Transcript BrightonRock Insurance - ISDA

Risk & Risk Sharing
Solvency 2, Insurance and Pensions
ISDA – PRMIA
London July 2008
Con Keating
1
Risk Measures
VaR and Shortfall
1
ES  VaR  I 3

VaR 1   F
1
(1  )
Regulatory Mechanisms
Pruin 
1

2
,
where  
C  N
 N
.
• Value at Risk is simply an application of insurance ruin theory
• It dates from 1963 and William Baumol rather than the 1990s
• If we wish to regulate the probability of ruin, there are variables other
than capital (C) we may utilise.
• The loading factor (λ) but this is product regulation
• The number of risks (N) but this has competition implications
• The variability of individual risks (σ), again product regulation
• The regulator favours institutional over product regulation.
• The regulator also favours principles over prescriptive rules
Solvency 2
• Remember Risk = Likelihood x Consequence
• By increasing the capital of an insurer, we lower the likelihood of
insolvency and the risk to a policyholder
• The regime is effective
• But for a pension scheme with recourse to its sponsor
• If we capitalise the pension scheme, we lower the consequence
• At the cost of the sponsor, raising the likelihood of their insolvency
• Risk may increase.
• And an orphaned pension scheme has a long residual life facing
uncertainty
• For which funding or over-capitalisation is advisable
• This is a genuine problem of corporate finance
A choice game
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Choose between receiving
A) €100 with certainty
B) €200 / €0 on the flip of a coin
And now paying
C) €100 with certainty
D) €200 / €0 on the flip of a coin
Most choose A and D
Reversal of attitude
Does your choice change with repetition?
Risk and Value
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The game illustrates the differing role of uncertainty for assets and liabilities.
For our asset uncertainty reduces current and future value.
This does not require “risk aversion” - It is a property of repeated games
But that which hurts our asset helps our liability
Liabilities – the long term aspect is good not bad.
Equity is preferable to short term bank loans
A consequence – the more certain a liability is, the greater its current cost
A liability differs from its asset counterpart in location and symmetry
Multiplication by -1, a rigid rotation. Not a translation on the returns line
Certainty Equivalent Premium
Geometric Mean =
Arithmetic Mean –
0.5*Variance
10% volatility = 0.5%
20% volatility = 2.0%
Property of repeated
games
Volatility / Risk has a cost
Fat Tails and Asymmetry
Fat Tails – Often but not always
lower – reverts reasonably
(-ve) Asymmetry – strictly lower
very slow to revert
Volatility
It is far too high for fundamentals to explain
Annual Dividend Volatility is of
the order of 3-4%
Retail price and wage inflation
volatility is similarly low
But Bond Price Index Volatility is 6 12%
Equity Index Volatility 12 – 30%
Empirical Volatility
Volatility possesses a holding period term structure
Campbell and Viceira
The obvious explanation is
that markets represent a costly
option on liquidity
But that is heresy to the
fundamentalist economists
If we use market prices for assets and liabilities, what does this do?
N(7,25)
N(5,15)
Rebalanced
Initial
Mean
0.0682
0.0499
0.0591
0.0546
St.Dev.
0.251
0.149
0.147
0.179
Skew
-0.245
-0.032
-0.097
-0.188
Kurtosis
0.045
-0.029
-0.186
0.588
Diversification
& Strategy
Diversification and Strategy
1E+23
1E+20
Normal(0.07,0.25)
Normal(0.05,0.15)
EW Rebal. Portfolio
EW Initial Portfolio
1E+17
Value
1E+14
1E+11
1E+08
100000
100
0.1 0
100
200
300
400
500
Sample
600
700
800
900
1000
Why does this matter?
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Erb & Harvey – Geometric Returns
Commodity index returns
Diversification matters in more than a risk mitigation sense.
It enhances the geometric return of the portfolio
And this result is not dependent upon risk premia
In the case of jointly normal assets
Expected equally weighted rebalanced portfolio diversification
return is:
1
1 2
E{EWRP DR}  1    1   
2
K
Strategies now matter
Risk-Sharing
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Suppose we can split volatility between two parties
Then the total cost diminishes
20% = 2% yield cost, but 2* (10%) = 2*(0.5%) = 1% yield cost
But we can’t.
Which leaves only risk transfer as the sharing mechanism
And one man’s asset is another’s liability
Risk-sharing is costly to one or other.
What about risk diminution?
Pension Sensitivity and Hedging
The relation between real return, longevity and
contribution cost
Contribution, Longevity and Investment Rate
40 Years Contributions: 2/3 Final Salary
45%
40%
35%
30%
Contribution % Salary
25%
20%
15%
10%
5%
35
0%
30
0.01
0.02
25
0.03
20
0.04
Real Investment Return
0.05
Longevity at
65
Returns and Risk
Real Rates, Contribution Costs and Risks
2/3 Replacment Salary
500
120
9.00 - One Real
4.33 - Three Real
Low Risk
High Risk
400
100
Value of Fund
350
80
300
250
60
200
40
150
100
20
50
0
0
1
11
21
31
41
Year
51
61
Absloute Risk
450
ILG and RPI
A hedge using the 15+ ILG index?
Partial autocorrelogram (ILG)
1
1
0.8
0.8
0.6
0.6
0.4
0.2
0
-0.2
0
1
2
3
4
5
6
7
-0.4
8
9
10
11
12
13
14
Partial autocorrelation
Partial autocorrelation
Partial autocorrelogram (RPI)
0.4
0.2
0
-0.2
0
1
2
3
4
5
6
7
-0.4
-0.6
-0.6
-0.8
-0.8
-1
-1
Lag
Lag
Fundamentally different dynamics
8
9
10
11
12
13
14
Lags?
Cross-correlations - correlations among series at varying lags
Cross-correlations (ILG / RPI)
The result is volatility
1
But holding a single ILG
certainly pays inflation plus
to maturity
Cross-correlation
0.8
0.6
0.4
0.2
0
-0.2
-14 -12 -10 -8
-6
-4
-2
0
-0.4
-0.6
-0.8
-1
Lag
2
4
6
8
10 12 14
Some further volatility effects
• Excess volatility in financial markets is one of the great puzzles of
financial theory
• If we expressly introduce this into scheme funding requirements, for
example by the use of target funding levels such as the OECD’s
recommended 100% we see that the costs of the scheme rise
• This is an explicit cost of myopia, short-term-ism.
• We show a fifty year scheme with liabilities increasing at 5% per
annum deterministically and assets increasing at 6% pa with
volatility at 10%
• We also show the “make-good” portfolio which requires additional
contributions whenever the scheme falls below 100% funded.
• Perhaps the most important volatility effect is perversely the advent
of Liability Driven Investment
Funding Rules
The additional contributions
needed to maintain full
funding have a net present
value of 46% of the fund’s
initial value
And this is raised in times
when the cost of capital is
higher than the average
We can also show that deficit based rules are, in general, inefficient
This is an illustration of the principle that path dependent processes
are inefficient
Survival Times
Cash-flow Life
(Years)
Interest rate
Three
Five
Seven
Ten
50% Funded
18
13
10
7
60% Funded
22
17
13
10
70% Funded
29
21
17
13
80% Funded
36
27
22
17
90% Funded
49
38
30
23
100% Funded
NM
NM
NM
NM
The interesting feature of this stylised model is that the lower interest
rates are, the longer one has to rectify deficits
It also suggests that scheme specific funding requirements for pensions
should be interest rate dependent.
Finally it demonstrates the inadequacy of the view of risk management
as concerned only with the immediate
Real Equity Prices and
Insolvency Rates
1.60%
1.40%
1.20%
Insolvency Rate
1.00%
0.80%
0.60%
0.40%
0.20%
0.00%
0
50
100
150
200
250
300
Re al Pr ice Inde x
No obvious relationship between real equity prices and insolvency
rates
In Changes
60.00%
No obvious relation
between change in
market prices and
changes in insolvency
rates
Change in Insolvency Rate
40.00%
20.00%
-80.0%
-60.0%
-40.0%
-20.0%
0.00%
0.0%
20.0%
40.0%
-20.00%
-40.00%
Change in Real Equity Price
Another nail in the coffin of market prices as fair value
60.0%
80.0%
100.0%
Basic Company
& Scheme
Company
Returns
Volatility
Income
One Year
15
10
12.75
97.75
Assets
85
Equity
85
Debt
0
7.5
0
0
Liabilities
50
5
2.5
52.5
Assets
65
8
5.2
70.2
97.75
Scheme
20
Group
Assets
150
15.16575
167.95
Equity
100
97.75
Liabilities
50
52.5
Funding
Rules
Ne gative Corre lation
14
12
Distance from Default
10
8
6
No Debt Correl: 0
4
No Debt Correl: 1
Correl: -1 Co Negative
2
Correl: -1 Scheme Negative
0
0
10
20
30
40
Sche m e Funding
50
60
70
The Funding and Debt Level Relation
Distance from Default
Correlation 0
12
10
8
6
4
2
0
-2
140
100
120
Debt Level
80
60
40
20
-4
0
Distance
(StDevs)
5
15
25
35
45
55
65
Scheme
Funding
Debt and Equity Volatility
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Suppose I have equity of 50 with a duration of 10 years
And I buy assets of 50 with a risk of 20
Then my equity risk exposure is 20
Now I borrow a further 50 at call, doubling the asset holding
My duration of liabilities is now 5 years and the risk is 40
The risk of Equity has increased fourfold
Insolvency likelihood has increased
Next suppose I borrow 50 long term with a duration of 30 years
Then the duration of liabilities is 20 years
And the risk of Equity is unchanged at 20 and insolvency likelihood is
unchanged
Doubling the long term leverage to 100 results in Equity risk of 25.71
And minor increases in insolvency likelihood
When the pension scheme is large relative to the company, borrowing from
it (leaving unfunded) lowers the aggregate risk
Risk – Sharing Consultation
• This would have us believe that the largest risks faced by UK
pension schemes are longevity and investment risk
• The truth is the primary risk is sponsor insolvency
• And all other risks are subordinate to that
• The PPF desire to add asset risk to its levy factors is yet another
illustration of focus upon a conditional risk
• And further illustrates that the PPF cannot resolve the corporate
finance paradox at the heart of pensions funding
• Solvency 2 would aggravate that paradox
• Insurance can resolve it fully and cost effectively.
Accounting standards
Assets and Capital assets
• Today’s market price may, perhaps, reflect current information
perfectly, but, even with the addition of rational expectations, that
does not mean that it embodies perfect information with respect to
future prices.
• That would require perfect foresight.
• A consumption good may be consumed immediately; the information
content of its current market price is close to complete.
• Though the option to defer consumption needs a little thought, as do
alternate possible uses as a store of value.
• The value relevance of a market price is high for such assets
• By contrast, the information content of a market price for a capital
asset is at best limited to that known today, which is far from
complete over the life of that capital asset
Capital assets
• Of course, for very long lived capital assets the information content
of today’s price may actually be very small and the value relevance
low.
• Obviously as the time dimension increases, so too does the
potential information incompleteness of a market price today with
respect to the future value.
• Each and every price may have differing information content, though
they all share a common set, today’s available information.
• The value relevance of today’s price may also differ for each and
every owner of the capital asset.
• Increasing the size of today’s information set, that which is available
today, will not remedy this incompleteness as that is based
predominantly in future information.
• The more incomplete the information content of a price the greater is
the potential for strategic behaviour, and far more substantial and
sustained departures of the market price from true value.
Accounting Models
• There are questions with all financial theories as to whether they
function as cameras, recording empirical regularities or as engines
influencing performance.
• Most important for these latter theories are the prescriptive actions
they generate to reinforce themselves. Or as the German sociologist
Max Weber expressed it: “To seal the ideological bondage”
• The criterion of decision usefulness puts the new accounting
squarely in the “engine” or positive camp
Mixed games
• A distinct co-ordination feature of financial markets – Keynes’
newspaper competition in which “the competitors have to pick out
the six prettiest faces from a hundred photographs, the prize being
awarded to the competitor whose choice most nearly corresponds to
the average preferences of the competitors as a whole; so that each
competitor has to pick not those faces which he himself finds
prettiest, but those he thinks likeliest to catch the fancy of other
competitors, all of whom are looking at the problem from the same
point of view.”
• Francis Galton’s study of the wagers placed on the weight of an ox
at a fair in 1906 is relevant in the context of aggregation of individual
beliefs – the average guess was 1,198 pounds and the actual weight
was 1,197 pounds.
• However these wagers had one important property; they were
independent – no-one knew anyone else’s wagers. But when a
crowd is permitted to know the wagers of others, we admit the
possibility of strategic behaviour.
Mixed games
• Strategic behaviour and Keynesian co-ordination have the effect of
making endogenous to the market new sources of risk and
uncertainty; this lowers the role of true information in price formation.
• In Galton’s example this might consist of placing wagers close to
those of the experts, the slaughter-men and butchers, or equally of
relying on rating opinions in a more recent context.
• The possibilities for hysteresis or feed-back in such situations are
obvious – and can result in very strange equilibria indeed. Certainly
there is no longer any reason to believe that the law of large
numbers will apply to this market, or that its elementary statistics will
be relevant, adequate descriptions.
• It is evident that financial markets are mixed games – they are partly
games against nature and partly games against others. Uncertainty
and risk have both exogenous and endogenous sources.
• In such situations the all powerful arbitrageur is as likely to behave
in a destabilising predatory manner as to arbitrage prices back to fair
value.
Regulations
• The accounting standards and regulations are driving much
economic behaviour in pensions
• Market prices induce myopia and strategic behaviour
• This is costly
• We should rectify these problems before transferring risks and costs
to pensioners
• The accounting can be rectified simply by applying a test to the use
of market prices
• A question:
• What is the value relevance of this price for this asset/liability
in this context?
Contact Details
[email protected]
• Website:
• www.brightonrockgroup.co.uk