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
101PD - Use of Efficient
Frontiers in Strategic
Asset Allocation Analysis
Presented to
October 28, 2014
Presented by
Efficient frontier (EF) modeling is an intuitive, convenient way to capture
the incremental trade-offs between object combinations in the two
dimensional space of risk and return.
TODAY’S DISCUSSION
 Traditional Mean-Variance EFs and Concepts
 Other Topical Uses of EFs
 EF Modeling Input
 EF Modeling Challenges
 Practical Limitations and “Taming the Optimizer”
141028 SOA Use of EF in SAA.ppt
2
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.
TRADITIONAL MEAN-VARIANCE EFs
 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.
141028 SOA Use of EF in SAA.ppt
Source: Investopedia.com, Cardinal Investment Advisors Analysis
3
EFs can be very sensitive to the componentry of which they are comprised.
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.
Illustrative Risk Reduction from New Asset Classes
Annualized Rate of Return
Annualized Rate of Return
Illustrative Return Gain from New Asset Classes
Return Gain
Frontier with existing assets
With new asset classes
Current allocation
With new asset classes
Risk % (Standard Deviation of Annual Returns)
141028 SOA Use of EF in SAA.ppt
Source: Cardinal Investment Advisors Analysis
Risk
Reduction
Frontier with existing assets
With new asset classes
Current allocation
With new asset classes
Risk % (Standard Deviation of Annual Returns)
4
EFs get to the heart of Modern Portfolio theory and the notion of
improving efficiency via diversification.
HARNESSING DIVERSIFICATION VIA EFs
 The inverse correlation
of the assets creates
higher returns at lower
risk than a simple
linear combination of
the assets.
Risk/Return of Efficient Portfolio Combinations
14%
12%
Annualized Return (%)
10%
Unconstrained Frontier
8%
 Adding new, potential
asset classes to the
mix will only improve
those efficiencies as
long as the correlations
are less than 1.0.
Current Target
6%
4%
2%
0%
0%
5%
141028 SOA Use of EF in SAA.ppt
10%
15%
20%
25%
30%
Risk (Annual Standard Deviation - %)
Source: Cardinal Investment Advisors, ProVal
5
35%
40%
The opportunity set of objects one can embed in an EF depends on the
limits imposed by state, federal, or other regulation.
REAL WORLD OF INSURANCE EFs
LOCATION, LOCATION, LOCATION!
141028 SOA Use of EF in SAA.ppt
Source: State Regulations, Cardinal Investment Advisors analysis
6
Actual implementable EFs can depart dramatically from conceptual
ones. Mundane factors such as taxes leverage constraints/risk controls
fundamentally change the shape of EFs.
INCLUDING REALISTIC FACTORS IN EFs
12%
30% Trade Finance
14% Small Cap
16% International
14% Private RE
3% Commodities
23% Private Equity
Expected Return (After-Tax)
10%
25% HY Bank LoansUnconstrained
75% Private Equity
8%
Unconstrained with Taxes
85% Cash
11% TIPS
2% Private Equity
6%
50% Investment Leverage
6% Basket Clause
4%
A-Policy Target
2%
0%
0%
5%
10%
15%
Risk (After-Tax Standard Deviation)
141028 SOA Use of EF in SAA.ppt
Source: Cardinal Investment Advisors
7
20%
25%
30%
EFs are frequently used to capture other concepts of risk vs. return, or
cost vs. benefit tradeoffs. Excess return vs. a liability is one.
OTHER TOPICAL EF CONCEPTS
 The “risk-equivalent” point
on the frontier in this
context is a very different
allocation than the-risk
equivalent from the meanvariance EF
Liability Tracking (Excess Return) Frontier
Excess Return (Over PBO Liability Return - %)
5%
4%
3%
Unconstrained
Frontier
2%
1%
0%
Current Allocation
-1%
-2%
Long Credit
Non US Devloped
Private Equity
US Small
PIMCO
Total
Excess Return
PBO Liability Tracking Error
43%
28%
12%
13%
4%
100%
1.4%
12.8%
-3%
0%
141028 SOA Use of EF in SAA.ppt
5%
10%
15%
20%
25%
30%
Tracking Error (Std Dev. of Excess Return - %)
Source: Cardinal Investment Advisors, ProVal
8
35%
Long Credit
Non US Developed
US Small
Low Volatility Equity
Private Real Estate
Private Equity
PIMCO
Commodities
Total
Compound Return
Volatility
35%
21%
17%
12%
6%
4%
4%
1%
100%
7.7%
11.4%
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.
OTHER TOPICAL EF CONCEPTS (continued)
141028 SOA Use of EF in SAA.ppt
Source: Voya
9
An age-old debate… Arithmetic means are biased high; Geometric means
are biased low. Converting between the two should be thoughtful.
INPUTS: ARITHMETIC VS. GEOMETRIC RETURNS
 Maclaurin series expansion
 Taylor series expansion
141028 SOA Use of EF in SAA.ppt
Source: CDI Advisors
10
Intuitive return forecasts based on drivers of value should be favored over
historic returns.
INPUTS: HISTORIC VS. FORWARD LOOKING RETURNS
Using Historic Averages to Forecast Future Returns
(10 Yr. Trailing S&P 500 vs. Future 10 Years)
25%
20%
Annualized Return
15%
10%
5%
RSQ = 0.04
0%
-5%
Forecast
Actual
141028 SOA Use of EF in SAA.ppt
Source: Cardinal Investment Advisors
11
Q4 2013
Q4 2011
Q4 2009
Q4 2007
Q4 2005
Q4 2003
Q4 2001
Q4 1999
Q4 1997
Q4 1995
Q4 1993
Q4 1991
Q4 1989
Q4 1987
Period Ending…
Q4 1985
Q4 1983
Q4 1981
Q4 1979
Q4 1977
Q4 1975
Q4 1973
Q4 1971
Q4 1969
Q4 1967
Q4 1965
Q4 1963
Q4 1961
Q4 1959
Q4 1957
Q4 1955
Q4 1953
Q4 1951
Q4 1949
Q4 1947
Q4 1945
-10%
Building blocks can be used to capture both the current environment and
typical mean reverting activity in asset return forecasts.
INPUTS: BASIC EQUITY RETURN FORECAST APPROACH
2.70%
4.95%
Current
Income
Component
Growth
Component
+
1.90%
Current
Dividend
Yield
.80%
Share
Repurchase
Yield
+
-0.25%
+
2.25%
2.70%
Long-Term
Expected
Inflation
Future
Dividend
Growth
+
Valuation
Component
-0.25%
Current vs.
Long-Term
P/E Multiple
Real GDP
growth rate
in US
2.00%
~
~
Speed of
Market
Mean
Implied
~ Inflation
~
Reversion
2.60%
2.20%
2.90%
Expert
Consensus
Forecasts
GDP
Component
Method
0.90%
Source: Cardinal Investment Advisors
2.60%
~
Trailing
Expert
Historic
Consensus
~ Averages ~ Forecasts
2.65%
2.00%
Labor Force
Growth in
the US
141028 SOA Use of EF in SAA.ppt
~
12
+
Productivity
Growth in
the US
=
7.40%
Large US
Equity
Projection
Long-term EFs should not be predicated on untenable short-term assumptions.
INPUTS: LOW YIELD ENVIRONMENT NEEDS TO BE ADDRESSED
Barclays Capital Agg and Long Credit
Yield to Worst and Subsequent 10-Year Returns
(Since Inception 1973 - 2013)
18
 Cardinal’s fixed
income asset class
return projections are
based on current
market yields as an
unbiased consensus
indicator of
anticipated bond
pricing. However…
16
14
Yield to Worst (%)
12
10
R² = 0.8156
8
6
4
2
0
0%
2%
4%
6%
8%
10%
12%
14%
Subsequent 10-Year Return
141028 SOA Use of EF in SAA.ppt
Source: Barclays, Cardinal Investment Advisors
13
16%
18%
20%
Forecasting bond returns may require a two-stage or reversion approach.
INPUTS: SECULAR TREND IN YIELDS OVER LONG-TERM
US Treasury Yield Curve
Domestic Core Fixed Income (Two-Stage)
8.0
2.60%
7.0
Core Bond
Return
Projection
Yield (%)
6.0
Long-term
downward
trend
5.0
4.0
2.30%
Current
Aggregate
YTM
3.0
2.0
Recent
stabilization
in rates
1.0
0.0
.5 1
2
5
Ave Last 10 Years
141028 SOA Use of EF in SAA.ppt
10
Term (Years)
Ave. Last 30 Years
30
6/30/2013
Source: Federal Reserve, Cardinal Investment Advisors
6/30/2014
14
3.30%
~
Aggregate
Reinvestment
Yield
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.
INPUTS: RISK REGIME CHANGES
Intermediate Bonds
Volatility Regime Change
Barclays Aggregate St Dev
1970 to
1980 to
1990 to
141028 SOA Use of EF in SAA.ppt
2013 6.96
1990 8.93
2013 4.99
15
Illiquid, private asset classes suffer from pricing biases that require “unsmoothing.”
INPUTS: ALTERNATIVE ASSET CLASSES UNDERSTATE RISK
Reported Real Estate Returns vs. Unsmoothed
15.00
10.00
5.00
Return (%)
0.00
-5.00
-10.00
St Dev
Reported
2.2
Unsmoothed 4.5
-15.00
Return
2.0
1.9
-20.00
-25.00
Q1 1982
Q4 1982
Q3 1983
Q2 1984
Q1 1985
Q4 1985
Q3 1986
Q2 1987
Q1 1988
Q4 1988
Q3 1989
Q2 1990
Q1 1991
Q4 1991
Q3 1992
Q2 1993
Q1 1994
Q4 1994
Q3 1995
Q2 1996
Q1 1997
Q4 1997
Q3 1998
Q2 1999
Q1 2000
Q4 2000
Q3 2001
Q2 2002
Q1 2003
Q4 2003
Q3 2004
Q2 2005
Q1 2006
Q4 2006
Q3 2007
Q2 2008
Q1 2009
Q4 2009
Q3 2010
Q2 2011
Q1 2012
Q4 2012
-30.00
Unsmoothed
141028 SOA Use of EF in SAA.ppt
Source: NCREIF, Cardinal Investment Advisors
Reported
16
Correlations often converge during periods of market stress.
INPUTS: CORRELATIONS ARE NOT ALWAYS STABLE
Historic Correlations to Investment Allocations
3-Year Centered Correlation Coefficient
1.00
High Convergence
Convergence
0.80
0.60
3
4
1
0.40
0.20
0.00
-0.20
2
-0.40
-0.60
5
-0.80
-1.00
Bull Mkt.
Bull Mkt.
Asset
Rolling
141028 SOA Use of EF in SAA.ppt
Source: Cardinal Investment Advisors
Bear Mkt.
Asset Ave.
17
 EFs require a
covariance structure.
 Using a single point
static value can hide
the impact of real
world convergences.
 Shock testing is
important.
“Artificial” constraints can be very costly and should be quantified.
ACKNOWLEDGING THE COST OF CONSTRAINTS
Comparative Frontiers - Typical Assets vs. Impairment Sensitive
 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.
10
Return (Annualized) - %
9
8
Typical Pension Asset Frontier
7
Imprudent levels of
asset concentration
6
5
Cost of constraints
4
Impairment Sensitive Frontier
3
2
1
0
0
2
4
6
8
10
12
14
16
Risk (Annual Standard Deviation) - %
141028 SOA Use of EF in SAA.ppt
18
18
20
Two, apparently, near-identical EFs appear below.
OPTIMIZERS ARE FICKLE – TESTING SENSITIVITY
Identical Frontiers?
10.0%
Efficient Frontier #2
9.0%
8.0%
Efficient Frontier #1
Nominal Return
7.0%
6.0%
5.0%
4.0%
3.0%
2.0%
1.0%
0.0%
0%
5%
10%
15%
20%
Standard Deviation of Nominal Return
141028 SOA Use of EF in SAA.ppt
19
25%
30%
Asset class return/risk assumptions only flexed +/- <20 bps. Can result in +/- 10%
allocation changes.
MINOR INPUT CHANGES CAN BE SIGNIFICANT
Efficient Frontier #1
Efficient Frontier #2
100%
100%
90%
90%
80%
80%
70%
70%
60%
60%
50%
50%
40%
40%
30%
30%
20%
20%
10%
10%
0%
0%
141028 SOA Use of EF in SAA.ppt
20
Objects flow in and out of the EF depending on constraints and relative efficiency.
DETERMINING WHAT IS BINDING
100%
5
Commodities
4
90%
80%
Private Equity FOF
2
Hedge FOF
3
Non US Emerging Equity
70%
60%
Non US Developed Equity
US Small Cap Equity
6
US Large Cap Equity
50%
Private Real Estate
LC Emerging Mkts Debt
40%
1
30%
High Yield Bonds
Long Gov/Credit
TIPS
20%
Core Bonds
10%
Cash
0%
4
Domestic and non-US equity’s low correlation to core bonds
pulls the asset into the frontier almost immediately.
TIPS enter immediately due low correlations. The 10% max binds
initially with allocations declining as correlation is offset by low returns.
5
Commodities’ high expected returns drive it to the max limit as
it quickly dominates hedge funds, REITs etc.
Real estate is prominent along the frontier as a high income diversifier.
6
The incremental yield pickup of Long Gov/Credit drive a max
allocation early in the frontier.
1
High Yield Bonds’ current yields are sufficiently high to maintain a
presence throughout most of the frontier.
2
3
141028 SOA Use of EF in SAA.ppt
21
ADDING AN OVERLAY
Projected Asset Class Risk/Return
14%
Annualized Return (%)
12%
US Small Cap
All Private Equity
Equity
Non-US Developed
US Mid Cap Equity
Equity
US Large Cap
Equity
Low Volatility
Equities
Non-US Emerging
Bonds
Commodities
Hedge Funds
Private Real Estate
High Yield
REITs (Public Real
Long Credit
Estate)
10%
8%
6%
Non-US Emerging
Equity
4%
Long Government
Domestic Bonds
2%
Market Return
TIPS
Cash
Active Mgmt Return
0%
0%
5%
10%
15%
20%
25%
30%
35%
Risk (Annual Standard Deviation of Returns - %)
141028 SOA Use of EF in SAA.ppt
22
40%
Cash
Domestic Bonds
Long Government
Long Credit
TIPS
High Yield
Hedge Funds
Private Real Estate
REITs (Public Real Estate)
US Large Cap Equity
US Large Cap (Passive)
US Mid Cap Equity
US Small Cap Equity
Non-US Developed Equity
Commodities
All Private Equity
Emerging Market Equity
Emerging Market Bonds
Low Volatility Equities
45%
Active Management
Alpha
TE
0.1%
0.2%
0.2%
0.5%
0.1%
0.5%
0.3%
0.5%
0.8%
3.5%
0.5%
2.0%
0.5%
2.5%
0.8%
3.8%
1.0%
5.0%
1.5%
5.0%
1.5%
5.0%
0.4%
1.5%
-
ALPHA OVERLAY ASSUMPTIONS
141028 SOA Use of EF in SAA.ppt
23
OTHER CONSIDERATIONS
 Non-normality
 Fat-tails (leptokurtosis)
 Correlation Convergences
 Shock-testing
 Historic Scenarios/Crisis
141028 SOA Use of EF in SAA.ppt
24
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
assumptions
141028 SOA Use of EF in SAA.ppt
25
SOA Annual Meeting
October 28, 2014
One Financial Plaza Hartford, CT 06103 | www.conning.com
Simulation Modeling Approach
Economic
Scenario
Generator (ESG)
Company Model - Projects Future States of the Company
Q1
Q2
Q3
Q4
…
Scenario 1
Models Future States
of the Economy &
Financial Markets
Scenario 2
WholeCompany
Outputs
Scenario 3
Accounting
Regulatory
Financials
Tax
Scenario 4
Company
Data Input
Start of
Simulation
Scenario n
Current Business State
 Current Financials
 Business Plans
 Actuarial Models
 Input from ERM
...
High Performance Business Computing
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
Source: Conning ADVISE
28
Economic Value (EV) Efficient Frontier
Transition
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
Economic Value (EV) Efficient Frontier
Current
Cash and Gov't
Corporate
Structured
CML/Private Placement
High Yield
US Equity
Alternative Assets
Total
Overall Duration
Economic Value ($MM)
Risk ($MM)
5%
65%
16%
11%
3%
100%
Benchmark
4%
40%
29%
20%
3%
1%
3%
100%
7.1
8.1
1,617
154
1,654
167
A
B
36%
16%
8%
6%
1%
-
-
-
-
-
-
21%
43%
100%
40%
43%
1%
100%
32%
44%
15%
1%
100%
31%
33%
29%
1%
100%
54%
14%
30%
1%
100%
52%
17%
30%
1%
100%
41%
26%
30%
3%
100%
35%
32%
30%
3%
100%
39%
28%
30%
3%
100%
50%
20%
26%
1%
3%
100%
59%
19%
15%
4%
3%
100%
6.7
1,577
122
C
6.8
1,590
122
D
6.5
1,603
124
E
6.6
1,616
128
F
6.8
1,629
136
G
7.4
1,642
146
H
7.7
1,656
158
I
8.5
1,669
171
J
9.7
1,681
185
K
11.0
1,694
204
12.2
1,709
228
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
Economic Value (EV) Duration Targeting
Market Value Balance Sheet
Modeled Assets and Liabilities
(Amount in $ millions)
Immunized
Book
Market
Effective
Effective
Value
Value
Duration
Duration
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
10,000
10,000
7.1
6.7
8,000
8,000
8.2
8.2
500
500
2.0
2.0
Total Liabilities
8,500
8,500
7.9
7.9
Total Surplus
1,500
1,500
2.4
0.0
Assets :
Total Invested Assets
Liabilities :
Liabilities
Other
Surplus :
MV Surplus % of MV Assets =
15%
31
Economic Value (EV) Duration Targeting
32
Economic Value (EV) Efficient Frontier
Not preferred from an SAA standpoint!
•
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
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
Source: Conning ADVISE
34
Economic Value (EV) Efficient Frontier
35
Economic Value (EV) Efficient Frontier – Minimum 4% High Yield
36
Expected Results and Range of Results
Probability Distribution
Return
Return
Efficient Frontier
+

90 - 95%
75 - 90%
50 - 75%
25 - 50%
10 - 25%
5 - 10%
+ mean
Risk

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?
Source: Conning Analysis
37
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
BM* means Benchmark Strategy
38
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)
Source: Conning Analytics
39
Economic Efficient Frontier
40
Initial-to-Initial vs. Initial-to-Normative
Average of 10-Yr Rates over 1,000 Scenarios
6.00%
5.00%
4.00%
3.00%
2.00%
Initial to Initial
Initial to Normative
1.00%
0.00%
0
2
4
6
8
10
Projection (Years)
12
14
16
18
20
Source: Conning Analysis
41
Example - Asset Model Calibration Parameters
Source: Conning Analysis
42
Example - Asset Model Calibration Parameters
Source: Conning Analysis
43
The question – to extend or not extend?
Economic Value ($millions)
Life Insurance Efficient Frontier Example
8,500
8,000
7,500
7,000
C
6,500
11
10
9
8
3 4 5 6 7
2
1
D
E F
I
H
G
J
K
B
6,000
A
5,500
5,000
1,100
1,200
1,300
1,400
Risk
1,500
1,600
1,700
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
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
Initial to Normative
Source: Conning analysis
44
The question – to extend or not extend?
Even Our Former Fed Chair Can’t Refi…
Source: U.S. Federal Reserve History. http://www.federalreservehistory.org/People/DetailView/12 Accessed on 10/23/2014
45
The Efficient Frontier — Progressive Analysis
Asset Only
Efficient
Frontier
• Examine Projection
Biases
• Standalone Asset
Performance
EV Efficient
Frontier
Optimization on
Total Return
• 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
ALM
Efficient
Frontier
• Incorporates Liabilities
and Solvency Constraints
• Asset classes include
Government Bonds,
Corporate Bonds and
Equity
Source: Conning Analysis
C11:2173029
46
Efficient Frontier Analysis – Optimization Metrics
Source: Conning Analysis
PVDE vs Economic Value (EV) Efficient Frontiers
EV Regime
PVDE Regime
80
250
60
200
40
20
Reward
Reward
150
0
-20
100
-40
-60
50
-80
0
0
100
200
300
Risk
400
500
-100
0
10
20
30
Risk
40
EV under EV
PVDE under PVDE
PVDE under EV
EV under PVDE
50
60
Source: Conning Analytics
48
Thank you for
your time!
Questions?
49
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