Weird distributions #1

Turn to any textbook treatment of the Black-Scholes model, and you will find a list of things that the model ‘assumes’. Wikipedia is no exception. These divide into assumptions about the market, such as no arbitrage, ability to short sell etc., which I shall set aside for now, and assumptions about the asset process. Foremost among these are that

  • Future returns are independent of past values, i.e. the process is random
  • Log returns are Gaussian, or normally distributed
  • Volatility is constant
  • Drift is constant

Now it is true that if these conditions are satisfied, then the model will work (I shall discuss an appropriate sense of ‘work’ below). That is, these are sufficient conditions (p implies q). But it is also commonly assumed1 that if they are not satisfied, then the model will not work (not p implies not q), i.e. it is assumed that the conditions are necessary, as well as sufficient.

Nothing could be further from the truth.

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Why I ignore the crash

 

Markets iffy last week but my shoulders shrug. I have a fixed price target for my portfolio, so what with all the market collapse my growth projection has increased. Moreover I discount all my future liabilities (paying gas bills, Sainsbury’s, ‘biting on granite’ worktops, garden shed, phone, new pair of trousers etc) by the same growth rate so my overall position is unchanged.

We should all do this.  After all, that’s what the Bank of England recommends.2

The Marcus Barnard Show

The Equity Release seminar that Dean and I presented at the London School of Economics on Monday October 1st got a good turnout and prompted a lively, and at times, stormy, discussion.3 The most entertaining contribution to the discussion came from NUMIS equity release analyst Marcus Bernard, who has been pushing Just Group hard as a buy.

Marcus and I are on opposite sides on this issue.

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Artificial stupidity

When someone mentions ‘Artificial Intelligence’ I usually ignore them completely. But the subject comes up so frequently that it is impossible to ignore. Andy Haldane fretted a few weeks ago that AI might cause ‘widespread unemployment, despite an Organisation for Economic Cooperation and Development report earlier this year saying that fears of mass unemployment for automation were ‘overblown’ as most jobs were harder to automate than previous studies had suggested.

One of the better articles came out yesterday (9 October) quoting Roger Schank who predicts a new AI winter, ‘a reference to the period in the early 1980s when disappointment over the progress of the technology led to a retreat from the field’.

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A for Anonymous

We received an email from Anonymous@hotmail.com (which doesn’t exist, of course) suggesting we look at slide 4 on page 2 of this presentation given at the Life Conference in November 2017. The presentation was given by Tom Kenny (of Just Group), and Gina Craske of KPMG (auditor of Just Group). The other members of the Party including a representative from each of the other three big accountancy firms, two members representing ERM providers, and only one academic that I could make out.

Many thanks, Anonymous, but we already knew this. See also this response to CP 13/18 by the Institute which identifies the other two Institutional bodies involved in replying to the PRA, namely the Life Standards and Consultations sub Committee, whose members are listed here, and the Life Insurance Board, whose members are listed here.

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Why the forward price has an interest rate term

Another day, and another challenge to the method we have proposed for the valuation of the no negative equity guarantee. In our presentation here (slide 9, equation 8) we use the term r-q in the calculation of the forward house price at time t, so aren’t we incorporating both a house price growth assumption (r = interest rate) and a net rental rate q? Thus aren’t we – implausibly – assuming that future house price growth will be equal to the interest rate?

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Casting magic upon daylight

A spokesman for UKAR got back to me saying I got the numbers wrong in this post. I said that the total loan value of the book bought by Rothesay Life, i.e. the original amount lent accrued at the loan rate is somewhat north of £1bn. Apparently not, for that value, which they call ‘unpaid balances on portfolios sold’, is £860m, hence somewhat south of £1bn. So there are five different values to choose from:

  • The loan value (i.e. original amount lent accrued at the loan rate) £860m
  • The book value of c. £750m
  • The amount that would have been paid if not for the NNEG
  • The amount paid by Rothesay, which UKAR cannot disclose, but which was greater than book value, and £200m less than the amount that would have been paid if not for the NNEG
  • Government loan repayment: over £1bn

Fans of linear algebra will spot that there are still too many unknown quantities to make any sense of this.

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Fundamentally broken


I was at a discussion today where we were asked whether corporate reporting faced any problems. Most hands went up. Then we were asked whether reporting faced any significant problems.  Only two hands went up, including mine. I briefly skirted around the problems with life company reporting.

My point was dismissed. Everyone agrees, said the room, that life company accounting is fundamentally broken, so that objection didn’t count. What else haven’t the Romans done for us, sort of thing.

To be sure, I have heard this many times, including in the corridors of power, even from life insurance accountants. But if everyone thinks that, why has no one done anything? Life insurance is about, well, our pensions and stuff. Could it really be too difficult to fix?

Our contact form is on the menu above, all suggestions welcome. Is there a problem? How do we fix it?