered for deposits with similar terms and risks. Fair value of our senior note liabilities and covered bonds is determined by referring to current market prices for similar instruments or using valuation techniques, such as discounted cash flows that use market interest rate curves and funding spreads.

•

For fixed rate deposits with no defined maturities, we consider fair value to equal carrying value, based on carrying value being equivalent to the amount payable on the reporting date.

•

For floating rate deposits, changes in interest rates have minimal impact on fair value since deposits reprice to market frequently. On that basis, fair value is assumed to equal carrying value.

A portion of our structured note liabilities that have coupons or repayment terms linked to the performance of interest rates, foreign currencies, commodities or equity securities have been designated at fair value through profit or loss. The fair value of these structured notes is estimated using internally validated valuation models and incorporates observable market prices for identical or comparable securities, as well as other inputs, such as interest rate yield curves, option volatilities and foreign exchange rates, where appropriate. Where observable prices or inputs are not available, management judgment is required to determine the fair value by assessing other relevant sources of information, such as historical data and proxy information from similar transactions.

Securities Sold But Not Yet Purchased

The fair value of these obligations is based on the fair value of the underlying securities, which can be equity or debt securities. As these obligations are fully collateralized, the method used to determine fair value would be the same as that used for the relevant underlying equity or debt securities.

Securitization and Structured Entities’ Liabilities

The determination of the fair value of securitization and structured entities’ liabilities is based on quoted market prices or quoted market prices for similar financial instruments, where available. Where quoted prices are not available, fair value is determined using valuation techniques, such as discounted cash flow models that maximize the use of observable inputs.

Subordinated Debt

The fair value of our subordinated debt is determined by referring to current market prices for the same or similar instruments.

Financial Instruments with a Carrying Value Approximating Fair Value

Short-term and Other Financial Instruments

Carrying value is assumed to be a reasonable estimate of fair value for our cash and cash equivalents.

The carrying value of certain financial assets and liabilities, such as interest bearing deposits with banks, securities borrowed or purchased under resale agreements, customers’ liability under acceptances, other assets, acceptances, securities lent or sold under repurchase agreements and other liabilities, is a reasonable estimate of fair value due to their short-term nature or because they are frequently repriced to current market rates.

Certain assets, including premises and equipment, goodwill and intangible assets, as well as shareholders’ equity, are not considered financial instruments and therefore no fair value has been determined for these items.

Fair Value Hierarchy

We use a fair value hierarchy to categorize financial instruments according to the inputs we use in valuation techniques to measure fair value.

Fair Value of Financial Instruments Not Carried at Fair Value on the Balance Sheet

Set out in the following tables are the fair values of financial instruments not carried at fair value on our Consolidated Balance Sheet.

(Canadian $ in millions)

2018

Carrying
value

Fair

value

Valued using
quoted market
prices

Valued using
models (with
observable inputs)

Valued using
models (without
observable inputs)

Securities

Amortized cost

6,485

6,288

429

5,795

Loans (1)

Residential mortgages

119,544

118,609

–

118,609

–

Consumer instalment and other personal

62,687

62,618

–

62,618

–

Credit cards

8,099

–

8,099

–

Business and government (2)

192,225

191,989

–

191,989

–

382,555

381,315

–

381,315

–

Deposits (3)

506,742

506,581

–

506,581

–

Securitization and structured entities’ liabilities

25,051

24,838

–

24,838

–

Subordinated debt

6,782

6,834

–

6,834

–

(1)

Carrying value of loans is net of allowance.

(2)

Excludes $1,450 million of loans classified as FVTPL upon adoption of IFRS 9 (refer to Note 28).

(3)

Excludes $15,309 million of structured note liabilities designated at FVTPL and accounted for at fair value.

This table excludes financial instruments with a carrying value approximating fair value, such as cash and cash equivalents, interest bearing deposits with banks, securities borrowed or purchased under resale agreements, customers’ liability under acceptances, other assets, acceptances, securities lent or sold under repurchase agreements and other liabilities.


(Canadian $ in millions)									2017
	Carrying value		Fair value		Valued using quoted market prices		Valued using models (with observable inputs)		Valued using models (without observable inputs)
Securities
Held to maturity		9,094		9,096		2,522		6,574		–

Loans (1)
Residential mortgages		115,165		114,821		–		114,821		–
Consumer instalment and other personal		61,465		61,470		–		61,470		–
Credit cards		7,828		7,828		–		7,828		–
Business and government		174,084		174,105		–		174,105		–
		358,542		358,224		–		358,224		–

Deposits (2)		466,118		466,441		–		466,441		–
Securitization and structured entities’ liabilities		23,054		23,148		–		23,148		–
Subordinated debt		5,029		5,255		–		5,255		–

(1)

Carrying value of loans is net of allowance.

(2)

Excludes $13,674 million of structured note liabilities designated at FVTPL and accounted for at fair value.

Certain comparative figures have been reclassified to conform with the current year’s presentation.

Valuation Techniques and Significant Inputs

We determine the fair value of publicly traded fixed maturity debt and equity securities using quoted prices in active markets (Level 1) when these are available. When quoted prices in active markets are not available, we determine the fair value of financial instruments using models such as discounted cash flows, with observable market data for inputs, such as yield and prepayment rates or broker quotes and other third-party vendor quotes (Level 2). Fair value may also be determined using models where significant market inputs are not observable due to inactive markets or minimal market activity (Level 3). We maximize the use of observable market inputs to the extent possible.

Our Level 2 trading securities are primarily valued using discounted cash flow models with observable spreads or broker quotes. The fair value of Level 2 FVOCI securities, previously classified as available-for-sale securities, is determined using discounted cash flow models with observable spreads or third-party vendor quotes. Level 2 structured note liabilities are valued using models with observable market information. Level 2 derivative assets and liabilities are valued using industry-standard models and observable market information.

The extent of our use of actively quoted market prices (Level 1), internal models using observable market information as inputs (Level 2) and models without observable market information as inputs (Level 3) in the valuation of securities, fair value liabilities, derivative assets and derivative liabilities is presented in the following tables:

Classified under IFRS 9

(Canadian $ in millions)

2018

Valued using
quoted market prices

Valued using
models (with
observable inputs)

Valued using
models (without
observable inputs)

Total

Trading Securities

Issued or guaranteed by:

Canadian federal government

9,107

1,213

–

10,320

Canadian provincial and municipal governments

4,013

4,689

–

8,702

U.S. federal government

9,465

–

9,517

U.S. states, municipalities and agencies

1,138

–

1,216

Other governments

1,210

201

–

1,411

NHA MBS and U.S. agency MBS and CMO

8,869

255

9,184

Corporate debt

2,973

6,218

9,198

Loans

–

199

–

199

Corporate equity

49,946

–

49,950

76,852

22,583

262

99,697

FVTPL Securities

Issued or guaranteed by:

Canadian federal government

328

103

–

431

Canadian provincial and municipal governments

219

727

–

946

U.S. federal government

–

NHA MBS and U.S. agency MBS and CMO

–

Corporate debt

178

6,643

–

6,821

Corporate equity

1,378

134

1,825

3,337

2,172

7,614

1,825

11,611

FVOCI Securities

Issued or guaranteed by:

Canadian federal government

11,978

827

–

12,805

Canadian provincial and municipal governments

3,315

3,547

–

6,862

U.S. federal government

16,823

–

16,823

U.S. states, municipalities and agencies

3,640

3,655

Other governments

3,143

1,647

–

4,790

NHA MBS and U.S. agency MBS and CMO

–

13,687

–

13,687

Corporate debt

1,959

1,797

–

3,756

Corporate equity

–

37,232

25,145

62,440

Business and Government Loans

–

1,450

Fair Value Liabilities

Securities sold but not yet purchased

26,336

2,468

–

28,804

Structured note liabilities and other note liabilities

–

15,309

–

15,309

Annuity liabilities

–

800

–

800

26,336

18,577

–

44,913

Derivative Assets

Interest rate contracts

8,959

–

8,977

Foreign exchange contracts

12,983

–

12,999

Commodity contracts

166

1,894

–

2,060

Equity contracts

286

1,872

–

2,158

Credit default swaps

–

486

25,718

–

26,204

Derivative Liabilities

Interest rate contracts

8,620

–

8,634

Foreign exchange contracts

11,852

–

11,854

Commodity contracts

295

1,161

–

1,456

Equity contracts

246

2,183

2,430

Credit default swaps

–

557

23,852

24,411

Classified under IAS 39


(Canadian $ in millions)	2017
	Valued using quoted market prices		Valued using models (with observable inputs)		Valued using models (without observable inputs)		Total
Trading Securities
Issued or guaranteed by:
Canadian federal government		8,712		2,115		–		10,827
Canadian provincial and municipal governments		3,177		4,150		–		7,327
U.S. federal government		9,417		56		–		9,473
U.S. states, municipalities and agencies		189		1,942		–		2,131
Other governments		630		193		–		823
NHA MBS, U.S. agency MBS and CMO		–		931		–		931
Corporate debt		1,485		10,278		–		11,763
Loans		3		150		–		153
Corporate equity		55,640		1		–		55,641
		79,253		19,816		–		99,069
Available-for-Sale Securities
Issued or guaranteed by:
Canadian federal government		8,283		897		–		9,180
Canadian provincial and municipal governments		920		2,707		–		3,627
U.S. federal government		14,269		–		–		14,269
U.S. states, municipalities and agencies		18		4,077		1		4,096
Other governments		2,290		1,268		–		3,558
NHA MBS, U.S. agency MBS and CMO		–		13,216		–		13,216
Corporate debt		1,551		2,972		2		4,525
Corporate equity		37		126		1,441		1,604
		27,368		25,263		1,444		54,075
Other Securities		–		–		333		333
Fair Value Liabilities
Securities sold but not yet purchased		22,992		2,171		–		25,163
Structured note liabilities and other note liabilities		–		13,674		–		13,674
Annuity liabilities		–		749		–		749
		22,992		16,594		–		39,586
Derivative Assets
Interest rate contracts		4		9,223		–		9,227
Foreign exchange contracts		17		17,196		–		17,213
Commodity contracts		232		846		–		1,078
Equity contracts		93		1,333		–		1,426
Credit default swaps		–		7		–		7
		346		28,605		–		28,951
Derivative Liabilities
Interest rate contracts		7		8,309		–		8,316
Foreign exchange contracts		6		14,967		–		14,973
Commodity contracts		239		835		–		1,074
Equity contracts		166		3,220		–		3,386
Credit default swaps		–		55		–		55
		418		27,386		–		27,804

Quantitative Information about Level 3 Fair Value Measurements

The table below presents the fair values of our significant Level 3 financial instruments, the valuation techniques used to determine their fair values and the value ranges of significant unobservable inputs used in the valuations. We have not applied any other reasonably possible alternative assumption to the significant Level 3 categories of private equity investments, as the net asset values are provided by the investment or fund managers.

As at October 31, 2018

(Canadian $ in millions, except as noted)

Reporting line in fair
value hierarchy table

Fair value
of assets

Valuation techniques

Significant
unobservable inputs

Range of input values (1)

Change in fair value

reasonably possible alternatives (2)

Low

High

Private equity (3)

Corporate equity

1,825

Net Asset Value

EV/EBITDA

Net Asset Value

Multiple

18x

na
na

Loans

Business and

government loans

1,450

Discounted
cash flows

Discount
margin

50 bps

175 bps

(1)

The low and high input values represent the highest and lowest actual level of inputs used to value a group of financial instruments in a particular product category. These input ranges do not reflect the level of input uncertainty, but are affected by the specific underlying instruments within the product category. The input ranges will therefore vary from period to period based on the characteristics of the underlying instruments held at each balance sheet date.

(2)

The impact of assuming a 10 basis point increase or decrease in discount margin for business and government loans.

(3)

Included in private equity is $889 million of Federal Reserve Bank and U.S. Federal Home Loan Bank shares that we hold to meet regulatory requirements.

– not applicable

Significant Unobservable Inputs in Level 3 Instrument Valuations

Net Asset Value

Net asset value represents the estimated value of a security based on valuations received from the investment or fund manager. The valuation of certain private equity securities is based on the economic benefit we derive from our investment.

EV/EBITDA Multiple

The fair value of private equity and merchant banking investments is derived by calculating an enterprise value (“EV”) using the EV/EBITDA multiple and then proceeding through a waterfall of the company’s capital structure to determine the value of the assets or securities we hold. The EV/EBITDA multiple is determined using judgment in considering factors such as multiples for comparable listed companies, recent transactions and company-specific factors, as well as liquidity discounts that account for the lack of active trading in these assets and securities.

Discount Margin

Loan and corporate debt yield is the interest rate used to discount expected future cash flows in the valuation model. The discount margin is the difference between an instrument’s yield and a benchmark instrument’s yield. Benchmark instruments have high credit quality ratings and similar maturities, such as government bonds. The discount margin therefore represents a market return required for uncertainty in future cash flows. Generally a higher or lower discount margin will result in a lower or higher fair value.

Significant Transfers

Our policy is to record transfers of assets and liabilities between fair value hierarchy levels at their fair values as at the end of each reporting period, consistent with the date of the determination of fair value. Transfers between the various fair value hierarchy levels reflect changes in the availability of quoted market prices or observable market inputs that result from changes in market conditions. The following is a discussion of the significant transfers between Level 1, Level 2 and Level 3 balances for the year ended October 31, 2018.

During the year ended October 31, 2018, $2,578 million of trading securities, $714 million of FVTPL securities and $2,266 million of FVOCI securities ($176 million of trading securities and $107 million of available-for-sale securities, respectively, in 2017) were transferred from Level 1 to Level 2 due to reduced observability of the inputs used to value these securities. During the year ended October 31, 2018, $4,122 million of trading securities, $742 million of FVTPL securities and $4,044 million of FVOCI securities ($156 million of trading securities and $56 million of available-for-sale securities, respectively, in 2017) were transferred from Level 2 to Level 1 due to increased availability of quoted prices in active markets.

During the year ended October 31, 2017, $33 million of available-for-sale securities were transferred from Level 3 to Level 1 due to the availability of observable prices used to value these securities. No such transfers happened in 2018.

Changes in Level 3 Fair Value Measurements

The tables below present a reconciliation of all changes in Level 3 financial instruments during the years ended October 31, 2018 and 2017, including realized and unrealized gains (losses) included in earnings and other comprehensive income.

Change in fair value

For the year ended October 31, 2018

(Canadian $ in millions)

Balance
November 1,
2017

Included in
earnings

Included

in other

compre-

hensive
income (1)

Purchases

Sales

Maturities/
Settlement

Transfers
into
Level 3

Transfers
out of
Level 3

Fair value as

at October 31,

2018

Change in

unrealized gains

(losses)

recorded in income
for instruments
still held (2)

Trading Securities

NHA MBS and U.S. agency MBS and CMO

–

)

306

(54

)

–

255

)

Corporate debt

–

Total trading securities

–

)

313

(54

)

–

262

)

FVTPL Securities

Corporate debt (3)

–

)

–

(74

)

–

Corporate equity (3)(4)

1,701

307

(161

)

–

(63

)

1,825

Total FVTPL securities

1,774

312

(161

)

–

(137

)

1,825

FVOCI Securities

Issued or guaranteed by:

U.S. states, municipalities and agencies

–

Corporate debt

–

)

–

Corporate equity

–

Total FVOCI securities

–

)

–

Business and Government Loans (5)

2,372

)

604

–

(1,548

)

–

1,450

–

Derivative Liabilities

Equity contracts

–

Credit default swaps

–

Total derivative liabilities

–

(1)

Foreign exchange translation on trading securities held by foreign subsidiaries is included in other comprehensive income, net foreign operations.

(2)

Changes in unrealized gains (losses) on FVTPL securities still held on October 31, 2018 are included in earnings for the year.

(3)

Includes $73 million of debt instruments and $260 million of equity instruments reclassified from other securities to FVTPL upon adoption of IFRS 9 (see Note 28).

(4)

Includes $1,441 million of equity instruments reclassified from available-for-sale to FVTPL upon adoption of IFRS 9 (see Note 28).

(5)

Business and government loans were reclassified from amortized cost to FVTPL upon adoption of IFRS 9 (see Note 28).

na – not applicable


			Change in fair value
For the year ended October 31, 2017 (Canadian $ in millions)	Balance October 31, 2016		Included in earnings			Included in other compre- hensive income (1)			Purchases		Sales			Maturities/ Settlement			Transfers into Level 3		Transfers out of Level 3			Fair value as at October 31, 2017		Change in unrealized gains (losses) recorded in income for instruments still held (2)
Trading Securities
Corporate debt		91		1			1			–		–			(93	)		–		–			–		–
Total trading securities		91		1			1			–		–			(93	)		–		–			–		–
Available-for-Sale Securities
Issued or guaranteed by:
U.S. states, municipalities and agencies		1		–			–			–		–			–			–		–			1		na
Corporate debt		4		–			–			–		(1	)		(1	)		–		–			2		na
Corporate equity		1,456		(40	)		(15	)		190		(117	)		–			–		(33	)		1,441		na
Total available-for-sale securities		1,461		(40	)		(15	)		190		(118	)		(1	)		–		(33	)		1,444		na
Other Securities		320		(9	)		(7	)		134		(102	)		(3	)		–		–			333		(8	)

(1)

Foreign exchange translation on trading securities held by foreign subsidiaries is included in other comprehensive income, net foreign operations.

(2)

Changes in unrealized gains (losses) on trading securities, derivative assets and derivative liabilities still held on October 31, 2017 are included in earnings for the year.

na – not applicable

Trading-Related Revenue

Trading assets and liabilities, including derivatives, securities and financial instruments designated at fair value through profit or loss, are measured at fair value, with gains and losses recognized in trading revenues, non-interest revenue, in the Consolidated Statement of Income. Trading-related revenue includes net interest income and non-interest revenue and excludes underwriting fees and commissions on securities transactions, which are shown separately in the Consolidated Statement of Income. Net interest income arises from interest and dividends related to trading assets and liabilities and is reported net of interest expense associated with funding these assets and liabilities in the following table.


(Canadian $ in millions)	2018			2017			2016
Interest rates		437			480			663
Foreign exchange		377			369			349
Equities		449			239			188
Commodities		63			84			66
Other		82			47			25
Total trading revenue		1,408			1,219			1,291
Reported as:
Net interest income (1)		(422	)		(133	)		99
Non-interest revenue – trading revenue		1,830			1,352			1,192
Total trading revenue		1,408			1,219			1,291

(1)

Amounts in brackets denote net interest expense.