Jules van Binsbergen and Michael Brandt€¦ · Optimal Asset Allocation in ALM Jules van Binsbergen and Michael Brandt Asset Allocation in Uncertain Times Conference Cass Business

Optimal Asset Allocation in ALM

Jules van Binsbergen and Michael BrandtAsset Allocation in Uncertain Times Conference

Cass Business School, July 2 2012

© Jules van Binsbergen & Michael Brandt, 2012All rights reserved without exception

Overview

Optimal Asset Allocation in ALM© Jules van Binsbergen & Michael W. Brandt, 2005

All rights reserved without exception− 3 −

Pension under-funding crisis

•US defined benefits pension system (2010 PBGC data)

Motivation

Funding Ratio

under 40% 483 2% 153,942 6%40-60% 4,798 18% 567,653 28%60-80% 11,053 56% 920,618 64%

80-100% 7,177 80% 733,928 92%100-120% 2,960 90% 146,694 98%120-140% 1,063 94% 28,724 99%over 140% 1,751 100% 18,043 100%

Plans Liabilities (in mm)



Pension protection act of 2006

•Changing rules to strengthen the pension system

– Accurate measurement of assets and liabilitiesLimit deviation of actuarial value of assets from mktvalue (smoothing within 80-120% of market value)Limit deviations of actuarial value of liabilities from mktvalue (discount rates within 90-100% of average 30-year government or corporate rate over last 4 years)

– Deficit reduction measuresDefinition of “underfunded” – 100% versus 90%If underfunded, deficit is amortized over 15-30 yearsMandatory additional financial contributions (AFCs) for underfunded plans as function of funding status

– Credits system

Motivation



Reporting

Issues

•Impact of the discount factor used for computing the PV of the liabilities on the reported financial position of pension plans has been heavily debated‒ discounting by current yields guarantees an accurate description of the

fund’s financial situation

‒ discounting by constant yields smoothens out temporary fluctuations in the PV of liabilities and allows the fund to have a longer term perspective

‒ current regulations prescribe a 4-year rolling average

•Emphasis of the debate has been on informativeness‒ when yields increase, a fund using a constant or smoothed discount rate

may seem under funded while in fact it is fully funded and vice versa

•What are the portfolio choice implications of smoothing yields from the fund manager’s perspective?



Ex-post versus ex-ante risk constraints

Issues

•Mandatory additional financial contributions (AFCs) act as ex-post or punitive risk control‒ fund manager is punished, either explicitly or through reputation cost, for

making a portfolio choice that ends up causing an underfunding

•Alternatively, a value-at-risk (VaR) or similar constraint acts as ex-ante or preventive risk control‒ fund manager is not allowed to make a portfolio choice that is likely, with

some fixed probability, to cause underfunding

•How different does a fund manager behave with preventive versus punitive risk controls?



Myopic versus dynamic portfolio choice

Issues

•Although fund managers make periodic investment choices, pension plans are by design very long term investors

•Two ways to make long-term investment decisions

1. Myopically => each period the fund manager optimizes a one-period objective ignoring the fact that the decision problem will be repeated next period

2. Dynamically => the fund managers solves a dynamic program that optimally takes into account the multi-period aspect of the problem

•When investment opportunities vary, dynamic versus myopic investment choices may be quite different (Merton, 1969)

•How important is dynamic optimization for ALM?



Questions

Questions

1. Do financial reporting rules have real effects on investment behavior (unconditionally and close to the AFC/VaR bound)?

2. Do punitive risk controls lead to the same investment behavior as preventive ones, and if not which is better?

3. How important is dynamic optimization for ALM, particularly with realistic reporting rules and AFC or VaR risk controls?



Answers

Answers

1. Do financial reporting rules have real effects on investment behavior (unconditionally and close to the AFC/VaR bound)?

Smoothed discount rates induce grossly suboptimal (more risky) investment decisions, both myopically and dynamically

2. Do punitive risk controls lead to the same investment behavior as preventive ones, and if not which is better?

Myopically, the two result in similar portfolio choices around funding ratios of 100% but dynamically, the portfolio choices are very different due to a kink in the preferences

3. How important is dynamic optimization for ALM, particularly with realistic reporting rules and AFC or VaR risk controls?

Gains from dynamic investing for standard ALM are small and even smaller with VaR constraints, but gains from dynamic investing with mandatory AFCs are very large

ALM problem


All rights reserved without exception

Roadmap

•Return dynamics

•Liabilities reporting

•Risk constraints

•Investment manager preferences

− 11 −

Roadmap



Return dynamics

•Investment opportunities comprised of stocks (S&P 500 index), bonds (15-year T-bond), and risk-free asset (1-year T-bill)

•Two state variables (indicated by zt)– 1-year T-bill yield y1,t

– 15-year T-bond yield y15,t

•Joint return and state variable dynamics describing the time-varying investment opportunity set

with

Model



Assets, liabilities and sponsor contributions

•Returns

•Liabilities

•Assets

•Funding ratiosponsor contributions

Model


All rights reserved without exception

0

2

4

6

8

10

12

14

16

1956 1961 1966 1971 1976 1981 1986 1991 1996 2001

%

Year

4-year rolling average

Market yield

Constant yield

− 14 −

Liabilities

Discount rate for PV computation



How 4-year averaging affects liability risk

t-4 t-3 t-2 t-1 t t+1 t+2

Average at time t

Average at time t + 1

•Averaging reduces the uncertainty of the liabilities‒ from time t to time t+1, only the innovation to the yield at t+1 is

uncertain; the other three values in the average stay the same

‒ liability risk is highly reduced to only 1/16 of the original variance, which makes bonds less attractive and assets that are uncorrelated with liabilities (like the risk free asset) more attractive

Liabilities



Three measures of liabilities (normalized)

•Actual

•Constant

•Smoothed

Liabilities



Value at Risk (VaR) constraint

•In each period the probability of being underfunded in the next period must be less than 2.5%

•When a fund is already underfunded, the probability of a worsening of the funding status must be less than 2.5%

•Depending on liability reporting rules, the VaR constraint is defined with respect to the

‒ratio of assets to actual liabilities

‒ratio of assets to smoothed liabilities

Risk constraints



Mandatory additional financial contributions (AFCs)

Risk constraints

•Whenever the plan is underfunded, the plan sponsor has to inject funds, which comes at a utility cost to the manager

•Depending on liability reporting rules, “underfunded” means that the assets are smaller than

‒actual liabilities

‒smoothed liabilities



Investment manager preferences

{ }( ) ⎥⎦

⎤⎢⎣

⎡−

−= ∑

=

−

=

T

tt

tTTttT cSEcSU

1

1

01 1, βλ

γ

γ

Maximize funding ratio atend of investment horizon

Minimize sponsorcontributions

Align incentives?

•Different assets interesting for different parts of utility function

Preferences



First-order risk aversion

•Kink in the utility function causes the investment manager to become first-order risk averse whenever the (reported) funding ratio approaches the critical threshold that triggers AFCs

•For actual discounting in 1-period problem

Preferences

( ) ( ){ }

( ){ } ( )⎥⎦

⎤⎢⎣

⎡−−

−=

⎥⎦

⎤⎢⎣

⎡−

−=

−

−

0,1max1

,1max

1,1max,

1

1

TT

TT

TT

SSE

cSEcSU

λγ

λγ

γ

γ

Numerical solution method



DP by simulation and parameterized expectations

•Even this highly stylized ALM problem is very difficult to solve– too many state variables

– path dependence

(much like a multi-asset American style option pricing problem)

•We use the simulation based method of Brandt et al (2005)– simulate many potential paths of the return and liability dynamics

– solve the problem backward on each simulated path using dynamic programming with parameterized (linear regression based) expectations

Preferences

Results: Smoothing yields



One-period ALM problem under a VaR constraint

Constant Discounting Actual Discounting 4-year Av. DiscountingSo Stocks Riskfree Bonds CE scaled Stocks Riskfree Bonds CE scaled Stocks Riskfree Bonds CE scaled<0.90 0.24 0.74 0.02 1.0734 0.24 0.00 0.76 1.0787 0.28 0.48 0.24 1.0787

0.99 0.24 0.74 0.02 1.0734 0.24 0.00 0.76 1.0787 0.28 0.48 0.24 1.07871.00 0.24 0.74 0.02 1.0734 0.24 0.00 0.76 1.0787 0.28 0.48 0.24 1.07871.01 0.30 0.70 0.00 1.0778 0.28 0.00 0.72 1.0815 0.32 0.40 0.28 1.08211.02 0.36 0.64 0.00 1.0824 0.34 0.00 0.66 1.0858 0.38 0.36 0.26 1.08641.05 0.50 0.46 0.04 1.0931 0.46 0.00 0.54 1.0940 0.54 0.22 0.24 1.09781.08 0.66 0.34 0.00 1.1040 0.58 0.00 0.42 1.1018 0.68 0.08 0.24 1.10751.10 0.74 0.22 0.04 1.1099 0.66 0.00 0.34 1.1069 0.78 0.00 0.22 1.11411.12 0.84 0.16 0.00 1.1162 0.74 0.00 0.26 1.1117 0.86 0.00 0.14 1.11881.15 0.96 0.02 0.02 1.1242 0.86 0.00 0.14 1.1188 0.98 0.00 0.02 1.1255

>1.20 1.00 0.00 0.00 1.1266 1.00 0.00 0.00 1.1266 1.00 0.00 0.00 1.1266






0.99 0.24 0.74 0.02 1.0734 0.24 0.00 0.76 1.0787 0.28 0.48 0.24 1.07871.00 0.24 0.74 0.02 1.0734 0.24 0.00 0.76 1.0787 0.28 0.48 0.24 1.07871.01 0.30 0.70 0.00 1.0778 0.28 0.00 0.72 1.0815 0.32 0.40 0.28 1.08211.02 0.36 0.64 0.00 1.0824 0.34 0.00 0.66 1.0858 0.38 0.36 0.26 1.08641.05 0.50 0.46 0.04 1.0931 0.46 0.00 0.54 1.0940 0.54 0.22 0.24 1.09781.08 0.66 0.34 0.00 1.1040 0.58 0.00 0.42 1.1018 0.68 0.08 0.24 1.10751.10 0.74 0.22 0.04 1.1099 0.66 0.00 0.34 1.1069 0.78 0.00 0.22 1.11411.12 0.84 0.16 0.00 1.1162 0.74 0.00 0.26 1.1117 0.86 0.00 0.14 1.11881.15 0.96 0.02 0.02 1.1242 0.86 0.00 0.14 1.1188 0.98 0.00 0.02 1.1255

>1.20 1.00 0.00 0.00 1.1266 1.00 0.00 0.00 1.1266 1.00 0.00 0.00 1.1266






0.99 0.24 0.74 0.02 1.0734 0.24 0.00 0.76 1.0787 0.28 0.48 0.24 1.07871.00 0.24 0.74 0.02 1.0734 0.24 0.00 0.76 1.0787 0.28 0.48 0.24 1.07871.01 0.30 0.70 0.00 1.0778 0.28 0.00 0.72 1.0815 0.32 0.40 0.28 1.08211.02 0.36 0.64 0.00 1.0824 0.34 0.00 0.66 1.0858 0.38 0.36 0.26 1.08641.05 0.50 0.46 0.04 1.0931 0.46 0.00 0.54 1.0940 0.54 0.22 0.24 1.09781.08 0.66 0.34 0.00 1.1040 0.58 0.00 0.42 1.1018 0.68 0.08 0.24 1.10751.10 0.74 0.22 0.04 1.1099 0.66 0.00 0.34 1.1069 0.78 0.00 0.22 1.11411.12 0.84 0.16 0.00 1.1162 0.74 0.00 0.26 1.1117 0.86 0.00 0.14 1.11881.15 0.96 0.02 0.02 1.1242 0.86 0.00 0.14 1.1188 0.98 0.00 0.02 1.1255

>1.20 1.00 0.00 0.00 1.1266 1.00 0.00 0.00 1.1266 1.00 0.00 0.00 1.1266






0.99 0.24 0.74 0.02 1.0734 0.24 0.00 0.76 1.0787 0.28 0.48 0.24 1.07871.00 0.24 0.74 0.02 1.0734 0.24 0.00 0.76 1.0787 0.28 0.48 0.24 1.07871.01 0.30 0.70 0.00 1.0778 0.28 0.00 0.72 1.0815 0.32 0.40 0.28 1.08211.02 0.36 0.64 0.00 1.0824 0.34 0.00 0.66 1.0858 0.38 0.36 0.26 1.08641.05 0.50 0.46 0.04 1.0931 0.46 0.00 0.54 1.0940 0.54 0.22 0.24 1.09781.08 0.66 0.34 0.00 1.1040 0.58 0.00 0.42 1.1018 0.68 0.08 0.24 1.10751.10 0.74 0.22 0.04 1.1099 0.66 0.00 0.34 1.1069 0.78 0.00 0.22 1.11411.12 0.84 0.16 0.00 1.1162 0.74 0.00 0.26 1.1117 0.86 0.00 0.14 1.11881.15 0.96 0.02 0.02 1.1242 0.86 0.00 0.14 1.1188 0.98 0.00 0.02 1.1255

>1.20 1.00 0.00 0.00 1.1266 1.00 0.00 0.00 1.1266 1.00 0.00 0.00 1.1266






0.99 0.20 0.70 0.10 1.0507 0.24 0.00 0.76 1.0748 0.22 0.40 0.38 1.06411.00 0.20 0.70 0.10 1.0507 0.24 0.00 0.76 1.0748 0.22 0.40 0.38 1.06411.01 0.26 0.64 0.10 1.0550 0.28 0.00 0.72 1.0765 0.26 0.34 0.40 1.06741.02 0.28 0.56 0.16 1.0591 0.34 0.00 0.66 1.0787 0.34 0.30 0.36 1.07081.05 0.42 0.38 0.20 1.0689 0.46 0.00 0.54 1.0818 0.44 0.10 0.46 1.07891.08 0.50 0.20 0.30 1.0765 0.58 0.00 0.42 1.0833 0.62 0.00 0.38 1.08341.10 0.58 0.08 0.34 1.0809 0.62 0.00 0.38 1.0834 0.62 0.00 0.38 1.08341.12 0.62 0.00 0.38 1.0834 0.62 0.00 0.38 1.0834 0.62 0.00 0.38 1.08341.15 0.62 0.00 0.38 1.0834 0.62 0.00 0.38 1.0834 0.62 0.00 0.38 1.0834

>1.20 0.62 0.00 0.38 1.0834 0.62 0.00 0.38 1.0834 0.62 0.00 0.38 1.0834




Ratio of certainty equivalents of 1-period ALM problem under two different VaR constraints: actual discounting vs constant discounting

0.9900

0.9950

1.0000

1.0050

1.0100

1.0150

1.0200

1.0250

1.0300

1.0350

1.0400

1.0450

0.95 1 1.05 1.1 1.15 1.2 1.25 1.3

Funding ratio S

γ=10

γ=8

γ=5

γ=1




One-period ALM problem with AFCs

Constant Discounting Actual DiscountingSo Stocks Riskfree Bonds CE scaled Stocks Riskfree Bonds CE scaled

0.90 1.00 0.00 0.00 1.0526 0.78 0.00 0.22 1.06060.92 0.97 0.00 0.03 1.0533 0.61 0.00 0.39 1.06280.95 0.81 0.00 0.19 1.0568 0.42 0.00 0.58 1.06910.97 0.75 0.00 0.25 1.0603 0.38 0.00 0.62 1.07340.98 0.72 0.00 0.28 1.0622 0.40 0.00 0.60 1.07520.99 0.70 0.00 0.30 1.0642 0.41 0.00 0.59 1.07661.00 0.67 0.01 0.32 1.0661 0.43 0.00 0.57 1.07781.01 0.66 0.01 0.33 1.0679 0.44 0.00 0.56 1.07881.02 0.65 0.01 0.34 1.0697 0.46 0.00 0.54 1.07961.05 0.62 0.00 0.38 1.0742 0.51 0.00 0.49 1.08141.08 0.61 0.00 0.39 1.0776 0.55 0.00 0.45 1.08231.10 0.61 0.00 0.39 1.0793 0.57 0.00 0.43 1.08271.12 0.61 0.00 0.39 1.0806 0.59 0.00 0.41 1.0831.15 0.61 0.00 0.39 1.0818 0.60 0.00 0.40 1.08321.20 0.62 0.00 0.38 1.0827 0.62 0.00 0.38 1.08341.50 0.63 0.00 0.37 1.0834 0.63 0.00 0.37 1.0834




One-period ALM problem with AFCs (cont)

Constant Discounting Actual DiscountingSo Stocks Riskfree Bonds CE scaled Stocks Riskfree Bonds CE scaled

0.90 0.69 0.28 0.03 0.9626 0.37 0.00 0.63 0.97880.92 0.48 0.49 0.03 0.9798 0.21 0.00 0.79 1.00580.95 0.13 0.86 0.02 1.0189 0.03 0.00 0.97 1.05860.97 0.16 0.78 0.06 1.0389 0.14 0.00 0.86 1.06710.98 0.21 0.70 0.09 1.0441 0.18 0.00 0.82 1.06970.99 0.26 0.62 0.12 1.0484 0.23 0.00 0.78 1.07191.00 0.29 0.56 0.15 1.0521 0.26 0.00 0.74 1.07361.01 0.33 0.50 0.17 1.0553 0.30 0.00 0.70 1.07511.02 0.36 0.45 0.19 1.0582 0.33 0.00 0.67 1.07641.05 0.43 0.32 0.25 1.0652 0.41 0.00 0.59 1.07921.08 0.49 0.21 0.30 1.0706 0.47 0.00 0.53 1.0811.10 0.51 0.15 0.34 1.0735 0.51 0.00 0.49 1.08181.12 0.55 0.07 0.38 1.0760 0.53 0.00 0.47 1.08231.15 0.58 0.00 0.42 1.0790 0.57 0.00 0.43 1.08281.20 0.61 0.00 0.39 1.0816 0.60 0.00 0.40 1.08331.50 0.63 0.00 0.37 1.0834 0.63 0.00 0.37 1.0834




Conclusion: Smoothing yields

•Smoothing liabilities can lead to a large utility loss, up to 4% of wealth per annum with constant discounting and up to 2% of wealth per annum for 4-year average discounting

•Investment manager is torn between 1. maximizing the (utility of the) funding ratio at the end of the investment

horizon which is based on actual liabilities

2. satisfying the VaR constraint and/or minimizing AFCs which are based on smoothed liabilities

•Smoothing induces a greater allocation to the riskless asset because it is a better hedge from a risk constrain perspective


Results: Dynamic investment



Hedging demands

•Dynamic and myopic decisions differ by hedging demands– strategic multi-period investor deviates from decisions that are optimal in a

single-period (or myopic) context in order to hedge against future changes in “investment opportunities” (Merton, 1969)

– intertemporal hedging is effective if asset returns are contemporaneously correlated with changes in investment opportunities

E.g., stock returns tend to be positive (negative) when investment opportunities deteriorate (improve) => stocks are an intertemporal hedge and hence a dynamic investor wants to hold more stocks than a myopic one

•Variation in investment opportunities can be– Physical = time-varying means, variances, correlations

– Perceived = time-varying beliefs, learning

– Preference induced = time-varying risk aversion




Hedging demands (cont)

•For standard CRRA investment problems, gains from dynamic as opposed to myopic investment are usually very small

•Even though the hedging demands themselves may be large in size (up to 25%), the utility impact of those hedging demands are not, i.e. the maximum of the utility function is very flat




Standard CRRA portfolio problem

•As first benchmark we solve a standard 10-year CRRA investment problem (no liabilities, no VaR, no AFCs)


gamma Stocks Riskfree Bonds CE scaled1 1.000 (0.000) 0.000 (0.000) 0.000 (0.000) 3.266 (0.012)5 0.942 (0.047) 0.012 (0.025) 0.046 (0.039) 2.560 (0.011)8 0.608 (0.070) 0.196 (0.087) 0.195 (0.068) 2.255 (0.014)

Dynamic

gamma CE Ratio Bp1 1.0000 (0.0000) 0.005 1.0044 (0.0011) 4.398 1.0088 (0.0032) 8.77


Myopic



Standard CRRA portfolio problem

•As first benchmark we solve a standard 10-year CRRA investment problem (no liabilities, no VaR, no AFCs)



Dynamic

gamma CE Ratio Bp1 1.0000 (0.0000) 0.005 1.0044 (0.0011) 4.398 1.0088 (0.0032) 8.77


Myopic



Standard ALM problem


•As second benchmark we solve a 10-year ALM problem without constraints (no VaR, no AFCs)


Dynamic


Myopic

gamma CE Ratio Bp1 1.0000 (0.0000) 0.005 1.0095 (0.0012) 9.468 1.0093 (0.0033) 9.26



Standard ALM problem


•As second benchmark we solve a 10-year ALM problem without constraints (no VaR, no AFCs)


Dynamic


Myopic

gamma CE Ratio Bp1 1.0000 (0.0000) 0.005 1.0095 (0.0012) 9.468 1.0093 (0.0033) 9.26



ALM under VaR constraint


•Dynamic ALM problem under a VaR constraint based on constant discounting for , but no AFCs

Myopic DynamicSo Stocks Risk free Bonds CE scaled Stocks Risk free Bonds CE scaled Ratio CE Gain in bp per year

<0.85 0.24 0.60 0.16 2.4042 0.24 0.60 0.16 2.4052 1.0004 0.40.90 0.24 0.60 0.16 2.4635 0.24 0.60 0.16 2.4669 1.0014 1.40.95 0.24 0.60 0.16 2.5224 0.24 0.60 0.16 2.5273 1.0019 1.90.99 0.24 0.60 0.16 2.5612 0.24 0.60 0.16 2.5669 1.0022 2.21.00 0.24 0.60 0.16 2.5684 0.24 0.60 0.16 2.5741 1.0022 2.21.01 0.28 0.50 0.23 2.5838 0.30 0.51 0.19 2.5899 1.0024 2.41.05 0.49 0.14 0.38 2.6261 0.54 0.16 0.30 2.6361 1.0038 3.81.10 0.60 0.00 0.40 2.6468 0.66 0.00 0.34 2.6590 1.0046 4.61.15 0.60 0.00 0.40 2.6550 0.71 0.00 0.29 2.6710 1.0060 6.01.20 0.60 0.00 0.40 2.6585 0.76 0.00 0.24 2.6783 1.0074 7.41.25 0.60 0.00 0.40 2.6604 0.79 0.00 0.21 2.6825 1.0083 8.31.30 0.60 0.00 0.40 2.6616 0.80 0.00 0.20 2.6850 1.0088 8.81.35 0.60 0.00 0.40 2.6622 0.80 0.00 0.20 2.6866 1.0092 9.11.40 0.60 0.00 0.40 2.6627 0.81 0.00 0.19 2.6877 1.0094 9.41.50 0.60 0.00 0.40 2.6631 0.81 0.00 0.19 2.6899 1.0101 10.01.60 0.60 0.00 0.40 2.6633 0.81 0.00 0.19 2.6916 1.0106 10.61.70 0.60 0.00 0.40 2.6634 0.81 0.00 0.19 2.6925 1.0109 10.91.80 0.60 0.00 0.40 2.6634 0.81 0.00 0.19 2.6934 1.0112 11.2

>2.00 0.60 0.00 0.40 2.6635 0.81 0.00 0.19 2.6945 1.0116 11.2



Conclusion: ALM under VaR constraint•Popular belief has it that constraints increases the value of

solving a dynamics vs corresponding myopic problem– strategic avoidance of the VaR constraint, in this case, would lead to utility

increases; specifically when the investment opportunity set is dynamic, the investment manager would want to avoid being constrained in his choices when investment opportunities are good

•Our results show the exact opposite: the VaR constraint decreases the gains to dynamic investment

– for low wealth, the dynamic investor wants to invest more in stocks (due to hedging demands) but is not allowed to

– for moderate wealth, the dynamic investor could choose to invest less in stocks today to avoid the constraint in the future, but the constraint already detracts from the optimal portfolio, so the cost of deviating even further is too big

– for high wealth, the current VaR constraint is already a sufficient remedy for avoid the VaR constraint in the future




ALM with AFCs


•The dynamic ALM problem with sponsor contributions based on constant discounting for , but no VaR constraint

Myopic DynamicSo Stocks Risk free Bonds CE scaled Stocks Risk free Bonds CE scaled Ratio CE Gain in bp per year

0.90 0.50 0.50 0.00 1.1768 0.80 0.10 0.10 1.1455 1.0237 27.00.95 0.05 0.95 0.00 1.7585 0.20 0.75 0.05 1.5223 1.1552 145.30.99 0.10 0.85 0.05 2.3513 0.25 0.60 0.15 1.8472 1.2732 244.51.00 0.10 0.80 0.10 2.3698 0.30 0.55 0.15 1.8751 1.2638 236.91.01 0.15 0.80 0.05 2.3886 0.30 0.50 0.20 1.9189 1.2448 221.41.05 0.25 0.65 0.10 2.4434 0.40 0.30 0.30 1.9933 1.2258 205.71.10 0.30 0.55 0.15 2.4923 0.50 0.10 0.40 2.0548 1.2129 194.91.15 0.40 0.45 0.15 2.5286 0.55 0.00 0.45 2.1655 1.1677 156.21.20 0.45 0.35 0.20 2.5540 0.60 0.00 0.40 2.3145 1.1035 99.01.25 0.55 0.30 0.15 2.5730 0.60 0.00 0.40 2.4213 1.0627 61.01.30 0.60 0.25 0.15 2.5879 0.65 0.00 0.35 2.4774 1.0446 43.71.35 0.60 0.15 0.25 2.5993 0.65 0.00 0.35 2.5173 1.0326 32.11.40 0.65 0.10 0.25 2.6085 0.65 0.00 0.35 2.5401 1.0269 26.61.50 0.75 0.05 0.20 2.6208 0.65 0.00 0.35 2.5612 1.0233 23.01.60 0.80 0.00 0.20 2.6276 0.65 0.00 0.35 2.5687 1.0229 22.71.70 0.85 0.00 0.15 2.6303 0.65 0.00 0.35 2.5702 1.0234 23.11.80 0.85 0.00 0.15 2.6308 0.65 0.00 0.35 2.5692 1.0240 23.7

>2.00 0.85 0.00 0.15 2.6310 0.65 0.00 0.35 2.5651 1.0251 24.9

MyopicDynamic



Conclusions

•Financial reporting and risk control rules have real effects on investment behavior that should not be overlooked

•Smoothing the discount rates for computing the PV of future liabilities can lead to grossly sub-optimal investment decisions

•The Importance of dynamic (as opposed to myopic) investment for ALM depends on the specifics of the problem

– In the unconstrained ALM problem the gains from dynamic investment are small even though the hedging demands can be large in magnitude

– The VaR constraint further decreases the small gains to being dynamic

– However, when the investment manager wishes to avoid AFCs from the plan sponsor, solving the dynamic problem can lead to large utility gains due to the first-order risk aversion induce by AFCs

Conclusions

Documents

Jules van Binsbergen and Michael Brandt€¦ · Optimal Asset Allocation in ALM Jules van Binsbergen and Michael Brandt Asset Allocation in Uncertain Times Conference Cass Business