Session 101 PD, Use of Efficient Frontiers in Strategic Asset Allocation Analysis Moderator: Ken Griffin, ASA, MAAA

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Session 101 PD, Use of Efficient Frontiers in Strategic Asset Allocation

Analysis

Moderator:

Ken Griffin, ASA, MAAA

Presenters:

Ken Griffin, ASA, MAAA

Sean Kane, CFA

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101PD - Use of Efficient

Frontiers in Strategic

Asset Allocation Analysis

Presented to

October 28, 2014

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141028 SOA Use of EF in SAA.ppt

TODAY’S DISCUSSION



Traditional Mean-Variance EFs and Concepts



EF Modeling Input



EF Modeling Challenges



Practical Limitations and “Taming the Optimizer”

Efficient frontier (EF) modeling is an intuitive, convenient way to capture

the incremental trade-offs between object combinations in the two

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TRADITIONAL MEAN-VARIANCE EFs

EFs are classically used to in a mean-variance context to create optimal portfolios

of assets as defined by the highest level of portfolio return at a given level of

standard deviation of portfolio return.



We can combine assets

together in optimal

portfolios using our

assumptions for risk, return,

and correlation.



The Efficient Frontier

represents all combinations

of assets that maximize

return for a given the level of

risk (optimal).

• Portfolio combinations

below or to the right of the

efficient frontier are

dominated by more

efficient portfolios along

the frontier.

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4

EXPANDING/CONTRACTING THE FRONTIER



Diversification with new assets can expand the efficient frontier and

add value in one of two fashions:

1. Generating incremental return in the portfolio at the same level of

risk.

2. Reducing portfolio risk without sacrificing return.

Risk % (Standard Deviation of Annual Returns)

A nn ua liz ed Rate of Retu rn

Return Gain

Illustrative

Return Gain

from New Asset Classes

Frontier with existing assets With new asset classes Current allocation With new asset classes

Risk % (Standard Deviation of Annual Returns)

A nn ua liz ed Rate of Retu rn

Risk

Reduc-tion

Illustrative

Risk Reduction

from New Asset Classes

Frontier with existing assets With new asset classes Current allocation With new asset classes

Source: Cardinal Investment Advisors Analysis

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5

HARNESSING DIVERSIFICATION VIA EFs

EFs get to the heart of Modern Portfolio theory and the notion of

improving efficiency via diversification.



The inverse correlation

of the assets creates

higher returns at lower

risk than a simple

linear combination of

the assets.



Adding new, potential

asset classes to the

mix will only improve

those efficiencies as

long as the correlations

are less than 1.0.

Source: Cardinal Investment Advisors, ProVal

Current Target 0% 2% 4% 6% 8% 10% 12% 14% 0% 5% 10% 15% 20% 25% 30% 35% 40% Annualiz ed R et urn (%)

Risk (Annual Standard Deviation - %)

Risk/Return of Efficient Portfolio Combinations

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6

REAL WORLD OF INSURANCE EFs

Source: State Regulations, Cardinal Investment Advisors analysis

LOCATION, LOCATION, LOCATION!

The opportunity set of objects one can embed in an EF depends on the

limits imposed by state, federal, or other regulation.

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A-Policy Target 0% 2% 4% 6% 8% 10% 12% 0% 5% 10% 15% 20% 25% 30% E x p e c te d R e tu rn ( A ft e r-T a x)

Risk (After-Tax Standard Deviation)

Unconstrained

Unconstrained with Taxes

50% Investment Leverage 6% Basket Clause

INCLUDING REALISTIC FACTORS IN EFs

85% Cash

11% TIPS

2% Private Equity

25% HY Bank Loans

75% Private Equity

30% Trade Finance

14% Small Cap

16% International

14% Private RE

3% Commodities

23% Private Equity

Source: Cardinal Investment Advisors

Actual implementable EFs can depart dramatically from conceptual

ones. Mundane factors such as taxes leverage constraints/risk controls

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EFs are frequently used to capture other concepts of risk vs. return, or

cost vs. benefit tradeoffs. Excess return vs. a liability is one.



The “risk-equivalent” point

on the frontier in this

context is a very different

allocation than the-risk

equivalent from the

mean-variance EF

Long Credit 35% Non US Developed 21% US Small 17% Low Volatility Equity 12% Private Real Estate 6% Private Equity 4% PIMCO 4% Commodities 1% Total 100% Compound Return 7.7% Volatility 11.4%

Source: Cardinal Investment Advisors, ProVal

Current Allocation -3% -2% -1% 0% 1% 2% 3% 4% 5% 0% 5% 10% 15% 20% 25% 30% 35% Ex c es s R et urn (Ov er PBO Liabilit y R et urn -%)

Tracking Error (Std Dev. of Excess Return - %)

Liability Tracking (Excess Return) Frontier

Unconstrained Frontier Long Credit 43% Non US Devloped 28% Private Equity 12% US Small 13% PIMCO 4% Total 100% Excess Return 1.4%

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EF analysis is used to determine the appropriate tradeoff of investment

risk as manifest in retirement Income Replacement Ratios in the

defined contribution/401k plan space.

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INPUTS: ARITHMETIC VS. GEOMETRIC RETURNS

An age-old debate… Arithmetic means are biased high; Geometric means

are biased low. Converting between the two should be thoughtful.



Maclaurin series expansion



Taylor series expansion

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INPUTS: HISTORIC VS. FORWARD LOOKING RETURNS

Intuitive return forecasts based on drivers of value should be favored over

historic returns.

-10% -5% 0% 5% 10% 15% 20% 25% Q 4 1 94 5 Q 4 1 9 4 7 Q 4 1 9 4 9 Q 4 1 9 5 1 Q 4 1 95 3 Q 4 1 95 5 Q 4 1 95 7 Q 4 1 95 9 Q 4 1 96 1 Q 4 1 96 3 Q 4 1 96 5 Q 4 1 96 7 Q 4 1 96 9 Q 4 1 97 1 Q 4 1 97 3 Q 4 1 97 5 Q 4 1 97 7 Q 4 1 97 9 Q 4 1 98 1 Q 4 1 98 3 Q 4 1 98 5 Q 4 1 98 7 Q 4 1 98 9 Q 4 1 99 1 Q 4 1 99 3 Q 4 1 99 5 Q 4 1 99 7 Q 4 1 99 9 Q 4 2 00 1 Q 4 2 00 3 Q 4 2 00 5 Q 4 2 00 7 Q 4 2 00 9 Q 4 2 01 1 Q 4 2 01 3 A nn ua liz ed Retu rn Period Ending…

Using Historic Averages to Forecast Future Returns

(10 Yr. Trailing S&P 500 vs. Future 10 Years)

Forecast

Actual

RSQ = 0.04

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INPUTS: BASIC EQUITY RETURN FORECAST APPROACH

Building blocks can be used to capture both the current environment and

typical mean reverting activity in asset return forecasts.

Current Income Component Growth Component Valuation Component

+

=

Large US Equity Projection Current Dividend Yield Share Repurchase Yield Long-Term Expected Inflation Future Dividend Growth Current vs. Long-Term P/E Multiple Speed of Mean Reversion Market Implied Inflation Expert Consensus Forecasts Real GDP growth rate in US Expert Consensus Forecasts GDP Component Method Trailing Historic Averages Productivity Growth in the US Labor Force Growth in the US

+

~

1.90%

+

.80% 2.25%

+

2.60%

~

2.00%

~

2.20% 2.70% 2.70% 4.95% -0.25% 7.40% 0.90% 2.00% 2.90%

~

2.65%

~

2.60% -0.25%

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INPUTS: LOW YIELD ENVIRONMENT NEEDS TO BE ADDRESSED

Long-term EFs should not be predicated on untenable short-term assumptions.



Cardinal’s fixed

income asset class

return projections are

based on current

market yields as an

unbiased consensus

indicator of

anticipated bond

pricing. However…

R² = 0.8156

0 2 4 6 8 10 12 14 16 18 0% 2% 4% 6% 8% 10% 12% 14% 16% 18% 20% Y iel d t o W o rst ( % )

Subsequent 10-Year Return

Barclays Capital Agg and Long Credit

Yield to Worst and Subsequent 10-Year Returns

(Since Inception 1973 - 2013)

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INPUTS: SECULAR TREND IN YIELDS OVER LONG-TERM

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0

Y

ield

(%

)

Term (Years)

US Treasury Yield Curve

Ave Last 10 Years

Ave. Last 30 Years

6/30/2013

6/30/2014

30 10 5 2 1 .5

Long-term

downward

trend

Recent

stabilization

in rates

Forecasting bond returns may require a two-stage or reversion approach.

Core Bond Return Projection

2.60%

Domestic Core Fixed Income (Two-Stage)

Aggregate Reinvestment Yield Current Aggregate YTM 2.30% 3.30%

~

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INPUTS: RISK REGIME CHANGES

Time series can experience regime changes or persistent shifts. If these can be

linked to underlying drivers that are persistent, the future may be very different

and adjustment should be made.

Intermediate Bonds

Volatility Regime Change

Barclays Aggregate St Dev

1970 to

2013 6.96

1980 to

1990 8.93

1990 to

2013 4.99

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INPUTS: ALTERNATIVE ASSET CLASSES UNDERSTATE RISK

Illiquid, private asset classes suffer from pricing biases that require “unsmoothing.”

-30.00 -25.00 -20.00 -15.00 -10.00 -5.00 0.00 5.00 10.00 15.00 Q 1 1 9 8 2 Q 4 1 9 8 2 Q 3 1 9 8 3 Q 2 1 9 8 4 Q 1 1 9 8 5 Q 4 1 9 8 5 Q 3 1 9 8 6 Q 2 1 9 8 7 Q 1 1 9 8 8 Q 4 1 9 8 8 Q 3 1 9 8 9 Q 2 1 9 9 0 Q 1 1 9 9 1 Q 4 1 9 9 1 Q 3 1 9 9 2 Q 2 1 9 9 3 Q 1 1 9 9 4 Q 4 1 9 9 4 Q 3 1 9 9 5 Q 2 1 9 9 6 Q 1 1 9 9 7 Q 4 1 9 9 7 Q 3 1 9 9 8 Q 2 1 9 9 9 Q 1 2 0 0 0 Q 4 2 0 0 0 Q 3 2 0 0 1 Q 2 2 0 0 2 Q 1 2 0 0 3 Q 4 2 0 0 3 Q 3 2 0 0 4 Q 2 2 0 0 5 Q 1 2 0 0 6 Q 4 2 0 0 6 Q 3 2 0 0 7 Q 2 2 0 0 8 Q 1 2 0 0 9 Q 4 2 0 0 9 Q 3 2 0 1 0 Q 2 2 0 1 1 Q 1 2 0 1 2 Q 4 2 0 1 2 Retu rn (%)

Reported Real Estate Returns vs. Unsmoothed

Unsmoothed Reported

St Dev Return

Reported

2.2 2.0

Unsmoothed 4.5 1.9

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INPUTS: CORRELATIONS ARE NOT ALWAYS STABLE



EFs require a

covariance structure.



Using a single point

static value can hide

the impact of real

world convergences.



Shock testing is

important.

Correlations often converge during periods of market stress.

5

Historic Correlations to Investment Allocations

-1.00 -0.80 -0.60 -0.40 -0.20 0.00 0.20 0.40 0.60 0.80 1.00 3 -Ye a r Cen te red Corr e la tio n Coe ffic ie nt

Asset

Rolling

Asset Ave.

Bull Mkt.

Bear Mkt.

Convergence

High Convergence

3 4 2 1

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ACKNOWLEDGING THE COST OF CONSTRAINTS

Comparative Frontiers - Typical Assets vs. Impairment Sensitive

0 1 2 3 4 5 6 7 8 9 10 0 2 4 6 8 10 12 14 16 18 20

Risk (Annual Standard Deviation) - %

Re

turn

(An

nu

al

iz

ed

)

-

%

Impairment Sensitive Frontier

Typical Pension Asset Frontier

Imprudent levels of

asset concentration

Cost of constraints

“Artificial” constraints can be very costly and should be quantified.



Any constraint will,

by definition, reduce

and shift the EF.



Operating constraints

related to

accounting, audit

complexity etc. can

be quantified and a

business case made.

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OPTIMIZERS ARE FICKLE – TESTING SENSITIVITY

Two, apparently, near-identical EFs appear below.

0.0% 1.0% 2.0% 3.0% 4.0% 5.0% 6.0% 7.0% 8.0% 9.0% 10.0% 0% 5% 10% 15% 20% 25% 30%

Nom

ina

l

Ret

u

rn

Standard Deviation of Nominal Return

Identical Frontiers?

Efficient Frontier #1

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MINOR INPUT CHANGES CAN BE SIGNIFICANT

Efficient Frontier #1

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

Efficient Frontier #2

Asset class return/risk assumptions only flexed +/- <20 bps. Can result in +/- 10%

allocation changes.

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DETERMINING WHAT IS BINDING

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% Commodities Private Equity FOF Hedge FOF

Non US Emerging Equity Non US Developed Equity US Small Cap Equity US Large Cap Equity Private Real Estate LC Emerging Mkts Debt High Yield Bonds Long Gov/Credit TIPS Core Bonds Cash 4 1 2 5

High Yield Bonds’ current yields are sufficiently high to maintain a

presence throughout most of the frontier.

TIPS enter immediately due low correlations. The 10% max binds

initially with allocations declining as correlation is offset by low returns.

Real estate is prominent along the frontier as a high income diversifier.

3

Domestic and non-US equity’s low correlation to core bonds

pulls the asset into the frontier almost immediately.

Commodities’ high expected returns drive it to the max limit as

it quickly dominates hedge funds, REITs etc.

The incremental yield pickup of Long Gov/Credit drive a max

allocation early in the frontier.

6 1 2 3 4 5 6

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ADDING AN OVERLAY

Cash

Domestic Bonds Long Government

Long Credit

TIPS

High Yield

Hedge Funds _{Private Real Estate}

REITs (Public Real Estate) US Large Cap

Equity US Mid Cap Equity

US Small Cap Equity

Non-US Developed Equity

Commodities

All Private Equity Non-US Emerging _Equity

Non-US Emerging Bonds Low Volatility Equities 0% 2% 4% 6% 8% 10% 12% 14% 0% 5% 10% 15% 20% 25% 30% 35% 40% 45% A nn ua liz ed Retu rn (%)

Risk (Annual Standard Deviation of Returns - %)

Projected Asset Class Risk/Return

Market Return

Active Mgmt Return

Alpha

TE

Cash

0.1%

0.2%

Domestic Bonds

0.2%

0.5%

Long Government

0.1%

0.5%

Long Credit

0.3%

0.5%

TIPS

-

-High Yield

0.8%

3.5%

Hedge Funds

-

-Private Real Estate

-

-REITs (Public Real Estate)

0.5%

2.0%

US Large Cap Equity

0.5%

2.5%

US Large Cap (Passive)

-

-US Mid Cap Equity

0.8%

3.8%

US Small Cap Equity

1.0%

5.0%

Non-US Developed Equity

1.5%

5.0%

Commodities

-

-All Private Equity

-

-Emerging Market Equity

1.5%

5.0%

Emerging Market Bonds

0.4%

1.5%

Low Volatility Equities

-

-Active Management

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OTHER CONSIDERATIONS



Non-normality



Fat-tails (leptokurtosis)



Correlation Convergences



Shock-testing



Historic Scenarios/Crisis

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CONCLUSIONS



EFs can be simple / intuitive



EFs can capture trade-offs



EFs are conducive to what-if

analysis



EFs can be very sensitive



EFs are classic GIGO



EFs include some simplifying

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One Financial Plaza Hartford, CT 06103 | www.conning.com

SOA Annual Meeting

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Simulation Modeling Approach

Current Business State



Current Financials



Business Plans



Actuarial Models



Input from ERM

Company

Data Input

Company Model - Projects Future States of the Company

Start of

Simulation

Q 1

Q 2

Q3

Q 4 …

Scenario 1 Scenario 2 Scenario 3 Scenario 4 Scenario n

...

High Performance Business Computing

Whole-

Company

Outputs

Accounting

Regulatory

Financials

Tax

Economic

Scenario

Generator (ESG)

Models Future States

of the Economy &

Financial Markets

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Economic Value (EV) Efficient Frontier

Integrated ALM



Identify investment strategy

to meet specific risk/reward

profile



Maximize economic value -

not just investment returns

- for various levels of risk



Provides a platform for

aggregating enterprise

risks

28

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Economic Value (EV) Efficient Frontier

The efficient frontier does not reflect the deduction of estimated investment management and transaction fees that the client may incur. * All dividends and other earnings are assumed to be reinvested semi-annually. Source: Conning analysis

29

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Economic Value (EV) Efficient Frontier

The efficient frontier does not reflects the deduction of estimated investment management and transaction fees that the client may incur. All dividends and other earnings are assumed to be reinvested semi-annually.

Source: Conning Analysis

30

Current Benchmark A B C D E F G H I J K

Cash and Gov't 5% 4% 36% 16% 8% 6% 1% - - - -Corporate 65% 40% 21% 40% 32% 31% 54% 52% 41% 35% 39% 50% 59% Structured 16% 29% 43% 43% 44% 33% 14% 17% 26% 32% 28% 20% 19% CML/Private Placement 11% 20% - 1% 15% 29% 30% 30% 30% 30% 30% 26% 15% High Yield 3% 3% - - - -US Equity - 1% - - - 1% 4% Alternative Assets - 3% - - 1% 1% 1% 1% 3% 3% 3% 3% 3% Total 100% 100% 100% 100% 100% 100% 100% 100% 100% 100% 100% 100% 100% Overall Duration 7.1 8.1 6.7 6.8 6.5 6.6 6.8 7.4 7.7 8.5 9.7 11.0 12.2 Economic Value ($MM) 1,617 1,654 1,577 1,590 1,603 1,616 1,629 1,642 1,656 1,669 1,681 1,694 1,709 Risk ($MM) 154 167 122 122 124 128 136 146 158 171 185 204 228

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Economic Value (EV) Duration Targeting

31

Modeled Assets and Liabilities

(Amount in $ millions)

Immunized

Book Market Effective Effective

Value Value Duration Duration

Assets :

US Corp 6,000 6,000 9.0 8.4 US Structured Securities 3,000 3,000 4.5 4.5 Other Invested Assets 1,000 1,000 3.0 3.0

Total Invested Assets 10,000 10,000 7.1 6.7

Liabilities : Liabilities 8,000 8,000 8.2 8.2 Other 500 500 2.0 2.0 Total Liabilities 8,500 8,500 7.9 7.9 Surplus : Total Surplus 1,500 1,500 2.4 0.0 MV Surplus % of MV Assets = 15%

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Economic Value (EV) Duration Targeting

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Economic Value (EV) Efficient Frontier

• The efficient frontier does not reflects the deduction of estimated investment management and transaction fees that the client may incur.

All dividends and other earnings are assumed to be reinvested semi-annually. Source: Conning Analysis

33

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Economic Value (EV) Efficient Frontier

34

Integrated ALM



Identify investment

strategy to meet

specific risk/reward

profile



Maximize economic

value - not just

investment returns - for

various levels of risk



Provides a platform for

aggregating enterprise

risks

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Economic Value (EV) Efficient Frontier

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Economic Value (EV) Efficient Frontier – Minimum 4% High Yield

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Expected Results and Range of Results



Each point on the efficient frontier, defined by a single risk and a single reward measure, is based on the results of

1,000s of scenarios



We usually want the investment strategy that on average gives the "best" reward for a given level of risk



However, we also want to know the downside risk - how bad could results be?



We evaluate this risk by looking at the range of potential results; for example, how bad is the 5% probability level (1

year in twenty), and can we accept that much risk?

37

Efficient Frontier

 Ret u rn Risk

Probability Distribution

+ Ret u rn + mean 90 - 95% 75 - 90% 50 - 75% 25 - 50% 10 - 25% 5 - 10%

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Expected Results and Range of Results

Observations



Benchmark economic value is

improved over the Current

allocation at nearly every percentile



Extreme tail events are similar

between the Benchmark and

Current allocations



Tail risk exceeds the Current

allocation in the longest duration

and riskiest portfolios J and K

*The efficient frontier does not reflects the deduction of estimated investment management and transaction fees that the client may incur. All dividends and other earnings

Source: Conning Analytics

38

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Investment Optimization Tool (IO) - Risk Measures

Additional Risk Measures



Pull down menu selection



Standard deviation



Coefficient of variation



Minimum



Semi-standard deviation



Conditional standard deviation



Average



Percentiles



Conditional Tail Expectation

(CTE)

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Economic Efficient Frontier

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Initial-to-Initial vs. Initial-to-Normative

0.00% 1.00% 2.00% 3.00% 4.00% 5.00% 6.00% 0 2 4 6 8 10 12 14 16 18 20 Projection (Years)

Average of 10-Yr Rates over 1,000 Scenarios

Initial to Initial

Initial to Normative

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Example - Asset Model Calibration Parameters

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Example - Asset Model Calibration Parameters

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The question – to extend or not extend?

Source: Conning analysis

44

A

B

C

D

E

F

G

5,000

5,500

6,000

6,500

7,000

7,500

8,000

8,500

1,100

1,200

1,300

1,400

1,500

1,600

1,700

Ec

onom

ic

V

alue

($m

illions

)

Risk

H

I

J

K

1

2 3 4 5 6

7 8 9

10

11 Life Insurance Efficient Frontier Example

Initial to Initial

Asset Allocation:

A

B

C

D

E

F

G

H

I

J

K

Overall Duration

3.6

4.5

5.9

6.5

7.1

7.7

8.3

8.9

9.5

10.1

10.7 Initial to Normative

Asset Allocation

1

2

3

4

5

6

7

8

9

10

11 Overall Duration

2.7

3.3

3.6

4.7

5.3

5.9

6.5

7.7

8.3

9.5

10.7

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The question – to extend or not extend?

45

Even Our Former Fed Chair Can’t Refi…

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The Efficient Frontier — Progressive Analysis

Source: Conning Analysis C11:2173029 46

Asset Only

Efficient

Frontier

• Examine Projection Biases • Standalone Asset Performance

EV Efficient

Frontier

• MV of Assets minus PV of Liabilities • Incorporate Liabilities and Liability

Constraints

• Asset classes include Government Bonds, Corporate Bonds and Equity

PVDE

Efficient

Frontier

• Profit based Efficient Frontier

• Incorporates Liabilities and Solvency Constraints • Asset classes include

Government Bonds, Corporate Bonds and Equity

Optimization on

Total Return

ALM

Efficient

Frontier

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Efficient Frontier Analysis – Optimization Metrics

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PVDE vs Economic Value (EV) Efficient Frontiers

48 -100 -80 -60 -40 -20 0 20 40 60 80 0 10 20 30 40 50 60 Re w a rd Risk

PVDE Regime

PVDE under PVDE EV under PVDE 0 50 100 150 200 250 0 100 200 300 400 500 Rew ar d Risk

EV Regime

EV under EV PVDE under EV

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Thank you for

your time!

Questions?

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Session 101 PD, Use of Efficient Frontiers in Strategic Asset Allocation Analysis Moderator: Ken Griffin, ASA, MAAA