1. Portfolio Construction and Risk Management
g
Consider the portfolio selection model:
where
Quantifying the inputs to the optimization is good discipline.
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2. Portfolio Construction and Risk Management
g
Risk Management
Start with quantification of what you know (risk)
S f f ( )
Prepare for what is not knowable (uncertainty)
Challenge simplifying assumptions
C f
1) Only care about the mean and variance of the
probability di t ib ti of portfolio returns
b bilit distribution f tf li t
a) Ignore skewness (asymmetry) and kurtosis (fat tails)
b) Event risk
c) Market failure
d) Government Intervention
e) Investment horizon – liquidity demand versus
provision 2
3. Portfolio Construction and Risk Management
g
2) Parameter Stationarity (or one period model)
a) Regime Change
b) Time variation characteristics (bonds)
c) Cuspiness (securitized asset tranches)
d) Dynamic interaction (liquidity->fundamentals-
>liquidity => downward spiral
e) Time-varying covariance structure (i.e., correlations
Time varying
increase during crisis periods)
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4. Portfolio Construction and Risk Management
g
Risk Management Approaches
1) Multi-Dimentional Risk Analysis (calculate sensitivity exposures
to state variables)
2) Stress tests on each exposure
3) Value-in-Stress (multiple scenario analysis)
4) Value at Risk (VaR) is probabalistic
a)
) Requires covariance matrix estimation
q
b) i.e., 95% VaR is L= –V x 1.645 x portfolio standard deviation .
There is a 5% chance of loosing more than L.
c) Distributional assumption for tail risk
d) Parameter estimation
i. Historical data (with or without forward looking adjustments)
ii. Forward simulation
e) Model the tail of the distribution
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5. Portfolio Construction and Risk Management
g
Dealing with the unknowable
1) Stop Loss (then what?)
2) Flight to quality hedges
3) Long/short strategies (no net market or macro-factor
macro factor
exposures)
4) L k
Lock-ups
5) Portfolio Insurance
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6. Portfolio Construction and Risk Management
g
General Valuation Equation
x1 x2 xN
V0 = + + ...+
(1+ R1 ) (1+ R1 )(1+ R2 ) (1+ R1 )...(1+ RN )
For bonds, the cash flows in the numerator are expected coupons
and principal payment(s) in each period.
For common stock, N is infinity and the numerator contains
stock
expected cash flows to equity holders.
The R' s are the per period expected required rates of return to
compensate investors for the riskiness of their respective cash
flows.
Risk Premi m is a function of priced risk factors and the sec rit ’s
Premium f nction security’s
sensitivity to those exposures.
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9. Pension Plan Asset-Liability Management
2006 Pension Protection Act
Requires underfunded plans to move toward a 100% funding level
d f d d l d f d l l
Provisions come into effect on a rolling schedule over several years
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10. Pension Plan Asset-Liability Management
Provisions combined with market performance trends are affecting asset
allocations now
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11. Pension Plan Asset-Liability Management
Major Factors Affecting Pension Plan Funding Status
Performance of assets
Performance of assets
Company contributions
Number of employees covered and cost per employee
Discount rates used to calculate the present value of
Discount rates used to calculate the present value of
future obligations
AA rated Long‐dated corporate bonds
AA rated Long dated corporate bonds
Average of AAA, AA, and A rated corporate bonds
Note that the discount factors have fallen sharply during 2009 =>
Note that the discount factors have fallen sharply during 2009 =>
increase in PV of future obligations
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12. Pension Plan Asset-Liability Management
Asset Allocation: Select a portfolio that minimizes the
standard deviation of the plan’s surplus
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13. Pension Plan Asset-Liability Management
Liabilities rate of return series:
Rate of change in the present value of future liabilities for the
change in discount rates (AAA‐A corporate bond rates
g ( p
prescribed by the 2006 pension protection act).
The term structure of liabilities in this example is that of the
The term structure of liabilities in this example is that of the
average pension plan.
The riskiness of the plan’s liabilities in the time‐series of
Th i ki f h l ’ li bili i i h i i f
returns is defined by the time period selected.
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14. Pension Plan Asset-Liability Management
Asset Allocation: Select a portfolio that minimizes the
standard deviation of the plan’s surplus
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