The Asset Return - Funding Cost Paradox: The Case for LDI

“My message is simple: Almost every corporate pension fund should be entirely in fixed dollar investments.”

Fischer Black, Financial Analysts Journal 1980

The Asset Return - Funding Cost Paradox

The Case for Liability Driven Investment

Dr. Norman Ehrentreich

10 April 2023

Overview

The Current State of DB Pension Plans and the Return – Volatility Trade-Off of LDI Strategies

The Asset Return – Funding Cost Paradox

Proof of its Existence: A Simple Example Why can the Asset Return – Funding Cost Paradox arise? The Step from Possibility to Reality – Why is it likely to arise? Can we Quantify the Effects?

Volatility Risk Return Risk

Initial Poll

Is it possible that a higher returning equity strategy leads to higher funding costs for a DB pension plan than a lower returning LDI strategy?

PLANSPONSOR / RiverSource Investments study (August 2008)(21 questions to 4,090 DB plan sponsors, responses from 98 corporate plans and 52 non-corporate plans)

Do You Think that Higher Returns in a Given Period Automatically Translate into Lower Funding Costs?

Non-Corporate Defined Benefit Plans

Corporate Defined Benefit Plans

30%

55%

15%

Yes No Don't know

24%

69%

7%

Yes No Don't know

/ RiverSource Investments

Initial Poll


Is it likely?

Can a fully funded DB Pension Plan that earns, on average, its discounting rate over a certain investment period, be bankrupt at the end of that period?

To fund the pension liability

At the lowest cost to the plan sponsor

Subject to reasonable risk

Pension Fund Objectives

To achieve these objectives, asset returns should be the primary source to fund these liabilities, not contributions to the pension fund.

The Current State of DB Pension Plans

Lowest-ever funding levels of U.S. corporate pension plans (Watson Wyatt, January 2009) An asset plunge of $445 billion in 2008 for the 450 DB plans of

the Fortune 1000 companies A $78 billion aggregate surplus turned into a $366 billion deficit For 2008, about 61% of pension plans will have funding levels

between 50% and 70% (only 5% of plans were in that range a year earlier)

Similar, if not worse, for public pension plans Underfunded Pension Benefit Guarantee Corporation

Underfunded by $11.2 billion (fiscal year 2008, ended in Sep ‘08)

Social Security (???)

Why Not more LDI? The Volatility-Return Trade-Off

Pros: LDI strategies avoid large funding shortfalls,

reduce funding status volatility, and hence

balance sheet volatility (FAS 158),

and contribution volatility (PPA of 2006).

Cons: Supposed to lock-in an eventual funding deficit

Interest rates are at historic lows

Pure LDI solutions are fixed income based and thus have lower expected returns than equity

Lower expected returns are supposed to lead to higher funding costs

“Not sure plans will be able to stomach performance of LDI in a rising rate environment.”

“Why would a plan adopt an LDI strategy when equities are expected to outperform over long periods of time. It's a strategy that's "too safe" for most plans.”

“The best hedge against future liabilities is a strong record of portfolio total return.”

“… politicians will care much more about maximizing return and minimizing contribution rates than short term swings in funding status.”

“LDI raises the cost of the DB plan in the low rate environment we are in.”

“We are in for the long term.” “A 3% difference in expected return would increase the cost of a

defined benefit plan to employers by 30% over ten years.”

“Heard on the Street” − Opinions from Plan Sponsors, Managers, and Investment Analysts

The Asset Return – Funding Cost Paradox

It is possible for a lower yielding bond portfolio to require lower average contribution payments than a higher returning equity portfolio.

Higher average asset returns do not automatically translate into lower average funding costs for DB pension plans since the requirements to convert an eventual equity risk premium into lower funding costs are regularly violated in practice.

I have yet to see any problem, however complicated, which, when you look at it in the right way, did not become more complicated.”

Poul W. Anderson

The asset weighted average returns of fully funded LDI strategies tend to beat asset weighted average

returns of traditional asset allocation strategies.

Funding Cost Scenarios for a Simple DB Pension Plan

Liabilities of a Simple DB Pension Plan

0

25

50

75

100

1 2 3

Period

Lia

bili

ties

Year ReturnLiability payment

End of year asset value

End of year funding status

Bonds: 6% annualized rate of return

Scenario 1: Return sequence 6%, 6%, and 6%

0 133.58 100.0 %

1 6 % 25.00 116.59 100.0 %

2 6 % 100.00 23.58 100.0 %

3 6 % 25.00 0.00 N/A

Stocks: 8% annualized rate of return


0 128.73 100.0 %

1 8 % 25.00 114.03 100.0 %

2 8 % 100.00 23.15 100.0 %

3 8 % 25.00 0.00 N/A

The “Traditional” View






0 133.58 100.0 %

1 6 % 25.00 116.59 100.0 %

2 6 % 100.00 23.58 100.0 %

3 6 % 25.00 0.00 N/A



0 128.73 100.0 %

1 8 % 25.00 114.03 100.0 %

2 8 % 100.00 23.15 100.0 %

3 8 % 25.00 0.00 N/A

The “Traditional” View What Else Could Happen?




Stocks: 8% annualized rates of return

Scenario 3: Return sequence of 10%, 10%, and 4%

0 128.73 100.0 %

1 10 % 25.00 116.60 102.3 %

2 10 % 100.00 28.26 122.1 %

3 10 % 25.00 +4.39 N/A








0 128.73 100.0 %

1 10 % 25.00 116.60 102.3 %

2 10 % 100.00 28.26 122.1 %

3 10 % 25.00 +4.39 N/A

Scenario 4a: Return sequence of 4%, 4%, and 16%

0 128.73 100.0 %

1 4 % 25.00 108.88 95.5 %

2 4 % 100.00 13.23 57.2 %

3 16 % 25.00 – 9.59 N/A






0 133.58 100.0 %

1 6 % 25.00 116.59 100.0 %

2 6 % 100.00 23.58 100.0 %

3 6 % 25.00 0.00 N/A



0 128.73 100.0 %

1 8 % 25.00 114.03 100.0 %

2 8 % 100.00 23.15 100.0 %

3 8 % 25.00 0.00 N/A








0 128.73 100.0 %

1 10 % 25.00 116.60 102.3 %

2 10 % 100.00 28.26 122.1 %

3 10 % 25.00 +4.39 N/A


0 128.73 100.0 %

1 4 % 25.00 108.88 95.5 %

2 4 % 100.00 13.23 57.2 %

3 16 % 25.00 – 9.59 N/A

Scenario 4b: Return sequence of 4%, 4%, and 16%

0 133.58 103.8 %

1 4 % 25.00 113.92 99.9 %

2 4 % 100.00 18.47 79.8 %

3 16 % 25.00 – 3.57 N/A

“… there is no way to reduce the ex ante cost by taking risk. Taking risk can only change future outcomes, not the present value of costs.”

Zvi Bodie (2005)







0 133.58 100.0 %

1 6 % 25.00 116.59 100.0 %

2 6 % 100.00 23.58 100.0 %

3 6 % 25.00 0.00 N/A



0 128.73 100.0 %

1 8 % 25.00 114.03 100.0 %

2 8 % 100.00 23.15 100.0 %

3 8 % 25.00 0.00 N/A







0 DW-ARR: 9.45% 128.73 100.0 %

1 10 % 25.00 116.60 102.3 %

2 10 % 100.00 28.26 122.1 %

3 10 % 25.00 +4.39 N/A


0 DW-ARR: 4.62% 128.73 100.0 %

1 4 % 25.00 108.88 95.5 %

2 4 % 100.00 13.23 57.2 %

3 16 % 25.00 – 9.59 N/A

Scenario 4b: Return sequence of 4%, 4%, and 16%

0 DW-ARR: 4.78% 133.58 103.8 %

1 4 % 25.00 113.92 99.9 %

2 4 % 100.00 18.47 79.8 %

3 16 % 25.00 – 3.57 N/A

What matters are dollar-weighted rates of return and not average asset returns.







0 DW-ARR: 6.00% 133.58 100.0 %

1 6 % 25.00 116.59 100.0 %

2 6 % 100.00 23.58 100.0 %

3 6 % 25.00 0.00 N/A



0 DW-ARR: 8.00% 128.73 100.0 %

1 8 % 25.00 114.03 100.0 %

2 8 % 100.00 23.15 100.0 %

3 8 % 25.00 0.00 N/A

The Asset Return – Funding Cost Paradox arises because of volatile asset returns current benefit payments (Intra-period cash flows, in particular

benefit payments, break the link between average returns and average funding costs, reverse dollar cost averaging)

Funding costs for DB pension plans are path dependent on the sequence of asset returns.

To compare competing investment strategies, one needs to look at dollar weighted rates of return

To convert an eventual equity risk premium into lower funding cost, DB pensions plans need to be, on average, fully funded.

Intermediate Results

The Asset Return – Funding Cost Paradox: How Likely Is It?

In reality, DB pension plans tend to be, on average, underfunded. Therefore, they are not in a position to profit from an eventual equity risk premium.


Average Funding Levels over the last 10 Years

1% 1%

6%

30%

36%

13%

12%

13%

3%

20%

25%

18%

5%

18%

0%

10%

20%

30%

40%

<=60% <=70% <=80% <=90% <=100% <=110% >110%

Corporate Non-Corporate

Inability to close arising funding gapsThrough above-average asset returns following an

asset slump (reverse dollar cost averaging)

Reasons for Persistent Underfunding

Liability Profiles of Seven DB Pension Plans

(normalized to $100 million present value of liabilities at 6%)

0

2

4

6

8

10

12

14

16

18

0 10 20 30 40 50 60 70

Mill

ions

Years from Now

Liab

ility

Pay

men

ts /

Yea

r in

Plan A (Duration 8.9) B (12.2) C (10.0) D (8.0) E (22.7) F (14.0) G (16.9)

S&P-500 (TRI) vs. S&P-500 Investment Strategies

0%

20%

40%

60%

80%

100%

120%

140%

160%

Fu

nd

ing

Sta

tus

/ S

&P

-500

S&P500 (TRI) E (21.1) B (11.7) C (9.7) D (6.8)

Pension Fund’s Asset Value = Present Value of Liabilities x Funding Status

Case 1: Benefit Payments at the End of the Period

Case 2: Benefit Payments at the Beginning of the Period

1t1t1tttt FS )PV(LiabAVFS )PV(LiabAV

1 FS )PV(Liab

BPFS )PV(Liabi

BPi)(1AVAV

t

t1t

tt1t

1BPFS )PV(Liab

FS )PV(Liabi

)i1( )BPAV(AV

tt

1t

tt1t

Required Asset Returns to Maintain Funding Status

4.00%

6.00%

8.00%

10.00%

12.00%

14.00%

16.00%

18.00%

20.00%

22.00%

150% 140% 130% 120% 110% 100% 90% 80% 70% 60% 50%

Funding Status

Req

uir

ed R

etu

rn t

o M

ain

tain

Fu

nd

ing

Sta

tus

Plan A (7.8) Plan B (10.7) Plan C (8.7) Plan D (7.0) Plan F (20.2) Plan E (12.7)

Required Asset Returns to Maintain Funding Status

Inability to close arising funding gapsThrough above-average asset returns following an

asset slump (reverse dollar cost averaging)Through additional contributions

Large funding gaps usually arise under adverse business conditions

Pension Relief Bill (WRERA 2008) Asset and Liability Smoothing

Reasons for Persistent Underfunding (continued)

mask the true economic funding status of a pension plan. needed to minimize balance sheet & contribution

volatility (i.e., to defer necessary contributions) Introduce a wedge between “accounting” and “economic”

funding levels Huge differences between reported funding levels and

funding levels on a termination basis Bethlehem Steel 2002: 84% vs. 45%US Airways 2003: 94% vs. 35%

Not needed for LDI strategies as funding gaps are usually small and not systematically correlated with the business cycle.

A Note on Asset and Liability Smoothing

Non-Corporate Defined Benefit Plans

Corporate Defined Benefit Plans

52%48%

Yes No

82%

18%

Yes No

Have You Smoothed Asset and Liability Values?


Inability to close arising funding gapsThrough above-average asset returns following an asset

slump (reverse dollar cost averaging)Through additional contributions

Large funding gaps usually arise under adverse business conditions

Pension Relief Bill (WRERA 2008) Asset and Liability Smoothing

Funding cushions to prevent new shortfalls are not acquired during good economic times Minimum funding policies (Mercer 2008) contribution holidays Benefit bargaining Tax treatment

Reasons for Persistent Underfunding (continued)

Intended to prevent corporate takeover / raiding / plan terminations of overfunded plans in the early 1980ies

1985: 15%, 50% in 1990 Changed the property rights to excess pension assets Led to a fall in average funding status (Ippolito 2002)

through contribution holidays and minimum funding policies (Mercer Sep. 2008)

Disfavors DB Plans by increasing their after-tax costs in comparison to cash balance & DC plans

“It is hard to imagine a public policy that has engendered a result so contrary to its original intent.” (Ippolito 2002)

Reversion Tax on Excess Pension Assets

Quantifying the Effects of Volatile Asset Returns

Monte Carlo Simulation

Our seven DB pension plans (A to G), hard frozen, no contributions Generate random monthly return paths with a given annualized total

rate of return

− Simulation structure:

For all plans and all return pathsInitialize plans with xx% of the PV(Liabilities)For i = 1 to 120 months

Earn returnPay out benefit

Next iAnalyze terminal funding levels

Identifying the Components of Risky Asset Returns

Return Risk: The range of investment outcomes

stemming solely from differences in non-

volatile asset returns.

Volatility Risk: For any given average rate of return over

a specific investment period, volatility risk

is the range of investment outcomes (e.g.,

final funding levels for DB pension plans)

stemming solely from intra-period return

volatility.

0 1 2 3 4 5 6 7 8 9 100.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

2.2

2.4

Years

Sto

ck P

rice

s75 random asset price paths (annual rate of return =8%, sigma=4.2%)

Volatility Risk: Uncertainty about the Path towards the (Realized) Expected Return



100 random asset price paths with no intra-period volatility. The realized average returns are normally distributed around the expected return.

Return Risk: Uncertainty about the Realized Rate of Return at the Investment Horizon

0 0.5 1 1.5 20

500

1000

1500

2000

2500Plan D, Duration 6.8

0 0.5 1 1.5 20

500

1000

1500

2000


0.5 1 1.50

500

1000

1500

2000

2500Plan C, Duration 9.7

0.5 1 1.50

1000

2000

3000

4000


0.5 1 1.50

500

1000

1500

2000

2500Plan F, Duration 13.3

0.5 1 1.50

2000

4000

6000

8000


Distribution of Fundig Levels when the Realized (No-Volatility) Returns are Normally Distributed Around Their Expected Returns (i.e., "Return Risk" for 70/30 S&P-500/Barclays Agg Strategies)

Distribution of Final Funding Levels When Plans Earn, on Average, Their Discounting Rate (i.e., "Volatility Risk" for 70/30 S&P-500/Barclays Agg Strategies, monthly asset return volatility = 3%)

Return Risk

0 0.5 1 1.5 20

500

1000

1500

2000


0 0.5 1 1.5 20

500

1000

1500

2000


0.5 1 1.50

500

1000

1500

2000


0.5 1 1.50

1000

2000

3000

4000


0.5 1 1.50

500

1000

1500

2000


0.5 1 1.50

2000

4000

6000

8000


Distribution of Fundig Levels when the Realized (No-Volatility) Returns are Normally Distributed Around Their Expected Returns (i.e., "Return Risk" for 70/30 S&P-500/Barclays Agg Strategies)

Distribution of Final Funding Levels When Plans Earn, on Average, Their Discounting Rate (i.e., "Volatility Risk" for 70/30 S&P-500/Barclays Agg Strategies, monthly asset return volatility = 3%)

Return Risk versus Volatility Risk

Conclusions The Asset Return – Funding Cost Paradox is real. Low duration

plans are more likely to experience it.

LDI strategies minimize the risk of creating large funding deficits from which it is hard to recover.

Funding costs are a function of asset returns and funding levels.

By continuing to use unmatched strategies, underfunded plans have a slight chance of improving their funding status, yet run the risk of failing even earlier (Russian roulette).

Even if average return expectations materialize, non-LDI plans have a positive risk of failing if no further contributions are made.

The volatility risk due to volatile asset returns is not sufficiently compensated in today’s market place

In my opinion, plans have no viable alternative to LDI in terms of risk management and funding costs.

Exit Poll


Is it likely?

Can a fully funded DB Pension Plan that earns, on average, its discounting rate over a certain investment period, be bankrupt at the end of that period?

Cited Sources and Additional Materials

Allen J. (2008): “Do You Have a Funding Policy? … And Is It Working?”, Mercer US Retirement Perspective (September).

Bodie, Z. (2005): “On the Time Dimension of Investing”, Boston University School of Management Working Paper No. 2005-28.

Black, F. (1980): “The Tax Consequences of Long-Run Pension Policy”, Financial Analysts Journal 36(4), p. 21-28.

Ippolito, R.A. (2002): “The Reversion Tax’s Perverse Results”, Securities and Investments, 25(1), p. 46-53.

Watson Wyatt (2008): “Dramatic Drops in Interest Rates Forecast Much Lower DB Plan Funding Status on Accounting Basis for 2008”, Insider February 2009.

Plansponser/RiverSource (2008): “The Funding Cost Paradox – Higher returns don’t always result in better funding outcomes”, Plansponsor, August 2008, p. 18 – 20.

For questions or comments contact Dr. Norman Ehrentreich [email protected], 612-706-7819

Economy & Finance

The Asset Return - Funding Cost Paradox: The Case for LDI