Category Archives: complexiy

Actuarial sloppiness

An actuary I know once made me cringe by saying “It doesn’t matter how an Economic Scenario Generator is constructed, if it meets all the calibration tests then it’s fine. A machine learning black box is as good as any other model with the same scores.” The idea being that if the model outputs correctly reflect the calibration inputs, the martingale test worked and the number of simulations generated produced an acceptably low standard error then the model is fit for purpose and is as good as any other model with the same “test scores”.

This is an example of actuarial sloppiness and is of course quite wrong.

There are at least three clear reasons why the model could still be dangerously specified and inferior to a more coherently structured model with worse “test scores”.

The least concerning of the three is probably interpolation. We rarely have a complete set of calibration inputs. We might have equity volatility at 1 year, 3 year, 5 year and an assumed long-term point of 30 years as calibration inputs to our model. We will be using the model outputs for many other points and just because we confirmed that the output results are consistent with the calibration inputs says nothing about whether the 2 year or 10 year volatility are appropriate.

The second reason is related – extrapolation. We may well be using model outputs beyond the 30 year point for which we have a specific calibration. A second example would be the volatility skew implied by the model even if none were specified – a more subtle form of extrapolation

A typical counter to these first two concerns is to use a more comprehensive set of calibration tests. Consider the smoothness of the volatility surface and ensure that extrapolations beyond the last calibration point are sensible. Good ideas both, but already we are veering away from a simplified calibration test score world and introducing judgment (a good thing!) into the evaluation.

There are limits to the “expanded test” solution. A truly comprehensive set of tests might well be impossibly large if not infinite with increasing cost to this brute force approach.

The third is a function of how the ESG is used. Most likely, the model is being used to value a complex guarantee or exotic derivative with a set of pay-offs based on the results of the ESG. Two ESGs could have the same calibration test results, even calculating similar at-the-money option values but value path-dependent or otherwise more exotic or products very differently due to different serial correlations or untested higher moments.

It is unlikely that a far out-of-the-money binary option was part of the calibration inputs and tests. If it were, it is certain that another instrument with information to add from a complete market was excluded. The set of calibration inputs and tests can never be exhaustive.

It turns out there is an easier way to decreasing the risk that the interpolated and extrapolated financial outcomes of using the ESG are nonsense: Start with a coherent model structure for the ESG. By using a logical underlying model incorporating drivers and interactions that reflect what we know of the market, we bring much of what we would need to add in that enormous set of calibration tests into the model and increase the likelihood of usable ESG results.

Sanral with blinkers on and no imagination

I read Nazir Alli’s opinion piece on BDLive this morning. Unsurprisingly, he talks up tolling as the best way to fund roads.

Now, I don’t have as strong a view as some that etolls are Universally Bad. Frankly, I also feel that many people who complain about etolls are still complaining about having to pay. The arguments against etolls have become more sophisticated over time, but I can’t shake the suspicion that many of those who support fuel levies would have been almost equally outraged if an increased fuel levy had been used instead of etolls.

Let’s take a look at some of the more egregious comments from Mr Alli:

There should be agreement that the fuel levy is not an option, especially in the context of reducing inequality, though that is what the populists and dissenters keep punting. That leaves us with three options.

Starting with the end in mind? It’s a bold claim that “there should be agreement that the fuel levy is not an option”. As far as I can tell, there is no justification for this in the piece.  The plea to reduce inequality is also vague – I can think of several mechanisms that could be used to mitigate the increased burden on the poor. There are more complex, more subtle interventions than the simple, single-lever ideas Mr Alli imagines.

Then there is the capacity-related backlog in and around our metropolitan areas. These are the roads that are reaching their maximum capacity during peak hour, resulting in increased congestion, which in turn contributes to driver frustration, decreased safety and negative economic consequences. To alleviate congestion, additional lanes or new roads need to be built. For this, Sanral needs a further R120bn.

This is a separate point for Mr Alli and for me. The need for funding doesn’t talk to how that funding should be raised. This paragraph does provide a fascinating insight into the 20th century mindset on dealing with road congestion. Congestion? More roads! The answer to congestion is actually fewer parking spaces and increased public transport. Think about it, if you have nowhere to park your vehicle, you won’t drive to work. If there are a range of efficient, reliable, safe and cost-effective public transport options available, then you have the carrot as well.

It gets better:

These are huge sums of money but if one takes into account that about 87% of all goods and services move by road, it is really important to keep road traffic moving. In light of the needs elsewhere in the economy, it is unlikely such funding will be forthcoming.

Yes, roads are used, overused, for transport in South Africa. One can hardly blame Sanral for the decline in our rail network, but the 87% needs to be decreased as part of a coherent national transport and logistics plan.

Mr Alli says “it is unlikely such funding will be forthcoming”.  All the funding comes from South African citizens and corporations. If Mr Alli believes that the only way to raise funds is via etolling, then it’s hardly surprising that he is so fixated on etolls as the “right answer”. There are other options, even if Mr Alli can’t conceive of them.

The growth in the length of roads Sanral has to manage is not matched by an increased allocation from the Treasury, which means the agency must be innovative, smart and prudent with allocated funds.

I’m waiting for a recognition that the etolling infrastructure is extremely expensive and doesn’t really talk to “prudent” at all.

Keeping in mind the large sums required for road construction and maintenance, it is obvious that the levy would have to rise by between R1.35/l and R2.80/l, depending on the time frames in which the backlogs should be addressed

I would like to see the analysis behind this – and get a view on how these compares to the etolls in terms of their ability to deal with backlogs of funding.

That will hit the poor really hard, given the long distances people have to travel to get to work. In Gauteng, nearly 64% of commuters rely on minibus taxis — the preferred mode of the poor — which receive no transport subsidy at present, yet are exempt from e-tolling. Increasing the fuel levy may result in increasing pressure from the taxi industry for a transport subsidy.

There is nothing inherently pro-poor about etolls. The exemption for taxis is pro-poor. A taxi transport subsidy would be pro-poor.  What exactly is the point being made here?

An important toll principle is that those who use a road should directly pay for it — the direct user-pays principle.

My Alli apparently believes this principle, but it is not a natural law of the universe. It is one principle out of many. And ironically, isn’t particularly pro-poor which seems to be so important to Mr Alli. It also doesn’t talk to the complications of who ultimately pays for the etolls – business will increase prices to be born by consumers so it’s not only those individuals who happen to be driving who will bear the cost anyway.

In simple terms, if you live in Springbok, you will not pay for the road between Johannesburg and Pretoria if it is a toll road. Also, a cost-benefit study has shown that those in the higher income brackets will be paying about 94% of the passenger vehicle toll — in other words, those who can afford it.

There are two points here. The first is that individuals who don’t personally use a road don’t benefit from it. I am happy to pay for a road network, as we have all done in this country and other countries for decades. On the 94%, it is an interesting number. I’m curious to know which income brackets have been used, what the comparable number would be for the fuel levy AND what the number would be without the exemptions factored into current etolls.

We need to understand that the e-tolling system enables different tariffs to be charged for time of day and day of the week, providing a mechanism to reduce demand during peak hours and thus for costly capacity upgrades — which is not possible with the fuel levy.

Finally, an excellent and valid point. I’m also a fan of using etags more broadly – paying for parking automatically amongst others.

Going the fuel levy route or waiting for the Treasury to find the considerable sums needed would have a simple and often overlooked consequence: it would be virtually impossible to deliver large infrastructure projects in short time periods when they are needed — due to the very high fuel levy that would be required to achieve this. It would also encourage people not to use public transport.

Alternative funding mechanisms are possible. Sanral could be permitted to borrow to repay the borrowings out of future income, amongst others.  The second point is more ridiculous – Mr Alli is comparing etolls with exemptions for public transport to fuel levies without subsidies for public transport. That is not a fair comparison.

With the fuel levy, the present generation needs to pay in full for infrastructure that has a 20-or 30-year life expectancy, which may result in less infrastructure being built than needed.

No, it doesn’t. Again, alternative funding mechanism are possible with the fuel levy performing the same function as the etolls in providing income to finance the roads over time.

Where is the mention of the relative efficiency of collecting money via etolls and the fuel levy? The saved costs of etolling infrastructure, call centres, debt collectors an advertising? Where is the imagination to see how other options might work (or at least, might have worked)? Where is the discussion of the forex expenditure and trade deficit implications of paying significant money to foreign companies?

Mr Alli has a position to argue and he’s done it narrowly and with a single-mindedness that is terrifying.

The debate over etolls is a complex one. This doesn’t help.


When is revenue lost?

In respect for Nelson Mandela’s death and funeral, many retailers closed yesterday for the day. This Business Day article claims a R300m loss for the retail industry as a result.

Except, no. Some fraction of those sales might be permanently lost, but the income hasn’t been spent and the cash still sits in shoppers’ pockets. The R300m is mostly just delayed.

There will be some impact where closed shops sacrifice sales to open shops.

There might even be some small amount of decreased consumption and therefore increased saving. The article headline wasn’t, “Retailers sacrifice means an increase of R300m in personal savings.”

This is part of an ongoing trend (probably for hundreds of years) for journalists, even respected financial journalists working at a respect newspaper, to seek the most impressive headline. It also reflects our very human tendency to ignore second order effects. Which is a pity because that’s where the really interesting analysis lies.

Link shortening madness

URL shorteners are handy when space is limited, but each one adds another fatal point of failure. To make the point, if I want you to read about New Business Margin on Revenue. And by the way you should because it’s an important newish concept, the link will work provided your internet connection is working, the relevant DNS is working and my server is running.

Let’s look at an extreme alternative:

  • First shorten link at gets to
  • Then take and shorten at to get
  • Then gets
  • Then TinyURL gets

Interestingly, didn’t want to shorten the link. TinyURL has a longish URK, but does have the awesome ability to provide your own shortened URL like

I’m not provide embedded links for all of those because it’s a bit silly. But you can see when you click on the last link as it backtracks through each of the shorteners before arriving at the destination. Each step is the chance for catastrophic failure.

So please don’t use link shorteners in ordinary web content. It’s not necessary and makes the internet increasingly fragile.

Intrade and the Prisoner’s Dilemma

Ok, it’s not exactly the Prisoner’s Dilemma, but it tastes the same.  Members of prediction market Intrade, have to decide whether to cooperate or be selfish.

The exchange is insolvent. It seems like the operator didn’t separate member money from its own money and then spent it. This basically makes it a ponzi scheme. It can keep operating as long as it keeps operating. There are sufficient member balances that it still has positive cash. As soon as it accounts for these liabilities to members, it is insolvent.

So, members are offered the chance to agree to a voluntary reduction in their claim and/or conversion to long-term investment. If nobody agrees, the exchange will be liquidated and everyone loses out and any inherent value in the exchange disappears. If enough agree, then those who don’t agree get to withdraw their full funds.

Under this argument, the incentive is for each member to be selfish. Let’s see why.

There are two scenarios – enough accept the terms, too few accept the terms.

If too few accept the terms, the payout is the same whether you agreed to accept the terms or not. So that won’t affect the decision. If there are enough who accept the terms, those who declined will get paid out in full.  The only way it makes sense or an individual to accept the terms is if the value of accepting the terms is greater than 100% of their account balance. This might be the case if they were converted to an equity value in the business and believed in its ongoing sustainability, but seems pretty unlikely.

The equity value has been massively damaged by the damage to brand value of the exchange. Outside parties or existing members wishing to take an equity stake need to consider carefully the extent of brand damage already and the $700,000 shortfall needed to restore solvency let alone any capital for future operations and investment.

Bye bye inTrade.

Eskom, inflation and early onset dementia

Everyone has totally lost the plot.

The proportion of people who speak sense has declined to the lowest level recorded since ever.

“If Eskom puts up its prices too high we’ll have higher inflation. Inflation is bad therefore Eskom shouldn’t put up electricity prices so much.”

Oh really? What happens to the cost of producing electricity when Eskom puts up its prices by 16% rather than 8%? Nothing. Well actually the cost goes down, but then I’m being sneaky – raising the price will reduce consumption, which in turn will decrease the total amount of electricity produced, thus reducing the aggregate cost of electricity production. Yes, it’s sneaky because we all knew I meant the “cost per unit” of electricity.

But wait, if we consume less electricity, Eskom presumably would have to use less gas-turbine powered emergency and oh-so-very-expensive sources of electricity to fill in at peak times. So just maybe the cost per unit of electricity would go down if Eskom were allowed to raise it’s prices by 16% and not 8%.

Another good way to lower inflation would be for government to add a 1% subsidy on everything this year. Everything will be 1% cheaper because you mail (fax?) your receipts to Pravin and Government will mail you a postal order for 1% of the value back in.  Instantly effective prices are 1% lower and inflation is more under control.

Hell, why stop at 1%? Let’s have a 2% reduction.  And a further 2% next year and so on.