Deterministic and Stochastic: the Great Modelling Face-off

By December 14, 2020 No Comments
devil angel shoulder deterministic stochastic

Deterministic and stochastic shouldn’t be dirty words! 

If deterministic and stochastic modelling were football teams, they would be Man United and Liverpool.  Or maybe Liverpool and Man City, in recent years.  OK, maybe Spurs and Chelsea in 2020-21? 

If they were computer systems, they would be PC and Mac, during the Gates/Jobs era. 

If they were games consoles, they would be Playstation and Xbox… 

You get the picture.  There are those who swear that one is the Holy Grail, while the other is a load of rubbish.  Meanwhile, the truth is that neither is either.   

If you, like us, are sick of experts telling you that one is “right” while the other is “wrong”; or that one is “misleading” to clients, or the other “confusing”, maybe this blog will help shed light on some of these mysteries. 

Don’t worry, turns out they’re both wrong! 


What is stochastic modelling? 

According to Google (and/or Wikipedia) Stochastic modelling: 

is a tool for estimating probability distributions of potential outcomes by allowing for random variation in one or more inputs over time. The random variation is usually based on fluctuations observed in historical data for a selected period using standard time-series techniques. 

In other words: you look at historic variations of one of the inputs in your model and use these to look at how the future might take shape.   

Might being the operative word here.  Of course, we’re all familiar with COBS 4.6 but, in case you don’t know it by rote, here’s the relevant disclaimer from COBS 4.6.7 (b): any indication of possible future performance based on historic data must include: “a prominent warning that such forecasts are not a reliable indicator of future performance“. 

In a stochastic model, one or more of the assumptions will vary over the course of projection.  Clients will typically see outcomes both in monetary terms and in the form of a probability of success or failure.  This is often accompanied by a chart illustrating a range of likely outcomes.

The idea is that, rather than the potentially misleading “certainty” of a specific predicted outcome, they get a spread of possible outcomes and a likelihood of achieving their goals. 


business chart falling stochastic deterministic cashflow model

What is deterministic modelling? 

While stochastic modelling works by looking at variations of one or more of the inputs in your model, deterministic modelling takes a single, average growth rate and assumes this will be the same for each year.  On average.   

In other words: an investment of £100,000 growing at 4% per annum will be worth £104,000 after one year; £108,160 after two years, etc. 

Just like with stochastic modelling, you will be using past performance to gauge potential future performance.  An example: 

  • You have a client aged 45.   
  • You are helping them plan their cashflow up to age 100.   
  • Your client’s portfolio has grown at just 0.5% this year (thanks, Covid!) 
  • Average annualised growth on the portfolio over the last 5 years is 4.2% 

What growth rate would you assume, for the next 55 years of your client’s lifetime? 




If you said 0.5% then congratulations.  You may be a glass-half-empty kind of person, but you will never be accused of over-estimating your clients’ potential future investment performance! 

If you said something in the region of 3-4% then you’re probably being a little more realistic.  Remember, this is a 55-year projection – we shouldn’t allow short-term dips to cloud our judgement.  We also shouldn’t ignore the possibility of similar risks in future… but this is something I’ll come back to shortly. 


The “illusion of certainty” 

So showing the client a range of likely outcomes sounds like a great option, doesn’t it?  And, in some ways, it is.  But in others, perhaps less so! 

It’s often suggested that deterministic models give the illusion of certainty.  I can definitely understand why.    

If someone didn’t adequately explain a deterministic model, it might look like it was trying to predict the future by telling me I’ll have exactly £932,123 in 40 years’ time.  BUT that isn’t the point of deterministic cashflow modelling.  The point of deterministic cashflow modelling is empowering decision making by illustrating the difference between route A and route B.  If all other assumptions stay the same, we can show whether one or the other provides a better outcome.   

Perhaps this comes down to training or knowledge, but an adviser using deterministic modelling with clients probably shouldn’t be telling them that it’s a crystal ball.  The projection should be caveated in some way (“based on the agreed assumptions…”) or it should be explained that this is just a model and all models are wrong! 

The “illusion of certainty” criticism is always directed at deterministic models, never stochastic.  But is this really fair?  If you’re a competent user of a deterministic cashflow tool, and explain its purpose to your clients, there is no illusion of certainty.  If, on the other hand, you’re presenting them with a model that tells them they have a 63.8% chance of succeeding with their chosen withdrawal strategy, could that not also be construed as an illusion of certainty?! 


stochastic cashflow illusion certainty confusing clients“Stochastic modelling confuses clients” 

This is another one we hear a lot.  Deterministic modelling is “simpler” or “less confusing”.   

Neither is necessarily true!  Either type of model, used well and presented well, can be simple and unambiguous.  Either type of model, used poorly and presented badly, will confuse clients.   

Deterministic modelling is, perhaps, more familiar to clients.  Most people are au fait with the idea of taking an investment and rolling its value forward or putting together a budget.  Stochastic modelling is, perhaps, more foreign to them.  The idea of ESGs or discrete rolling return historic periods is unlikely to be familiar to even the most financially-savvy clients.   

What does this mean?   

I don’t think stochastic is necessarily “confusing”, but advisers using stochastic modelling with clients will need to bridge the gap in clients’ understanding by means of their own skill in explaining and presenting the model.    

Deterministic modelling is perhaps more forgiving in this respect because clients “just get it”.  That doesn’t mean you can get away with using the model poorly or presenting it badly, just that it might perhaps be more intuitive to clients than a more technical stochastic model. 


If X, then Y 

I mentioned above that in a stochastic model one or more of the assumptions will vary.  One of the issues with this is that there is no interdependence between these assumptions.   

For example, look at what’s happened to inflation during the Coronavirus pandemic.  There’s an excellent article on the Bank of England website which discusses this here. 

A deterministic model might anticipate inflation averaging e.g. 2% over a 30 year period and inflation growth averaging e.g. 4% over the same period (I.e. 2% real return). 

What assumptions will vary in the stochastic model?  Will it be assumed that inflation is a constant 2%, while investment return can vary stochastically alongside it?  If so, when investment return hits 15%, will clients be benefitting from 13% real return in these years?  Conversely, when investment returns show –20% will inflation adjust accordingly (see BoE post, above)? 

In reality, most of the other assumptions in the model will vary (either proportionately or inversely) as a result of market change.  With poor market returns recently, we’ve seen record lows of inflation (disinflation, even); stalling business growth and public-sector pay freezes… is it giving clients a “more accurate” picture if you’re varying investment returns each year stochastically, but still making a deterministic assumption about inflation, earnings increase, property values, and business growth? 


Spurious accuracy vs accurate spuriocity 

In case you’re wondering: no, spuriocity ISN’T a word.  But it should be!

The other key difference we’ve found between stochastic and deterministic modelling is their approach to lifestyle and spending.  In most stochastic tools, there’s an assumption that clients have an “income need”.  For example, they might want £80k per annum to spend, in retirement. 

This is all well and good, but who spends exactly £80,000 every year?  Surely our lifestyles aren’t that linear? 

While deterministic modelling advocates using a single average growth rate for investment return, it also allows for more specific plans around future spending.  This might include, for example, mortgages being paid off; holiday homes being bought (or sold); grandchildren’s uni fees being paid, or any number of the kind of things that happen in real life.   

If I had to define, in layman’s terms, the difference between stochastic and deterministic modelling, here’s how I’d put it: 

Stochastic = average of lifestyle expenses; accurate investment returns. 
Deterministic = accurate lifestyle expenses; average investment returns. 

Note: both use averages.  Neither is without its flaws, but we should be cautious about “accurately” modelling one variable while making blanket assumptions about others, i.e. sacrificing accuracy on all other points for the sake of “accurately” modelling investment return.  Is there any tangible value in knowing that even the worst returns of the last 100 years would have met my notional Income Need of £80k/annum if, in reality, that’s not what I need? 


This morning at Tesco (a conclusion, of sorts!?)

On average, I probably spend £100 a week on groceries.  Sometimes it’s £120, others £80.  This morning, I spent £140.  That’s a long way off the average…

cope market fall stochastic deterministic cashflow

Just like the age-old investment performance caveats, what I spent last month on groceries cannot be used to guarantee future grocery spending performance.   There’s no truly accurate way of predicting either future investment returns OR future spending – if I can’t predict what my weekly supermarket shop will come to, what chance do I have of guesstimating an Income Need I may or may not have in 30 years’ time?  

Both stochastic and deterministic are wrong.Do your clients care if you prefer Playstation or Xbox, or if you support Liverpool?  Will it help reach their goals any quicker?  What matters isn’t the tools you use, but the ongoing service you provide. 

Is there a sensible middle-ground?  Yes, certainly!  Many Truth users stress-test the growth assumptions in their deterministic models using stochastic tools (in fact, we have a stochastic calculator built into Truth).  This allows you to sense check the assumptions in your deterministic model and (if necessary) adjust in line with what your stochastic tools tell you about the likely probability of success. 

The point is that cashflow modelling isn’t about predicting the future, it’s about helping clients facilitate their lifestyle goals.  Whether or not this involves recommending products or investments; whether or not it uses Stochastic or Deterministic illustrations doesn’t really matter… it’s simply about planning.