Quiet summer, with the Coalition bedding in nicely, and having the good sense to ignore calls to abuse lower bond yields to pay for more government spending. They've also dropped a few pensions bombshells; the first was the suggestion that DC pensions should be linked to the cost of living inflation index (CPI) rather than the retail price index (RPI). Since CPI runs on average about 1% less per year than CPI, this has quite an impact over the timescale of a pensioner's life.

The other less reported move - but in its way just as interesting - was the effective abolition of transfers from defined benefit (ie final salary) scemes to defined contribution. This is quite important as many DB schemes have looked to reduce their long term liabilities by offering their members a transfer, often with a bonus of some kind, to a DC scheme. The selling of these transfers has been of variable quality, with some rather dodgy remuneration structures at times. For example, IFAs have been paid based on the number of members who chose to transfer. Not much incentive for mis-selling there, then. DB scheme promises are usually very valuable, since they are typically inflation protected, may have built-in increases, and their future value is quite easy to calculate.

In other news, the Faculty and Institute have now merged, and have gone down the pragmatic road of becoming the Institute and Faculty of Actuaries.

## Wednesday, August 25, 2010

## Tuesday, June 22, 2010

### Public sector pension discount rates

Interesting post from the BBC's Robert Peston, discussing public sector pension liabilities. He makes the interesting point that a lot of these schemes use a discount rate which is higher than the rate the government can actually borrow at, and so is likely to be too high.

## Thursday, June 17, 2010

### Debt, asset bubbles, and fiat currency versus gold

I am still somewhat bemused by the resurgence of Keynesian thinking in recent years. I am still convinced that much of the action taken during the financial crisis was wrong and the state could have been a far more intelligent actor than it was. Likewise, I distrust those who claim that the only answer is a return to the gold standard; I cannot see the value in something that cannot be eaten, worn, lived in, or burnt. But this Buttonwood post makes a convincing argument that the globe is still working through the aftershocks of the collapse of the gold standard and the Bretton Woods system in the 70s.

## Tuesday, June 15, 2010

### Uh oh

None of these data points look very good. I don't think we've seen the last of the liquidity crunches, and is government (in general) going to shore the system up again?

## Monday, May 31, 2010

### Words from the sage

Quite:

We make no attempt to predict how security markets will behave; successfully forecasting short term stock price movements is something we think neither we nor anyone else can do.

## Friday, May 28, 2010

### Retiring is weird

Great post from the Economist's Free Exchange blog on the history and structure of pension provision.

I agree with this, but I'd go one step further. I'd like to see the concept of a retirement age thrown out all together. People would simply accrue retirement benefits that got more valuable as they got older, and every individual could decide at what point they wanted to make the trade-off.

...governments must address their demographic time bombs sooner rather than later. Not only to get their fiscal houses in order, but to re-adjust retirement expectations. A later retirement age, indexed to life-expectancy, should be part of any plan. This will give individuals more certainty about one significant part of their retirement income and the appropriate retirement age. These facts are necessary to make a good decision about how much you need to save. For most people working longer and saving more is their only shot at a comfortable retirement.

I agree with this, but I'd go one step further. I'd like to see the concept of a retirement age thrown out all together. People would simply accrue retirement benefits that got more valuable as they got older, and every individual could decide at what point they wanted to make the trade-off.

## Wednesday, May 26, 2010

### Faculty & Institute to merge

Passed. Not really surprising news; it has been on the cards for a long time and I suppose it is on balance a good thing. However, as a dyed in the wool Scot I am disappointed that (unless events move glacially) I will never be a member of a uniquely Scottish actuarial body.

Mention should be made of Patrick Lee who did much to scrutinise the detail of proposals and to ensure that the new body would operate under a set of rules that would allow effective governance but still allow the membership to retain effective control.

Mention should be made of Patrick Lee who did much to scrutinise the detail of proposals and to ensure that the new body would operate under a set of rules that would allow effective governance but still allow the membership to retain effective control.

### Andrew Moss takes tea

For all that its sales are worldwide, the Economist (my internal style guide insists on a small 't' in the definite article) has a somewhat British approach to some things. Hence they dragged in the CEO of Aviva (or Norwich Union, as old fogeys like remember it) and grilled him lightly on the role of private pensions in public provision and Aviva's approach to emerging markets. While drinking tea.

## Friday, May 21, 2010

### Modelling equities returns

It's a tricky business. We don't actually have all that much information to make statistical judgements about equity performance, and because we know so much about the underlying economics, it's very tempting to cherry-pick your data in order to come up with some sort of "correct" model.

This is important because the return equities generate is of huge importance in long term planning. Many pension funds are invested in equities, for example. The return such a fund earns over forty years or so is very sensitive to the long term rate. In practice, though, assigning a number to this rate has been more art than science:

The real problem is modelling the tail risk. If you take annual stock market returns, you have a random variable with quite a convincing bell-like distribution. However, if you fit a particular distribution to them, you get a good fit for a number of distributions in the bulk of observations, but the extreme data values - the ones that are really of interest - do not model well. Getting these wrong mean your knowledge of the risk you are taking is not adequate.

This is important because the return equities generate is of huge importance in long term planning. Many pension funds are invested in equities, for example. The return such a fund earns over forty years or so is very sensitive to the long term rate. In practice, though, assigning a number to this rate has been more art than science:

I recently spoke to an auditor who described the difficulty involved in calculating today's equity premium. If you use recent history in your estimation, you may end up with a zero or negative equity premium. No one wants to use this in their forecasts; otherwise projections look pretty dismal. If you're selling a financial product or strategy that involves equity investment, a zero equity premium will not entice investors.

Some state pension plans have not adjusted their risk premium either since the financial crisis. They expect their equity portfolios to earn them more than 8% per year, a risk premium a bit larger than 5%. The state plans also have no incentive to lower their equity premium. If they do, their projected assets will fall and liabilities will rise. This means their funding ratios will plummet and they will have to start making larger contributions to the plan, which would likely mean higher taxes.

The real problem is modelling the tail risk. If you take annual stock market returns, you have a random variable with quite a convincing bell-like distribution. However, if you fit a particular distribution to them, you get a good fit for a number of distributions in the bulk of observations, but the extreme data values - the ones that are really of interest - do not model well. Getting these wrong mean your knowledge of the risk you are taking is not adequate.

Labels:
academics,
data,
economics,
maths,
probability,
risk,
shares,
statistics

## Sunday, May 16, 2010

### More models causing problems

I've managed to lose the blogpost that linked me to this old, but fascinating article on the structure of the CDO crisis. Apologies to you, nameless blogger.

## Monday, May 10, 2010

### Are you rational?

Chris Dillow points to a fascinating piece of research:

The interesting thing is that the subjects *never* figured this out and carried on making sacrifices for as long as they played.

Are you rational?

In ancient times, sacrifices were at the centre of many religions. The Greeks and Romans offered their gods food and animals. The Aztecs and Mayans sacrificed humans, and Abraham was prepared to kill his own son. All were attempts to placate potentially angry gods and to win fertility, good harvests or luck in battle.

Today, we know this is just irrational babble. We’d never do anything so stupid, would we?

Oh, yes we would, as this paper by Paul Frijters and Juan Baron shows. They got a group of Australian students to play a series of public goods games, with a quirk. After each round of the ordinary game, subjects were told that their pay-offs would depend upon an unknown rule set by “Theoi”, and they were asked to choose to make a sacrifice (or not) of the money they’d made in the game to Theoi before playing the game again.

The subjects made large sacrifices. This is despite the fact that Theoi did not exist, and the pay-off was just random.

The interesting thing is that the subjects *never* figured this out and carried on making sacrifices for as long as they played.

Are you rational?

## Sunday, May 9, 2010

### Facebook privacy

Not particularly relevant, I suppose, but this graphic would have worked better as an animation. Interesting stuff, though.

## Friday, May 7, 2010

### Justifying the risk free rate

One of the commonest assumptions in financial mathematics is that the yield on government bonds represents a risk free rate which can be used to benchmark return versus risks on other investments. In good times, it's a fair assumption; when the markets are falling like dominoes, it's not.

Buttonwod muses on the issue:

Buttonwod muses on the issue:

A related issue is the use of government bonds as the core holding for pension funds, on the grounds that these are the closest match to the company's liabilities. Again, it may be the case that, say, Shell's promise to pay its pensioners is stronger than the British or Dutch government's pledge to repay its debts in full. (There is a philosophical point, as well. The rationale for private sector pension funds is that they reduce the burden on future taxpayers. But a fund investing in government bonds is simply a claim on future tax revenues.)

## Sunday, May 2, 2010

### How to avoid revising

Pick holes in the statistical arguments of the mainstream media instead. I've been taking issue with the Independent's John Rentoul (if you're not familiar with him, check out his series, Questions to Which the Answer is No) over his treatment of opinion polls.

Essentially, John is taking a number of opinion polls (an estimate of the voting intentions of the population) and taking their average, and hoping that this is somehow a better estimate of the intentions of the population than any individual poll. Indeed, if the polls follow an identical methodology, then this approach is mathematically valid - however, it is still effectively a poll, with a random value. The variance will have decreased slightly, but in real terms, not that much. If the methodologies are different, then we are averaging apples and oranges.

Essentially, John is taking a number of opinion polls (an estimate of the voting intentions of the population) and taking their average, and hoping that this is somehow a better estimate of the intentions of the population than any individual poll. Indeed, if the polls follow an identical methodology, then this approach is mathematically valid - however, it is still effectively a poll, with a random value. The variance will have decreased slightly, but in real terms, not that much. If the methodologies are different, then we are averaging apples and oranges.

## Tuesday, April 27, 2010

### More data visualisation porn

From McKinsey via a stats blog at Columbia University comes this chart, which paints a pretty stark picture of the worth of analyst's predictions:

## Saturday, April 24, 2010

### A motorway metaphor for financial risk

Democracy in America has a nice little discussion about why it is that financial innovations that can help hedge risk don't actually reduce overall risk levels: simply, people make riskier transactions to raise the level of overall risk to what it was before hedging.

### Some bedtime reading

Something I've been plowing through lately is Warren Buffet's annual shareholder letters, which are archived on the Berkshire Hathaway website - whether you think Buffet is an investment genius or just the kind of outlier that one might expect to see one or two of in any distribution, they make for fascinating reading. They also act as a great potted history of the last thirty-odd years in business and finance.

## Thursday, April 22, 2010

### Mmmm

This /. story has the potential to cause a massive hoo-hah. I can't really disagree with the principle behind it, but it will be hell of a culture shock for a lot of academics.

## Wednesday, April 21, 2010

### On the unspeakable coolness of numbers

This is an interesting little question, stolen shamelessly from xkcd, as many interesting things often are.

I choose two real numbers, A and B, using some process which I do not share with you. I tell you one of the numbers, chosen by means of a fair coin toss. Your task is to guess whether the other number is higher or lower than the one I have shared with you.

The question, of course is whether or not there is a strategy that is going to give you a better chance of being correct than borrowing my coin and flipping it. Is there?

Highlight for hint:

Since the set of reals is

Highlight for answer:

Given that the number you have been given is x, calculate p(x)=1/(1+e^-x). Now pick a random number from U(0,1). If this number is lower than p(x), guess that the unseen number is lower than the number you are given, and vice versa.

Highlight for explanation:

Consider p(x). It tends to zero on the left and 1 on the right and is monotonic in between. Sound familiar? It is, of course, a cumulative distribution function. Consider two distinct real numbers m,n with m<n, so that p(m)<p(n). Now we were shown one of m or n at random: what is the probability that we selected the lower one? This is just P(lower)=0.5*(1-p(m))+0.5*p(n), since we pick each with 50% probability. Working through, this gives P(lower)=0.5+0.5(p(n)-p(m)). And since p(m)<p(n), we have P(lower)>0.5. Pretty cool, huh?

I choose two real numbers, A and B, using some process which I do not share with you. I tell you one of the numbers, chosen by means of a fair coin toss. Your task is to guess whether the other number is higher or lower than the one I have shared with you.

The question, of course is whether or not there is a strategy that is going to give you a better chance of being correct than borrowing my coin and flipping it. Is there?

Highlight for hint:

Since the set of reals is

**uncountably**infinite, it follows that a finite process cannot choose a real number with equal probability (since you can't biject between a finite domain and an infinite codomain). This is a rather long way of saying that both A and B are likely to be closer to one, than, say Graham's Number.Highlight for answer:

Given that the number you have been given is x, calculate p(x)=1/(1+e^-x). Now pick a random number from U(0,1). If this number is lower than p(x), guess that the unseen number is lower than the number you are given, and vice versa.

Highlight for explanation:

Consider p(x). It tends to zero on the left and 1 on the right and is monotonic in between. Sound familiar? It is, of course, a cumulative distribution function. Consider two distinct real numbers m,n with m<n, so that p(m)<p(n). Now we were shown one of m or n at random: what is the probability that we selected the lower one? This is just P(lower)=0.5*(1-p(m))+0.5*p(n), since we pick each with 50% probability. Working through, this gives P(lower)=0.5+0.5(p(n)-p(m)). And since p(m)<p(n), we have P(lower)>0.5. Pretty cool, huh?

## Tuesday, April 20, 2010

### The Greek saga drags on

Quiet on the blogging front? Never apologise, never explain.

Free Exchange quotes an interview from

The point is that many financial institutions hold a mix of sovereign debt to match long term liabilities. Many Euro area bonds trade in step with each other, with a spread correlating to perceived risk. A Greek default will increase the yield on everyone else's bonds, and this could lead to a second, more serious financial crisis. The first one was resolved by backing it with the might of the dollar: it's not clear if the unique conditions of the Euro area could create a credible European equivalent.

Free Exchange quotes an interview from

*Der Spiegel:*SchÃ¤uble: [W]e have experienced a financial crisis from which we in Europe must draw a clear lesson: We cannot allow the bankruptcy of a euro member state like Greece to turn into a second Lehman Brothers.

SPIEGEL: You are exaggerating. In past years, it's happened again and again that a country couldn't pay its debts, and yet that hasn't led to a collapse of the global financial system. Why should this be different in Greece's case?

SchÃ¤uble: Because Greece is a member of the European monetary union. Greece's debts are all denominated in euros, but it isn't clear who holds how much of those debts. For that reason, the consequences of a national bankruptcy would be incalculable. Greece is just as systemically important as a major bank.

The point is that many financial institutions hold a mix of sovereign debt to match long term liabilities. Many Euro area bonds trade in step with each other, with a spread correlating to perceived risk. A Greek default will increase the yield on everyone else's bonds, and this could lead to a second, more serious financial crisis. The first one was resolved by backing it with the might of the dollar: it's not clear if the unique conditions of the Euro area could create a credible European equivalent.

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