CFA® LEVEL III SMARTSHEETFUNDAMENTALS FOR CFA® EXAM SUCCESS

2018CFA® EXAM REVIEW

WCID184

CRITICAL CONCEPTS FOR THE

CFA EXAM

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ETHICAL AND PROFESSIONAL STANDARDSSTANDARDS OF PROFESSIONAL CONDUCT

• Thoroughly read the Standards, along with related guidance and examples.

ASSET MANAGER CODE OF PROFESSIONAL CONDUCT

• Firm-wide, voluntary standards• No partial claim of compliance.• Compliance statement: “[Insert name of fi rm] claims

compliance with the CFA Institute Asset Manager Code of Professional Conduct. This claim has not been verifi ed by CFA Institute.”

• Firms must notify CFA Institute when claiming compliance.

• CFA Institute does not verify manager’s claim of compliance.

• Standards cover: • Loyalty to clients• Investment process and actions• Trading• Risk management, compliance, and support• Performance and valuation• Disclosures

BEHAVIORAL FINANCEBEHAVIORAL FINANCE PERSPECTIVE

• Prospect theory• Assigns value to changes in wealth rather than levels

of wealth.• Underweight moderate- and high-probability

outcomes.• Overweight low-probability outcomes.• Value function is concave above a wealth reference

point (risk aversion) and convex below a wealth reference point (risk seeking).

• Value function is steeper for losses than for gains.• Cognitive limitations

• Bounded rationality: deciding how much will be done to aggregate relevant information and using rules of thumb.

• Satisfi cing: fi nding adequate rather than optimal solutions.

• Traditional perspective on portfolio construction assumes that managers can identify an investor’s optimal portfolio from mean-variance eff icient portfolios.

• Consumption and savings• Mental accounting: wealth classifi ed into current

income, currently owned assets, PV of future income.• Framing: source of wealth aff ects spending/saving

decisions (current income has high marginal propensity to consume).

• Self-control: long-term sources unavailable for current spending.

• Behavioral asset pricing models• Sentiment premium included in required return.• Bullish (bearish) sentiment risk decreases (increases)

required return.• Behavioral portfolio theory

• Strategic asset allocation depends on the goal assigned to the funding layer.

• Uses bonds to fund critical goals in the domain of gains.

• Uses risky securities to fund aspirational goals in the domain of losses.

• Adaptive markets hypothesis• Must adapt to survive (bias towards previously

successful behavior due to use of heuristics).• Risk premiums and successful strategies change over

time.

BEHAVIORAL BIASES

• Cognitive errors (belief persistence biases)• Conservatism: overweight initial information and fail to

update with new information.• Confi rmation bias: only accept belief-confi rming

information, disregard contradictory information.• Representativeness: extrapolate past information into

the future (includes base-rate neglect and sample-size neglect).

• Illusion of control: believe that you have more control over events than is actually the case.

• Hindsight bias: only remember information that reinforces existing beliefs.

• Cognitive errors (information-processing biases)• Anchoring and adjustment: develop initial estimate

and subsequently adjust it up/down.• Mental accounting: treat money diff erently depending

on source/use.• Framing: make a decision diff erently depending on

how information is presented.• Availability bias: use heuristics based on how readily

information comes to mind.• Emotional biases

• Loss aversion: strongly prefer avoiding losses to making gains (includes disposition eff ect, house-money eff ect and myopic loss aversion).

• Overconfi dence: overestimate analytical ability or usefulness of their information (prediction overconfi dence and certainty overconfi dence).

• Self-attribution bias: self-enhancing and self-protecting biases intensify overconfi dence.

• Self-control bias: fail to act in their long-term interests (includes hyberbolic discounting).

• Status quo bias: prefer to do nothing than make a change.

• Endowment bias: value an owned asset more than if you were to buy it.

• Regret aversion: avoid making decisions for fear of being unsuccessful (includes errors of commission and omission).

• Goals-based investing• Base of pyramid: low-risk assets for obligations/needs.• Moderate-risk assets for priorities/desires; speculative

assets for aspirational goals.• Behaviorally modifi ed asset allocation

• Greater wealth relative to needs allows greater adaptation to client biases

• Advisor should moderate cognitive biases with high standard of living risk (SLR).

• Advisor should adapt to emotional biases with a low SLR.

INVESTMENT PROCESSES

• Behavioral biases in portfolio construction• Inertia and default: decide not to change an asset

allocation (status quo bias).• Naïve diversifi cation: exhibit cognitive errors resulting

from framing or using heuristics like 1/n diversifi cation.• Company stock investment: overallocate funds to

company stock.• Overconfi dence bias: engage in excessive trading

(includes disposition eff ect).• Home bias: prefer own country’s assets.• Mental accounting: portfolio may not be eff icient due

to goals-based investing as each layer of pyramid is optimized separately.

• Behavioral biases in research and forecasting• Representativeness: due to excessive structured

information.• Confi rmation bias: only accept supporting evidence.• Gamblers’ fallacy: overweight probability of mean

reversion.• Hot hand fallacy: overweight probability of similar

returns.• Overconfi dence, availability, illusion of control, self-

attribution and hindsight biases also possible.• Market behavioral biases

• Momentum eff ects due to herding, anchoring, availability and hindsight biases.

• Bubbles due to overconfi dence, self-attribution, confi rmation and hindsight biases.

• Value stocks have outperformed growth stocks; small-cap stocks have outperformed large-cap stocks.

PRIVATE WEALTH MANAGEMENTINVESTMENT POLICY STATEMENT

• Return calculation• To maintain real value of portfolio, the required real

aft er-tax return is calculated as:

Annual after-tax withdrawal from the portfolio / Asset base

• To convert aft er-tax withdrawal to a pre-tax withdrawal

Pre-tax withdrawal = After-tax withdrawal / (1 – Tax rate on withdrawals)

• Nominal return = Real return + Infl ation rate• If investor wishes to grow portfolio, use TVM worksheet

to compute I/Y over investment horizon.• Risk tolerance

• Above-average ability if longer time horizon or large asset base compared with needs.

• Willingness based on psychological profi le.• Overall tolerance is a combination of ability and

willingness.• Time horizon constraint: length and number of stages.• Liquidity constraint: ongoing needs, one-time

expenditures, emergencies.• Tax constraint: diff erent rates may apply to diff erent

sources of income and capital gains.• Legal and regulatory constraint: less of a concern for

individuals, restricted trading periods may apply to corporate insiders.

• Unique constraint: client-imposed restrictions, e.g. socially responsible investing, client-directed brokerage.

• Psychological profi ling• More risk averse: methodical (thinking), cautious

(feeling).• Less risk averse: individualist (thinking), spontaneous

(feeling).• Strategic asset allocation

• Return: eliminate portfolios that do not meet return objective. May need to convert a pre-tax nominal return to an aft er-tax real return.

After-tax real return = Pre-tax nominal return × (1 – Tax rate) – Inflation rate

• Risk: eliminate portfolios that do not meet shortfall or other risk objectives.

• Constraints: eliminate portfolios that do not meet constraints, e.g. cash holding for liquidity.

• Of the remaining portfolios, select portfolio with highest risk-adjusted performance, usually on Sharpe ratio.

Sharpearpear ratio is:(expected return – rturn – rtur iskn – riskn – r -free rate)

expected standardndardnda deviation

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TAXES AND PRIVATE WEALTH MANAGEMENT

• Future value factor with accrual taxes

[1 1 ]

pre-tax

after-tax pre-tax

FVIF rprF rpre-taxF re-taxFVIF rFVI

FVIF r[1F r[1afteF rafter-F rr-taxF rtax prF rprFVIF rFVI

n

n

( )1( )1 pr( )pre-tax( )e-taxF r( )F r1F r1( )1F r1 prF rpr( )prF rpr

( )1 ]( )1 ]1 ]t1 ]( )1 ]t1 ]I( )I1 ]I1 ]( )1 ]I1 ]

F r= +F rF r( )F r= +F r( )F r1F r1( )1F r1= +1F r1( )1F r1

F r= +F r[1F r[1= +[1F r[1 1 ]( )1 ]−1 ]( )1 ]

• Future value factor when deferring taxes on capital gains (B is cost basis as a proportion of current market value)

FVIFCG = (1 + rpre‐taxrpre‐taxr )n (1 − tCG) + tCGBCGBCG

• Future value factor with annual wealth tax

1 1FVIF rFVIF rFVI W W1 1W W1 1W WF rW WF rW W

n( )1 1( )1 1F r( )F r1 1F r1 1( )1 1F r1 1( )pr( )prW W( )W W1 1W W1 1( )1 1W W1 1prW Wpr( )prW Wpr1 1pr1 1W W1 1pr1 1( )1 1pr1 1W W1 1pr1 1e-taxW We-tax( )e-taxW We-tax1 1e-tax1 1W W1 1e-tax1 1( )1 1e-tax1 1W W1 1e-tax1 11 1F r1 1W W1 1F r1 1( )1 1F r1 1W W1 1F r1 11 1pr1 1F r1 1pr1 1W W1 1pr1 1F r1 1pr1 1( )1 1pr1 1F r1 1pr1 1W W1 1pr1 1F r1 1pr1 1( )1 1( )1 1 t( )tW W( )W W1 1W W1 1( )1 1W W1 1 tW Wt( )tW WtF r= +F rF rW WF r= +F rW WF rF r( )F r= +F r( )F r1 1F r1 1( )1 1F r1 1= +1 1F r1 1( )1 1F r1 1F rW WF r( )F rW WF r= +F rW WF r( )F rW WF r1 1F r1 1W W1 1F r1 1( )1 1F r1 1W W1 1F r1 1= +1 1F r1 1W W1 1F r1 1( )1 1F r1 1W W1 1F r1 1F r= +F rF rW WF r= +F rW WF r ( )−( )F rF rF r= +F rF r= +F rF rW WF r= +F rW WF rF rW WF r= +F rW WF rW WW WF rW WF r= +F rW WF rF rW WF r= +F rW WF rF r= +F rF r= +F rF r= +F rF r= +F rF rW WF r= +F rW WF rF rW WF r= +F rW WF rF rW WF r= +F rW WF rF rW WF r= +F rW WF r

• Eff ective annual aft er-tax return aft er taxes interest, dividends and realized capital gains

*r r*r r* T Ir rT Ir r ( )1( )1 P t( )P t P t( )P t P t( )P tT I( )T I1T I1( )1T I1 P tT IP t( )P tT IP tI D( )I DP tI DP t( )P tI DP tD C( )D CP tD CP t( )P tD CP tG C( )G CP tG CP t( )P tG CP t G( )G= −r r= −r rT I= −T Ir rT Ir r= −r rT Ir r ( )= −( )1( )1= −1( )1T I( )T I= −T I( )T I1T I1( )1T I1= −1T I1( )1T I1( )− −( )P t( )P t− −P t( )P t

• Eff ective capital gains tax rate

1

1T t*T t*

P P P

P t P t P tCGI DP PI DP P CGPCGP

I DP tI DP t P tI DP tD CP tD CP tG CP tG CP t G

T t=T t− −P P− −P P −

− −P t− −P t −

• Future value factor with blended tax regime

(1 *) (1 ) * (1 )after-taxFVIF r(1F r(1afteF rafter-F rr-taxF rtaxFVIF rFVI T T*T T*)T T) t B(1t B(1n) (n) ( CGt BCGt BF r= +F r(1F r(1= +(1F r(1 − +T T− +T T*T T*− +*T T*)T T)− +)T T) − −t B− −t B(1t B(1− −(1t B(1

• Accrual equivalent aft er-tax return

1

0

0

V V

rV

V0V0

n A0n A0V Vn AV V0V V0n A0V V0n

AErAErnVnV

n

( )1( )1 r( )rn A( )n Arn Ar( )rn Ar E( )E= +0= +0V V= +V V0V V0= +0V V0n A= +n A0n A0= +0n A0V Vn AV V= +V Vn AV V0V V0n A0V V0= +0V V0n A0V V0 ( )= +( )1( )1= +1( )1n A( )n A= +n A( )n A1n A1( )1n A1= +1n A1( )1n A1

= −= −= −n= −n

• Accrual equivalent tax rate

( )= −( )= −( )= −

r r= −r r= −( )T( )T

r

r

AEr rAEr r ( )AE( )( )T( )AE( )T( )

AETAET AErAEr

( )1( )( )= −( )1( )= −( )1= −1= −

• Measure of tax drag = Diff erence between accrual equivalent aft er-tax return and the actual return of the portfolio.

• Tax-deferred accounts (TDAs): contributions from untaxed ordinary income, tax-free growth during the holding period, taxed at time of withdrawal

FVIFTDA = (1 + r)n (1 – tn)

• Tax-exempt accounts (TEAs): aft er-tax contributions, tax-free growth during the holding period, no future tax liabilities.

( )FVIF r( )F r( )= +F r= +( )= +( )F r( )= +( )FVIF rFVI TEF rTEF rAF rAF rTEATEF rTEF rAF rTEF r n( )1( )( )F r( )1( )F r( )( )= +( )F r( )= +( )1( )= +( )F r( )= +( )

• TDA off ers aft er-tax return advantage over TEA if tax rate at withdrawal is lower than tax rate at initial contribution.

• Investor’s shared of investment risk on a taxed return

( )σ = σ −( )σ −( )( )t( )ATσ =ATσ = ( )1( )( )σ −( )1( )σ −( )

ESTATE PLANNING

• Core capital• Assets for maintaining lifestyle, funding desired

spending goals and providing emergency reserve.• Joint survival probability for a couple

p s l p al p s l

p s l p alJ Hl pJ Hl p W

H Wl pH Wl p

( )p s( )p sur( )urviva( )vivaurvivaur( )urvivaur l p( )l pl pJ Hl p( )l pJ Hl p( )rviv( )rvival( )alJ H( )J HsuJ Hsu( )suJ HsurvivJ Hrviv( )rvivJ HrvivalJ Hal( )alJ Hal ( )p s( )p sur( )urviva( )vivaurvivaur( )urvivaur l( )lW( )W

( )viva( )vival p( )l p( )p s( )p sur( )urviva( )vivaurvivaur( )urvivaur l p( )l pl pH Wl p( )l pH Wl p( )su( )surviv( )rvival( )alH W( )H WsuH Wsu( )suH WsurvivH Wrviv( )rvivH WrvivalH Wal( )alH Wal

= +l p= +l pJ H= +J Hl pJ Hl p= +l pJ Hl p( )= +( )su( )su= +su( )surviv( )rviv= +rviv( )rvival( )al= +al( )alJ H( )J H= +J H( )J HsuJ Hsu( )suJ Hsu= +suJ Hsu( )suJ HsurvivJ Hrviv( )rvivJ Hrviv= +rvivJ Hrviv( )rvivJ HrvivalJ Hal( )alJ Hal= +alJ Hal( )alJ Hal

l p− ×l pl pH Wl p− ×l pH Wl p− ×p s− ×p s( )− ×( )p s( )p s− ×p s( )p sur( )ur− ×ur( )urviva( )viva− ×viva( )vivaurvivaur( )urvivaur− ×urvivaur( )urvivaur l p( )l p− ×l p( )l pl pH Wl p( )l pH Wl p− ×l pH Wl p( )l pH Wl p

• PV of joint spending needs

( )( ) ( )

(1 )1

PV sp( )sp( )ending( )ending( )p s( )p s( )( )ur( )( )viva( )( )ur( )viva( )ur( )l s( )l s( ) ( )l s( )pending( )pending( )l spendingl s( )l s( )pending( )l s( )

rJ( )J( ) J J( )J J( ) ( )J J( )l sJ Jl s( )l s( )J J( )l s( ) ( )l s( )J J( )l s( )pendingJ Jpending( )pending( )J J( )pending( )( )l s( )pending( )l s( )J J( )l s( )pending( )l s( )t

t

N

∑=l s×l sl sJ Jl s×l sJ Jl s

+=

• Relative aft er-tax value of a tax-free gift

[1 (1 )]

[1 (1 )] (1 )RV

FV

FV

r t(1r t(1r t

r t(1r t(1 TtaRVtaRV x ftax fta rx frx f eeGiftreeGiftrGFVGFV ift

BequestFVBequestFVg i(1g i(1r tg ir t(1r t(1g i(1r t(1 g

n

e i(1e i(1r te ir t(1r t(1e i(1r t(1 en

eTeT= == =

+ −r t+ −r t(1r t(1+ −(1r t(1r tg ir t+ −r tg ir t(1r t(1g i(1r t(1+ −(1r t(1g i(1r t(1

+ −r t+ −r t(1r t(1+ −(1r t(1r te ir t+ −r te ir t(1r t(1e i(1r t(1+ −(1r t(1e i(1r t(1 −x f−x f

• Relative aft er-tax value of a gift taxable to the recipient

[1 (1 )] (1 )

[1 (1 )] (1 )RV

FV

FV

r t(1r t(1 T

r t(1r t(1 TtaxablRVtaxablRV e GiftGFVGFV ift

BequestFVBequestFVg i(1g i(1r tg ir t(1r t(1g i(1r t(1 g

ngTgT

e i(1e i(1r te ir t(1r t(1e i(1r t(1 en

eTeT= == =

+ −r t+ −r t(1r t(1+ −(1r t(1r tg ir t+ −r tg ir t(1r t(1g i(1r t(1+ −(1r t(1g i(1r t(1 −+ −r t+ −r t(1r t(1+ −(1r t(1r te ir t+ −r te ir t(1r t(1e i(1r t(1+ −(1r t(1e i(1r t(1 −

• Trusts• Revocable: owner (settlor) retains right to assets and

can use trust assets to settle claims against settlor.• Irrevocable: owner forfeits right to assets and cannot

use trust assets to settle claims against settlor.• Double taxation

• Credit method: residence country provides a tax credit for taxes paid in source country.

tCM =Max CM =Max CM (tRCtRCt , tRC, tRC SC, tSC, t )

• Exemption method: residence country exempts foreign source income from tax.

t tEMt tEMt tSCt t=t t

• Deduction method: residence country allows deduction for tax paid in source country.

t t t t tDMt tDMt tRC SCt tSCt tRC SC= +t t= +t tRC= +RC t t−t t

CONCENTRATED SINGLE-ASSET POSITIONS

• Objectives: risk reduction (diversifi cation), monetization, tax optimization, control.

• Considerations: illiquidity, triggering taxable gains on sale, restrictions on amount and timing of sales, emotional and cognitive biases.

• Monetization strategies• Monetization by (1) hedging the position, and (2)

borrowing against hedged position.• Hedging for monetization strategies can be achieved

by: (1) short sale against the box (least expensive); (2) total return equity swap; (3) short forward or futures contract; (4) synthetic short forward (long put and short call).

• Hedging strategies• Buy puts (protect downside and keep upside while

deferring capital gains tax).• Use zero-premium collars (long put and short call with

off setting premiums) to reduce costs vs buying puts.• Use prepaid variable forward (combine hedge and

margin loan in same instrument), with number of shares delivered at maturity dependent on share price at maturity.

• Yield enhancement strategies:• Write covered calls to generate income.• Does not reduce downside risk.

• Tax optimized equity strategies• Index-tracking separately managed portfolio: designed

to outperform benchmark from an investment and tax perspective.

• Completeness portfolio: tracks index given concentrated portfolio characteristics and new investments.

• Exchange fund: investors with concentrated positions contribute these positions in exchange for a share in a diversifi ed fund (non-taxable event).

• Monetization strategies for concentrated private shares• Strategic buyers: gain market share and earnings

growth.• Financial buyers: acquire and manage companies using

private equity fund.• Leveraged recapitalization: private equity fi rm uses

debt to purchase majority of owner’s stock for cash.• Management buyout: management borrow money to

purchase owner’s stock.• Divestiture of noncore assets: owner uses proceeds to

diversify asset pool.• Sale or gift to family members.• Personal line of credit secured by company shares.• Initial public off ering.• Employee share ownership plan (ESOP) exchange:

company buys owner’s shares for ESOP distributions.• Monetization strategies for real estate

• Mortgage fi nancing (no tax consequences and can use proceeds to diversify).

• Donor-advised funds (contribute property now for tax deduction).

• Sale and leaseback (frees up capital for diversifi cation but sale triggers taxable gain).

RISK MANAGEMENT FOR INDIVIDUALS

• Financial capital: includes all tangible assets including family home

• Human capital: PV of future expected labor income (higher income volatility requires higher discount rate).

• Income volatility risk can be diversifi ed by appropriate fi nancial capital, e.g. if human capital is equity-like, fi nancial capital should contain more bonds.

• Economic (holistic) balance sheet• Assets: fi nancial capital, personal property, human

capital, pension value.• Liabilities: total debt, lifetime consumption needs,

bequests.• Net wealth is the diff erence between total assets and

total liabilities.• Young family has high % of economic assets in human

capital. As the household ages, weight of human (fi nancial) capital will decrease (increase).

• Risks to human and fi nancial capital• Earnings risk: protect against earnings risk related to

injury with disability insurance.• Premature death (mortality risk): protect with life

insurance.• Longevity risk: protect with annuities.• Property risk: protect with homeowner’s insurance.• Liability risk: protect with liability insurance.• Health risk: protect with health insurance.

• Risk management techniques

Loss Characteristics High Frequency Low Frequency

High severity

Low severity

Risk avoidance

Risk reduction

Risk transfer

Risk retention

• Adequacy of life insurance• Human life value method: estimates the PV of earnings

that must be replaced.• Needs analysis method: estimates fi nancial needs of

dependents.

INSTITUTIONAL INVESTORSDEFINED BENEFIT PENSION PLAN

• Risk tolerance: greater ability to assume risk if• Plan surplus• Lower sponsor debt and/or higher current profi tability• Lower correlation of plan asset returns with company

profi tability• No early retirement and lump sum distributions

options• Greater proportion of active versus retired lives• Higher proportion of younger workers

• Risk objective: usually related to shortfall risk of achieving funding status.

• Return objective: to achieve a return that will fully fund liabilities (infl ation-adjusted), given funding constraints.

• Liquidity: to meet required benefi t payments.• Time horizon: usually long-term and could be multi-

stage.

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• Tax: investment income and capital gain usually tax-exempt.

• Legal/regulatory: plan trustees have a fi duciary responsibility to benefi ciaries under ERISA (US).

• Unique: limited resources for due diligence, ethical constraints.

FOUNDATIONS

• Risk tolerance/objective: higher risk tolerance due to noncontractually committed payout.

• Return objective: to cover infl ation-adjusted spending goals and overheads not countable toward required spending minimum.

r %spend %management % inflation

or

(1 % spend)(1 %management)(1 % inflation) 1

= +%s= +%spend= +pend t %+t %

= +(1= +(1 + +1 %+ +1 %management+ +management)(+ +)(1 %+ +1 % −

• Liquidity: to quickly fund spending needs (including noncountable overheads) greater than current contributions.

• Time horizon: usually infi nite.• Tax: investment income and capital gain taxable.• Legal/regulatory: UPMIFA (US).• Unique: May use swap agreements or other transactions

to diversify returns if funding is primarily via large blocks of stocks.

ENDOWMENTS

• Risk tolerance/objective• Greater ability to take risk due to infi nite time horizon

and if adopting spending rules based on smoothed averages of return and previous spending.

• Lower ability to take risk if high donor contributions as a % of total spend.

• Lower ability to take risk if contributing a signifi cant % to a company’s annual spending or if company relies on endowment to cover high fi xed costs.

• Return objective: same as for foundations. Annual spend may be calculated in a number of ways.

Spendingt = Spending rate × Ending market valuet−1

Spendingt = Spending rate × 1⁄1⁄13⁄3⁄ [Ending market valuet−3

+ Ending market valuet−2 + Ending market valuet−1]

Spendingt = Smoothing rate × [Spendingt−1 × (1 + Inflationt−1)] + [(1 − Smoothing rate) × (Spending rate × Beginning market valuet−1)]

• Liquidity: to fund gift s and planned capital distributions for construction projects as well as to allow portfolio rebalancing. No minimum spending requirement.

• Time horizon: usually infi nite (maintain principal in perpetuity).

• Tax: not taxable unless they are unrelated business taxable income.

• Legal/regulatory: UPMIFA (US).• Unique: types of investments constrained by size or

board member sophistication.

LIFE INSURANCE COMPANIES

• Risk tolerance/objective• Liquidity risk: arises from changes in investment

portfolio that aff ects reserves.• Interest rate risk: reinvestment risk and valuation

risk (due to duration mismatch between assets and liabilities).

• Credit risk of bond investments.• Cash volatility risk: relates to timely receipt and

reinvestment of cash.• Disintermediation risk: policy owners withdraw

funds to reinvest with other intermediaries in higher-returning assets.

• Return objective: minimum return requirement (based on rate initially specifi ed to fund life insurance contract) and net interest spread.

• Liquidity: limited liquidity needs since cash infl ows exceed cash outfl ows, but need to consider disintermediation risk (when interest rates are rising) and asset marketability risk.

• Time horizon: diff erent product lines have diff erent time horizons and will be funded by duration-matched assets.

• Tax: pay corporate tax.• Legal/regulatory: regulations on eligible investments,

prudent investor rule, NAIC risk-based capital (RBC) and asset valuation reserve (AVR) requirements.

• Unique: look out for restrictions on illiquid investments.

NON-LIFE INSURANCE COMPANIES

• Risk tolerance/objective• Policyholder reserves use lower-risk assets due to

unpredictable operating claims.• Maintaining surplus during high-volatility markets

reduces ability to accept higher risk.• Risk measured against premiums-to-capital and

premiums-to-surplus ratios.• Return objective

• Investment earnings on surplus assets must be suff icient to off set periodic losses and to maintain policyholder reserves.

• Larger companies use active management strategies for total return rather than yield or investment income strategies.

• Liquidity: to meet policyholder claims.• Time horizon: generally shorter duration than life

insurance companies.• Tax: pay corporate tax.• Legal/regulatory: regulations on eligible investments,

risk-based capital (RBC) requirements.• Unique: look for restrictions on illiquid investments.

BANKS

• Risk tolerance/objective• Below-average risk tolerance.• Leverage-adjusted duration gap (LADG) measure

overall interest rate exposure.

LADG D kDD kDD k

k V VA LD kA LD kDA LDD kDD kA LD kDD k

L Ak VL Ak V VL AV/L A/L A

= −D k= −D kD kA LD k= −D kA LD k

k V=k V

• Value at risk (VAR) measures minimum loss expected over a specifi ed time period at a given level of probability.

• Credit risk in the bank’s loan portfolio.• Return objective: interest income allocation focuses on

positive spread over cost of funds, with the remaining allocation focusing on higher total return.

• Liquidity: driven by demand for loans and net outfl ows of deposits.

• Time horizon: duration spread of assets over liabilities constrains time horizon for securities portfolio to an intermediate-term.

• Tax: pay corporate tax.• Legal/regulatory

• Large % of securities portfolio in government securities as pledge against reserves.

• Regulators restrict allocation to common shares and below-investment-grade bonds.

• Risk-based capital requirements.• Unique: Lending activities may be infl uenced by

community needs and historical banking relationships.

ECONOMIC ANALYSISCAPITAL MARKET EXPECTATIONS

• Expected return on equity from Gordon growth model

E RD g

Pg

D

Pg( )E R( )E R

( )D g( )D g=D g( )D g+D g( )D g

+ =g+ =g +0D g0D g

0P0P1

0P0P

( )1( )D g( )D g1D g( )D g

• Expected return on equity from Grinold-Kroner model

( ) % %E R( )E R( )D

PS I% %S I% %NF% %NF% %S INFS I% %S I% %NF% %S I% %L g% %L g% %NFL gNF% %NF% %L g% %NF% % PEr% %r% %≈ −≈ − ∆ +% %∆ +% %% %S I% %∆ +% %S I% %% %+ +% %% %L g% %+ +% %L g% %% %r% %+ +% %r% %∆PE∆PE

• Risk premium (buildup) approach• Fixed income buildup modelFixed income buildup model( )E R( )E R( ) RP RP RP RP RPb F( )b F( ) INRP RP RP RP RPINRP RP RP RP RPFLRP RP RP RP RPFLRP RP RP RP RPINFLINRP RP RP RP RPINRP RP RP RP RPFLRP RP RP RP RPINRP RP RP RP RPDefault LRP RP RP RP RPt LRP RP RP RP RPiquidityRP RP RP RP RPiquidityRP RP RP RP RPMaturity TaRP RP RP RP RPTaRP RP RP RP RP xTaxTa= +rr= +rrb F= +b Frrb Frr= +rrb Frr RP RP RP RP RP+ +RP RP RP RP RPRP RP RP RP RPDRP RP RP RP RP+ +RP RP RP RP RPDRP RP RP RP RPRP RP RP RP RPefaulRP RP RP RP RP+ +RP RP RP RP RPefaulRP RP RP RP RPRP RP RP RP RPt LRP RP RP RP RP+ +RP RP RP RP RPt LRP RP RP RP RPRP RP RP RP RP+ +RP RP RP RP RPRP RP RP RP RPMaRP RP RP RP RP+ +RP RP RP RP RPMaRP RP RP RP RPRP RP RP RP RPturityRP RP RP RP RP+ +RP RP RP RP RPturityRP RP RP RP RP

• Equity buildup modelEquity buildup modelE R R ERP YTM ERPe F year Trer Trer T asuryasuryasur( )E R( )E Re F( )e FE Re FE R( )E Re FE R = +R= +Re F= +e FRe FR= +Re FR = +YTM= +YTM yea= +year T= +r Tre= +rer Trer T= +r Trer T asur= +asury= +yasuryasur= +asuryasur−10= +10= +

• ICAPM (Singer-Terhaar)• Expected return

( ) ) ]E R( )E R( ) R E ) ]R R) ]i F( )i F( ) i M F) ]F) ]= +R E= +R Ei F= +i FR Ei FR E= +R Ei FR Eβ −[ (β −[ ( ) ]β −) ]β −R Eβ −R E[ (R E[ (β −[ (R E[ (β −) ]β −) ]R Rβ −R R) ]R R) ]β −) ]R R) ]i Mβ −i M[ (i M[ (β −[ (i M[ (R Ei MR Eβ −R Ei MR E[ (R E[ (i M[ (R E[ (β −[ (R E[ (i M[ (R E[ (R Ri MR Rβ −R Ri MR R

• Asset class risk premium in a 100% fully integrated market

COVi

i MCOVi MCOV

M

i M i M

M

i

Mi M

,i M,i M2

,i M,i M2 ,i M,i Mβ =iβ =i σ

=σ σi Mσ σi Mρ

σ=

σσ

ρ

RPRP

iRPiRP MRPMRP

Mi i M=

σ

σ ρi iσ ρi i,

• Asset class risk premium in a completely segmented market

RPRP

i iRPi iRP MRPMRP

M

= σi i= σi i σ

• Expected return with less than 100% integration and a liquidity risk premium (where RPi

* is the weighted average of perfectly integrated and completely segmented asset class risk premiums)

( ) *E R( )E R( ) R RP R*P R* Pi F( )i F( ) i LP Ri LP RPi LP iquidity= +R R= +R Ri F= +i FR Ri FR R= +R Ri FR RP R+P RP Ri LP R+P Ri LP R

• Taylor rule

= + × − + ×[0.5 (× −(× −GDP GDP× −GDP GDP× − ) 0+ ×) 0+ ×.5+ ×.5+ × ( )]R R= +R R= + g gGDP GDPg gGDP GDP× −GDP GDP× −g g× −GDP GDP× − ( )I I( )−( )−I I−( )−OpR ROpR RtimalR RtimalR RNeut= +Neut= +ra= +ra= +l F= +l F= + × −l F× −[0l F[0.5l F.5 (l F(× −(× −l F× −(× −GDP GDPl FGDP GDP× −GDP GDP× −l F× −GDP GDP× −g gl Fg gGDP GDPg gGDP GDPl FGDP GDPg gGDP GDP× −GDP GDP× −g g× −GDP GDP× −l F× −GDP GDP× −g g× −GDP GDP× −org gorg gGDP GDPg gGDP GDPorGDP GDPg gGDP GDP× −GDP GDP× −g g× −GDP GDP× −or× −GDP GDP× −g g× −GDP GDP× −l Forl Fg gl Fg gorg gl Fg gGDP GDPg gGDP GDPl FGDP GDPg gGDP GDPorGDP GDPg gGDP GDPl FGDP GDPg gGDP GDP× −GDP GDP× −g g× −GDP GDP× −l F× −GDP GDP× −g g× −GDP GDP× −or× −GDP GDP× −g g× −GDP GDP× −l F× −GDP GDP× −g g× −GDP GDP× −ecastg gecastg gGDP GDPg gGDP GDPecastGDP GDPg gGDP GDP× −GDP GDP× −g g× −GDP GDP× −ecast× −GDP GDP× −g g× −GDP GDP× −orecastorg gorg gecastg gorg gGDP GDPg gGDP GDPorGDP GDPg gGDP GDPecastGDP GDPg gGDP GDPorGDP GDPg gGDP GDP× −GDP GDP× −g g× −GDP GDP× −or× −GDP GDP× −g g× −GDP GDP× −ecast× −GDP GDP× −g g× −GDP GDP× −or× −GDP GDP× −g g× −GDP GDP× − Trend F+ ×d F+ ×) 0d F) 0+ ×) 0+ ×d F+ ×) 0+ ×.5d F.5+ ×.5+ ×d F+ ×.5+ × ( )d F( )( )I I( )d F( )I I( )or( )or( )( )I I( )or( )I I( )d Ford F( )d F( )or( )d F( )( )I I( )d F( )I I( )or( )I I( )d F( )I I( )ecast( )ecast( )( )I I( )ecast( )I I( )orecastor( )or( )ecast( )or( )( )I I( )or( )I I( )ecast( )I I( )or( )I I( )Ta( )Ta( )rg( )rg( )et( )et( )

• Exchange rate forecasting• Relative PPP: exchange rates off set infl ation

diff erentials

∆ ≈ −%∆ ≈FX∆ ≈ INFLINFLIN INFLINFLINf d∆ ≈f d∆ ≈/f d/∆ ≈/∆ ≈f d∆ ≈/∆ ≈ f dINf dINFLf dFLINFLINf dINFLIN

• Relative economic strength: increasing growth attracts portfolio investment capital, increasing short-term demand for domestic currency.

• Capital fl ows forecasting: higher relative direct and long-term portfolio investment causing currency appreciation.

• Savings-investment imbalance: current account defi cits must be met with capital account surplus as foreign investors provide funds to off set domestic savings defi cit.

EQUITY MARKET VALUATION

• Cobb-Douglas economic growth with constant returns to scale

(1 )Y

Y

A

A

K

K

L

L

∆ ≈ ∆A∆A + α ∆ + −(1+ −(1 α ∆L∆L

• H-model for equity market valuationH-model for equity market valuation

200V0V0

D

r g

N

LL S2L S2

( )g g( )g gL S( )L Sg gL Sg g( )g gL Sg gL( )L( )1( )1 g( )gL S( )L S=r g−r g

+ +L S+ +L S( )+ +( )g( )g+ +g( )gL S( )L S+ +L S( )L Sg g( )g g−g g( )g g

• Relative value models• Fed model: equity market undervalued if S&P earnings

yield > 10-year Treasury note yield (but ignores equity risk premium and earnings growth).

• Yardeni model: equity markets undervalued if model’s justifi ed earnings yield < market’s earnings yield.

1

0

E

P0P0y d LTEGBy dBy d= −y d= −y dy dBy d= −y dBy d ×

• Cyclically adjusted P/E (CAPE) ratio• 10-year moving average CAPE ratio controls for

business cycle eff ects and is mean reverting.

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• CAPE value is current-year real S&P 500 index value divided by average real earnings over previous 10 years.

• Asset-based models• Tobin’s q: market value of debt and equity capital

divided by replacement cost of assets (undervalued if q ratio < 1 assuming mean reversion).

• Equity q: market value of equity divided by replacement cost of net assets (undervalued if q ratio < 1 assuming mean reversion).

ASSET ALLOCATIONASSET ALLOCATION APPROACHES

• Asset-only: does not explicitly model liabilities• Liability-relative (liability-driven investing): aims at an

asset allocation that can pay off liabilities when they come due.

• Goals-based investing: specifi es sub-portfolios aligned with a specifi c goal (sum of all sub-portfolio asset allocations results in an overall strategic asset allocation).

PRINCIPLES OF ASSET ALLOCATION

• Mean variance optimization (MVO)• Produces an eff icient frontier based on returns,

standard deviation of returns and pairwise correlations.

• Find optimal asset allocation mix that maximizes client’s utility.

( ) 0.005 2U E R A( )R A( ) 0.00R A0.005R A5p p( )p p( )U Ep pU E( )R A( )p p( )R A( ) p= −( )= −( )U E= −U E R A= −R A( )R A( )= −( )R A( ) × ×R A× ×R A σ

• MVO limitations• Asset allocations are highly sensitive to small changes

in input variables.• Asset allocations can be highly concentrated.• Only focuses on mean and variance of returns.• Sources of risk may not be well diversifi ed.• Asset-only strategy.• Single-period framework and ignores trading/

rebalancing costs and taxes.• Does not address evolving asset allocation strategies,

path-dependent decisions, non-normal distributions.• Approaches to improve quality of MVO asset allocation

• Use reverse optimization to compute implied returns and improve quality of inputs, e.g. Black-Litterman model.

• Adding constraints to incorporate short-selling and other real-world restrictions into optimization.

• Resampled MVO technique combining MVO and Monte Carlo approaches to seek the most eff icient and consistent optimization.

• Monte Carlo simulation and scenario analysis• Used in a multiple-period framework to improve

single-period MVO.• Provides a realistic picture of distribution of potential

future outcomes.• Can incorporate trading/rebalancing costs and taxes.• Can model non-normal distributions, serial and cross-

sectional correlations, evolving asset allocations, path-dependent decisions, non-traditional investments, human capital.

• Risk budget• Identifi es total amount of risk and allocates risk to

diff erent asset classes.• Asset allocation is optimal when ratio of excess return

to MCTR is the same for all assets.

= ×Marginal contricontricont bution to total risk (MCTR) A= ×A= ×sse= ×sse= ×t b= ×t b= ×et= ×et= ×a P= ×a P= × ortfortfor oliotfoliotf standardndardnda deviation

Absolute contribution to total risk Asset weight MCTR

Ratio of excess return teturn tetur o MCTR (Expected return Risk-free rate)/MCTR

( )AC( )ACTR( )TR = ×A= ×Asse= ×sset w= ×t weigh= ×eight M= ×t M

= −R (= −R (Expected= −Expected re= −retu= −turn= −rn

• Liability-relative asset allocation approaches

Surplus optimization two-Portfoliotwo-Portfoliot Integrated Asset-liability

Simplicity Simplicity Increased complexity

Linear correlation Linear or nonlinear correlation Linear or nonlinear correlation

All levels of risk Conservative level of risk All levels of risk

Any funding ratio Positive funding ratio for basic approach

Any funding ratio

Single period Single period Multiple periods

• Goal-based asset allocations• Creation of diff erentiated portfolio modules based on

capital market expectations.• Identifying clients’ goals and matching the goals to

appropriate sub-portfolios and modules.

ASSET ALLOCATION WITH REAL-WORLD CONSTRAINTS

• Constraints on asset allocation due to:• Asset size: more acute issue for individual rather than

institutional investors.• Liquidity: liquidity needs of asset owner and liquidity

characteristics of diff erent asset classes.• Time horizon: asset allocation decisions evolve

with changes in time horizon, human capital, utility function, fi nancial market conditions, characteristics of liability and the asset owner’s priorities.

• Regulatory: fi nancial markets and regulatory entities oft en impose additional constraints.

• Taxes• Place less tax-eff icient assets in tax-advantaged

accounts to achieve aft er-tax portfolio optimization.

r p r t p ratr patr pd pr td pr tt dr tt dr t a pp ra pp r t cg(1r t(1r tt d(1t dr tt dr t(1r tt dr t ) (p r) (p ra p) (a pp ra pp r) (p ra pp r t c) (t c1 )t1 )tt c1 )t ctt ct1 )tt ct g1 )gr t= −r tr tt dr t= −r tt dr t= −r p= −r p r t= −r td p= −d pr td pr t= −r td pr tr tt dr t= −r tt dr tr t(1r t= −r t(1r tr tt dr t(1r tt dr t= −r tt dr t(1r tt dr t + −t c+ −t c) (+ −) (p r) (p r+ −p r) (p ra p) (a p+ −a p) (a pp ra pp r) (p ra pp r+ −p ra pp r) (p ra pp r t c) (t c+ −t c) (t c1 )+ −1 )t c1 )t c+ −t c1 )t c

• Rebalancing range for a taxable portfolio (Rtaxable) can be wider than those of an otherwise identical tax-exempt portfolio (Rtax exempt).

= −R R= −R R= −/ (= −/ (= −1 t= −1 t= − )taxableR RtaxableR Rtax= −tax= −exempt= −exempt= −

• Revision to asset an allocation• Changes in goals• Changes in constraints• Changes in investment beliefs

• Tactical asset allocation (TAA) approaches• Discretionary TAA: uses market timing skills to avoid or

hedge negative returns in down markets and enhance positive returns in up markets.

• Systematic TAA: uses signals to capture asset-class-level return anomalies that have been empirically demonstrated as producing abnormal returns.

• Behavioral biases in asset allocation• Loss aversion: mitigate by framing risk in terms of

shortfall probability or funding high-priority goals with low-risk assets.

• Illusion of control: mitigate by using the global market portfolio as a starting point and using a formal asset allocation process based on long-term return and risk forecasts, optimization constraints anchored around asset class weights in the global market portfolio, and strict policy ranges.

• Mental accounting: goal-based investing incorporates this bias directly into the asset allocation solution by aligning each goal with a discrete sub-portfolio.

• Recency or representativeness bias: mitigate by using a formal asset allocation policy with prespecifi ed allowable ranges.

• Framing bias: mitigate by presenting the possible asset allocation choices with multiple perspectives on the risk-reward tradeoff .

• Familiarity or availability bias: mitigate by using the global market portfolio as the starting point in asset allocation and carefully evaluating any potential deviations.

CURRENCY MANAGEMENT

• Domestic return on global asset (where exchange rate is expressed as SDC/FC)

(1 )(1 ) 1R R(1R R(1 1 )R1 )DCR RDCR RFC FX)(FC FX)(1 )FC FX1 )R R= +R R(1R R(1= +(1R R(1 + −1 )+ −1 )1 )R1 )+ −1 )R1 )1 )FC FX1 )+ −1 )FC FX1 )1 )R1 )FC FX1 )R1 )+ −1 )R1 )FC FX1 )R1 )

• Portfolio return in domestic currency terms

[ (1 )(1 ) w (1 )(1 )] 11 1[ (1 1[ (1 )1 11 ) 1 2) w1 2) w 2 21 )2 21 )R w[ (R w[ ( R R1 )R R1 )(1R R(1 R R)(R R)(1 )R R1 )1 )2 21 )R R1 )2 21 )DCR wDCR w FC FX1 )FC FX1 )(1FC FX(11 1FC FX1 11 )1 11 )FC FX1 )1 11 )R RFC FXR R FC FX2 2FC FX2 2)(2 2)(FC FX)(2 2)(1 )2 21 )FC FX1 )2 21 )1 )2 21 )R R1 )2 21 )FC FX1 )2 21 )R R1 )2 21 )[ (= ×[ ([ (1 1[ (= ×[ (1 1[ (R w= ×R w[ (R w[ (= ×[ (R w[ (1 )+ +1 )1 )1 11 )+ +1 )1 11 )R R+ +R R1 )R R1 )+ +1 )R R1 )(1R R(1+ +(1R R(11 )1 11 )R R1 )1 11 )+ +1 )1 11 )R R1 )1 11 )R RFC FXR R+ +R RFC FXR R1 )R R1 )FC FX1 )R R1 )+ +1 )R R1 )FC FX1 )R R1 )(1R R(1FC FX(1R R(1+ +(1R R(1FC FX(1R R(11 )1 11 )R R1 )1 11 )FC FX1 )1 11 )R R1 )1 11 )+ +1 )1 11 )R R1 )1 11 )FC FX1 )1 11 )R R1 )1 11 ) + ×) w+ ×) w1 2+ ×1 2) w1 2) w+ ×) w1 2) w + +R R+ +R R)(R R)(+ +)(R R)(1 )R R1 )+ +1 )R R1 )2 2R R2 2+ +2 2R R2 2)(2 2)(R R)(2 2)(+ +)(2 2)(R R)(2 2)(1 )2 21 )R R1 )2 21 )+ +1 )2 21 )R R1 )2 21 )R RFC FXR R+ +R RFC FXR R2 2R R2 2FC FX2 2R R2 2+ +2 2R R2 2FC FX2 2R R2 2)(2 2)(R R)(2 2)(FC FX)(2 2)(R R)(2 2)(+ +)(2 2)(R R)(2 2)(FC FX)(2 2)(R R)(2 2)(1 )2 21 )R R1 )2 21 )FC FX1 )2 21 )R R1 )2 21 )+ +1 )2 21 )R R1 )2 21 )FC FX1 )2 21 )R R1 )2 21 )] 1−] 1

• Variance of the domestic return

( ) ( ) ( ) [2 ( ) ( ) ( , )]2 2( )2 2( ) 2R R( )R R( )2 2R R2 2( )2 2( )R R( )2 2( ) R R( )R R( ) [2R R[2 ( )R R( ) R R( )R R( ) ( ,R R( ,RDC( )DC( ) FC FX( )FC FX( ) ( )FC FX( ) FC FX FC FX( )FC FX FC FX( ) ( )FC FX FC FX( ) ( ,FC FX FC FX( ,R RFC FX FC FXR R( )R R( )FC FX FC FX( )R R( ) ( ,R R( ,FC FX FC FX( ,R R( ,RFC FX FC FXRσ ≈( )σ ≈( )2 2σ ≈2 2( )2 2( )σ ≈( )2 2( )R Rσ ≈R R( )R R( )σ ≈( )R R( )2 2R R2 2σ ≈2 2R R2 2( )2 2( )R R( )2 2( )σ ≈( )2 2( )R R( )2 2( )( )DC( )σ ≈( )DC( )( )R R( )DC( )R R( )σ ≈( )R R( )DC( )R R( ) σ +( )σ +( )R Rσ +R R( )R R( )σ +( )R R( )2 2R R2 2σ +2 2R R2 2FC FXσ +FC FX( )FC FX( )σ +( )FC FX( ) σ +( )σ +( )2σ +2 R Rσ +R R( )R R( )σ +( )R R( )FC FXσ +FC FX( )FC FX( )σ +( )FC FX( )( )R R( )FC FX( )R R( )σ +( )R R( )FC FX( )R R( ) × σ × σ( )× σ × σ( )R R× σ × σR R( )R R( )× σ × σ( )R R( )FC FX FC FX× σ × σFC FX FC FX( )FC FX FC FX( )× σ × σ( )FC FX FC FX( ) R R× ρR RFC FX FC FX× ρFC FX FC FXR RFC FX FC FXR R× ρR RFC FX FC FXR R

• Factors favouring more currency hedging• Signifi cant short-term objectives, e.g. income/liquidity

requirements.• Global fi xed-income investments.• Markets with high currency or asset volatility.• High risk aversion.• Doubt about value of currency return potential.• Lower possibility of regret if the hedge is not profi table.• Low costs of hedging.

• Hedging strategies• Passive hedging: manager protects portfolio with full

hedging.• Discretionary hedging: manager reduces risk with

hedging but has discretion to make currency bets for return enhancement.

• Active currency management: manager seeks alpha by making currency bets.

• Currency overlay: currency management outsourced to specialists.

• Active currency management• Economic fundamentals: real exchange rate will

eventually converge to fair market values, with short-term increases in the domestic currency due to (1) increase in domestic currency’s real purchasing power, (2) higher domestic interest rates, (3) higher expected foreign infl ation, and (4) higher foreign risk premiums.

• Technical analysis: based on belief that historical currency patterns will repeat over time and those repetitions are predictable.

• Carry trade: borrow in lower interest rate (or forward premium) currencies and invest in higher interest rate (or forward discount) currencies, based on assumption that uncovered interest rate parity does not hold.

• Roll yield: positive when trading the forward rate bias (buying base currency at forward discount or selling base currency at forward premium); negative when trading against the forward rate bias (selling base currency at forward discount or buying base currency at forward premium).

F S1 (i )i )

1 (i )i )

F S1 (i )i )

1 (i )i )

FCF SFCF S/DF S/DF SC FF SC FF S C/DCC/DCC/FCi )FCi )Ai )Ai )ctuali )ctuali )360i )360i )

DCi )DCi )Ai )Ai )ctuali )ctuali )360i )360i )

PCF SPCF S/BF S/BF SC PF SC PF S C/BCPCi )PCi )Ai )Ai )ctuali )ctuali )360i )360i )

BCi )BCi )Ai )Ai )ctuali )ctuali )360i )360i )

= ×F S= ×F SC F= ×C FF SC FF S= ×F SC FF S C/= ×C/DC= ×DCC/DCC/= ×C/DCC/+ ×1 (+ ×1 (i )+ ×i )i )FCi )+ ×i )FCi )

+ ×1 (+ ×1 (i )+ ×i )i )DCi )+ ×i )DCi )

= ×F S= ×F SC P= ×C PF SC PF S= ×F SC PF S C/BC= ×C/BC+ ×1 (+ ×1 (i )+ ×i )i )PCi )+ ×i )PCi )

+ ×1 (+ ×1 (i )+ ×i )i )BCi )+ ×i )BCi )

• Volatility trade: long (short) straddle or strangle if volatility expected to increase (decrease).

• Currency management tools

CurrenCy ManageMent: an IntroduCtIon

r19.indd 108 12 August 2017 11:54 PM

108 © 2018 Wiley

options expire within that range. The “short” position comes from the fact that the out-of-the-money put and call in the seagull spread have been shorted.

Exotic Options

Exotic options are those that are creative in nature and cannot be categorized as being “plain.” Exotic strategies provide the lowest cost investment to achieve a specific outcome. These options are quite helpful for clients with significant unique circumstance constraints in the investment policy statement or who have specific income needs that cannot be produced by traditional financial securities.

One commonly used exotic option is a knock‐in option in which the option does not actually exist until a barrier spot rate is realized. Keep in mind that the barrier rate is not the same as the strike price. For example, consider a call option with an exercise rate of CAD1.15/USD and a barrier rate of CAD1.12/USD. If the spot rate is currently CAD1.10/USD, the option does not even exist until the spot rate rises to CAD1.12/USD. It works like a regular option, but if the barrier rate is never realized, it’s as if the option never existed. A knock-out option ceases to exist when the exchange rate touches the barrier. Think of a put option of the base currency with a barrier slightly below the strike price. If the base currency appreciates above the barrier, then the option no longer exists. These exotics are cheaper than regularly traded options and offer less protection.

Exhibit 5‐1: Select Currency Management Strategies

Forward Contracts Over‐/under‐hedging Profit from market view

Option Contracts OTM options Cheaper than ATM

Risk reversals Write options to earn premiums

Exotic Options Put/call spreads Write options to earn premiums

Seagull spreads Write options to earn premiums

Knock‐in/out features Reduced downside/upside exposure

Digital options Extreme payoff strategies

A digital option, which might also be called an “all‐or‐nothing” or binary option, earns a predetermined, fixed payout if the underlying reaches the strike price at any time during the life of the option. It does not have to cross the strike price, nor does it have to remain in‐the‐money until expiration to earn the payoff amount. This feature makes the option more appropriate for currency speculation than hedging.

• Minimum variance hedge ratio for a cross-hedge• Obtained from a regression of change in value of

underlying asset in domestic currency terms against change in value of the hedging security.

• Beta (slope coeff icient) of the regression equation is the optimal hedge ratio.

• Basis risk occurs due to imperfect correlation between currency price movement and hedging instrument.

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MARKET INDEXES

• Market cap weighted index: weight of each security is security’s capitalization value as a % of total index market cap.• Advantages: broad acceptance; requires less

rebalancing as index remains properly weighted aft er a price change.

• Disadvantages: overly infl uenced by overpriced securities; price movements overly concentrated in a few large companies.

• Price weighted index: weight of each security is proportional to its price (represents portfolio holding one share of each security).• Advantages: simple; long track record.• Disadvantages: not relevant to most strategies;

infl uenced by highest priced securities; must be rebalanced aft er stock splits.

• Equal weighted index: all securities are held in equal weights at rebalancing (represents portfolio holding an equal $ amount of each security).• Advantages: more diversifi ed away from highest-priced

companies.• Disadvantages: must be rebalanced frequently to

maintain weighting; price movements of smaller companies may be overrepresented.

• Fundamental weighted index: uses accounting data or other valuation metrics to weight the securities.• Advantages: better representation of economic

importance.• Disadvantages: rely on creator’s subjective judgment;

restrictive valuation screens may result in less diversifi cation; investability constraints of smaller companies; not transparent because of proprietary valuation weightings.

FIXED INCOME PORTFOLIO MANAGEMENTINTRODUCTION

• Fixed-income returns model• Expected return decomposition

≈+

∆−+

E(R) Yield income

Roll down return

+ E( P∆( P∆ rice due to yields and spreadreadr s)

E(Credit losses)

E(Currency gains and losses)

• Yield income equals current yield assuming no reinvestment income

Current yield =Annual coupon payment

Bond pricpricpr e

• Rolldown return: value change as bond approaches maturity (pull to par)

=Roll-down returneturnetur 1 0

0

B B−B B−1 0B B1 0

B

• Expected price change due to change in yield or spread

∆ = − × ∆ + × ∆E(% P∆ =% P∆ =) (∆ =) (∆ = D Y− ×D Y− × ∆ +D Y∆ +) (∆ +) (∆ + C 0× ∆C 0× ∆.5× ∆.5× ∆Y )MoD YMoD Y− ×D Y− ×Mo− ×D Y− ×dD YdD Y− ×D Y− ×d− ×D Y− × 2Y )2Y )

• Expected credit losses

• Eff ect of leverage on portfolio return

rPortfolio return

Portfolio equity

r (V V ) r V

V

V

V(r r )

PrPrI Er (I Er (V VI EV VB BV VB BV V ) rB B) r BVBV

EVEV

IBVBV

EVEVI B(rI B(r r )I Br )

=

= + −V V+ −V V ) r+ −) rB B+ −B BV VB BV V+ −V VB BV V ) rB B) r+ −) rB B) r

= +r= +rI= +IrIr= +rIr −

• Leverage with futures

Leverage =Notional value – Margin

MarginFutures

LIABILITY-DRIVEN STRATEGIES

• Immunization: reduces or eliminates the risks to liability funding arising from interest rate volatility over the planning horizon.

• Immunizing a single liability• Market value of assets is greater than or equal to PV of

liability• Macaulay duration of assets matches liability’s due

date• Convexity of asset portfolio is minimized.• Portfolio needs rebalancing as time passes.• Risk: non-parallel shift s in yield curve (risk is reduced

by minimizing convexity).• Cash fl ow matching for multiple liabilities

• Portfolio has cash fl ows matching the amount and timing of liabilities.

• Duration matching for multiple liabilities• Market value of assets is greater than or equal to the

market value of liabilities.• Asset basis point value (BPV) equals the liability BPV.• Dispersion of cash fl ows and convexity of assets are

greater than those of the liabilities.• Derivatives overlay

• Uses bond futures contracts to immunize liabilities.

Liability portfolioportfoliopor BPV – Asset portfolioportfoliopor BPV

Futures BPV

Futures BPV

N

BPV

CF

f

CTBPVCTBPV DCTDCT

CTCFCTCF DCTDCT

=

≈

• Contingent immunization• Active management if surplus (assets less liabilities) is

above a designated threshold.• If the surplus falls below threshold, revert to a pure

immunization strategy.• Use gains on actively managed funds to reduce cost of

meeting liabilities.• Horizon matching: cash fl ow matching for short-term

liabilities (< 5 years), duration matching for long-term liabilities.

• Interest rate swap overlay to reduce duration gap

NPLiability portfolio BPV – Asset portfolioportfoliopor BPV

Swap BPV100= ×= ×

Liability= ×Liability po

= ×po por

= ×por

• Risks when managing portfolio against a liability structure: model risk, spread risk, counterparty credit risk.

INDEX-BASED STRATEGIES

• Total return mandates• Pure indexing (full replication): match benchmark

weights and risk factors by owning all bonds in the index with the same weighting.

• Enhanced indexing: sampling approach to match primary risk factors; slight mismatch with benchmark weights to achieve a higher return compared to full replication.

• Active management: aggressive mismatches with benchmark weights and primary risk factors to achieve outperformance.

• Laddered bond portfolio• Maturities and par values spread evenly along the yield

curve.• Protection from yield curve shift s and twists by

balancing the position between cash fl ow reinvestment and market price volatility.

• Suited to stable, upwardly sloped yield curve environments.

• Higher convexity and liquidity.

YIELD CURVE STRATEGIES

• Stable yield curve strategies

• Buy and hold: choose parts of curve where yield changes will not aff ect return or purchase longer-duration/higher-yield securities.

• Rolldown: riding the yield curve when yield curve is upward-sloping.

• Selling convexity: sell lower-yielding higher-convexity bonds if expecting low interest rate volatility.

• Carry trade: buy longer-maturity, higher-yielding securities and fi nance them with shorter-maturity, lower-yielding securities.

• Changing yield curve strategies• Duration management: shorten (lengthen) duration if

expect yield increases (decreases).• Buying convexity: with falling yields, portfolios with

greater convexity will increase more in value than portfolios with less convexity; with rising yields, portfolios with greater convexity will decrease less.

• Bullet and barbell structures

Relative Outperformance Given Scenario

Yield Curve Scenarios Structure

Level change Parallel shift Barbell

Slope change FlatteningSteepening

BarbellBullet

Curvature change Less curvatureMore curvature

BulletBarbell

Volatility change Decreased volatilityincreased volatility

BulletBarbell

• Duration management methods• Buy (sell) bond futures to increase (decrease) duration.

= −# Contracts required

PVBP PVBP

PVBPT PBPT PBP PVT PPVBPT PBP

FBPFBP

where the subscripts on PVBP indicate the target value T, actual portfolio value P, and futures value F.

• Use leverage to increase durationAdditional PVBP

of bonds10,000Leveraged

Modifiedodifiedodif

= ×= ×VLeveVLeve D

New OldEquity Leveraged

Equity

D DNeD DNew OD Dw O

V VEquityV VEquity LeveV VLeveVEquityVEquity

= ×w O= ×w Old= ×ldD D= ×D Dw OD Dw O= ×w OD Dw O

V V+V V

• Use interest rate swaps: receive-fi xed, pay-fl oating swaps increase duration; pay-fi xed, receive-fl oating swaps reduce duration.

• Convexity management methods• Shift bonds in portfolio (diff icult with large portfolios).• Buying callable bonds and MBS (equivalent to selling

convexity).• Portfolio positioning strategy

• Parallel upward shift : bonds with forward implied yield change greater than forecast yield change will enjoy higher return as they roll down the yield curve (upward sloping).

• Parallel yield change of uncertain direction: increase convexity by using barbell strategy.

• Using butterfl ies: long the wings (barbell) and short the body (bullet) if fl attening curve, volatile interest rates, buying convexity or parallel yield curve increase; short the wings and long the body if steepening curve, stable interest rates or selling convexity.

• Using options: sell convexity bonds (30-year maturity) and purchase call options to outperform in both rising and falling rate scenarios.

CREDIT STRATEGIES

• Risk considerations• High yield bonds: credit risk (includes default risk and

loss severity).• Investment grade bonds: interest rate risk, credit

migration risk, spread risk.

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• Spread duration (measure of spread risk): percentage increase in bond price for a 1% decrease in spread.

• Credit spread measures• G-spread: bond’s yield to maturity less interpolated

yield of correct maturity benchmark bond.• I-spread: uses swap rates rather government bond

yields.• z-spread: spread added to each yield-curve point so

that PV of bond’s cash fl ows equals price.• Option-adjusted spread (OAS) for bonds with

embedded options: spread added to one-period forward rates that sets arbitrage-free value equal to price

• Excess return and expected excess return on credit securitiesXR ( )s t( )s t ( )s S( )s SD( )Ds SDs S( )s SDs S≈ ×( )≈ ×( )s t( )s t≈ ×s t( )s t − ∆( )− ∆( )s S( )s S×s S( )s S

EXR s SD ts SD ts S p L( )s t( )s t – ( ) (D t) (D t )≈ ×( )≈ ×( )s t( )s t≈ ×s t( )s t ∆ ×s S∆ ×s S − ×D t− ×D tD t) (D t− ×D t) (D t p L×p L

• Bottom-up approach to credit strategy (security selection): for two issuers with similar credit risks, purchase bond with greater spread to benchmark rate.

• Top-down approach to credit strategy: macro approach to determine and overweight sectors with better relative value.

• Managing liquidity risk• Cash• Liquid, non-benchmark bonds (higher incremental

return vs cash).• Credit default swaps index derivatives (more liquid

than credit markets).• ETFs (liquid but unpredictable price movements in

volatile markets).• Tail risk

• Assess tail risk by modelling unusual return patterns and using scenario analysis (historical and hypothetical).

• Manage tail risk using (1) diversifi cation strategies and (2) hedges using options and credit default swaps.

• Advantages of using structured fi nancial securities such as ABSs, MBS, CDOs and covered bonds• Higher returns vs other types of bonds.• Improved portfolio diversifi cation.• Diff erent exposures to investment grade and high yield

bonds.

EQUITY PORTFOLIO MANAGEMENT

• Approaches to managing equity portfolios• Passive management: try to match benchmark

performance.• Active management: seek to outperform benchmark

by buying outperforming stocks and selling underperforming stocks.

• Semiactive management (enhanced indexing): seek to outperform benchmark with limited tracking risk (highest information ratio).

• Approaches to constructing an indexed portfolio• Full replication: minimal tracking risk but high costs.• Stratifi ed sampling: retains basic characteristics of

index without costs associated with buying all the stocks.

• Optimization: seeks to match portfolio’s risk exposures (including covariances) to those of the index but can be misspecifi ed if historical risk relationships change over time.

• Value style investing: low P/E, contrarian, high yield.• Growth style investing: consistent growth, earnings

momentum.• Market-oriented (blend or core style) investors: market-

oriented with a value bias, market-oriented with a growth bias, growth at a reasonable price, style rotators.

• Market cap approach: small-cap, mid-cap, large-cap investors.

• Investment style analysis• Holdings-based: analyses characteristics of individual

security holdings.

• Returns-based: regressing portfolio returns on returns of a set of securities indices (betas are the portfolio’s proportional exposure to the particular style represented by index).

• Price ineff iciency on the short side• Restrictions to short selling.• Management’s tendency to deliberately overstate

profi ts.• Sell-side analysts issue fewer sell recommendations.• Sell-side analysts are reluctant to issue negative

opinions.• Sell disciplines

• Substitution: opportunity cost sell and deteriorating fundamentals sell.

• Rule-driven: valuation-level sell, down-from-cost sell, up-from-cost sell, target price sell.

• Semiactive equity strategies• Derivative-based semiactive equity strategies:

exposure to equity market through derivatives and enhanced return through non-equity investments, e.g. fi xed income.

• Stock-based enhanced indexing strategies: portfolio looks like benchmark except in those areas on which the manager explicitly wishes to bet on (within risk limits) to generate alpha.

• Information ratio (Grinold and Kahn)

IR IC Breadth≈

• Core-satellite portfolio: index and semiactive managers constitute core holding while active managers represent satellites.

• Total active return and risk• Manager’s true active return = Manager’s return –

Manager’s normal benchmark• Manager’s misfi t active return = Manager’s normal

benchmark – Investor’s benchmark• Total active riskManager’s totalactiveriserise r k

(Manager’s “tru“tru“t e” active rise rise r k) (Manager’s “misfit” active rise rise r k)2 2(M2 2(Manager2 2anager’s2 2’s “m2 2“mis2 2isfi2 2fit”2 2t” activ2 2active r2 2e ris2 2ise rise r2 2e rise r k)2 2k)

=

+2 2+2 2

• Information ratio as measure of manager’s risk adjusted performance

IRManager’s “truetruetr ” active returneturnetur

Manager’s “truetruetr ” active rise rise r k=

ALTERNATIVE INVESTMENTS

• Common features of alternative investments• Relative illiquidity• Diversifying potential• High due diligence costs• Diff icult performance appraisal• Informationally less eff icient markets

• Real estate• Direct investment: ownership in residences,

commercial real estate, agricultural land.• Indirect investment: real estate companies, REITs,

ETFs, mutual funds, CREFs, infrastructure funds.• Benchmarks: NCREIF (sample of commercial

properties), NAREIT.• Private equity

• Direct private equity investment is structured as convertible preferred stock: provides priority for dividends and liquidation claims over common shares; buyout or acquisition of the common equity will trigger conversion of convertible prefs into common shares.

• Indirect investment primarily through private equity funds (venture capital and buyout funds).

• Formative-stage investment: seed, start-up, fi rst stage capital.

• Expansion-stage investment: second stage, third stage, pre-IPO (mezzanine) capital.

• Buyout funds seek to add value by: restructuring operations and improving management; purchasing

companies at a discount to intrinsic value; capturing gains from debt structuring.

• Compensation to fund manager of private equity fund consists of management fee plus incentive fee (carried interest).

• Benchmarks: IRR, benchmarks for VC funds and buyout funds provided by Cambridge Associates and Thomson Venture Economics.

• Commodities• Direct investment: purchase of physical commodities

and commodity derivatives.• Indirect investment: companies specializing in

commodity production.• Energy and precious metals provide signifi cant

infl ation hedge.• Benchmarks: RJ/CRB, S&P GSCI, DJ-AIGCI and S&P CI

are indices based on futures prices.• Hedge funds

• Broad range of strategies• Compensation structure consists of management fee

plus incentive fee and may include high-water mark and hurdle rate.

• Diff erences in hedge fund indices due to: selection criteria, style classifi cation, weighting scheme, rebalancing scheme, investability, survivorship bias, backfi ll bias.

• Hedge fund performance appraisal measures• Sharpe ratio (inappropriate with illiquid holdings

and when returns are asymetrical/skewed or serially correlated).

• Sortino ratio

Sortino ratio = (Annualized rate of return - Minimum acceptable return)/Downside deviation

• Gain-to-loss ratioGain-to-loss ratio (Number months with positive reture reture r nseturnsetur / Number months

with negative returnseturnsetur ) (Average up-month rmonth rmont eturn /eturn /eturAverage down-month rmonth rmont eturn)eturn)etur

=) (×) (

• Distressed securities• Hedge fund structure or private equity fund structure.• Risks: event risk, market liquidity risk, market risk,

J-factor risk (past judicial precedents on bankrupt proceedings).

RISK MANAGEMENT

• Financial risks: market, credit, liquidity, asset price, exchange rate, interest rate.

• Non-fi nancial risks: operational, model, settlement (Herstaat), regulatory, legal/contract, tax, accounting, sovereign/political.

• VaR• Minimum amount we expect to lose in a given

reporting period with a given level of probability.• Analytical (variance-covariance) method: assumes

normality in asset return distributions.

Miniumum $ VaR V EP PV EP PV E[ ]( )[ ]( )V E[ ]V E R Z[ ]R Z( )R Z( )[ ]( )R Z( )P P[ ]P P( )P P( )[ ]( )P P( )V EP PV E[ ]V EP PV E( )R Z( )P P( )R Z( )[ ]( )R Z( )P P( )R Z( ) P[ ]P= ×V E= ×V EV EP PV E= ×V EP PV E[ ]− σ[ ]R Z[ ]R Z− σR Z[ ]R Zα[ ]α[ ][ ]− σ[ ]α[ ]− σ[ ]

• Historical method: VaR estimates based on historical realizations of past returns.

• Monte Carlo method: uses a probability distribution for each variable to randomly generate portfolio returns and to compute VaR based on the simulated returns.

• Limitations: can be diff icult to estimate; considers only downside risk; may be based on invalid distributional assumptions.

• Stress testing as a complement to VaR• Used to identify unusual conditions that would lead to

losses in excess of a threshold.• Can be based on stylized scenarios (historical or

hypothetical), stressing models, maximum loss optimization and worst-case scenario analysis.

• Credit risk• Current credit risk (jump-to-default): risk of ongoing or

pending default in the immediate future.• Potential credit risk: risk of possible default in the

future.

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• Credit VaR: minimum expected loss due to a negative credit event with a given probability during a period of time.

• Forwards: counterparty with positive value has credit risk.• Interest rate and equity swaps: potential credit risk is

highest during the middle of swap’s life.• Currency swap: potential credit risk is highest between

the middle and end of swap’s life.• Options: option buyers hold credit risk.

• Managing risk: apply eff ective risk governance model; use ERM system; use risk budgeting; reduce or transfer risk.

• Performance evaluation• Sharpe ratio• Risk-adjusted return on capital (RAROC)• Return over maximum drawdown (RoMAD)• Sortino ratio

RISK MANAGEMENT APPLICATION OF DERIVATIVESFORWARD AND FUTURES

• Managing equity market risk and changing equity asset allocation by beta adjustment

=β − β

β

NS

ffT Sβ −T Sβ − βT Sβ

f

• Creating synthetic stock index fund or converting equity into cash

Round(1 )*N

V r(1V r(1

fqf

T

= V r+V r

where V is the amount of money to be invested, V is the amount of money to be invested, V r is the risk-free rate, r is the risk-free rate, r T is the T is the Tinvestment horizon, q is the futures contract price multiplier, f is the stock index f is the stock index ffutures price, and *N f is an integer representing the number of long stock index futures contracts to convert a cash position to an equity position or the number of short stock index futures contracts to convert an existing equity position into a cash position.

• Changing bond asset allocation

=−

βNMDURMDURM MDURMDURM

MDURMDURM

B

fBfT SMT SMDURT SDURMDURMT SMDURM

f Bf BDURf BDUR ff Bfy

OPTIONS

• Option strategies

Strategy Construction using European options

Motivation

Covered call

Own underlying share and sell call on share.

Earn premium to cushion losses.

Protective put

Own underlying share and buy put on share.

Downside protection with upside potential.

Bull spread

Buy call at lower strike and sell call at higher strike (can use puts instead of calls)

Speculation on stock price increase in a range

Bear spread

Buy call at higher strike and sell call at lower strike (can use puts instead of calls)

Speculation on stock price decrease in a range

Butterfl y spread

Buy call at lower strike, buy call at higher strike, sell two calls at strike halfway between strikes of long calls (can use puts instead of calls)

Bet on low volatility

Collar Buy stock, buy put and sell call. (zero-cost collar if call and put premiums are the same)

Downside protection and with limited upside

Straddle Buy call and put with same strike

Bet on high volatility

Strap Buy two calls and one put with same strike

Bet on high volatility (stock price rise more likely)

Strip Buy one call and two puts with same strike

Bet on high volatility (stock price fall more likely)

Strangle Buy call and put, put has different exercise price

Bet on high volatility

Box spread

Bull call spread and bear put spread

Replicate risk-free return or make arbitrage profi t

• Interest rate options• Buy interest rate call option to protect a future

borrowing against interest rate increases.Interest rate call option payoff Nayoff Nayof otional principal max (Underlying rate at

expiration Exercise rate,0)Days in underlying rate

360

= ×f N= ×f Notiona= ×otional p= ×l pri= ×rincipal= ×ncipal

− ×n E− ×n Exe− ×xerc− ×rcis− ×ise r− ×e rat− ×ate,− ×e,0)− ×0)

• Buy interest rate put option to protect a future lending (or investing) transaction against interest rate declines.

Interest rate put option payoff Nayoff Nayof otional principal max (Exercise rate

Underlying rate at expiration,0)Days in underlying rate

360

= ×f N= ×f Notiona= ×otional p= ×l pri= ×rincipal= ×ncipal

− ×U− ×Unde− ×nderl− ×rlying− ×ying ra− ×rate− ×te at− ×at expi− ×expira− ×ratio− ×tion,− ×n,0)− ×0)

• Cap: series of interest rate call options.• Floor: series of interest rate put options.• Interest rate collar to protect a future borrowing: buy

interest rate cap and sell interest rate fl oor.• Option Greeks

• Option delta: positive for long call; negative for long put

= == = ∆∆

Option deltaChange in option price

Change in underlying stock price

c

S

• Option gamma: greatest for options that are at-the-money and close to expiration.money and close to expiration.

=Option gammaChange in option delta

Change in underlying stock price

SWAPS

• Duration of interest rate swapsDuration [Pay fixedy fixedy f and receive floating interesnteresnter t rate swap]wap]wa Duration(Floating-rate bond)

Duration (Fixed-rate bond)=

−

Duration [pay floatiny floatiny f g and receive fixed interesnteresnter t rate swap]wap]wa Duration (Fixed-rate bond)Duration (Floating-rate bond)

=−

• Use pay fl oating and receive fi xed interest rate swap to increase duration of bond portfolio.

• Use pay fi xed and receive fl oating interest rate swap to reduce duration of bond portfolio.

• Duration management using an interest rate swap

= −

NP VMDURMDURM MDURMDURM

MDURMDURMPVPVT PMT PMDURT PDURMDURMT PMDURM

S

• Uses of currency swap• Convert loan in one currency into a loan in another

currency.• Convert foreign cash receipts into domestic currency.

• Uses of equity swap• Diversify a concentrated portfolio.• Achieve international diversifi cation.• Change asset allocation between stocks and bonds.

• Swaptions• Payer swaption: holder has right to enter interest rate

swap as fi xed-rate payer (in-the-money when interest rates go up).

• Receiver swaption: holder has right to enter interest rate as fi xed-rate receiver (in-the-money when interest rates go down).

TRADING, MONITORING AND REBALANCINGEXECUTION OF PORTFOLIO DECISIONS

• Eff ective spread

Effectivffectivff e spread 2 Execution price(Bid pricpricpr e Ask pricpricpr e)

2= ×2 E= ×2 E − e A+e A2 E2 E

2 E

2 E2 E2 E2 E2 E2 E2 E

2 E

2 E2 E

2 E

• Market quality• Liquidity: resilience, quote depth, narrow bid-ask

spreads.• Transparency: pre-trade and post-trade• Assured completion: trade completion is guaranteed.

• Execution costs

• Explicit: commissions, exchange fees, duties and taxes.• Implicit: bid-ask spread, market impact, missed trade

opportunity cost, delay (or slippage) costs.• Volume-weighted average price (VWAP)

• Advantages: easy to compute/understand; useful for comparing smaller trades in nontrending markets.

• Disadvantages: Does not include costs of delayed/cancelled trades; misleading for large trades; can be gamed by delaying trades; not sensitive to trade size or market conditions.

• Implementation shortfall (IS)• IS is the return diff erence between the return on a

notional portfolio and the actual portfolio’s return, expressed as a % of the investment in the notional portfolio.

• Explicit costs (for purchases)

=Expicit costsCommissions, taxes, and feesfeesf

S P×S P×H HS PH HS P×S P×H H×S P×

• Realized profi t/loss (for purchases)

= ( )× −( )× −RPL

S P× −S P× −( )S P( )× −( )× −S P× −( )× −( )P( )

S P×S P×E R( )E R( )× −( )× −E R× −( )× −( )S P( )E R( )S P( )× −( )× −S P× −( )× −E R× −( )× −S P× −( )× −( )P( )E R( )P( )

H HS PH HS P×S P×H H×S P×

• Delay or slippage costs (for purchases)

=Delay( )× −( )× −( )S P× −S P× −( )S P( )× −( )× −S P× −( )× −( )P( )

S P×S P×R H( )R H( )× −( )× −R H× −( )× −( )S P( )R H( )S P( )× −( )× −S P× −( )× −R H× −( )× −S P× −( )× −( )P( )R H( )P( )

H HS PH HS P×S P×H H×S P×

• Unrealized profi t/loss or missed trade opportunity cost (for purchases)

= − ×( )− ×( )− × ( )UPLUPLUP

( )S S( )− ×( )− ×S S− ×( )− × ( )P P( )−( )−P P−( )−S P×S P×

H L− ×H L− ×( )H L( )− ×( )− ×H L− ×( )− × ( )H L( )( )S S( )H L( )S S( )− ×( )− ×S S− ×( )− ×H L− ×( )− ×S S− ×( )− × ( )P P( )H L( )P P( )H( )H( )( )P P( )H( )P P( )

H HS PH HS P×S P×H H×S P×

• IS is the sum of explicit costs, RPL, delay costs and UPL (for sales, reverse the prices used in the numerator).

• Advantages: relates execution costs to value of investment idea; recognizes tradeoff between immediacy and price; attribution of execution costs; can be used to optimize turnover and improve performance; cannot be gamed.

• Disadvantages: requires extensive data collection; unfamiliar framework.

• Types of traderstrader trader t type Motivation Preference Holding Period

Information Unassimilated information Time Minutes/hours

Value Valuation errors Price Days/weeks

Liquidity Divest securities, invest cash, buy things

Time Minutes/hours

Passive Rebalance (to index) Price Days/weeks

Dealers/Day traders Accommodate other traders Indifferent Minutes/hours

• Trading tactics

Focus Purpose costs Advantages Disadvantages

Liquidity at any cost

Immediately execute large blocks

Upsetting supply/demand

Guaranteed execution

Information leakage and market impact possible

Need trustworthy agent

Low level advertising on large trades; possible hazardous situation

Higher commissions; information leakage

Price improvement due to ability to wait

Lose trade control

Costs are not important

Certain execution

Spread; potential price impact

Market‐ determined price

Lose trade control

Advertise to draw liquidity

Large trades without information advantage

High (organizational and operational) cost

Market‐ determined price

Possible front running

Low cost whatever the liquidity

Indifferent to timing; non‐ informational trades

High search and monitoring costs; low commission

Favorable price possible

Execution uncertainty; possible movement away from price point results in “chasing” the market with limit orders

• Algorithmic trading• Simple logical participation strategies: VWAP strategy

aims to match expected volume for the stock; TWAP strategy breaks order up for exposure at various time periods during the day; percentage of volume strategy makes trades as some % of overall market volume until completed.

• Implementation shortfall (arrival price) strategies:

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minimize execution costs by front-loading executions into the early part of the trading day.

• Opportunistic strategies: involve passive holdings and opportunistically seizing liquidity.

• Specialized strategies: smart routing, “hunter” strategies and benchmark-based algorithms.

MONITORING AND REBALANCING

• Rebalancing disciplines• Calendar rebalancing: simple but unrelated to market

behavior.• Percentage-of-portfolio (or interval) rebalancing:

provides tighter control and triggers rebalancing related to market performance.

• Calendar and percentage-of-portfolio: rebalancing occurs at calendar intervals only if corridors have been exceeded (lower monitoring and rebalancing costs).

• Equal probability rebalancing: corridors are based on a common multiple of asset class standard deviation; does not address transaction costs or correlations.

• Tactical rebalancing: less frequent rebalancing during trending markets; more frequent rebalancing during reversals.

• Optimal corridor width of asset class

Factor EffectHigher transaction costs Wider corridorHigher risk tolerance Wider corridorHigher correlation with rest of portfolio

Wider corridor

Higher volatility of asset class Narrower corridorHigher volatility of remaining portfolio

Narrower corridor

• Rebalancing strategiesconstant Mix buy‐and‐hold cPPI

Market conditionsUP—Momentums Underperform Outperform Outperform

FLAT—Reversals Outperform Neutral Underperform

DOWN — Momentums Underperform Outperform Outperform

ImplicationsPayoff curve Concave Linear Convex

Portfolio insurance Selling insurance None Buying insurance

Multiplier 0 < m < 1 m = 1 m > 1

PERFORMANCE EVALUATION

• Characteristics of a valid benchmark: unambiguous, investable, measurable, appropriate, refl ective of current investment opinions, specifi ed in advance, acknowledged.

• Types of benchmarks: absolute return, manager universe, broad market index, investment style index, factor-model-based, return-based, custom security-based.

• High quality benchmark: low systematic bias; minimal tracking error; similar risk exposure to portfolio; signifi cant overlap of holdings with portfolio; low turnover; positive active positions.

• Macro attribution (fund sponsor level)• Net contributions• Risk-free rate• Asset categories• Benchmarks• Investment managers• Allocation eff ects

• Micro attribution (investment manager level)• Explains three components of value-added return

(diff erence between the returns on the portfolio and the benchmark).

[( ) ( )] [ ( )]1 1 1

r r r w r w[(r w[( w r) (w r) ( r w)]r w)] [ (r w[ (r rv Pr rv Pr r B Pr wB Pr wi

S

Pi Biw rBiw rPiw rPiw r Bir wBir w1 1i1 1i1 1i1 1

S

Bi[ (Bi[ ( Pir rPir rBir rBir ri

S

∑ ∑[(∑ ∑[( ) (∑ ∑) ( )]∑ ∑)]r w∑ ∑r w[(r w[(∑ ∑[(r w[( w r∑ ∑w r) (w r) (∑ ∑) (w r) ( r w∑ ∑r w)]r w)]∑ ∑)]r w)]B P∑ ∑B P[(B P[(∑ ∑[(B P[(r wB Pr w∑ ∑r wB Pr w[(r w[(B P[(r w[(∑ ∑[(r w[(B P[(r w[( i B∑ ∑i Bw ri Bw r∑ ∑w ri Bw ri B∑ ∑i B) (i B) (∑ ∑) (i B) (w ri Bw r∑ ∑w ri Bw r) (w r) (i B) (w r) (∑ ∑) (w r) (i B) (w r) ( i B∑ ∑i Br wi Br w∑ ∑r wi Br w ∑r w∑r w= − =r r= − =r r r w= − =r wv P= − =v Pr rv Pr r= − =r rv Pr r r wB Pr w= − =r wB Pr w∑ ∑− ×∑ ∑) (∑ ∑) (− ×) (∑ ∑) (w r∑ ∑w r− ×w r∑ ∑w r) (w r) (∑ ∑) (w r) (− ×) (w r) (∑ ∑) (w r) (i B∑ ∑i B− ×i B∑ ∑i Bw ri Bw r∑ ∑w ri Bw r− ×w ri Bw r∑ ∑w ri Bw rw ri Bw r∑ ∑w ri Bw r− ×w ri Bw r∑ ∑w ri Bw r) (w r) (i B) (w r) (∑ ∑) (w r) (i B) (w r) (− ×) (w r) (i B) (w r) (∑ ∑) (w r) (i B) (w r) (∑ ∑− +∑ ∑)]∑ ∑)]− +)]∑ ∑)]r w∑ ∑r w− +r w∑ ∑r w)]r w)]∑ ∑)]r w)]− +)]r w)]∑ ∑)]r w)]i B∑ ∑i B− +i B∑ ∑i Br wi Br w∑ ∑r wi Br w− +r wi Br w∑ ∑r wi Br w − ×) (− ×) (w r− ×w r) (w r) (− ×) (w r) (w rBiw r− ×w rBiw r − +)]− +)]r w− +r w)]r w)]− +)]r w)]r wBir w− +r wBir w × −[ (× −[ (r r× −r rr rPir r× −r rPir r1 1= =1 1= =1 1= =1 11 1i1 1= =1 1i1 1 =

• First term is pure sector allocation eff ect.• Second term is allocation/selection interaction eff ect.• Third term is stock selection eff ect.

• Fixed income micro attribution• Decomposes total return of a fi xed-income portfolio

into two groups of components: eff ect of external interest environment (out of manager’s control) and contribution of the investment manager.

• Eff ect of external interest environment: return on the default-free benchmark, assuming no change in forward rates; return due to changes in forward rates.

• Contribution of the investment manager: return from interest rate management; return from sector/

quality management; return from selection of specifi c securities; return from trading activities.

• Risk-adjusted performance measures• Ex post alpha

( )R r ( )R r( )t fR rt fR r t Mt ft Mt f t f( )t f( )( )R r( )t f( )R r( )t Mt ft M t t( )t t( )t ft tt f( )t f( )t t( )t f( )− =R r− =R rt f− =t fR rt fR r− =R rt fR r t M− =t Mt ft Mt f− =t ft Mt f α +t Mα +t Mβ −( )β −( )( )R r( )β −( )R r( )t Mβ −t M( )t M( )β −( )t M( )( )R r( )t M( )R r( )β −( )R r( )t M( )R r( )t fβ −t f( )t f( )β −( )t f( )( )R r( )t f( )R r( )β −( )R r( )t f( )R r( )t Mt ft Mβ −t Mt ft M( )t M( )t f( )t M( )β −( )t M( )t f( )t M( )( )R r( )t M( )R r( )t f( )R r( )t M( )R r( )β −( )R r( )t M( )R r( )t f( )R r( )t M( )R r( )+ εt t+ εt t

• Treynor measure

TR rR r

ATATA fR rA fR r

A�=

R r−R r

β

• Sharpe ratio

SharpeSharpeShar ratioR rR r

AA fR rA fR r

A�=R r−R r

σ

• M2

2M rM r2M r2 R rR rf

A fR rA fR r

AM��= +M r= +M rf= +fM rfM r= +M rfM r

R r−R r

σ

σ

• Ex post alpha and Treynor measure provide the same conclusion on manager performance as they are based on systematic risk.

• Sharpe ratio and M2 provide the same conclusion on manager performance as they are based on total risk.

• Information ratio

IRR R

AA BR RA BR R

A B�= R R−R R

σA B−A B

• Manager continuation policies• Type I error: keeping (or hiring) managers who do not

have investment skills.• Type II error: fi ring (or not hiring) managers who do

have investment skills.

GLOBAL INVESTMENT PERFORMANCE STANDARDS

• Focus on required disclosures, and presentation and reporting requirements and recommendations of GIPS.

• Be able to identify and correct errors in a performance presentation that claims to be GIPS compliant.

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