October 24, 2024 • 55 mins
My guest for Episode 100 is David Wilkie, CBE, FFA, FIA, FSS, FIMA, Hon D Sc, Hon D Math, Chairman at InQA Limited.
The theme for the episode is 𝗔𝗰𝘁𝘂𝗮𝗿𝗶𝗲𝘀 𝗶𝗻 𝗥𝗲𝘀𝗲𝗮𝗿𝗰𝗵 - 𝗣𝗮𝗿𝘁 𝟮.
David and I covered the following topics in 𝗣𝗮𝗿𝘁 𝟮 of this historic episode:
✅ Modeling uncertainty within insurance, finance, and risk mgmt
✅ Shortcomings of the Black-Scholes option pricing model
✅ The origins and evolution of the Wilkie Model for economic variables
✅ Realistic disaster scenarios for marine insurance
✅ The financial crisis, agency risk, and model hazard
✅ Helping to shape actuarial standards and practice globally
✅ David’s new unreleased research paper
𝗣𝗮𝗿𝘁 𝟮 Time Markers
1:25: Random walk hypothesis and modern financial economics.
2:49: Unit-linked life insurance policies and connection to share price uncertainty.
6:30: Foundations of the first Wilkie Model (retail prices, dividends, dividend yields, and long-term interest rates).
8:40: Limitations of Black-Scholes option pricing model assumptions (share price, transactions costs, and hedging constraints).
13:25: The key innovation for the first Wilkie Model (incorporating stochastic framework, variability, variable interrelations, and autoregressive methods).
16:30: The second Wilkie Model (short-term interest rates, property, property yields, and foreign exchange rates).
19:05: Index-linked yields and modifying long-term interest rate assumptions.
22:02: Incorporating company earnings and payout ratios (dividend payout and price/earnings) into Wilkie Model.
23:56: Realistic disaster scenarios, evaluating extreme losses for oil industry, and Lloyd’s syndicate as-if reserves.
30:16: Incorporating parameter uncertainty into Wilkie Model (hyper model approach).
32:51: Using fatter tail distributions (Normal, hyperbolic, and Laplace) for variables with extreme values and high kurtosis.
38:06: Transparency challenges around economic scenario generation.
39:03: Packaging of mortgages leading up to 2008 financial crisis and resulting implications.
42:32: Misaligned incentives in corporate taxation (interest
payment deductions).
46:33: Involvement with actuarial and scientific organizations.
50:30: Approved directive for life insurance valuation principles to address country-level disconnects.
52:26: Research that David hasn’t done yet but intends to do.
If you are an actuary interested in research, modeling, and programming, you want to listen to this.
My Website: maverickactuary.com
The theme for the episode is 𝗔𝗰𝘁𝘂𝗮𝗿𝗶𝗲𝘀 𝗶𝗻 𝗥𝗲𝘀𝗲𝗮𝗿𝗰𝗵 - 𝗣𝗮𝗿𝘁 𝟮.
David and I covered the following topics in 𝗣𝗮𝗿𝘁 𝟮 of this historic episode:
✅ Modeling uncertainty within insurance, finance, and risk mgmt
✅ Shortcomings of the Black-Scholes option pricing model
✅ The origins and evolution of the Wilkie Model for economic variables
✅ Realistic disaster scenarios for marine insurance
✅ The financial crisis, agency risk, and model hazard
✅ Helping to shape actuarial standards and practice globally
✅ David’s new unreleased research paper
𝗣𝗮𝗿𝘁 𝟮 Time Markers
1:25: Random walk hypothesis and modern financial economics.
2:49: Unit-linked life insurance policies and connection to share price uncertainty.
6:30: Foundations of the first Wilkie Model (retail prices, dividends, dividend yields, and long-term interest rates).
8:40: Limitations of Black-Scholes option pricing model assumptions (share price, transactions costs, and hedging constraints).
13:25: The key innovation for the first Wilkie Model (incorporating stochastic framework, variability, variable interrelations, and autoregressive methods).
16:30: The second Wilkie Model (short-term interest rates, property, property yields, and foreign exchange rates).
19:05: Index-linked yields and modifying long-term interest rate assumptions.
22:02: Incorporating company earnings and payout ratios (dividend payout and price/earnings) into Wilkie Model.
23:56: Realistic disaster scenarios, evaluating extreme losses for oil industry, and Lloyd’s syndicate as-if reserves.
30:16: Incorporating parameter uncertainty into Wilkie Model (hyper model approach).
32:51: Using fatter tail distributions (Normal, hyperbolic, and Laplace) for variables with extreme values and high kurtosis.
38:06: Transparency challenges around economic scenario generation.
39:03: Packaging of mortgages leading up to 2008 financial crisis and resulting implications.
42:32: Misaligned incentives in corporate taxation (interest
payment deductions).
46:33: Involvement with actuarial and scientific organizations.
50:30: Approved directive for life insurance valuation principles to address country-level disconnects.
52:26: Research that David hasn’t done yet but intends to do.
If you are an actuary interested in research, modeling, and programming, you want to listen to this.
My Website: maverickactuary.com
Mark as Played
Transcript
Episode Transcript
Available transcripts are automatically generated. Complete accuracy is not guaranteed.
Speaker 1 (00:00):
So let's pick up the conversation, David. In the first
half of the conversation, we talked about your backgrone, We
talked about your early days using the power programming to
develop models and utilize them. No, we want to take
things that step. Let's take things that step further and
not just talk about modeling, but let's talk about modeling uncertainty,
(00:21):
which is something that you're known for. So you're a
pioneer in modeling uncertainty within insurance, finance and risk management.
When did the idea of stochastic modeling start to get
traction or broadly speaking.
Speaker 2 (00:36):
Well, you're coming now onto what people call the Wilky model,
which I published in nineteen eighty four, quite a long
time ago now, But I bet I need to go
back a bit before that. I mentioned that sometime in
the early seventies I had become economist research manager of
(01:00):
the oft Standard Life looking at the economy was to
three other economists to advise the investment department about what
the economic future might be. And this part number of
companies had done this sort of bringing in economists to
(01:20):
assist the investment department, and I was put in charge
of this, and I expected what I was doing one
time to my friend Sidney Benjamin, sadly died some years ago,
but was his his paper on for probably in nineteen sixties,
(01:41):
what Actories can Do with Computers is still a very
useful paper to go for anybody to go back to.
It said, all sorts of things in it, ideas in it,
and certainly modeling uncertainty was in there a lot, But
he said, I said totally what they were seeing. He said,
(02:01):
but it's all random, isn't it. I said, what do
you mean? He'd say to me about the random walk
hypothesis and the sort of modern financial economics which I
hadn't come across myself before. And when it was mentioned
to investment management people, they were very skeptical about it.
It couldn't possibly be that if it was all random,
(02:23):
then they were no use at all, which was really
what the economists were saying. But there's a come back
to that. They are not entirely the investment managers, by
new means useless. But Sydney Benjamin then produced a paper
that was I don't think ever published. In the early seventies,
(02:48):
quite a lot of life offices in Britain had written
unit linked policies. This is where the premiums and minus
maybe or charge were invested in units of a unit
trust or a hypothetical unit fund and measured the values
(03:09):
in terms of the units. This had an idea to
come in from South Africa, but it was a very
useful way of people who are writing or managing unit
trusts are writing regular savings plans as if there were
life insurance policies and getting the tax relief which was great,
(03:31):
but it was vague worthwhile tax relief on life assurned
premiums in those days now because of course, as they knew,
everybody knows, share prices only go up. So they said
they had said, what will pay a maturity is the
value of the units or the value of the premiums
(03:52):
who put in whichever is the greater, and of course
about thinking themselves the value of the units what will
always be bigger? Anyway, and Sydney Benjamin pointed out that
if you used some past history, the share prices could
go down instead of up, and the value of the
option was quite substantial, and that it was not all
(04:14):
right just to ignore the possibility that the unit prices
might be down a lot. Well, this was probably about
seventy two. In seventy three, share prices went down a
little bit, and seventy four they went down enormously, about
(04:35):
a third of their previous high in the UK because
of the results of the seventy three Israeli Egypt War
and the blockage of the Sewers Canal and the oil
price being multiplied by four and people being very unsure
(04:56):
about what's going to happen in the British share market.
In January and February seventy five it shot back up again,
so there was no It wasn't a serious disaster, but
any linked policy maturing in the Sevenber sixty four would
have definitely needed supplementing. The unit price would have not
(05:18):
been big enough. So Sydney wrote another paper, and I
wrote a similar for this nineteen seventy six Japan International Congress,
and I wrote, I said, well, I don't like the
idea of picking out just the last the past history,
because you can't go outside it, and things could be
(05:43):
in nineteen seventy two. You've never seen anything as about
as seventy four, so you wouldn't have allowed for things
about as seventy four. So I said, it's better to
use the random walk model and use a normal distribution,
which can go infinitely either way. So I wrote a
paper and congress about just random walks and guarantees, and
(06:06):
then the Institute of actually set up a working party,
a number of different working parties one after another, but
the final maturity Guarantee Guarantees working PARTIAG included myself and
Sydney Benjamin now produce a large report in nineteen eighty
(06:27):
which was quite influential, I think. But it had been
pointed out that if if share prices were a random
walk had been a surprisingly straight one, hadn't they gone up,
They should have gone up and down a lot more.
And so we looked at it and thought, well, there's dividends,
(06:51):
company dividends. We've got a dividend yield. So what we
could do is model the dividend yields as a random walk,
and then the UH share price as the dividend yield,
the ratio of the dividend the share price as a
not a regressive model. And about the same time a
(07:14):
textbook on time series analysis by Box and William William
Jenkins had been published, and this was a very comprehensive book,
bringing in a lot of statistical ideas about time series,
so I didn't think had been looked out very sadly
by statisticians previously, and that that was influencing actress too.
(07:39):
They were all looking at boxing Jenkins method, so I
did too and used used their ideas in modeling. So
now we had a dividend series and a h I
yielded bobbled up and down, so the prices went and
(08:00):
down even more. One of my colleagues described that the
share prices that were doing a drunken stagger about a
random walk, which seemed rather good. And then at the
meeting to discuss maturity anti his working party report, someone said,
(08:25):
shouldn't you take inflation into account as well? That surely
affects a dividends. And another point that was made the
meeting come up later was that option pricing was just
coming in. Black Controls have published their paper about nineteen
seventy two, I think, and the argument was you didn't
(08:46):
need to worry about special reserves because what you did
was one option pricing strategy. You held appropriate mix of
units and cash, changing that as you went along. And
somebody points out if a large number of life offices
had these maturity guarantees, and share prices went down. Then
(09:14):
in order because we were following the option pricing rules,
they had sell shares, so so share prices would go
further down, and so on. They had to sell more shares,
and this obviously was unstable, so on had to have
separate reserves not align for the option pricing. Much later on,
(09:40):
Howard Waters and Iron someone else had forgotten his name
now wrote a paper or allowing for hedging and the
costs of the costs of transactions, the fact that you
couldn't hedge simultaneously had to do it to some extent
(10:00):
in arrears, you couldn't hedge accurately, and so on. You
didn't know what the black Show sigma value was and
making a lot of practical allowances for it. Anyway, that
was much it later, so I went back and thought, well,
it's all really while thinking about shares for life office,
(10:24):
we need to know about bonds as well. So I
got data for I got data for share prices and
dividend yields, and got data for long term interst rates,
short term interest rates using the yield and consoles and
bank rate, and also the race of inflation, and got
(10:45):
in touch with Grinham Jenkins's firm that happened to be
in Lancaster, where I had been brought up and where
my mother was still living, And so I went and
visited Willham Jenkins was very ill and died not long afterwards,
but also his assistant Gordon McCloud and also visited my
(11:08):
mother and got them got Grenn Jenkins's affirm to do
some analysis of the data I've got, and I use
their results as the basis of the first wiky model,
missing out part of it because bank rates had been
going on up and they assumed that this or bank
(11:31):
rate had been rising quite a lot. Short term interest
rates has been rising a lot over the period, and
they assumed they would carry on up instead of going
back down sometimes. And I said, well, that doesn't make
sense the way they're doing it. By the year two thousand,
you'll be paying one hundred percent in your mortgages. That
(11:51):
doesn't make sense. So I missed that bit out and
put it into the first work mod model structure these
four variables retail prices, dividends, dividend yield and long term
infrast rates. Published that in the paper in nineteen eighty four.
(12:13):
Again I had been involved in the working party of
the faculty which was looking at valuation methods, and I
wanted to we wanted to start looking at value life
office valuations taking into account the variability of investments. And
so what I did for in in producing the first
(12:36):
Willkie model was for the benefits of that working party.
Again the practical use of investmental some modeling, but was
the practical purpose of helping her a model for life
office valuation. Well, that's how it started. And it also
(13:00):
seems to be in the first economic model that put
together shares and investment and interest rates into one, one
single model.
Speaker 1 (13:11):
And so would it be fair just real quickly, Dave,
would be fair to say then? It's one of the
things I'm trying to understand is the key innovation with
the Wilki model. The first well, let's start with the
first Wilki model. First thing is that it was stochastic,
so it wasn't deterministic, it wasn't fixed. It allowed for variability,
(13:34):
and it sounds like it it was you're able to
analyze interrelation of variables as well. Would that be fair?
Speaker 2 (13:41):
Yes, yes, it was using entirely boxing Jenkins time series methods.
Also aggressive methods, or looking back at the past series
of the same data, looking back at the past errors,
and looking back at the relating one series to another
by smoothing past data. It entirely was using box and
(14:06):
drinkings methods, trying to simply making it as simple as
possible and not bringing in correlations that might be not significant.
And yeah, actually you using never less quite a lot
of the mathematics I was using for fitting or had
(14:29):
previously been using for fitting mortality rates max, some likelihood
methods on the series the fit a series of values
in one case a series by age, the other case
the series by time. That was the purpose of it,
And indeed, and the investment manager at Standard Life looked
(14:53):
at it quite a lot and decided that a sensible
policy for Standard Life, since it had some nonprofit business
and some with and some with profit business with heavy
bonus loadings, was to think of matching the extent of
investing the the non profit business. Imagine the nonprofit business
(15:19):
invested in match bonds, but the with profit business invested
one hundred, one hundred and ten in shares with a
ten percent negative in bonds which was borrowed therefore from
the with profit bit true matching, but over investment in
(15:39):
shares that was and that was using the markets was
around as well. His ideas were were coming into the
market its model which were not time series models, but
were allowing for combinations of different securities and fixing a
(16:04):
suitable minimum resu port eoarlier and then I over the
course of the years when I've moved from Watson's, from
Sand's Life to Watson's and then produced the second version,
(16:25):
the more on the Stochastic Investment Model paper nineteen mid
nineteen nineties, ninety five or ninety six, and that brought
in short term interest rates in the It's what I
thought was a sensible way and property and property and
(16:49):
property yields, and a bit on foreign exchange rates because
I've included some other countries in it. And from you
see in the early years it hasn't ought enough data
and foreign exchange because the old Breton Wood system had
been abandoned only in nineteen seventy one. So by nineteen
(17:12):
eighty four that was in the thirteen or probably twelve
years of data I could have used, which wasn't enough.
By nineteen ninety five there was now the ten years
of data. Now there's now the thirty years of data,
which is good. So that was stage two and the
(17:35):
also in Dexcellink. The bonds had been invented by then,
and I was involved in the introduction in the Excellent
bonds too, because I've been allowed while I was at
Standard Life to write an article for them about Financial Times,
thinking they were a very good idea, and it was
(17:55):
unusual for someone from within industry to say they were
a good idea. The academics had been mentioning them for
some time, but they could be paying any attention. And
then the Institute asked me to write a paper on
index linking, which was to be presented in March nineteen
(18:16):
eighty one. I think well about a fortnight before the
paper was due to be presented, the then Chancellor, Jeffrey
Howe announced the issue of the first index Link bond.
Was the bids for it taking place I think on
the Friday after my paper on the Monday. So my
(18:36):
paper was packed out with people in staple Inn coming
to find out what the right price to bid for
this Indexinc. Bond was and I described as Professor index Linking.
One stage anyway, I brought in the Indexinc. Yield, and
I've had to change the model because I assumed indexcellent
(19:01):
yields would say positive and they didn't. They went negative
and at some stage, so in a more recent revision,
I've had to change that so they can be positive
or negative. And I think long term interest rates I'd
assumed were always a bit higher than expected inflation, but
(19:23):
over the last over recent years, they've been lower than
expected inflation. They've inspected inflation was in two percent for
a long period in the last fifteen years. Then bond
yields have been done to one percent, which didn't make sense.
So I'm going to have to modify that bit of
(19:43):
the long term yield model too to allow for negative
for additions to past inflation. So the when I was
supervising students at PhD students at Terry, it was a
(20:04):
bit cheaty. I supervised PhD students, haven't done a PhD myself.
The honorary degrees I got honorary they're not they're not
for doing the work. I was supervisor student called Shuley
Shaheen from a lady from Turkey who wanted to do
(20:25):
some work on the Wilkie model, and she did and
for the last fifteen years or so, she and I
have been working together on doing yet more improvements the
Wilkie model and the whole series of yet more, yet
more on papers with a whole series of different editions
(20:47):
pointing out that the I think at one place the
estimation the parameters depended very much from the time you
were looking at it, and over certain periods the parameters
very read a lot. Other parameters are pretty stable regardless
of the period you were looking at at them. And
(21:07):
then we introduced we looked at monthly data and there's
a system called stochastic bridging where you have you know,
you're beginning and end points, and you are way of
stask fitting monthly data conditional on finishing at the right
(21:30):
end point. And those are Brandian bridges or in our
case what we're called up auto aggressive bridges and UH
normally distributed residuals throughout throughout the months. So that was
another paper on stochastic bridging. And then the I hadn't
(21:56):
used company earnings in eighty four because the All Share
index had not got an index of company earnings to
begin with on the but the Industrial Index had. The
(22:17):
problem was in Britain, financial companies were not obliged to
produce true and fair earnings, so that the earnings published
by banks and insurance companies and others were not not sensible,
and that until they changed, I think about nineteen ninety
(22:41):
there was a change in that, and so the All
Share Index got an earnings yield or a PE ratio
to the Recipric audit. And so using the Industrial index
and then running it into the the All Share index,
we were able to look at earnings as well as
(23:04):
dividends and all the different ratios, the payout ratios, dividends
divided by earnings, PE ratios, price divided by earnings, undividend yielders.
They were then divided by price. So the three of
them multiplied together are always one or one hundred, which
how will you express it. There's really only two variables
(23:26):
in that which give you automatically the third. So we
produced an earnings model as well, and the whole string
of other things we would like to do, which I
can go and talk about. You who'd like me to.
Speaker 1 (23:46):
Yeah, thanks for the friend, Thanks for overviewing the model.
I'm going to circle back to that briefly a bit
further on in the conversation. But something else I want
to ask about is realistic disaster scenarios. Another area of
modeling uncertainty that you've touched on from a property and
casualty perspective.
Speaker 2 (24:07):
Well, that was something I have done and people don't
know about it because there's nothing published and because the
data was confidential. But when they was in Watson's, a
large oil company called BP had been advised by some
(24:30):
economists that they didn't need to ensure their risks was
small insurance companies because they were so much bigger than
the insurance companies that were better able to stand the
risks themselves, and they wanted some idea of what their
insurance risks were to say that BP would consist of
(24:53):
a lot of subsidiary companies, but one of their subsidiaries
was an insurance company, which it ensured all the other companies,
all the other bits of the other companies, and reinsured
extreme risks in the Lloyd's market. Well, I said, what
(25:16):
we need to do is have a look at the
number and size of the claims that BP have had.
And I looked through them and got a lot of
data and analyzed it and then said, but none of
the there was a certain area when none of the
(25:37):
claim seemed extremely large. But I knew that there had
been a disaster in the North Sea sometime in nineteen eighties,
probably in an oil ray called Piper Alpha, which had
gone on far and a lot of people on it
had been killed and had been a very serious disaster.
And then Exon had an oil tanker called the Valde
(26:00):
which had spilled a lot of oil in the north
of Alaska, and that had been a considerable problem. As
I said, let's have a look at all the extreme
losses that the oil industry has had and put a
fraction of them into BP. Because you were lucky that
it was Ecton's tanker and not your tanker. You were
(26:22):
lucky that it was Atlantic Richfield's Piper Alpha rig and
the North Sea you're not one of yours. And so
we did that. The person who was not at that
time but later working for BP found out about that
and got in touch with me some years later to
(26:44):
assist the international group of P and night clubs, and
I did that for some years. P and I Clubs
Protection Demnisty Clubs was about twelve of them the world.
They insure shipowners third party liabilities, not the whole not
(27:06):
the cargo, but the third party liability and all the
losses of a modest size they keep themselves. Oh, after
a certain they're limited I think was probably ten million
dollars at that time. They pooled them in through the
(27:29):
International Group, and about some higher limit, let's say one
hundred million. They can't remember what it actually was they
insured in the market. So I said, well, they wanted
advice as to how much the reinsurance premium might be,
so that that would help them in their negotiations with
(27:50):
the Lloyd's market, because I was told it's true or
not that the premium they paid was the largest single
premium in the year that Lloyd's ever got. Some night
in the premiums are roughly two hundred million, but at
that time or some time ago, it may be quite
different now. And so Ducal Goodman, who was the other person, said,
(28:16):
what we ought to be including is as you did
with BP. It's all the losses that they might have
had but haven't happened yet. So we went round the
the P and I clubs and said, please tell us
what you can think of as serious disasters that might
(28:39):
have happened but happened. Cruise liner hitting a rock in
the Antarctic in the middle of the night, boat hitting
a bridge bringing it down when there's a railway train
and bullet train going across it, that sort of thing,
(29:00):
ship sinking, blocking a harbor, a whole lot of things
like that, And we put them in with a sort
of modest probability because they tended to exaggerate the probabilities.
So it fitted them then as what we call realistic
disaster scenarios. And I believe I don't know for certain
(29:22):
that Lloyd syndicates have been encouraged to use the same thing,
not whether it was me or someone else was thinking
about it, but I didn't know, but put in reserve
as if you had had some unusual claims bigger and
then think that you've expected before. And so this seemed
(29:47):
quite quite a good idea, and the analysis was fairly straightforward.
One looked at some statistical model for the frequency of
claims and some statistical model for the size of claims
out pretty standard in general insurance, and I think as
on distribution for one and the burrito for the other
(30:08):
were appropriate. But as I say, that has never been published,
and it's another bit as I did include in at
that time was parameter uncertainty. Now this isn't difficult to
do if one estimates parameters through a hypermodel through maximum likelihood.
(30:36):
If you've got a maximum which is not constrained at
a boundary, your maximum likelihood. If it goes up to
a boundary, the properties are not so good. If it's
our top of a hill in the middle of a field,
as it were, with boundaries around the field, then obviously
(30:56):
the first derivatives in the first partial derivaties with respect
to each parameter a zero. But you take the matrix
of second partial derivatives and invert it and change the sign.
You get the covariance matrix of the parameter. Estimates the
(31:17):
value of the parameter are the the value of the
maximum of the parameters are the best estimates to use.
But the information matrixes it's called, gives you information about
the standard errors of those parameters. How and that i'd
(31:43):
use what I would call would call a hypermodel. Inventing
that word, where at the beginning of each simulation you
simulate the values of the parameters you're going to use
within the further simulations using the multivariate normal distribution with
(32:07):
the maximum likelihood values for the parameters as the means,
and then the covariance matrix to give thee the Suandard
deviations and the correlation coefficients and the technical ways of
simulating from that, and you can and then you can
then simulate the future, allowing for parameter uncertainty as well.
(32:33):
So what I'd like to do and haven't fully done yet,
was the Wookie model is to bring in parameter uncertainty
through a hypermodel. Now that's that's one bit of the
of the extra extensions I would like to put in.
The Other one is quite a lot of our variables
(32:58):
have high of some extreme values. They have high kurtosis,
that is the curtosis the fourth moment divided by the
fourth power of the standard aviation. And for a normal distribution,
the curtosis is three. For a laplus distribution, which is
two exponentials back to back, it's it's six, and in
(33:25):
many of our cases it were somewhere up to six,
but in other cases going up to fourteen and fifteen
huge They outside that area. And we've used as series
of distributions normal and hyperbolic laplace which have all got
nice properties of being related to comic sections in a
(33:48):
complicated way I shan't explain now, but I'd like to
bring in fatter tail distributions, and exactly as with the
time series modeling in mortality, where I had been looking
for fatter tail distributions, it's just the same problem. I
(34:11):
want fatter tailed distributions that fit the data better and
than the ones I've been using. And I then want
to use a hypermodel to allow for the uncertainty of
the parameters. And that's the next big paper for improving
the wiki model, but hasn't been written yet. Some of
(34:33):
it has been dropped, some it's been done, but it
still needs quite a bit of writing on that. So
but I had used that the hypermodel idea, and of
course we're looking at that pretty long tail distributions to
deal with the general insrurance claims. And general insurance actories
(34:56):
are quite familiar with one sided long tail distributions because
claims can get very big, and the other way of
doing is to say two of those and put them
back to back and say they can get get very
large negative as well as well as very large positive.
Speaker 1 (35:14):
So, David, when you were talking about the realistic disaster scenarios,
the one that you you talked about the ship in
the middle of the cruise liner in the middle of
the night hitting a bridge. It kind of reminds me
of the Baltimore Bridge.
Speaker 2 (35:29):
Well, there're two different and so there was a cruise
miner hitting a rock in the Antarctic, which indeed it
happened to a small cruse line of all hundred pastures
and crew got out safely onto a rock. Of the
helicopters came in from chileans took them out. But it
did mean that the cost of Concordia, which was a
(35:52):
cruise line of hitting a rock in broad daylight and
stranding itself quite nicely on rocks, which was good thing
for the captain to have done, because rather few people
were drowned. Comparatively few people had drowned as a results
of cost and ordiator. It cost an awful lot for
the salvage of it. And the other one, the Baltimore Bridge,
(36:17):
were a different ship, not a cruise liner. Cargo ship
had hit the bridge, the bridge collapsed and then fortunately
there were only six people drowned, I think because who
were workers working on the bridge that was That course
was sad, but it wasn't Several hundreds as if were
railway train had been going across at the same time
(36:42):
as it was the hay Bridge disaster in eighteen seventy
nine when the bridge did collapse and the rail and
the train went into the water, and it also blocked
the port for a while. So I know what the
costs of that would be to the your night clubs,
but it'll be it'll be in the billions somewhere.
Speaker 1 (37:06):
Yeah, So when I when when we look back, the
reason I brought up that analogies when we think of
the applicability of your work, So you talked about the
realistic disaster scenarios to account for situations like that. When
we shift, sorry, we shift gears back to the Wilkie
model now, which which has been used in pension funds,
for capital adequacy, for asset liability management, for economic scenario generation.
(37:33):
You know, can you think of of any areas like
based on you know, some of the areas that it's
been used in. Can you think of any any areas
that might be interesting for it to be used in?
Speaker 2 (37:47):
Well, I I one of the problems is that I
don't know what areas it has been used in. I've
been out of out of the direct involvement insurance or
pension funds for quite a while now. But one thing
I'm rather disappointed is that the people who produce economic
(38:13):
scenario generators and sell their results, no doubt quite profitably
to themselves, to insurance companies and others, don't publish what
they've done. I believe that they have probably used the
Wilkie model as the basis of all the modeling, but
they may have modified it and improved it. And you
(38:33):
don't get scientific progress if people keep their improvement secret.
So that I criticize the ESG companies for their excessive secrecy,
they probably publish quite a bit more without giving proms
a values, for example, about some of their methods. Some
(38:54):
organizations are very touchy about secrecy.
Speaker 1 (38:58):
Sure, and if you look, if you look back in hindsight,
were there have been several corporate failures for various reasons
and as a liability management and and some of like
I said, some of the areas where the Wilky model
has added value have been attributing reasons. So can you
(39:18):
think of any historical failures like corporate failures for instance,
where some of the principles of the Wilky model where
they might not have happened had those principles been applied.
Speaker 2 (39:33):
One big complications, which wasn't it was not really to
do with the Wilky model or that sort of modeling.
Was was the problems in two thousand and seven and
eight was the packaging of mortgages into different slices and
(40:00):
what was it called.
Speaker 1 (40:03):
Squares?
Speaker 2 (40:04):
Yes, yes, obligations that sort of thing. Now, one of
the problems was that was what I would call agency risk.
The if sufficient of it was reinsured, then why did
they the original lending There was no motiflication for the
(40:27):
original lending company to be very vigorous about collecting the
mortgage payments from the borrower because it didn't matter to
them whether they lost, whether they were paid or not,
because it all went through to the reinsurers or so
(40:48):
there's a there is a model hazard in reinsuring too much.
Just as for insurers, ordinary general insurance, they often like
people to carry a reasonable retention called an excess we
won't pay claims under five hundred pounds or under one
(41:11):
thousand pounds. That first helps avoid administrative complications, but it
also slightly encourages people to be fairly careful with that
property and not be too reckless, and so you need
to think of them with insurance and model housard about
(41:33):
what the insured person or any of the intermediate it's
what motivations they have for behaving in the way that
other people would like. It was also I think very
stupid of banks to take on so much of these
CDO liabilities without fully understanding them. I think they possibly
(41:59):
didn't quite understand quite what it was. I remember at
that time hearing a talk from someone, First, never sell
the product you don't really understand. Never sell the product
you wouldn't buy yourself, and never then turn if you
(42:19):
don't actually know what they'll know a lot about those
seemed very good backing principles, quite straightforward. Also with insurance
ones too. Another there is a problem with a lot
of companies, with many companies going bus it's nothing to
do with can modeled with taxation, which well I'd like
(42:42):
to raise. In Britain and I think in many other countries,
a company is taxed on this profit minus the expenses,
of course, and treating interest as an expense, so that
you take the net profits and you deduct interest and
(43:05):
then you pay corporation tax, and then you can pay
the profits netive corporation tax to the shareholders. Now, this
produces a distortion in the market. Shareholders and lenders, borrowers
and bondholders are both lending capital to the company, either
(43:31):
through a share or through a bond or through just
no bank over draft. And there's no reason why the
profits from that from that capital transaction should be taxed
in different ways. And it gives an incentive to a
(43:53):
company to say a British pension fund two fund a
subsidiary was one hundred pounds of share capital and ten
million pounds of loan capital, because you pay less tax
that way, and you probably get the same profit and
(44:14):
you're carrying the same risks since you've got the same
the same portfolio of ownership. And so I would suggest
that it would be much better for corporation tax to
be calculated without the deduction of interest payments, and you've
(44:37):
probably half the rate of corporation tax or some pract
reduced to some fraction, but charge on a much larger amount,
and this takes away the tax incentive to have too
much loans. There's a good reason, there are good reasons
probably for shareholders to raise bonds that raise money through
(45:01):
bonds through loans or through overdrafts and keep control in
the hands of the shareholders. But it's a pity to
have a tax advantage as well in it the tax
should be neutral here and a lot of companies simply
go bus property companies and others because they have too
(45:24):
much loan capital too little share capital. But that's nothing
that's to do with risks. The risks are there are
depending on how much loan how much share capital there is,
doesn't make any difference to the profits of the business,
(45:44):
not directly. It may indirectly have secondary effects on profits
of the business. They take more or less risks, but
all it's doing is sharing the profit, sharing the profits
between shareholders and bondholders in different way, and the tax
I think that's the tax advantage should be taken away.
Speaker 1 (46:08):
The last thing, last thing I want to ask about
is I want to shift gears a bit because I
know not only have you worked on research around models
and modeling uncertainty, but beyond the publication of academic papers,
another avenue of thought leadership for you is your work
with actuarial organizations. In what ways have you helped actuarial
(46:32):
organizations to shape standards and practices globally.
Speaker 2 (46:37):
Uh well, let me think, haven't they. The stuff for
the CMI in Britain was to help the actorial professional
professional bodies and the actories to advise life insurance companies
(46:58):
about their mortality better. So it's helping the similar the
indices now really controlled by a foot see rather than
the actress they were helping. There was something done by
the profession in order to help the companies to understand
(47:19):
their investments better. Quite separately, I've been involved with both IOKA,
the National Assation and Consulting Actors in the past and
with AFIA for a long time, and I've been involved
with the Scientific Organization of conferences. I was looked looked
(47:45):
after the scientific program with three IOCA conferences in the
nine nineteen nineties I think, and with an awful loss
of the AFIA colloquials. I helped to be involved in
scientific sides of lots lots of conferences, and that's just
(48:07):
helping the professional body. But it's not there's I mean,
somebody has to do it, and somebody who has some knowledge,
reasonable knowledge of people's papers, whether they're sensible or not.
I'm probably a bit out of dating you for doing that,
because there will be a lot of new papers I
(48:27):
don't understand much about. And the first thing one has
to say when somebody sends in the paper for conferences,
is this actually for the right conference or is it
has it got Is it all about veterary science and
has arrived from the partly by mistake for the wrong
(48:47):
conference altogether? Or is it is it for an investment
conference and it's really about tame's management in general insurance
that sort. That's the first thing. Is it the right
on the right topic? Is it adequately written? Doesn't it
make reasonably good sense? Not a matter of scrutinizing it,
(49:10):
see whether it's a perfect paper, but is it a
plausible paper to book before people for discussion. That's what
one needs to do, and then organize some papps into
classify them. So I've helped the progressions there. I've also
I was on the consultative group of the European Acturary
(49:32):
Associations at it's now called the Actuary Association of Europe,
and there's a much bigger body because in the eighties,
eighties and nineties it was a smaller organization with two
actories from each of the professional associations in Europe. Getting
(49:55):
together in order to talk to the EU Commission. The
EU Commission would only talk to international bodies. It couldn't
talk to the French or German, Italian or British Actuarial Society,
and so that in the course of that I got
(50:20):
involved in one piece of research. The problem in life
insurance was that all the countries thought that their valuation
systems were good ones and didn't trust other people's valuation systems.
And I think I did some research which found out
that really the valuation systems for life offices that were
(50:43):
used by all the different countries were equally similarly safe.
Some of them were based on they were all based
on different methods, different principles, but in practice they worked
out pretty much the same. And so with two Dutch colleagues,
they rang me up and said could you come and
(51:04):
have a discussion this weekend and I said no, I'm
fownling to Switzerland. And they said, well, couldn't you change
planes such as scavening and talked to us. So I did.
I flew probably flew from Edinburgh or London to Scathing
and met them in the restaurant there and carried on
to euryth in the afternoon, and we drafted a set
(51:28):
of principles for life Office valuation, and that was just
the first draft. We tidied it up, presented it to
the Consulative Group's Life Committee, who had to look at it,
presented Salted Group had looked at it and tinkered with
it further, sent it into the European Commission and had
(51:51):
to look with it, tinkered with it further, and published
it in the first draft of the third Life Directive
as the valuation principles, and those eventually got into and
approved directive. That was modified quite a lot on the way,
but some of my words were still there. That has
(52:13):
all been replaced by Solvency two. But that's what you
might have called Solvency one. And I was amused. I
found it amusing that my words had I had actually
written part of the direct two. More things, yes, we have,
we haven't discussed, and that's for some future date. I
prom on my conference my ninetieth birthdat I write a
(52:35):
paper on research I haven't done yet but would like
to do. And that paper is almost drafted and will
I hope you published as a dozen al so different
suggestions in that. And we have haven't talked with anything
very much about AI, which I don't know an awful lot,
but have got some views on. But that's some other
(52:58):
discussion that some much later date.
Speaker 1 (53:00):
Sure, So just real quickly quickly on the on the paper,
Where can when, when is it going to commote and
where can we find it?
Speaker 2 (53:07):
It's it submitted to the British Annals of Actorial Science.
There's a special number of the animals to commemorate my
ninetieth birthday, which is will I think papers are supposed
to be in by about the end of the year
and it will be published sometime during next year. But
(53:30):
one of the problems with the British profession is that
stuff gets published in British Actuarial Journal and Annals Actorial
Science and nobody ever knows. There's never any announcements by
the actuarial body that the more papers or another volume
has been published.
Speaker 1 (53:49):
So anything anything I can do on social media to
help promote that, let me know.
Speaker 2 (53:53):
When I don't know what happens in America with the
with the transactions of society to factories or the atmosphous
transactions with casualty act of society. They're probably published online
these days rather than the specifically.
Speaker 1 (54:09):
Yeah, yeah, digitally. Well, David, you know, we've covered quite
a lot of ground today. We've learned about your actuarial background,
how you got into the profession. We explored your seventy
three year career journey through your early adoption into programming
and utilizing that for modeling, doing mortality forecasting, working on
(54:33):
share indices, income protection, multi state modeling. We've talked about
your renowned Wilkie model that's used to model uncertainty, touch
briefly on realistic disaster scenarios for properly and casualty insurance,
and you know, spoken about some of the applicability some
(54:54):
of the practical applications themselves. So just want to thank
you so much for your time and lending expertise.
Speaker 2 (55:01):
Okay, well, thank you for talking to me and giving
me the opportunity of spouting off my views and the
waves allowed me my pleasure.
Speaker 1 (55:12):
I have a wonderful rest of the day. Hi,
So let's pick up the conversation, David. In the first
half of the conversation, we talked about your backgrone, We
talked about your early days using the power programming to
develop models and utilize them. No, we want to take
things that step. Let's take things that step further and
not just talk about modeling, but let's talk about modeling uncertainty,
(00:21):
which is something that you're known for. So you're a
pioneer in modeling uncertainty within insurance, finance and risk management.
When did the idea of stochastic modeling start to get
traction or broadly speaking.
Speaker 2 (00:36):
Well, you're coming now onto what people call the Wilky model,
which I published in nineteen eighty four, quite a long
time ago now, But I bet I need to go
back a bit before that. I mentioned that sometime in
the early seventies I had become economist research manager of
(01:00):
the oft Standard Life looking at the economy was to
three other economists to advise the investment department about what
the economic future might be. And this part number of
companies had done this sort of bringing in economists to
(01:20):
assist the investment department, and I was put in charge
of this, and I expected what I was doing one
time to my friend Sidney Benjamin, sadly died some years ago,
but was his his paper on for probably in nineteen sixties,
(01:41):
what Actories can Do with Computers is still a very
useful paper to go for anybody to go back to.
It said, all sorts of things in it, ideas in it,
and certainly modeling uncertainty was in there a lot, But
he said, I said totally what they were seeing. He said,
(02:01):
but it's all random, isn't it. I said, what do
you mean? He'd say to me about the random walk
hypothesis and the sort of modern financial economics which I
hadn't come across myself before. And when it was mentioned
to investment management people, they were very skeptical about it.
It couldn't possibly be that if it was all random,
(02:23):
then they were no use at all, which was really
what the economists were saying. But there's a come back
to that. They are not entirely the investment managers, by
new means useless. But Sydney Benjamin then produced a paper
that was I don't think ever published. In the early seventies,
(02:48):
quite a lot of life offices in Britain had written
unit linked policies. This is where the premiums and minus
maybe or charge were invested in units of a unit
trust or a hypothetical unit fund and measured the values
(03:09):
in terms of the units. This had an idea to
come in from South Africa, but it was a very
useful way of people who are writing or managing unit
trusts are writing regular savings plans as if there were
life insurance policies and getting the tax relief which was great,
(03:31):
but it was vague worthwhile tax relief on life assurned
premiums in those days now because of course, as they knew,
everybody knows, share prices only go up. So they said
they had said, what will pay a maturity is the
value of the units or the value of the premiums
(03:52):
who put in whichever is the greater, and of course
about thinking themselves the value of the units what will
always be bigger? Anyway, and Sydney Benjamin pointed out that
if you used some past history, the share prices could
go down instead of up, and the value of the
option was quite substantial, and that it was not all
(04:14):
right just to ignore the possibility that the unit prices
might be down a lot. Well, this was probably about
seventy two. In seventy three, share prices went down a
little bit, and seventy four they went down enormously, about
(04:35):
a third of their previous high in the UK because
of the results of the seventy three Israeli Egypt War
and the blockage of the Sewers Canal and the oil
price being multiplied by four and people being very unsure
(04:56):
about what's going to happen in the British share market.
In January and February seventy five it shot back up again,
so there was no It wasn't a serious disaster, but
any linked policy maturing in the Sevenber sixty four would
have definitely needed supplementing. The unit price would have not
(05:18):
been big enough. So Sydney wrote another paper, and I
wrote a similar for this nineteen seventy six Japan International Congress,
and I wrote, I said, well, I don't like the
idea of picking out just the last the past history,
because you can't go outside it, and things could be
(05:43):
in nineteen seventy two. You've never seen anything as about
as seventy four, so you wouldn't have allowed for things
about as seventy four. So I said, it's better to
use the random walk model and use a normal distribution,
which can go infinitely either way. So I wrote a
paper and congress about just random walks and guarantees, and
(06:06):
then the Institute of actually set up a working party,
a number of different working parties one after another, but
the final maturity Guarantee Guarantees working PARTIAG included myself and
Sydney Benjamin now produce a large report in nineteen eighty
(06:27):
which was quite influential, I think. But it had been
pointed out that if if share prices were a random
walk had been a surprisingly straight one, hadn't they gone up,
They should have gone up and down a lot more.
And so we looked at it and thought, well, there's dividends,
(06:51):
company dividends. We've got a dividend yield. So what we
could do is model the dividend yields as a random walk,
and then the UH share price as the dividend yield,
the ratio of the dividend the share price as a
not a regressive model. And about the same time a
(07:14):
textbook on time series analysis by Box and William William
Jenkins had been published, and this was a very comprehensive book,
bringing in a lot of statistical ideas about time series,
so I didn't think had been looked out very sadly
by statisticians previously, and that that was influencing actress too.
(07:39):
They were all looking at boxing Jenkins method, so I
did too and used used their ideas in modeling. So
now we had a dividend series and a h I
yielded bobbled up and down, so the prices went and
(08:00):
down even more. One of my colleagues described that the
share prices that were doing a drunken stagger about a
random walk, which seemed rather good. And then at the
meeting to discuss maturity anti his working party report, someone said,
(08:25):
shouldn't you take inflation into account as well? That surely
affects a dividends. And another point that was made the
meeting come up later was that option pricing was just
coming in. Black Controls have published their paper about nineteen
seventy two, I think, and the argument was you didn't
(08:46):
need to worry about special reserves because what you did
was one option pricing strategy. You held appropriate mix of
units and cash, changing that as you went along. And
somebody points out if a large number of life offices
had these maturity guarantees, and share prices went down. Then
(09:14):
in order because we were following the option pricing rules,
they had sell shares, so so share prices would go
further down, and so on. They had to sell more shares,
and this obviously was unstable, so on had to have
separate reserves not align for the option pricing. Much later on,
(09:40):
Howard Waters and Iron someone else had forgotten his name
now wrote a paper or allowing for hedging and the
costs of the costs of transactions, the fact that you
couldn't hedge simultaneously had to do it to some extent
(10:00):
in arrears, you couldn't hedge accurately, and so on. You
didn't know what the black Show sigma value was and
making a lot of practical allowances for it. Anyway, that
was much it later, so I went back and thought, well,
it's all really while thinking about shares for life office,
(10:24):
we need to know about bonds as well. So I
got data for I got data for share prices and
dividend yields, and got data for long term interst rates,
short term interest rates using the yield and consoles and
bank rate, and also the race of inflation, and got
(10:45):
in touch with Grinham Jenkins's firm that happened to be
in Lancaster, where I had been brought up and where
my mother was still living, And so I went and
visited Willham Jenkins was very ill and died not long afterwards,
but also his assistant Gordon McCloud and also visited my
(11:08):
mother and got them got Grenn Jenkins's affirm to do
some analysis of the data I've got, and I use
their results as the basis of the first wiky model,
missing out part of it because bank rates had been
going on up and they assumed that this or bank
(11:31):
rate had been rising quite a lot. Short term interest
rates has been rising a lot over the period, and
they assumed they would carry on up instead of going
back down sometimes. And I said, well, that doesn't make
sense the way they're doing it. By the year two thousand,
you'll be paying one hundred percent in your mortgages. That
(11:51):
doesn't make sense. So I missed that bit out and
put it into the first work mod model structure these
four variables retail prices, dividends, dividend yield and long term
infrast rates. Published that in the paper in nineteen eighty four.
(12:13):
Again I had been involved in the working party of
the faculty which was looking at valuation methods, and I
wanted to we wanted to start looking at value life
office valuations taking into account the variability of investments. And
so what I did for in in producing the first
(12:36):
Willkie model was for the benefits of that working party.
Again the practical use of investmental some modeling, but was
the practical purpose of helping her a model for life
office valuation. Well, that's how it started. And it also
(13:00):
seems to be in the first economic model that put
together shares and investment and interest rates into one, one
single model.
Speaker 1 (13:11):
And so would it be fair just real quickly, Dave,
would be fair to say then? It's one of the
things I'm trying to understand is the key innovation with
the Wilki model. The first well, let's start with the
first Wilki model. First thing is that it was stochastic,
so it wasn't deterministic, it wasn't fixed. It allowed for variability,
(13:34):
and it sounds like it it was you're able to
analyze interrelation of variables as well. Would that be fair?
Speaker 2 (13:41):
Yes, yes, it was using entirely boxing Jenkins time series methods.
Also aggressive methods, or looking back at the past series
of the same data, looking back at the past errors,
and looking back at the relating one series to another
by smoothing past data. It entirely was using box and
(14:06):
drinkings methods, trying to simply making it as simple as
possible and not bringing in correlations that might be not significant.
And yeah, actually you using never less quite a lot
of the mathematics I was using for fitting or had
(14:29):
previously been using for fitting mortality rates max, some likelihood
methods on the series the fit a series of values
in one case a series by age, the other case
the series by time. That was the purpose of it,
And indeed, and the investment manager at Standard Life looked
(14:53):
at it quite a lot and decided that a sensible
policy for Standard Life, since it had some nonprofit business
and some with and some with profit business with heavy
bonus loadings, was to think of matching the extent of
investing the the non profit business. Imagine the nonprofit business
(15:19):
invested in match bonds, but the with profit business invested
one hundred, one hundred and ten in shares with a
ten percent negative in bonds which was borrowed therefore from
the with profit bit true matching, but over investment in
(15:39):
shares that was and that was using the markets was
around as well. His ideas were were coming into the
market its model which were not time series models, but
were allowing for combinations of different securities and fixing a
(16:04):
suitable minimum resu port eoarlier and then I over the
course of the years when I've moved from Watson's, from
Sand's Life to Watson's and then produced the second version,
(16:25):
the more on the Stochastic Investment Model paper nineteen mid
nineteen nineties, ninety five or ninety six, and that brought
in short term interest rates in the It's what I
thought was a sensible way and property and property and
(16:49):
property yields, and a bit on foreign exchange rates because
I've included some other countries in it. And from you
see in the early years it hasn't ought enough data
and foreign exchange because the old Breton Wood system had
been abandoned only in nineteen seventy one. So by nineteen
(17:12):
eighty four that was in the thirteen or probably twelve
years of data I could have used, which wasn't enough.
By nineteen ninety five there was now the ten years
of data. Now there's now the thirty years of data,
which is good. So that was stage two and the
(17:35):
also in Dexcellink. The bonds had been invented by then,
and I was involved in the introduction in the Excellent
bonds too, because I've been allowed while I was at
Standard Life to write an article for them about Financial Times,
thinking they were a very good idea, and it was
(17:55):
unusual for someone from within industry to say they were
a good idea. The academics had been mentioning them for
some time, but they could be paying any attention. And
then the Institute asked me to write a paper on
index linking, which was to be presented in March nineteen
(18:16):
eighty one. I think well about a fortnight before the
paper was due to be presented, the then Chancellor, Jeffrey
Howe announced the issue of the first index Link bond.
Was the bids for it taking place I think on
the Friday after my paper on the Monday. So my
(18:36):
paper was packed out with people in staple Inn coming
to find out what the right price to bid for
this Indexinc. Bond was and I described as Professor index Linking.
One stage anyway, I brought in the Indexinc. Yield, and
I've had to change the model because I assumed indexcellent
(19:01):
yields would say positive and they didn't. They went negative
and at some stage, so in a more recent revision,
I've had to change that so they can be positive
or negative. And I think long term interest rates I'd
assumed were always a bit higher than expected inflation, but
(19:23):
over the last over recent years, they've been lower than
expected inflation. They've inspected inflation was in two percent for
a long period in the last fifteen years. Then bond
yields have been done to one percent, which didn't make sense.
So I'm going to have to modify that bit of
(19:43):
the long term yield model too to allow for negative
for additions to past inflation. So the when I was
supervising students at PhD students at Terry, it was a
(20:04):
bit cheaty. I supervised PhD students, haven't done a PhD myself.
The honorary degrees I got honorary they're not they're not
for doing the work. I was supervisor student called Shuley
Shaheen from a lady from Turkey who wanted to do
(20:25):
some work on the Wilkie model, and she did and
for the last fifteen years or so, she and I
have been working together on doing yet more improvements the
Wilkie model and the whole series of yet more, yet
more on papers with a whole series of different editions
(20:47):
pointing out that the I think at one place the
estimation the parameters depended very much from the time you
were looking at it, and over certain periods the parameters
very read a lot. Other parameters are pretty stable regardless
of the period you were looking at at them. And
(21:07):
then we introduced we looked at monthly data and there's
a system called stochastic bridging where you have you know,
you're beginning and end points, and you are way of
stask fitting monthly data conditional on finishing at the right
(21:30):
end point. And those are Brandian bridges or in our
case what we're called up auto aggressive bridges and UH
normally distributed residuals throughout throughout the months. So that was
another paper on stochastic bridging. And then the I hadn't
(21:56):
used company earnings in eighty four because the All Share
index had not got an index of company earnings to
begin with on the but the Industrial Index had. The
(22:17):
problem was in Britain, financial companies were not obliged to
produce true and fair earnings, so that the earnings published
by banks and insurance companies and others were not not sensible,
and that until they changed, I think about nineteen ninety
(22:41):
there was a change in that, and so the All
Share Index got an earnings yield or a PE ratio
to the Recipric audit. And so using the Industrial index
and then running it into the the All Share index,
we were able to look at earnings as well as
(23:04):
dividends and all the different ratios, the payout ratios, dividends
divided by earnings, PE ratios, price divided by earnings, undividend yielders.
They were then divided by price. So the three of
them multiplied together are always one or one hundred, which
how will you express it. There's really only two variables
(23:26):
in that which give you automatically the third. So we
produced an earnings model as well, and the whole string
of other things we would like to do, which I
can go and talk about. You who'd like me to.
Speaker 1 (23:46):
Yeah, thanks for the friend, Thanks for overviewing the model.
I'm going to circle back to that briefly a bit
further on in the conversation. But something else I want
to ask about is realistic disaster scenarios. Another area of
modeling uncertainty that you've touched on from a property and
casualty perspective.
Speaker 2 (24:07):
Well, that was something I have done and people don't
know about it because there's nothing published and because the
data was confidential. But when they was in Watson's, a
large oil company called BP had been advised by some
(24:30):
economists that they didn't need to ensure their risks was
small insurance companies because they were so much bigger than
the insurance companies that were better able to stand the
risks themselves, and they wanted some idea of what their
insurance risks were to say that BP would consist of
(24:53):
a lot of subsidiary companies, but one of their subsidiaries
was an insurance company, which it ensured all the other companies,
all the other bits of the other companies, and reinsured
extreme risks in the Lloyd's market. Well, I said, what
(25:16):
we need to do is have a look at the
number and size of the claims that BP have had.
And I looked through them and got a lot of
data and analyzed it and then said, but none of
the there was a certain area when none of the
(25:37):
claim seemed extremely large. But I knew that there had
been a disaster in the North Sea sometime in nineteen eighties,
probably in an oil ray called Piper Alpha, which had
gone on far and a lot of people on it
had been killed and had been a very serious disaster.
And then Exon had an oil tanker called the Valde
(26:00):
which had spilled a lot of oil in the north
of Alaska, and that had been a considerable problem. As
I said, let's have a look at all the extreme
losses that the oil industry has had and put a
fraction of them into BP. Because you were lucky that
it was Ecton's tanker and not your tanker. You were
(26:22):
lucky that it was Atlantic Richfield's Piper Alpha rig and
the North Sea you're not one of yours. And so
we did that. The person who was not at that
time but later working for BP found out about that
and got in touch with me some years later to
(26:44):
assist the international group of P and night clubs, and
I did that for some years. P and I Clubs
Protection Demnisty Clubs was about twelve of them the world.
They insure shipowners third party liabilities, not the whole not
(27:06):
the cargo, but the third party liability and all the
losses of a modest size they keep themselves. Oh, after
a certain they're limited I think was probably ten million
dollars at that time. They pooled them in through the
(27:29):
International Group, and about some higher limit, let's say one
hundred million. They can't remember what it actually was they
insured in the market. So I said, well, they wanted
advice as to how much the reinsurance premium might be,
so that that would help them in their negotiations with
(27:50):
the Lloyd's market, because I was told it's true or
not that the premium they paid was the largest single
premium in the year that Lloyd's ever got. Some night
in the premiums are roughly two hundred million, but at
that time or some time ago, it may be quite
different now. And so Ducal Goodman, who was the other person, said,
(28:16):
what we ought to be including is as you did
with BP. It's all the losses that they might have
had but haven't happened yet. So we went round the
the P and I clubs and said, please tell us
what you can think of as serious disasters that might
(28:39):
have happened but happened. Cruise liner hitting a rock in
the Antarctic in the middle of the night, boat hitting
a bridge bringing it down when there's a railway train
and bullet train going across it, that sort of thing,
(29:00):
ship sinking, blocking a harbor, a whole lot of things
like that, And we put them in with a sort
of modest probability because they tended to exaggerate the probabilities.
So it fitted them then as what we call realistic
disaster scenarios. And I believe I don't know for certain
(29:22):
that Lloyd syndicates have been encouraged to use the same thing,
not whether it was me or someone else was thinking
about it, but I didn't know, but put in reserve
as if you had had some unusual claims bigger and
then think that you've expected before. And so this seemed
(29:47):
quite quite a good idea, and the analysis was fairly straightforward.
One looked at some statistical model for the frequency of
claims and some statistical model for the size of claims
out pretty standard in general insurance, and I think as
on distribution for one and the burrito for the other
(30:08):
were appropriate. But as I say, that has never been published,
and it's another bit as I did include in at
that time was parameter uncertainty. Now this isn't difficult to
do if one estimates parameters through a hypermodel through maximum likelihood.
(30:36):
If you've got a maximum which is not constrained at
a boundary, your maximum likelihood. If it goes up to
a boundary, the properties are not so good. If it's
our top of a hill in the middle of a field,
as it were, with boundaries around the field, then obviously
(30:56):
the first derivatives in the first partial derivaties with respect
to each parameter a zero. But you take the matrix
of second partial derivatives and invert it and change the sign.
You get the covariance matrix of the parameter. Estimates the
(31:17):
value of the parameter are the the value of the
maximum of the parameters are the best estimates to use.
But the information matrixes it's called, gives you information about
the standard errors of those parameters. How and that i'd
(31:43):
use what I would call would call a hypermodel. Inventing
that word, where at the beginning of each simulation you
simulate the values of the parameters you're going to use
within the further simulations using the multivariate normal distribution with
(32:07):
the maximum likelihood values for the parameters as the means,
and then the covariance matrix to give thee the Suandard
deviations and the correlation coefficients and the technical ways of
simulating from that, and you can and then you can
then simulate the future, allowing for parameter uncertainty as well.
(32:33):
So what I'd like to do and haven't fully done yet,
was the Wookie model is to bring in parameter uncertainty
through a hypermodel. Now that's that's one bit of the
of the extra extensions I would like to put in.
The Other one is quite a lot of our variables
(32:58):
have high of some extreme values. They have high kurtosis,
that is the curtosis the fourth moment divided by the
fourth power of the standard aviation. And for a normal distribution,
the curtosis is three. For a laplus distribution, which is
two exponentials back to back, it's it's six, and in
(33:25):
many of our cases it were somewhere up to six,
but in other cases going up to fourteen and fifteen
huge They outside that area. And we've used as series
of distributions normal and hyperbolic laplace which have all got
nice properties of being related to comic sections in a
(33:48):
complicated way I shan't explain now, but I'd like to
bring in fatter tail distributions, and exactly as with the
time series modeling in mortality, where I had been looking
for fatter tail distributions, it's just the same problem. I
(34:11):
want fatter tailed distributions that fit the data better and
than the ones I've been using. And I then want
to use a hypermodel to allow for the uncertainty of
the parameters. And that's the next big paper for improving
the wiki model, but hasn't been written yet. Some of
(34:33):
it has been dropped, some it's been done, but it
still needs quite a bit of writing on that. So
but I had used that the hypermodel idea, and of
course we're looking at that pretty long tail distributions to
deal with the general insrurance claims. And general insurance actories
(34:56):
are quite familiar with one sided long tail distributions because
claims can get very big, and the other way of
doing is to say two of those and put them
back to back and say they can get get very
large negative as well as well as very large positive.
Speaker 1 (35:14):
So, David, when you were talking about the realistic disaster scenarios,
the one that you you talked about the ship in
the middle of the cruise liner in the middle of
the night hitting a bridge. It kind of reminds me
of the Baltimore Bridge.
Speaker 2 (35:29):
Well, there're two different and so there was a cruise
miner hitting a rock in the Antarctic, which indeed it
happened to a small cruse line of all hundred pastures
and crew got out safely onto a rock. Of the
helicopters came in from chileans took them out. But it
did mean that the cost of Concordia, which was a
(35:52):
cruise line of hitting a rock in broad daylight and
stranding itself quite nicely on rocks, which was good thing
for the captain to have done, because rather few people
were drowned. Comparatively few people had drowned as a results
of cost and ordiator. It cost an awful lot for
the salvage of it. And the other one, the Baltimore Bridge,
(36:17):
were a different ship, not a cruise liner. Cargo ship
had hit the bridge, the bridge collapsed and then fortunately
there were only six people drowned, I think because who
were workers working on the bridge that was That course
was sad, but it wasn't Several hundreds as if were
railway train had been going across at the same time
(36:42):
as it was the hay Bridge disaster in eighteen seventy
nine when the bridge did collapse and the rail and
the train went into the water, and it also blocked
the port for a while. So I know what the
costs of that would be to the your night clubs,
but it'll be it'll be in the billions somewhere.
Speaker 1 (37:06):
Yeah, So when I when when we look back, the
reason I brought up that analogies when we think of
the applicability of your work, So you talked about the
realistic disaster scenarios to account for situations like that. When
we shift, sorry, we shift gears back to the Wilkie
model now, which which has been used in pension funds,
for capital adequacy, for asset liability management, for economic scenario generation.
(37:33):
You know, can you think of of any areas like
based on you know, some of the areas that it's
been used in. Can you think of any any areas
that might be interesting for it to be used in?
Speaker 2 (37:47):
Well, I I one of the problems is that I
don't know what areas it has been used in. I've
been out of out of the direct involvement insurance or
pension funds for quite a while now. But one thing
I'm rather disappointed is that the people who produce economic
(38:13):
scenario generators and sell their results, no doubt quite profitably
to themselves, to insurance companies and others, don't publish what
they've done. I believe that they have probably used the
Wilkie model as the basis of all the modeling, but
they may have modified it and improved it. And you
(38:33):
don't get scientific progress if people keep their improvement secret.
So that I criticize the ESG companies for their excessive secrecy,
they probably publish quite a bit more without giving proms
a values, for example, about some of their methods. Some
(38:54):
organizations are very touchy about secrecy.
Speaker 1 (38:58):
Sure, and if you look, if you look back in hindsight,
were there have been several corporate failures for various reasons
and as a liability management and and some of like
I said, some of the areas where the Wilky model
has added value have been attributing reasons. So can you
(39:18):
think of any historical failures like corporate failures for instance,
where some of the principles of the Wilky model where
they might not have happened had those principles been applied.
Speaker 2 (39:33):
One big complications, which wasn't it was not really to
do with the Wilky model or that sort of modeling.
Was was the problems in two thousand and seven and
eight was the packaging of mortgages into different slices and
(40:00):
what was it called.
Speaker 1 (40:03):
Squares?
Speaker 2 (40:04):
Yes, yes, obligations that sort of thing. Now, one of
the problems was that was what I would call agency risk.
The if sufficient of it was reinsured, then why did
they the original lending There was no motiflication for the
(40:27):
original lending company to be very vigorous about collecting the
mortgage payments from the borrower because it didn't matter to
them whether they lost, whether they were paid or not,
because it all went through to the reinsurers or so
(40:48):
there's a there is a model hazard in reinsuring too much.
Just as for insurers, ordinary general insurance, they often like
people to carry a reasonable retention called an excess we
won't pay claims under five hundred pounds or under one
(41:11):
thousand pounds. That first helps avoid administrative complications, but it
also slightly encourages people to be fairly careful with that
property and not be too reckless, and so you need
to think of them with insurance and model housard about
(41:33):
what the insured person or any of the intermediate it's
what motivations they have for behaving in the way that
other people would like. It was also I think very
stupid of banks to take on so much of these
CDO liabilities without fully understanding them. I think they possibly
(41:59):
didn't quite understand quite what it was. I remember at
that time hearing a talk from someone, First, never sell
the product you don't really understand. Never sell the product
you wouldn't buy yourself, and never then turn if you
(42:19):
don't actually know what they'll know a lot about those
seemed very good backing principles, quite straightforward. Also with insurance
ones too. Another there is a problem with a lot
of companies, with many companies going bus it's nothing to
do with can modeled with taxation, which well I'd like
(42:42):
to raise. In Britain and I think in many other countries,
a company is taxed on this profit minus the expenses,
of course, and treating interest as an expense, so that
you take the net profits and you deduct interest and
(43:05):
then you pay corporation tax, and then you can pay
the profits netive corporation tax to the shareholders. Now, this
produces a distortion in the market. Shareholders and lenders, borrowers
and bondholders are both lending capital to the company, either
(43:31):
through a share or through a bond or through just
no bank over draft. And there's no reason why the
profits from that from that capital transaction should be taxed
in different ways. And it gives an incentive to a
(43:53):
company to say a British pension fund two fund a
subsidiary was one hundred pounds of share capital and ten
million pounds of loan capital, because you pay less tax
that way, and you probably get the same profit and
(44:14):
you're carrying the same risks since you've got the same
the same portfolio of ownership. And so I would suggest
that it would be much better for corporation tax to
be calculated without the deduction of interest payments, and you've
(44:37):
probably half the rate of corporation tax or some pract
reduced to some fraction, but charge on a much larger amount,
and this takes away the tax incentive to have too
much loans. There's a good reason, there are good reasons
probably for shareholders to raise bonds that raise money through
(45:01):
bonds through loans or through overdrafts and keep control in
the hands of the shareholders. But it's a pity to
have a tax advantage as well in it the tax
should be neutral here and a lot of companies simply
go bus property companies and others because they have too
(45:24):
much loan capital too little share capital. But that's nothing
that's to do with risks. The risks are there are
depending on how much loan how much share capital there is,
doesn't make any difference to the profits of the business,
(45:44):
not directly. It may indirectly have secondary effects on profits
of the business. They take more or less risks, but
all it's doing is sharing the profit, sharing the profits
between shareholders and bondholders in different way, and the tax
I think that's the tax advantage should be taken away.
Speaker 1 (46:08):
The last thing, last thing I want to ask about
is I want to shift gears a bit because I
know not only have you worked on research around models
and modeling uncertainty, but beyond the publication of academic papers,
another avenue of thought leadership for you is your work
with actuarial organizations. In what ways have you helped actuarial
(46:32):
organizations to shape standards and practices globally.
Speaker 2 (46:37):
Uh well, let me think, haven't they. The stuff for
the CMI in Britain was to help the actorial professional
professional bodies and the actories to advise life insurance companies
(46:58):
about their mortality better. So it's helping the similar the
indices now really controlled by a foot see rather than
the actress they were helping. There was something done by
the profession in order to help the companies to understand
(47:19):
their investments better. Quite separately, I've been involved with both IOKA,
the National Assation and Consulting Actors in the past and
with AFIA for a long time, and I've been involved
with the Scientific Organization of conferences. I was looked looked
(47:45):
after the scientific program with three IOCA conferences in the
nine nineteen nineties I think, and with an awful loss
of the AFIA colloquials. I helped to be involved in
scientific sides of lots lots of conferences, and that's just
(48:07):
helping the professional body. But it's not there's I mean,
somebody has to do it, and somebody who has some knowledge,
reasonable knowledge of people's papers, whether they're sensible or not.
I'm probably a bit out of dating you for doing that,
because there will be a lot of new papers I
(48:27):
don't understand much about. And the first thing one has
to say when somebody sends in the paper for conferences,
is this actually for the right conference or is it
has it got Is it all about veterary science and
has arrived from the partly by mistake for the wrong
(48:47):
conference altogether? Or is it is it for an investment
conference and it's really about tame's management in general insurance
that sort. That's the first thing. Is it the right
on the right topic? Is it adequately written? Doesn't it
make reasonably good sense? Not a matter of scrutinizing it,
(49:10):
see whether it's a perfect paper, but is it a
plausible paper to book before people for discussion. That's what
one needs to do, and then organize some papps into
classify them. So I've helped the progressions there. I've also
I was on the consultative group of the European Acturary
(49:32):
Associations at it's now called the Actuary Association of Europe,
and there's a much bigger body because in the eighties,
eighties and nineties it was a smaller organization with two
actories from each of the professional associations in Europe. Getting
(49:55):
together in order to talk to the EU Commission. The
EU Commission would only talk to international bodies. It couldn't
talk to the French or German, Italian or British Actuarial Society,
and so that in the course of that I got
(50:20):
involved in one piece of research. The problem in life
insurance was that all the countries thought that their valuation
systems were good ones and didn't trust other people's valuation systems.
And I think I did some research which found out
that really the valuation systems for life offices that were
(50:43):
used by all the different countries were equally similarly safe.
Some of them were based on they were all based
on different methods, different principles, but in practice they worked
out pretty much the same. And so with two Dutch colleagues,
they rang me up and said could you come and
(51:04):
have a discussion this weekend and I said no, I'm
fownling to Switzerland. And they said, well, couldn't you change
planes such as scavening and talked to us. So I did.
I flew probably flew from Edinburgh or London to Scathing
and met them in the restaurant there and carried on
to euryth in the afternoon, and we drafted a set
(51:28):
of principles for life Office valuation, and that was just
the first draft. We tidied it up, presented it to
the Consulative Group's Life Committee, who had to look at it,
presented Salted Group had looked at it and tinkered with
it further, sent it into the European Commission and had
(51:51):
to look with it, tinkered with it further, and published
it in the first draft of the third Life Directive
as the valuation principles, and those eventually got into and
approved directive. That was modified quite a lot on the way,
but some of my words were still there. That has
(52:13):
all been replaced by Solvency two. But that's what you
might have called Solvency one. And I was amused. I
found it amusing that my words had I had actually
written part of the direct two. More things, yes, we have,
we haven't discussed, and that's for some future date. I
prom on my conference my ninetieth birthdat I write a
(52:35):
paper on research I haven't done yet but would like
to do. And that paper is almost drafted and will
I hope you published as a dozen al so different
suggestions in that. And we have haven't talked with anything
very much about AI, which I don't know an awful lot,
but have got some views on. But that's some other
(52:58):
discussion that some much later date.
Speaker 1 (53:00):
Sure, So just real quickly quickly on the on the paper,
Where can when, when is it going to commote and
where can we find it?
Speaker 2 (53:07):
It's it submitted to the British Annals of Actorial Science.
There's a special number of the animals to commemorate my
ninetieth birthday, which is will I think papers are supposed
to be in by about the end of the year
and it will be published sometime during next year. But
(53:30):
one of the problems with the British profession is that
stuff gets published in British Actuarial Journal and Annals Actorial
Science and nobody ever knows. There's never any announcements by
the actuarial body that the more papers or another volume
has been published.
Speaker 1 (53:49):
So anything anything I can do on social media to
help promote that, let me know.
Speaker 2 (53:53):
When I don't know what happens in America with the
with the transactions of society to factories or the atmosphous
transactions with casualty act of society. They're probably published online
these days rather than the specifically.
Speaker 1 (54:09):
Yeah, yeah, digitally. Well, David, you know, we've covered quite
a lot of ground today. We've learned about your actuarial background,
how you got into the profession. We explored your seventy
three year career journey through your early adoption into programming
and utilizing that for modeling, doing mortality forecasting, working on
(54:33):
share indices, income protection, multi state modeling. We've talked about
your renowned Wilkie model that's used to model uncertainty, touch
briefly on realistic disaster scenarios for properly and casualty insurance,
and you know, spoken about some of the applicability some
(54:54):
of the practical applications themselves. So just want to thank
you so much for your time and lending expertise.
Speaker 2 (55:01):
Okay, well, thank you for talking to me and giving
me the opportunity of spouting off my views and the
waves allowed me my pleasure.
Speaker 1 (55:12):
I have a wonderful rest of the day. Hi,
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