[Skip to content]

Sign up for our daily newsletter
The Actuary The magazine of the Institute & Faculty of Actuaries
.

Spread-betting and reserving techniques

The typical cradle-to-grave life-cycle
of the loss ratio for a given class of
business goes through the following
stages:
? business plan;
? incurred BornhuetterFerguson method;
? incurred chain-ladder method;
? paid chain-ladder development;
? paid claims.
Some stages last longer than others, some
are bypassed, and sometimes exposure-based
methods are required. What has any of this got
to do with spread-betting? (See the box ‘Spreadbetting
markets’ below.)
Business planning
For our purposes we are going to focus on a simple
supremacy bet in a typical super league
rugby match. The average score in St Helens’
first 17 matches is a win for Saints by 3216,
and in Wakefield matches it is a loss for the
Wildcats by 2126. Let us say that the St Helens
supremacy market is quoted at 2023.
The factors that will go into the initial
supremacy market offered by a spread-betting
firm will include:
? recent performances and results;
? relative impact of home advantage;
? predicted weather conditions;
? continuity of players;
? experience of players;
? injuries;
? suspensions;
? head-to-head records;
? relative importance of outcome;
? forthcoming fixtures;
? market prices.
There is an obvious translation for certain of
these issues into business planning in general
insurance.
Tracking expectations
Thinking about the development of the
supremacy margin from t (time) = 0, to 0 at
t = final hooter at any point during the game,
it is possible to take the current score and add
the unearned supremacy margin to get the midmarket
price.
Events such as tries (or hurricanes) have an
impact on expectations. They shift them in a
discontinuous fashion. A penalty will immediately
shift the actual supremacy margin by two
points, and also the market price by two. Landfalling
major hurricanes will do the same thing
to ultimate loss ratios, and usually by more than
two points.
Initial expectations and early doors
Before we get to the final outcome after 80 minutes
of end-to-end action, we are confronted by
the most interesting part of the issue. Between
kick-off and the final whistle the market is ‘inrunning’.
At all points during the game the spreadbetting
company will quote a bidoffer spread
for the St Helens supremacy. Primarily the price
will be related to the current score and the time
left in the game. Basically there is a predetermined
decay pattern that the additional
supremacy margin above the current score will follow. The decay pattern can be plotted over
time and will form a continuous line from 21.5
at t = 0, to 0 at t = final hooter.
As it turns out there is no score after 15 minutes,
and the St Helens supremacy at that point
was expected to be four points. As such the market
price is now St Helens 1619.
At such an early stage of development the
spread-betting firm is relying on its prior expectations
and an expected development pattern
of St Helens supremacy; a rugby league
BornhuetterFerguson method, if you will.
Changing positions
If you opened a position, say buying St Helens
before kick-off, you do not have to wait for the
final hooter to close out your bet. You can do
so at any time, although you have to pay the
full bidoffer spread rather than just half of it.
During the game you can close out part of
your position or all of your position, you can
also increase your position or even reverse your
position. All actions are possible.
So you can lock into a given level of profit or
put in place stop-loss protection. You can use
your judgement at every point to take advantage
of any perceived value in the market price.
Unfortunately no such equivalent readily
exists for the ultimate loss ratio for an underwriting
year. The closest you could get would be
a mid-year stop-loss reinsurance policy, whether
things were either going well or going badly.
Red card?
Back to the action, just before half-time a high
tackle is committed by feisty Wakefield Trinity
Wildcats prop forward, Adam Watene. The referee
as per usual did not have a good view of
the incident and takes the easy way out and
places the incident ‘on report’. What would
have happened if the player had been sent off?
The score at that point was 124 with a market
price of 1922, ie an eight-point lead plus a 12.5
expected future ‘cost’ plus the bidoffer spread.
Playing a full half of football without a player
is quite difficult and will typically lead to gaps
opening up wide later in the game. The loss is
incurred at the point when the player is sent off,
but the final cost is only reported over the next
40 minutes.
Spread-betting firms are prepared and have an
estimate of the value of losing any given player
for 40 minutes; the value here might be 18
points. So if Adam had been sent off, the market
price would have moved from 1922 to 3740.
Suffice it to say that hurricanes, among other things, have a lot in common with red cards.
Large risk losses are more like yellow cards: ten
minutes in the sin bin. Hurricane Katrina was
to loss ratios what Adam Watene almost was to
St Helens’ supremacy margin.
Reaching ultimate
Moving along to the last quarter of the game,
St Helens has just broken loose and is now leading
by 3610 thanks to a Jon Wilkin hat trick.
The St Helens supremacy at that point was
expected to be 13.5 points. As such, the market
price at that point is St Helens 32.535.5.
At such a late stage of development the
spread-betting firm is still stubbornly relying on
its prior expectations. You might think that if a
team was playing well on the day, the betting
firm would switch to the chain-ladder method,
ie if Wakefield was 12 points ahead with a quarter
of the match to go then the market quoted
would be something like Wakefield 14.517.5,
that is 4/3 times the current supremacy margin
plus the bidoffer spread.
Typically the spread-betting firms do not
change their view of the ability of a team during
a single match. Such a short period of observation
is regarded as not being sufficiently credible.
Ultimately the final score in the game is
reached after the full 80 minutes. In our example,
St Helens broke down a tired Wakefield
defence and ran in three converted tries in the
last 20 minutes, including one on the final play
of the game, to win by a score of 5410, giving
a final supremacy of 44 points. Anyone who bought St Helens at any point has won, and
anyone who sold them has lost.
A difference with reserving is that, short of a
scheme of arrangement, an underwriting year
never actually gets to ultimate. Rugby games
actually conclude.
From rugby to insurance
So there we are, I have highlighted some of the
(few) similarities between rugby league and general
insurance. The same approach works for
most sports.
For the record, Wakefield pulled off a bit of a
surprise by beating St Helens 2922 at home,
but they did lose at St Helens later in the season
by 3414. Adam Watene was neither sent off
nor placed on report.

Spread-betting markets
Spread-betting
There are many different spread-betting markets.
They all function in the same way, in that for a given
market there is a buy price, a sell price and a bidoffer
spread. The two most common types of betting
market are supremacy and index bets. In all instances
the counterparty to every trade is the spread-better.
This situation is different from fixed-odds betting
with betting exchanges, where the counterparty is
another individual.
Supremacy bets
A supremacy bet can be a simple ‘winning-margin’ bet.
So, using a rugby example, if St Helens were playing
the Wakefield Trinity Wildcats the spread-betting
firm might quote a supremacy market of St Helens
2023. That is to say, they think that St Helens will
win the match by 21.5 points and that there is a threepoint
bidoffer spread.
So if you buy St Helens at 23 for £10 a point and
they go on to win the match by 40 points, you will
win £170, being: (final price buy price) × unit stake,
or (40 23) × £10. This is referred to as ‘going long’
on St Helens.
If you fancy Wakefield to do better than lose by
20 points then you could sell St Helens at 20 for £15
a point. If St Helens win by 40 then you will lose
£300, being: (sell price final price) × unit stake, or
(20 40) × £15. This is referred to as ‘going short’ on
St Helens.
The final price is the price at which you close out
your position: if you bought then it is the final selling
price, if you sold then it is the final buying price. There
is no spread on the final price.
Index bets
An index bet can be a simple win/lose bet, often but
not always with only a binary outcome. An example
of a binary market would be Chelsea vs Liverpool, with
Chelsea conceding a half-goal handicap with an index
of 50 for a win and nothing for a loss. There being half
a goal handicap ensures that a draw is not possible.
Alternatively if Liverpool was playing Chelsea then
the spread-betting firm might quote an index market
of Liverpool 1013. The index is 50 points for a win,
25 points for a draw, and no points for a loss. The
Chelsea index market would have to be priced at
3740 in order to be consistent with the pricing of
the Liverpool index market.
So if you buy Liverpool at 13 for £20 a point and
they manage a draw (no doubt through a dodgy lastminute
penalty at the Kop end) then you will win
£240, ie (25 13) × £20.
More markets
Many other markets exist; however, they are all
tweaks of the above markets or sometimes combinations
of supremacy and index markets. A typical
combination might be a football index based on 20
points for winning plus 10 points per goal scored.

Jargonbuster
Scheme of arrangement
a compromise or arrangement between a
company and some or all of its creditors,
governed by section 425 of the Companies
Act 1985. A scheme needs to be sanctioned
by the court. It is a way of achieving finality.

07_10_28-29.pdf