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Gilt yield movements – why the BoE had to intervene


In the Men’s, it can be no real surprise that Djokovic comes out on top. We expect him on average to at least reach the 4th round of Wimbledon. In fact, using Djokovic’s calculated win probability, we can estimate that he has a 17% chance of winning the whole thing. The 6-time champion has been so dominant over the last few years and he is still the man to beat. Nadal follows closely in second place, indicating that we are still in the era of the tournaments being dominated by the greats.

With both of the authors of this article being based in the Edinburgh APR office, you may be surprised to see that Andy Murray misses out on the top 10. In fact, we actually have him ranked 31st. Statistics aside, we just use this as proof that we have not been swayed by any confirmation bias when creating these models!

After her long winning streak, it seems sensible that Iga Świątek has come out as our favourite to win the title in the Women’s draw. We would expect her to make it to at least the quarter-finals (further than Djokovic, perhaps a bold prediction given her past form on grass). This prediction translates to a 42% chance of her winning the tournament, which emphasises the extent of her domination just now.

The caveat that comes with the Women’s results is an absence of a prediction for Serena Williams due to her lengthy injury period. However using our “expert judgement”, as actuaries are so often asked to do, it seems unlikely she would make our top 10 with a lack of recent match practice behind her.

Lastly, in case you thought we’d forgotten, the Men’s model predicts that Richard Gasquet will win any given match with probability of 48.5% – which almost translates as an expected trip to the 2nd round for the decorated Frenchman. In fact, his estimated number of rounds is 1.94 and he has a probability of winning the tournament of 0.64% – well, you never know.

Now it’s time for us all to sit back, enjoy the Championships and sincerely hope that Djokovic and Świątek don’t make shock first-round exits – our credibility depends on it!

Addendum – written on 19th July, after Wimbledon 2022 had finished

So, how did we do? They say hindsight is a wonderful thing, but they probably haven’t tried predicting a tennis tournament. There were upsets, there were disappointments, there were shocks, and of course there were truckloads of strawberries and cream.

In the Men’s Singles, the drama began to unfold when our Number 5 pick, Berrettini, had to withdraw due to COVID-19 in the first round. At this point, we were starting to get worried. Casper Ruud (Number 4) and Stefanos Tsitsipas (Number 3) bowed out in the second and third rounds respectively, leaving us with a depleted stock from our top 10.

Fortunately, three of them – Cameron Norrie, Nadal and Djokovic all made it to the semi-finals. However, our model failed to predict the injury-forced withdrawal of Nadal at this point which left us with an unexpected Djokovic-Kyrgios final. Kyrgios, who our model predicted 20th most likely to win, had a characteristically explosive tournament, but he was no match for Djokovic. The Serb’s 7th Wimbledon title and 21st Grand Slam never really looked in doubt, and we can say we knew that all along.

It’s good that we can say that, because we certainly can’t say that we had full confidence (or much at all really) that Elena Rybakina would win the Women’s tournament, as she did. Our model had her as 18th most likely to take the title, but bear in mind that Wimbledon’s own seedings placed her in 17th before the tournament, so we weren’t far off the official list. We consoled ourselves with this fact after the heartbreak of seeing Iga Swiatek – our predicted favourite by some distance – end her 37-match winning streak in style with a huge loss to Alizé Cornet in the third round. We’re yet to face up to the “I told you so” that will be coming our way from the reviewer of this article and APR colleague, John Nicholls, so that’s something to look forward to…

Before you decide to chuck our model into whatever the equivalent of a dustbin is for mathematical models, you should know that our number 2 pick, Ons Jabeur, did actually make it to the final. She became the runner-up to Rybakina after a three-set battle that swung both ways. Our reputation just about remains intact. 

Modelling aside, it was yet another glorious instalment in the Wimbledon saga as far as the tennis was concerned. As obsessed as we were with outcomes matching our predictions, we still managed to find some moments of solace to sit back and appreciate the quality of tennis going on. Richard Gasquet even made it to the third round!

But the question on everybody’s lips is: were our models actually any good? It’s difficult to say with certainty – we only ever said who was more likely to win any given match. So we won some and we lost some. Djokovic was victorious and Swiatek bombed out. What is certain is that we will need to ruin tennis once again next year…

Ross Witney-Hunter and Josh Payne

June 2022

[1] Number of matches and wins relate to WTA250 level or above, (i.e. any wins at lower-level tournaments don’t contribute).


Wordle – how to maximise your chances of getting it in two

Table 1

DL had historically accounted for only a small part of AI in academia, but its explosive growth in the past 10 years has seen it become one of the most prominent machine learning techniques in use today. Many new AI applications are driven by neural networks.

The degree to which the distinctions between each of these four terms matter depends on the people involved.

It should be noted that neural networks can also be used to tackle problems outside of AI – for example nonlinear function approximation – but that will be the subject of a future article.

Types of neural networks

There are many different types of neural networks, but the three basic (most popular) types are referred to as Artificial, Convolutional and Recurrent (Table 2). This terminology is somewhat confusing, as Convolutional and Recurrent neural networks are clearly ‘artificial’ in the sense that they are not biological. In the early literature, ANNs referred to any non-biological neural networks. However, since the development of modern CNNs (LeNet-16, 1989) and RNNs (1989), most people now use the abbreviation ANN as the name for standard neural networks (Figure 2), especially when CNN and RNN are mentioned at the same time.

Table 2

ANNs are the simplest neural networks and sometimes also called standard/fully-connected neural networks. As shown in Figure 2, nodes (neurons) in the network are connected to others with right arrows. The first (left-hand) column represents the input data. Each column in the middle is a layer that detects and extracts the data relations from the previous layer. The last (right-hand) column is the output that we require, either a predicted value or some probabilities. Again, note that we plan to write a subsequent article focusing on the technical aspects of ANNs, so no further detail is given here.

Figure 2

A CNN works like a scanner on images with several different filters (usually squared). Each filter generates a new smaller image after scanning, as shown in Figure 3. Therefore, CNNs can ‘read’ the image and extract features automatically for further analysis. These extracted features are then used to recognise contents in the image, through an ANN. Because of the ability of image feature extraction, CNNs are powerful tools for image-related applications.

Figure 3

RNNs are the only neural networks that involve time variables. That is why it works for sequence data like sentences, sounds, rhythms and time series. A RNN processes the sequence data (x1, x2, x3) one by one and returns a sequence of data (y1, y2, y3), as shown in Figure 4.

Figure 4

We emphasise that CNNs and RNNs are not subsets of ANNs, as they are fundamentally different structures. It is common for a CNN or RNN to be followed by a shallow ANN, which is used to make the final predictions. Neural networks composed of more than one type of neural network are called hybrid neural networks. Complex real-world applications, such as autonomous driving and speech recognition, rely on hybrid neural networks.

In practice, there is no universally best architecture for neural networks and it all depends on the specific applications and the data types involved. This is a famous concept in the AI industry known as “No Free Lunch”.

Are DL and neural networks universally applicable?

Some people (including me) see DL as a universally powerful tool for all applications as long as sufficient data is involved. However, in practice the answer to this question is no. I explain the main reasons below.

First, for most applications, to train a neural network we need adequate data. As illustrated in Figure 2, the larger the dataset, the better performance we have. Whilst researchers and computer scientists in academia continue developing sophisticated algorithms and neural network architectures to achieve better performance on limited or existing datasets, in practice significantly improved performance is only possible by collecting and using more data and by utilising larger neural networks.

Figure 5

Second, neural networks are black boxes to humans. To explain this statement we start with an example. We know that humans recognise animals by features like shapes, colours and more. CNNs recognise images by features as well. But if we print out the features extracted by CNNs, these features appear mysterious to us and are not comprehensible. E.g. Figure 6 is a CNN filtered image which is recognised as a magpie by the machine. Because we do not understand the internal processes within neural networks we cannot explain the results or decisions made by neural networks. In the worst scenario, a decision made solely by machines without explanation may be illegal according to GDPR’s “right to explanation”. Besides, for the insurance industry, regulators require that insurers have a proper understanding of their models and products, something that is inconsistent with the black box nature of neural networks. This is probably one of the key factors behind the relatively limited uptake of deep learning techniques within the insurance industry to-date. Fortunately, a new but active field known as “Explainable AI” may be able to overcome this drawback by providing new explainable algorithms and better explanation for existing algorithms.

Figure 6

Third, the cost of implementing DL is non-trivial, especially for business-level applications. Anyone who plans to employ neural networks in business should consider doing so carefully. Designing and training a neural network from scratch is both time consuming and challenging, with no guarantee of a successful outcome. This may be another reason why insurance companies themselves are more conservative in their attitudes towards AI than insurtechs – a lack of both professionals familiar with AI and computing resources.


In summary, DL and neural networks are handy and powerful tools for data-related tasks. Although the black box nature and data/expertise requirements of neural networks are current obstacles, their use is likely to grow significantly in the future as we live in an era of data explosion, with an unprecedented amount of data being generated and captured every day globally. From this perspective, we can expect more applications in various industries, some of which may be game-changing. In the insurance industry, more and more insurtech companies are appearing in the market and provide AI-based solutions to pricing, underwriting, and claims processing. As experts who deal with data on a daily basis, all actuaries should be somewhat prepared for this rapidly evolving technology.

Chaofan Sun

February 2022


Lemonade’s Claim Automation

No Free Lunch Theorem for Machine Learning
Géron, Aurélien. Hands-on machine learning with Scikit-Learn, Keras, and TensorFlow: Concepts, tools, and techniques to build intelligent systems. ” O’Reilly Media, Inc.”, 2019.
LeCun, Yann, et al. “Backpropagation applied to handwritten zip code recognition.” Neural computation 1.4 (1989): 541-551.
Rumelhart, David E., Geoffrey E. Hinton, and Ronald J. Williams. “Learning representations by back-propagating errors.” Nature 323.6088 (1986): 533-536.

What does the future hold for cash?

Figure 1: Number of UK payments in millions by payment method for cash and debit card payments. Note that this includes both in-person and online payments. Source: UK Payments Market Summary [4].

Don’t count cash out yet though – the Bank of England estimates that in 2017 there were £70 billion worth of notes in circulation and that demand for notes had doubled compared to 10 years previously. The Bank of England reckons that bank notes are distributed across a variety of places; some are being held in people’s houses as savings; a lot is in banks, shop tills and high street ATMs; some is overseas; and a large proportion is held for criminal activities [6].

Those that still use cash

There has long been a concern that the decreased use of cash, much like the closure of high street banks, will lead to a disenfranchised section of society. Those who are not technology savvy, or don’t have a bank account may be left behind as society becomes cashless.  To help preserve the use of cash the government announced, in the March 2020 budget, that it would legislate protections to access to cash using various measures such as preserving ATM machines in rural locations, protecting some high street bank branches, and encouraging stores to provide cash-back services.

Other sections of society are already adapting. Charities have adopted “tap-to-donate” collection methods using contactless card readers, since 2018 all registered buskers at the Edinburgh Festival have been issued with card readers for accepting payments, and since May 2021 the Big Issue has offered card readers to each of its sellers [7]. Whilst these methods work for registered traders there still remains a gap for groups such as the homeless, illegal buskers and others without the means of accessing a card reader.

Another section of society that uses a lot of cash is the “shadow economy” – a move to a cashless society raises problems for traders who typically conduct “cash in hand” business to avoid taxes, as well as criminals who deal in cash to avoid detection. If all payments are conducted digitally then it means there is at least some trace of the transaction having taken place and it may be harder for criminals to hide their activity. Although, increasingly, criminals are turning towards digital alternatives such as bitcoin which provide a refuge outside the regulated banking economy and may provide an equivalent space to cash for these types of transactions.

What are the risks and benefits of a cashless society?

Going cashless could save both consumers, businesses, and the treasury some money: throughout the UK up to 25% of ATMs charge a fee for withdrawing cash; businesses have to store cash securely on their premises and then pay for security services to help transport it safely to banks; the central bank and the treasury have to pay for the production and issuing of new notes and coins; and both public and private sectors have to adapt machines each time notes or coins are changed. For example, in 2019-2020 the estimated cost of producing and issuing notes and coins in the UK was £143m [8]. Overall, it’s estimated that running the cash system costs up to £5 billion a year [8]. Unfortunately, at the moment many of these are fixed costs, and so as cash usage decreases the costs of running the system remain the same.

One of the other benefits is reflected in the discussion of the shadow economy above. In the absence of a suitable alternative, then a lack of cash forces everyone into the banking system. This means that all payments are logged digitally and that illegal activities such as tax evasion become harder to hide. According to an IFoA report in 2017 the potential savings in tax evasion in the UK could be up to £6 billion a year [9].  Of course, the rise of digital payments has also been met with a rise in many types of fraud – any move to a completely cashless society would need to have improved safeguards against this.

The risks of a cashless society lie primarily within the vulnerable and/or older sections of society (highlighting why it is a politically sensitive topic): those who don’t have bank accounts from which to make digital payments, those who need every transaction not to be registered, and those who don’t have access to, or don’t know how to use, the alternative technologies available. Whilst an increasing fraction of UK society is cashless there are still 5.4 million adults who rely on cash for their day to day lives, with dependency highest in the over 85’s [5]. For these groups Sweden provides a cautionary tale. As one of the most cashless societies in the world, with public transport only accepting digital transactions and the eKrona backed by the Swedish central bank, Sweden has been heralded as a world leader in moving towards a fully cashless society. However, backlash in early 2020 led to the government legislating that banks must protect access to both ATMs and cash deposit facilities for those that need them. This will mean that several locations across the country will have to have ATMs re-introduced.

Looking forward

A totally cashless society could also pave the way for changes in the banking system; from negative interest rates, to benefits from greater transaction monitoring, to flat taxes on all money spent.

Overall, the experts seem to agree that whilst we might be heading towards a cashless society, we’re not ready to become completely digital just yet. Until we find a way to include everyone in the transition then the infrastructure surrounding the cash system will have to remain.

Still, as my eldest child tucks her first baby tooth under her pillow I can’t help but wonder: one day will I need to leave a card reader out for the tooth fairy instead?

Caroline Blackley

January 2022


  9. Achord, S & Chan, J & Collier, I & Nardani, S & Rochemont, Sabrina. (2018). A Cashless Society Benefits, Risks and Issues (Interim Paper).
  10. Rochemont, Sabrina. (2020). A Cashless Society in 2019.

APR Finalists at Investors in People Awards

Who are the Super-Predictors from Round 1 of the APR Life Conference Competition?

Jacob Warbrick analyses the results from the first round of APR’s Prediction Competition at the IFoA Life Conference last November.

VBA Mini-Series – Extensibility

In the third of our VBA mini-series, John Nicholls explains how to make your VBA better using its massively useful but little-known suite of extensions.

The Problem with Probability

Have you ever considered using probability to be problematic? In this article, Joe Barnett shares his experienced opinion on the matter.

The past, present and future of wearable technology in insurance

Matthias Wuest assesses the usefulness and reliability of data from wearable technology and explores it’s impact on the Insurance Industry.

Actuarial Modelling and Diversity & Inclusion

Mujtaba Syed discusses how a highly skilled and diverse group of people working on similar problems can contribute to very effective model building and problem solving.

VBA Mini-Series – Class Modules

In the first of our VBA mini-series, John Nicholls dives into class modules in a VBA context, comparing VBA to other languages with classes and recommending areas where regular actuarial work might benefit more from using them.

APR Wins Investors in People Gold Award

APR has recently been awarded the Gold award by Investors in People! James Nicholl discusses what this means to us and what’s still being done to make APR an even better employer.

VBA Mini-Series – An Introduction

In this article John Nicholls introduces a series of planned articles that will perform a shallow dive into some more advanced concepts in VBA and how they might be useful in an actuarial context.

Talking with Pythons: How to Debug Failing Code

Stressed by tech glitches? Ellen Weise has the secrets for mastering the art of debugging, so you’ll never pull your hair out over broken code again!

APR Charity Day 2023

After another successful Charity Day for APR, Jennifer Claybourn summarises the charities we have donated to, and our reasons why.