Download Omega:A Sharper Ratio

Pensions – Some Problems of Financial Analysis
10
9
Risk (4.5 , 9) Bond
Risk (6.5,17.5) Equity
Risk (8, 17.5) Equity
Risk (4.0,9)Bond
Risk (5.0, 9.0) Bond
8
7
6
5
4
3
2
1
0
0
10
20
30
40
50
60
70
80
90
100
London January 2006
ISDA / PRMIA
Con Keating
The Finance Development Centre
1
Valuation Methods
The Finance Development Centre
2
So what’s wrong with these?
•
•
•
•
•
•
•
•
•
•
•
•
•
•
What is and what isn’t included in the liabilities.
ABO versus PBO - FRS 17 and IAS 19 PBO
See SEI and Cardiff Business School Paper
Dutch System – ABO, UK – PBO
Source of the ABO-PBO difference is the desire to avoid a mathematical
discrepancy. Benefits are defined as fractions of service, premiums are
set level – so younger members do not receive good value for early
years contributions. Within such schemes there is generational risk
sharing.
FRS17 & IAS19 are mixed attribute systems - Different basis of valuation
Leads to bias and overstatement of deficits.
The liability that constitutes someone else’s asset is its image about
zero – symmetries reverse.
The principal difference between an asset and a liability is one of control
We may not without consent alter the characteristics of a liability
Liability management comes down to renegotiation or defeasement
The value of an asset is a function of its use.
First best use, Second best use
Value in use in general differs from value in exchange
The Finance Development Centre
3
A way to think about Market prices
•
•
•
•
•
•
•
•
•
•
•
•
•
For any asset to have a value it must generate future cash-flows
These future cash-flows are not known with certainty.
We may present value these cash-flows by discounting them
We are left with an expected present value and a range of uncertainty
We shall call this fundamental uncertainty
Markets serve to price this present value.
We might for example today bid 60 for a stream of cash-flows which
have a present value of 100 +/-10
We may be considered to be risk averse
Equally we may say that we are greedy.
This is the Market Risk Premium
This is the fear and greed of popular market parlance.
The amount by which markets discount present values varies with time.
The Market Risk Premium is in fact a distribution – today 60, tomorrow
65
The Finance Development Centre
4
Market Prices Cont.
•
•
•
•
•
•
•
•
•
•
There are two sources of uncertainty at work in the volatility of market
prices.
Fundamental Uncertainty
Market “Risk” Premium Uncertainty
This distinction is not reliant upon present values, we might equally
compare future values.
Fundamental Uncertainty is exogenous but the Market Risk Premium
Uncertainty is endogenous.
Fundamental Uncertainty may be viewed as a game against nature but
the Market Risk Premium Uncertainty is a game against others.
It is reasonable to assume that the higher the fundamental uncertainty,
the more variable the market risk premium may be.
Extending the investment tenor increases fundamental uncertainty.
The market risk premium may be considered as the incentive necessary
to attract speculators and dealers.
However, the question then is how much of this arises from fundamental
uncertainty and how much from market risk premium volatility.
The Finance Development Centre
5
Financial Economics
•
•
•
•
•
Many attempt to justify market prices from the basis of elementary
financial economics.
We can today exchange £100 of equities and bonds and we can do the
same tomorrow ad infinitum.
This gave us Modigliani Miller and Black Scholes and the no-arbitrage
replication techniques.
M&M is just a re-statement of its axiomatic truth that the value of A+B is
equal to the Value of A plus the Value of B
Black-Scholes and no-arbitrage techniques work simply because the
spanning set of securities contains the security on which the option is
written.
• And this contains its risk premium
•
•
•
The implied volatility of option pricing is simply a distortion of market
price volatility.
Market prices are risk adjusted values
All of these are true but….
The Finance Development Centre
6
Finance 102
•
•
•
•
•
•
•
•
•
Financial Institutions do not exist in this simple world.
They are merely collections of securities
Markets are complete – we can hedge any risk
Accounting standards don’t matter
Regulation does not modify our behaviour
This is not the real world
Pensions schemes exist to internalise things which cannot be done in
markets
Information is costly
There are problems of incentives, adverse selection and moral hazard
• Values are no longer unique
“Value estimates that are calibrated to observable market prices
may be “unbiased” with respect to market valuations. But those
same valuations, in turn, may well be biased (misaligned) with
respect to a counterfactual benchmark in which prices reflect the
right signals for economic behaviour.”
Borio and Tsatsaronis BIS
The Finance Development Centre
7
Finance 101 revisited
•
•
•
•
•
•
•
•
•
•
•
Pensions liabilities are bond like
They aren’t any more so than any other future cash-flow - Their
sensitivities are to salaries, wage and retail price inflation and longevity
The apparent sensitivity arises because we discount future cash-flows
using an interest rate curve
In theory the default risk free – but that does not exist
But this is just a functional to compare cash-flows distributed in time
In theory there are infinitely many such functionals - Including our
Omega!
One desirable attribute of any measure is that it is invariant – market
prices are not
The proliferation of regulated methods in pensions estimation results in
multiple scales being used in measurement – Remember the smaller the
scale, the greater the magnitude observed - Mandelbrot
Partial Analysis – pensions deficits are the result of falling interest rates
increasing liability values, increasing longevity, and poor equity
performance.
Complete Equilibrium analysis – falling interest rates make possible
projects which were not previously viable and increasing longevity
reduces uncertainty about future consumer demand
Governments collect more taxes and Companies face less uncertainty
about the future evolution of the economy
The Finance Development Centre
8
Market Prices
Yield curve and risk premium in Germany
(January 1995)
8.80%
Risk Premium and Curves
7.80%
6.80%
5.80%
4.80%
3.80%
2.80%
1.80%
0.80%
-0.20%
0
5
10
15
Horizon
Explanatory power:
Risk Premium Volatility /
Market Price Volatility
If we next consider holding periods, what does our exposure to these risk
sources look like?
If we are holding for immediate sale, then the exposure to market risk
volatility is total.
If we are holding intending to consume the future cash-flows as they
arrive, we are exposed only to the fundamental uncertainty
The Finance Development Centre
9
Risk Exposures
We begin with a comparison of equity total returns, price returns
and dividend returns.
The sample period is from March 1988 until March 2005
FTSE
Total
FTSE
Price
FTSE
Dividend
S&P
Total
S&P
Price
S&P
Dividend
StDev
4.33
4.32
0.21
3.90
3.89
0.10
Mean
0.93
0.61
0.32
1.00
0.81
0.19
We observe that price volatility is dominant.
If we are holding these securities to consume dividends, we are
not exposed to this price volatility in any economic sense.
We expect prices to vary with retained earnings, interest rate
shifts and changes in the risk premium.
The Finance Development Centre
10
Market Risk Premium Exposure
Zero coupon bonds and non-dividend paying equity
Return on Equity 10%, tax rate 35% - Expected return 6.5% Volatility
17.5%
Bond: Expected Return 4%, Volatility 9%
Likelihood of Loss and Holding Term
Years
1
0
10
20
30
40
50
60
70
80
90
100000
100
0.1
10000
Expected Value (log scale)
Likelihood of Loss (log scale)
0.01
0.001
0.0001
1000
0.00001
0.000001
Likelihood of Loss
Bond
Equity
0.0000001
100
The Finance Development Centre
11
Shortfall and Risk
Equity relative to a 4% p.a. target
Expected Shortfall and Risk
8
100000
Risk
Expected Shortfall
7
5
1000
4
100
3
2
Expected Shortfall - Log Scale
Risk ( Product of likelihood and
magnitude ES - %)
10000
6
10
1
0
0
10
20
30
40
50
60
70
80
90
1
100
Years
Expected shortfall increases over time, but risk – the product of the
expected shortfall and its likelihood - is complex and rapidly
declining.
The Finance Development Centre
12
Equities and bonds
10
9
Risk (4.5 , 9) Bond
Risk (6.5,17.5) Equity
Risk (8, 17.5) Equity
Risk (4.0,9)Bond
Risk (5.0, 9.0) Bond
8
7
6
5
4
3
2
1
0
0
10
20
30
40
50
60
70
80
90
100
A mix of different bonds and equities
Which is riskier? It depends upon the horizon and the terms and
conditions.
The Finance Development Centre
13
Cash-Flows and Holding Period
Dividend Paying Equity
7
10000
6
1000
Risk %
4
100
3
Expected Shortfall
5
Risk
2
CF adjusted Risk
10
Expected Shortfall
CF adjusted Expected Shortfall
1
0
0
10
20
30
40
50
60
70
80
90
1
100
Years
75% Pay-out in Dividends – Threshold 0
By ten years the risk is negligible
The Finance Development Centre
14
A base case
Threshold Zero, Dividend payout total and all held in cash
Dividend Paying Equity
7
1000
6
100
Risk %
4
3
Expected Shortfall
5
10
Risk
2
CF adjusted Risk
Expected Shortfall
CF adjusted Expected Shortfall
1
0
0
10
20
30
40
50
60
70
80
90
1
100
Years
Expected shortfall and risk are constant in time
The cash-flow adjusted expected shortfall rises and cash-flow
adjusted risk is negligible beyond year ten.
The Finance Development Centre
15
Does it work like this in the real world?
•
•
•
•
•
•
•
•
•
•
Yes - There is a very long history of academic research finding that
variations in fundamental uncertainty are unable to explain more than
a small fraction of market price volatility
Shiller, Mehra & Prescott and a host of others
And no mention here of mean reversion and lower volatility levels.
Go away and think about implied volatilities derived from option
prices
Go away and think about Merton based models of Credit
When these are based upon equity prices, you will need to calibrate
for both the likelihood and volatility of the likelihood of default.
Go away and think about where the excess returns come from in
those structured products.
Go away and think about hedge funds and whether you really want to
pay one up twenty for systematic risk premium collection
Under FRS 17 and IAS 19, these effects are transmitted to the
sponsor company balance sheet – debt on the sponsor and arbitrary
volatility in the STRGL
Under the Dutch system, where funds are treated as if they are
stand-alone companies, they are required to hold surpluses to
cushion against these effects – (30% of liability values)
The Finance Development Centre
16
Solvency Tests
A key feature of all new “Risk Based” Pensions regulation is the
presence of a recurrent solvency test.
It is obvious that at the point of insolvency of the sponsor we
should require 100% funding of the scheme.
But should this be applied elsewhere?
We might for example argue that a deficit aligns the interests of
company and employee.
It is also often argued that a strong funding ratio is a positive
signal to employees
But to be credible any signal must be costly
The Finance Development Centre
17
Costs of Solvency
The primary decision criterion for funding from the standpoint of
the finances of the company is that the (post-tax) rate of return on
assets within the fund should equal or exceed the (post-tax) rate
of return of assets within the business.
The credit rating agencies are influential and rate companies
lower in the presence of FRS 17 / IAS 19 deficits.
This raises the costs of finance for the firm.
The presence of a solvency test renders the investment process
path dependent.
An illustration of a path independent process is one where we
require a certain sum of money at a point in time in the future and
it does not matter how we get there.
The Finance Development Centre
18
The cost of path dependency
We might view path dependency as shortening the time horizon
available for investment from the term of the fund to the term of
the test.
Viewing the world in this manner would place the cost at around
2% per annum.
It is of course from the social welfare standpoint undesirable
Perhaps better is to model this as a requirement to fund, to raise
equity whenever deficits occur.
If we have a 60/40 Equity-Bond portfolio with annual returns of
8% and 4% and volatilities of 17% and 8% and correlation of 0.40
And we begin with a 100% funded scheme, we observe a cost of
around 60 basis points.
The Finance Development Centre
19
The cost of path dependency
Somewhat contra-intuitively if we have an all bond portfolio this
cost only declines to 50-55 basis points per annum
And the all bond strategy costs about 2.5% in expected return
For an all equity fund the cost approaches 1%
It is difficult not to conclude that these costs justify long run
smoothing techniques
Finally of course we should expect regulations to feed back into
the behaviour of the market risk premium.
The rate of change of regulation in both pensions and insurance
makes this an econometrically challenging and perhaps
intractable exercise
In the UK such analyses are further compounded by the removal
of Advanced Corporation Tax in 1997
The Finance Development Centre
20
ALM in Pensions
•
•
•
•
•
Stochastic duration – not the Macaulay or Modified
Models for the term structure
Partial durations wrt each term structure factor
Multiple partial convexities.
Under positive yield curves stochastic duration can vary by 10%-20%
from the modified figure.
• Regulation – protecting the beneficiary
• One of the few things we can do to reduce dependence upon the
projected evolution of the economic dependency ratio is to improve
productivity growth
• Productivity growth of around 1% p.a. will greatly mitigate this.
The Finance Development Centre
21
Productivity and Risk based regulation
•
•
•
•
•
•
•
•
•
•
One of the effects of risk based regulation is to encourage investment in bonds
rather than equity
Bonds are less volatile than equities in market price terms
This is encouraging public sector investment rather than private sector
investment
The European Central Bank has concerns that the availability of debt finance will
result in debt issuance as a tax substitute rather than for capital and
infrastructure investment
For the past twenty five years we have privatised everything that moves – Jon’s
presentation was about one current aspect of this.
The economic orthodoxy is that private sector investment is more productive
than public sector investment – the analysis is one of incentives.
There is no subtle risk adjustment here – the assets and markets are the same
before and after privatisation
The effect of risk based regulation will be to lower future productivity growth
And ensure that the economic dependency ratio that causes such concern
comes to pass.
That is I believe an unintended consequence
The Finance Development Centre
22
Further Work
Problems of Recognition
Newer developments in finance offer many potentially interesting
new solutions
It is clear also that some currently being offered are expensive
and inappropriate
Immunisation and Dedication approaches are among these.
Insurance as an inter-temporal smoothing mechanism is obvious
Hedge or Absolute Return Funds, where leverage and risk
premium smoothing are at work, are perhaps another
But that is the subject of the OECD/IOPS Jordan Conference.
[email protected]
The Finance Development Centre
23
A final thought…or two.
John Watson, Chairman, Boots Pensions
Letter to the F.T. February 19 2005
“Both trends [DC and LDI] are ill-conceived as long-run solutions,”
Robert Merton, I.P.E., January 6 2006
The Finance Development Centre
24