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Asset Allocation Decisions and
Sponsor Valuation
André F. Perold and Luis Viceira
Harvard Business School
Prepared for the Q Group Fall Seminar
La Quinta, Ca
October 18, 2004
A Typical Large Defined-Benefit
Pension Fund
• Ratio of pension assets to market
capitalization = 2:1
• 60% equity allocation means equities = 1.2
times market cap of firm
© André F. Perold, October, 2004
Page 1
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Funded Status of DB Pension Plans in the S&P 500
130%
+$280b
Historical
Fully Funded
120%
Percent Funded
110%
100%
90%
80%
-$219b
70%
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
Source: Standand & Poors
U.S. Pension Initiatives
• Accounting
– Elimination of smoothing of assets and liabilities
(FASB)
– Increased disclosure (FASB)
– Redefinition of core earnings (Ratings Agencies)
• Funding
– Use of Aa corporate bond yield (Congress)
– Use of unsmoothed corporate yield curve (Treasury)
• Credit Ratings
– PBO as corporate debt for credit rating of sponsor
• Pension Benefit Guaranty Corporation
– Insurance premiums based on equity allocation
© André F. Perold, October, 2004
Page 2
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PBGC Insurance Premia
• Since 2001:
– $19 per participant
– 0.9% of funding shortfall
• Under consideration:
– Premium = f(equity exposure)
General Motors Pension Fund
$ Billions
1999
2000
2001
2002
Pension Assets
87.5
85.3
73.7
66.8
Pension Liabilities
83.0
86.0
86.3
92.2
Net Pension Funding
4.5
(0.8)
(12.7)
(25.4)
Shareholders Equity
20.9
30.2
19.7
6.7
Market Value of Equity
39.7
25.4
25.6
20.4
© André F. Perold, October, 2004
Page 3
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What if Pension Funds Sell Their Stocks
and Buy Bonds?
• Who will buy the shares?
• Who will sell the bonds?
• Households?
• Corporations?
Approximate Ownership of U.S. Equities
By Defined Benefit Pension Funds (2003)
$ Trillions
Equity Market Value
14.0
U.S. Corporate DB Plans
0.9
U.S. Public DB Plans
1.2
Foreign DB Plans
0.5
Total Ownership by DB Plans
2.6
© André F. Perold, October, 2004
Page 4
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Asset Allocation Considerations for
Corporate Defined Benefit Plans
• Expected utility
• Modigliani & Miller
• Comparative advantage
– Tax shields
– Long time horizon
• Accounting
• Moral Hazard
Annual Co-Movement of U.S. Stocks and Bonds
100%
Same Direction
Opposite Direction
80%
60%
40%
20%
0%
1950s & 60s
© André F. Perold, October, 2004
1970s thru '98
99-04
Page 5
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Weekly Stock and Bond Returns in 2003
Weekly Stock and Bond Returns in 2004
8%
Stocks
Bonds
6%
4%
2%
0%
-2%
-4%
x
© André F. Perold, October, 2004
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
Page 6
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U.S. Stock-Bond Correlation
(rolling 3 yr, 1806-2004)
80%
60%
40%
20%
0%
-20%
-40%
-60%
-80%
1806
1823
1841
1859
1877
1895
1913
1931
1949
1967
1985
2003
U.K. Stock-Bond Correlation
(rolling 3 yr, 1806-2004)
100%
80%
60%
40%
20%
0%
-20%
-40%
-60%
1806
© André F. Perold, October, 2004
1823
1841
1859
1877
1895
1913
1931
1949
1967
1985
2003
Page 7
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The Changing Stock-Bond Correlation
1976-1998
1999-2004
US
30%
-31%
UK
38%
-18%
Australia
35%
-15%
France
35%
-35%
8%
-38%
Japan
12%
-23%
Sweden
28%
-30%
Germany
What explains the changing correlation?
• Interest rates and inflation are proxies for business
conditions
• When inflation is moderate and stable
– Bonds go up and stocks go down when the business
outlook gets worse, and vice versa when it gets better
• When inflation is high and volatile
– Unexpected inflation is bad/good for stocks as well as
bonds
© André F. Perold, October, 2004
Page 8
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U.S. CPI
16%
12%
8%
4%
0%
-4%
1948
1956
1964
1972
1980
1988
1996
2004
How Risky Are Stock-Bond Portfolios Today?
Risk (S.D.)
Allocation
Stocks
16%
60%
Bonds
14%
40%
Portfolio Risk (S.D.)
Individuals
DB PFs
DB Hedged
50%
13%
9%
10%
0%
11%
13%
10%
-20%
10%
14%
10%
Correlation
© André F. Perold, October, 2004
Page 9
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Pension Fund Payoffs
Fund Assets
Wealth
Put Option
FV L
Liabilities
Call Option
FV L
Fund Assets
Wealth Levels and Probability Ranges
$10,000,000
+ 2 sigma
$1,000,000
ERP 7%
$100,000
95%
Wealth
$10,000
- 2 sigma
$1,000
Riskfree
$100
$10
$1
$0
0
5
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
100
Years
© André F. Perold, October, 2004
Page 10
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Future Value vs. Present Value
0.60
Put Option
0.50
Probability
0.40
0.30
2% Risk Premium
0.20
0.10
7% Risk Premium
0.00
0
5
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
100
Years
Pension Claims
• Sponsor’s claim
= Call option
• Pension beneficiaries’ claim
= Promised benefits – Put option
(+ Government insurance)
© André F. Perold, October, 2004
Page 11
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Value of the Pension Put
•
•
•
•
•
•
•
•
•
Asset allocation
Interest rate process
Company and asset class returns
Nature of promised pension payments
Valuation of pension liabilities
Minimum funding requirements
Solvency of the sponsor
Costs of financial distress
Resolution of bankruptcy
Model of Pension Claims
Company XYZ
Operating
Business
$100
Pension
Assets $100
© André F. Perold, October, 2004
Debt
$50
Equity
$50
P. Liabilities
$100
Page 12
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Pension Benefits
• Steady state workforce
• Deterministic demographics
– Vesting begins at age 31
– Retirement at age 65
– Death at age 85
• One employee in each age cohort
• Wages grow with inflation
• Pension benefits are proportional to final wage
times years of service
Accrued Pension Benefits (ABO)
700
Retired lives
Active lives
ABO
Pension service
600
500
400
300
200
100
0
1
4
7
10
13
16
19
22
25
28
31
34
37
40
43
46
49
52
55
Years from from the present
© André F. Perold, October, 2004
Page 13
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Asset Returns and Asset Pricing*
Stochastic discount factor:
-mt+1 = xt + zt + υm,t+1
Value of a cash flow Ct:
E0{Ctexp mt}
State variables:
xt+1 = (1-φx)µx + φxxt + υx,t+1
zt+1 = (1-φz)µz + φzzt + υz,t+1
Inflation:
πt+1 = zt + υπ,t+1
Nominal short rate:
rt+1 = xt + zt + µr
Stock market return:
st+1 = rt+1 + µs + υs,t+1
Return on company assets:
at+1 = βast+1 + (1-βa)rt + µa + υa,t+1
Price of discount bond:
-ln(Pn,t) = An + B1,n xt + B2,n zt
*Campbell and Viceira (2001)
Capital Market Assumptions
•
•
•
•
•
•
Stock market volatility 16% p.a.
Bond market volatility 13% p.a.
Stock-bond correlation = 0.5 or –0.5
Equity risk premium = 5% or 3%
Asset mix = 60/40 or 0/100 stocks/bonds
Pension liability (ABO) is discounted at long-term
default-free rates
• Company assets: Beta = 0.5; Resid sigma = 20%
© André F. Perold, October, 2004
Page 14
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Pension Model (cont)
• YOY change in pension liability
= Liability return
- Benefit payments
+ Pension service
• YOY change in pension assets
= Investment return
- Benefit payments
+ Pension service
- Contribution holiday
+ Minimum funding requirement
Pension Model (cont.)
•
•
•
•
•
•
•
•
Benefit payments = $8.9
Pension service = $1.6
MFR = k (Assets – 0.9 Liabilities), k = 1/12 or 1/5
Contribution holiday provided that
Assets > 1.1 Liabilities
Sponsor is insolvent when
Op. Assets + A – L < Debt
Termination upon insolvency or T = 30
Bankruptcy costs = 0% or 20% of operating assets
No taxes
© André F. Perold, October, 2004
Page 15
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Broad Observations and Conclusions
• Proposed pension reforms will create
incentives to reduce equity exposure
• Low stock/bond correlations increase the risk
of equity exposure in a defined benefit pension
fund
• However, the “pension put” is valuable and
may be reflected in sponsor valuations
• Eliminating equity exposure may reduce
sponsor market value
The Put Option Aside:
• Shares owned by corporate pension funds are held
indirectly by households
• Individuals should be comfortable exchanging
bonds for these shares
• Corporate plan sponsors will have less risk offbalance sheet – they can take more risk on-balance
sheet through share repurchases
• But who will buy shares owned by public pension
funds?
© André F. Perold, October, 2004
Page 16
Simulation Results
A
B
C
D
E
F
G
H
I
J
Stock-bond correlation
0.5
-0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
Cost of financial distress
0%
0%
0%
0%
0%
0%
0%
20%
20%
0%
100%
$100
$50
100%
$100
$50
80%
$100
$50
80%
$100
$50
100%
$100
$50
120%
$100
$50
100%
$300
$50
100%
$100
$50
100%
$100
$50
100%
$100
$70
Asset allocation
60%
60%
60%
0%
0%
60%
60%
60%
0%
60%
Deficit at termination ("put")
$7.0
$12.2
$12.9
$9.3
$0.0
$4.3
$2.8
$7.3
$0.0
$7.1
$2.5
$10.7
$6.2
$0.0
$8.1
$11.2
$7.2
$0.0
$1.1
$3.4
$11.6
$20.0
$0.0
$0.0
$10.7
$20.0
$0.0
$0.0
$0.0
$0.0
$4.8
$24.5
$5.1
-$20.0
$3.0
$12.4
$12.6
$0.0
$2.3
$9.6
$4.6
$0.0
$0.0
$0.0
$0.0
$0.0
$2.3
$8.5
$3.7
$0.0
28%
44%
43%
56%
47%
14%
5%
37%
59%
48%
$50.0
$57.0
$50.0
$62.2
$30.0
$42.9
$30.0
$39.3
$50.0
$50.0
$70.0 $250.0
$74.3 $252.8
$50.0
$48.7
$50.0
$40.3
$30.0
$37.1
Initial pension funding
Initial operating assets
Initial company debt
Surplus at termination ("call")
Contribution holiday
Required funding
Initial unfunded liability
Bankruptcy probability
Initial consolidated net worth
Market value of equity