Black-Scholes: my "Buffett mistakes"

 A confession: I am the actuary who disagreed with this post by Dean Buckner, a former PRA official, which asserts that the Black-Scholes formula gives a good valuation of an option under the assumption of mean reversion in prices. In a follow-up post he said my critique was “ingenious” but “wrong” and that it was similar to an earlier “Buffett mistake”. ( I am also the “the firm-friendly friend” who previously drew his attention to Buffett’s views on the pricing of long-term options as described there.) I would very happy go on making “Buffett mistakes” for the rest of my life. But despite further discussion with Dean, I remain in disagreement with both the original post and the follow-up. This post explicates my view.

Suppose that as in my interpretation of the original post, the (95, 96, 95, 96…) price series is a prospectively assumed distribution. In this case, I say that a put option at 90 is always worth zero (except for the chance that our (95, 96, 95,96…) assumption may be wrong, which has nothing to do with Black-Scholes).

Suppose, alternatively, as in the interpretation put forward in the follow-up post, the (95, 96, 95, 96…) price series is a retrospectively observed single path. In this case, I say that we have not departed from the classical assumptions of Black-Scholes; we have not made a prospective assumption of mean reversion. (The 95,96, 95,96..) is merely one possible observed path amongst many under geometric Brownian motion. If we then value an option using the Black-Scholes formula at every time t, we are implicitly making a prospective assumption of geometric Brownian motion at every time t. I agree that hedging allows us to correct for the retrospectively observed single path up to time t; but it says nothing about the validity of Black-Scholes valuation at time t if we were to make a prospective assumption of mean reversion at that time.(*)  

In short, the original post does not show what it claims to show: that the Black-Scholes formula gives a good valuation of an option under a prospective assumption of mean reversion. Its criticisms of the Institute and Faculty of Actuaries (like much else on the Eumaeus website) are entertaining as slapstick, but also intemperate and wrong. And its claim that “The family of Black pricing models are amongst the most practical and robust models of reality that science possesses” is simply absurd.


(*) We may be able to fudge Black-Scholes by adjusting the volatility input to allow for mean reversion, for example as in  this paper. But fudged Black-Scholes is not the same as Black-Scholes!

Guy Thomas | Sunday 04 November 2018 at 1:03 pm | | Default | No comments

Black-Scholes: a navigational analogy

My previous post presumed some understanding not just of the Black-Scholes formula, but also of its derivation; in particular, of the hedging argument whereby the drift in the underlying asset can be ignored. My likely readers at this blog probably do understand this, but some other commentators may not. How to explain?  Here, with some trepidation, is an attempt at analogy (I say “with some trepidation” because no analogies are perfect, and this one works best for recreational sailors).

Suppose you are sailing your boat at sea on a misty day.  The mist briefly clears and in the distance you glimpse your friends, who are drift fishing on their boat.  You quickly take a compass bearing. Then the mist closes in again.

If you steer the compass heading from the bearing through the mist, you will in due course successfully rendezvous with your friends. You don’t need to worry about any lateral tidal drift, because both boats are subject to the same drift.  You have a rationale for ignoring the drift.


Now suppose instead that the sight you glimpsed through the mist was not a drifting boat, but a harbour entrance. In this case, if you take a compass bearing and then steer that heading thorough the mist, you will not successfully navigate to the harbour entrance.  The harbour doesn't drift with the tide. You have no rationale for ignoring the drift.

Summarising, we should ignore the drift when we have a rationale do so (in an option context: continuous hedging), and not ignore it when we don’t.

This analogy isn’t perfect. In particular, it doesn’t encompass (ha ha) the idea of a policy-driven reflecting barrier underpinning the assumed diffusion of house prices.  But it’s a start. I welcome any suggestions for better analogies.

Guy Thomas | Saturday 22 September 2018 at 1:40 pm | | Default | No comments

No-negative-equity guarantees: Black-Scholes and its discontents

no negative equity guarantee, lifetime mortgages

The Prudential Regulation Authority (PRA) has issued a consultation paper CP13-18 on valuation of the no-negative-equity guarantee (NNEG) in equity release mortgages.  I think the use of the Black-Scholes formula in this context is flawed, in ways which are more fundamental than suggested by the PRA’s rather bland observation that “some of the assumptions that allow the mathematical derivation of the formula…are not met.”  The prescribed approach is likely to over-estimate the value of NNEG. 


An equity release mortgage is a product where a home owner typically aged 60+ borrows 25-30% of the valuation of their house from an insurer. A fixed rate of interest is charged to the home owner, but not actually paid. On the home owner’s death or any earlier permanent vacation of the house (e.g. after they move into a care home), the loan plus accumulated interest is repayable from the sale proceeds of the house. The NNEG guarantees that the amount repayable will not exceed the sale proceeds of the house.

Equity release mortgages are typically parcelled up into ‘restructured ERM notes’ on an insurer’s balance sheet. The restructured notes earn a relatively high yield and closely match annuity liabilities, so firms are then allowed the regulatory benefit of the ‘matching adjustment’ – an increase in the discount rate which can be used to discount the liabilities when determining the firm’s regulatory solvency. The quantum of the matching adjustment depends on the spread above risk-free rates earned on the ERM notes. This spread is construed partly as an illiquidity premium, but also partly as a risk premium, including the risk of the NNEG; the latter should not in itself give rise to a matching adjustment benefit. The question then arises: in apportioning the spread between illiquidity and retained risks, how should firms value the NNEG? 

 CP 13-16 proposes to amend Supervisory Statement 3/17 to mandate the use of a Black-Scholes type model with prescribed parameter values to value the NNEG.[i] The previous version of SS3/17 was somewhat less prescriptive. In the proposed amendments, some lip service continues to be given to the possibility of alternative approaches[ii], but this is now limited by an implication that any results which differ from the prescribed Black-Scholes model will automatically be regarded as suspect.[iii]

The proposed option valuation formula is the Black (1976) formula for an option on a forward price, slightly restated in CP 13-18 as follows:[iv]





-         N() is the standard Normal cumulative distribution function

-         S is the spot price (current price) of the property

-         T is the term to maturity (the NNEG is evaluated separately for each possible future year of maturity, with deterministic assumptions for mortality, morbidity and voluntary repayments)

-         K is the loan plus rolled-up interest at time T

-         r is the prescribed Solvency II risk-free interest rate for maturity T

-         σ is the volatility of the property price, prescribed as 13%

-         q is the deferment rate, prescribed as 1%.

 Where does Black-Scholes come from?

 CP 13-18 includes a brief acknowledgement that “some of the assumptions that allow the mathematical derivation of the formula….are not met”[v], but then effectively mandates that formula anyway.  To assess how important the missing assumptions are in the context of NNEG, we need to step back and recall the fundamental constructs from which Black-Scholes is derived.

Black-Scholes is an intuitively very surprising formula.  A natural first thought is that the value of an option would depend on one’s expectation for the price of the underlying at expiry. But Black-Scholes says that this intuition of expectation-based pricing is wrong: the expected rate of growth of the underlying does not appear in the formula.

This surprising result arises from the constructs of dynamic hedging and arbitrage.  Black-Scholes derives a value for an option by considering a long-short hedge portfolio in the option and the underlying. If this is continuously adjusted as the price of the underlying changes, the value of the portfolio can be kept neutral to rate of growth of the underlying.  Black-Scholes then argues that this risk-free portfolio must earn the risk-free rate. Why? Because profit-seeking arbitrageurs make it so. If it were not so, an arbitrageur could go long the riskless hedge portfolio, short riskless zero coupon bonds (or vice versa) and so earn risk-free profits.  Since risk-free profits in practice seem thin on the ground, we conclude that market prices for options are generally set so as avoid such arbitrages. 

To an options market-maker, this no-arbitrage argument – avoiding the possibility that arbitrageurs can earn risk-free profits from our prices – is always more compelling than any expectations-based argument.  Even if the market-maker thinks he has some insight into the expected price at expiry, quoting an expectations-based price is perilous, because it creates an exposure to arbitrages against him.  In other words: no-arbitrage prices take precedence over expectations-based prices because for a market-maker, expectations-based prices are too dangerous to quote.

But the Black-Scholes argument just given depends crucially on the idea of dynamic hedging: the existence of liquid markets which give the ability to continuously adjust the hedge portfolio in underlying and the option. It also depends on the existence of arbitrageurs hungry for risk-free profits, and on market makers with limited capital who cannot afford to bleed risk-free profits to those arbitrageurs. All these elements are missing for housing. There are no markets in NNEGs.  There are no markets in the appropriate underlying, that is forwards (or alternatively futures) in housing.  There are no market makers or arbitrageurs.  Dynamic hedging is simply not possible in any shape or form. This is not a failure of ‘some assumptions’ of Black-Scholes; it is a failure of the whole construct of Black Scholes.

Recognising the absence of forward contracts, the PRA prescribed formula recasts the original Black (1976) formula by substituting the forward price discounted at the risk-free rate, F exp{–rt}, with the deferment price, S exp{–qt}, that is a price agreed now and paid now to take possession of the property in future.  The PRA comments that this substitution alleviates the problem of the lack of an observable forward price, because the deferment price can be readily estimated from the spot price (I will have more to say on this below).  But as far as dynamic hedging is concerned, this modification does nothing to help us: there are still no markets in which to construct the dynamic hedge.

It is sometimes argued (eg Derman and Taleb 2005) that although the Black-Scholes formula as formally derived by academics requires dynamic hedging, it can alternatively be justified by the existence of forward contracts, puts and calls, and the constraint of put-call parity (ie the avoidance by market makers of prices which give rise to static arbitrages).  But even this doesn’t help for housing: there are simply no markets in forward contracts, or puts and calls. If there are no puts and calls, it is hard to see how put-call parity could be a constraint.[vi]

 Geometric Brownian motion is unrealistic for house prices, especially in the lower tail

The PRA argues that although “some of the assumptions” (in my view: foundational assumptions) for Black-Scholes are not met, this doesn’t really matter:

 “The PRA is aware, as noted by respondents to DP 1/16, that some of the assumptions that allow the mathematical derivation of the formula in paragraph 3.20 for option valuation are not met in the residential property market. However, the PRA has not seen evidence that the approach set out in the proposed updated text of SS3/17 would automatically over- or under-estimate the allowance for NNEG, compared with other methods that are consistent with the four principles”[vii]

I think the PRA’s proposed approach will tend to over-estimate the allowance for NNEG (albeit ‘automatically’ is always going to be a stretch, and in that sense the PRA’s wording here may be carefully chosen). 

Black-Scholes assumes when constructing the dynamic hedge that the underlying in which we trade (a forward which doesn’t actually exist for housing!) follows a geometric Brownian motion.  For housing this would have a positive trend above the risk-free interest rate, but the trend then gets eliminated from consideration in option valuation by the construct of the hedge portfolio.  In effect, the value of the option is then evaluated as the expectation under a ‘risk-neutral measure’ where the underlying has an expected return equal to the risk-free rate, but wanders around that as per the Brownian motion, and in particular, can fall arbitrarily close to zero. The NNEG value resides in the possibility of outcomes in the lower tail.

 This model of the underlying seems reasonable for an option on a hedgeable single stock. The expected return on the stock above the risk-free rate (i.e, the equity risk premium) is eliminated for option valuation purposes by the dynamic hedging argument; and the price of a single stock can indeed fall to zero, because companies can indeed go bust.  But there are two reasons why a model in which price can fall arbitrarily close to zero is not a reasonable model for forwards on house prices.

First, the long-term experience in the UK has been that house prices have tended to increase ahead of risk-free interest rates (and also ahead of inflation and even earnings). We do not know to what extent this will continue, but it seems unreasonable – again, in the absence of the hedging argument – to give it no weight at all.[viii] 

Second, a deep and prolonged fall in house prices, with the attendant collapse in mortgage lending, widespread repossessions and distress in the electorate, seems overwhelmingly likely to induce a policymaker response. This is illustrated by the policymaker response to the modest fall in house prices following the 2008 financial crisis: policies such as purchasing first gilts and then corporate bonds (and even equities in Japan); the term funding scheme to revive mortgage lending; and policies such as help-to-buy and associated schemes providing blatantly direct support for house prices. And all this was in response to a quite modest and short fall in prices!  In a deeper or more prolonged slump, there are many more steps which policymakers can (and I believe will) take.  In a country with its own currency, the government can (and I believe will) ultimately print money and buy houses. The activities and statements of central bankers worldwide in relation to asset purchases in recent years provide further general support for this notion of a policy response to deep and prolonged falls in asset (and particularly house) prices.

This is not the same as saying that I think house prices will always go up, or that housing is a better investment than shares, or that you can never lose by buying a house.  I do not believe any of that. I just believe that overwhelmingly likely policymaker responses now provide a reflecting barrier under house prices, which makes geometric Brownian motion an unreasonable assumption for house prices in the lower tail. The level and firmness of that barrier is matter for reasonable debate, but it seems unrealistic to pretend – as the prescribed NNEG formula does – that it does not exist at all.

A couple of decades ago, I did not have this belief in a ‘policy put’.  My views have slowly changed, based on observation of public policy over the past 25 years, and especially the policy response to the relatively minor decline in house prices after 2008. I now recognise that for better or worse, I live in a country where most MP’s own more than one property, former prime ministers buy whole apartment blocks to let,[ix], senior Bank of England policymakers assert in unguarded moments that ownership of property is a far superior form of personal investment to pensions[x], etc etc. Policymaker ideologies and preferences can of course slowly change, for example as new generations of MPs are elected; if and when they do, I might slowly change my mind about the reflecting barrier.  But any change is likely to be very gradual, because the ideology amongst policymakers which substantiates the reflecting barrier runs much deeper than the political hue or personalities of any particular government.

One response to my beliefs about a ‘policy put’ on houses prices might be to say that whilst everyone is entitled to their own opinions, different people will have different opinions, and none of these should enter into consideration in option valuation. We should instead stick to the risk-free rate as a ‘neutral’ view. But in the absence of hedging, this purported neutrality is an illusion: assuming (in effect) growth at the risk-free rate is just another belief, and I see no reason to give it primacy.  In the absence of hedging, one has to take a view on the trend in prices; it cannot be conjured away as in the standard Black-Scholes. 

One notable investor has made statements suggesting a belief that analogous arguments hold good for long-term equity indices as well. In his 2008 annual report, Warren Buffett discussed long-term put options written by Berkshire Hathaway on various stock indices.  He gave an example of a 100-year put option on the Dow Jones index, and suggested that the Black-Scholes formula (with typical assumptions at the time of writing) very substantially over-valued this option. Cornell (2009) interprets Buffett’s commentary as reflecting  “ the belief that future nominal stock prices are not well approximated by a lognormal distribution, because inflationary policies of governments and central banks will limit future declines in nominal stock prices compared with those predicted by an historically estimated lognormal distribution”  (I agree with this interpretation.)[xi]

I also note that the Bank of England ‘stress tests’ for banks involve a scenario where house prices fall one-third in 3 years, but then resume their trend rate of growth. This completely rules out the deep and prolonged falls in house prices for which insurers are being asked to reserve on NNEGs.  It’s not obvious why the reserving requirements for insurers writing NNEGs should be much more stringent than those for banks underwriting ordinary mortgages.

 Deferment price less than spot price? Not necessarily.

In the prescribed NNEG formula quoted above, the PRA calls the quantity S exp{-qt}  the ‘deferment price’ of the property, that is the price payable now to take possession on a future date. There is no meaningful market in deferment prices over the periods of 20-40 years most relevant to NNEGs.[xii] The PRA nevertheless asserts that the deferment price must always be lower than the spot price of the property, on the following rationale:

“This statement is equivalent to the assertion that the deferment rate for a property is positive. The rationale can be seen by comparing the value of two contracts, one giving immediate possession of the property, the other giving possession (‘deferred possession’) whenever the exit occurs. The only difference between these contracts is the value of foregone rights (eg to income or use of the property) during the deferment period. This value should be positive for the residential properties used as collateral for ERMs.”[xiii]

In isolation, this appears a reasonable argument. But there are also reasonable counter-arguments.

Housing today is owned mainly by owner-occupiers.  They have a preference for a current interest to a deferred interest, because they need a roof over their heads, they like long-term security of occupation, they like being able to make their own choices on extensions and repairs, etc. In other words, they like the practical and sentimental benefits of home ownership.  A minority of owners are buy-to-let landlords: they like understandable form of the investment, the unusual ability to finance it largely with borrowed money, and perhaps the disengagement it facilitates from the distrusted pensions and savings industry.

For an insurer, on the other hand, these practical and sentimental benefits of a current interest in a house have no relevance.  The main potential benefit of a current (as opposed to deferred) interest is the potential income from letting. But a current interest also has several disbenefits: tenants need to be managed, houses need to be maintained, from time to time there are costs (Including possibly PR costs) of evicting tenants in arrears, and there is a possibility (through existing or new legislation) that tenants might acquire new rights. If on the other hand houses are kept vacant, this gives another set of problems: council tax, security and maintenance costs, and possibly very considerable PR costs of owning substantial amounts of empty housing.  These disbenefits are not fanciful; their materiality can be inferred from the observable fact that despite the excellent long-term performance of housing as an investment, neither insurers nor any other financial institutions have shown any enthusiasm over the past several decades for housing as an asset class.

So current interests in houses are evidently not attractive to insurers and other institutional investors. Deferred interest might well be more attractive, particularly if in the form of cash-settled financial contracts, so that all the problems of current interests are permanently avoided. Even if a deferred interest is not strictly preferred, the relative valuation of a deferred interest compared to a current interest seems very likely to be much higher for an insurer than a typical individual owner. 

Now if there were a substantial market for deferred interests, the money weight of individuals’ preference for current interests versus insurers’ preference for deferred interests would determine the relative market prices for the two types of interest (i.e. what the PRA calls the ‘deferment rate’). But we have the same problem as with the hedging arguments: the market for deferred interests does not exist on any meaningful scale.  And this is not mere happenstance or oversight; to create such a market would require the development of legal and governance frameworks covering maintenance, insurance, the rights of occupiers during and on maturity of deferred interests, etc.  In the absence of such a framework, the relative values of current interests and deferred interests remain a matter of conjecture. The PRA’s argument is a reasonable one, but not the only reasonable one, and therefore not as conclusive as CP 13-18 asserts.[xiv]

Negative deferment rates might offset omission of the reflecting barrier

The PRA argument that the deferment price should always be less than the corresponding spot price is sometimes characterised as a ‘positive deferment rate’ (i.e. the rate ‘q’ in the deferment price = S exp{–qt) is positive). The PRA says that some insurers may be using a deferment rate that is ‘too low’.  Separately, I also noted above that the assumption of geometric Brownian motion seems unrealistic for long-term house prices in the lower tail, and that it would be more realistic to have a reflecting barrier under prices to represent the likely policy response to a deep and prolonged fall in house prices.  Either the ‘error’ of omitting this reflecting barrier, or the ‘error’ of using a deferment rate that is ‘too low’, will act to reduce the NNEG valuation.  So a low (or even negative) deferment rate combined with omission of the reflecting barrier might arrive at approximately the right answer, albeit arguably for the wrong reasons.


(1)           In the context of NNEGs, the complete inapplicability of dynamic hedging (or even put-call parity) makes the prescribed Black-Scholes formula somewhat arbitrary.  At the very least, it seems unjustified to label this ‘correct’, and all other approaches ‘incorrect’.

(2)           A deep and prolonged fall in house prices is almost certain to lead to a policymaker response.  This means that that the geometric Brownian motion assumed in Black-Scholes is too heavy in the lower tail. Since most of the NNEG value arises from this tail, the prescribed approach seems likely to over-value the NNEG. There should be some implicit or explicit allowance in NNEG valuation for this policymaker response.    

(3)           Reserving requirements for insurers underwriting NNEGs should not be more stringent than those for banks underwriting ordinary mortgages.

(4)           The PRA’s argument that the (hypothetical, unobserved) deferment price should always be less than the spot price (specifically: a minimum ‘deferment rate’ of 1%pa over the term of the NNEG) is not as obvious as CP-13-18 suggests.  There are good counter-arguments, which may justify a lower (perhaps even negative) deferment rate.


[i] CP13-18 para 2.7 & proposed SS3/17 para 3.20.

[ii] CP13-18 para 2.6.

[iii] Eg. proposed SS3/17 para 3.22.

[iv] Proposed SS 3/17 para 3.20

[v] CP13-18 para 2.7.

[vi] Derman, E. and Taleb, N.N. (2005) ‘The illusion of dynamic replication’, Quantitative Finance, 5(4):323-326.. By way of simple example, consider an underlying which trades at 100, where the call option with a 105 strike trades at 8 and the put at 3 (i.e. a time value of 3 for each). Now suppose the underlying starts trending upwards.  Intuitively, we night guess that the call is now worth say 10 and the put is worth 2.  But given puts, calls and a forward  contract, this would create an arbitrage. Put-call parity in effect requires that the put and call are both independent of the trend in the underlying.

[vii] CP13-18 para 2.7.

[viii] One might wonder about a possible inconsistency of housing increasing ahead of earnings indefinitely.  Do housing costs eventually absorb 100% of earnings?  David Miles has thought about this. He suggests there are no compelling economic reasons why houses shouldn’t eventually become assets like jets: utilised by many people, but owned by only a very few. See Miles, D. and Sefton, J. (2018)  ‘Houses across time and across place’.

[ix] ‘Tony and Cherie Blair’s property portfolio worth estimated £27m’ The Guardian, 14 March 2016.

[x] ‘Property is better bet than a pension says Bank of England economist’ The Guardian, 28 August 2016.

[xi] Cornell, B. (2009) ‘Warren Buffett, Black-Scholes, and the valuation of long-dated options.’ Journal of Portfolio Management, Summer 2010: 107-11.

[xii] One might possibly refer to freehold reversions on short leaseholds, but this seems a feeble argument, because any market is realistically negligible.

[xiii] SS 3/17 proposed para 3.16.

[xiv] Eg SS3/17 proposed para 3.16.

Guy Thomas | Thursday 06 September 2018 at 11:37 pm | | Default | Five comments

Why I am not a value investor

The header is a playful provocation: in truth I am probably closer to a value investor than any other type. But I place little credence on the historical superiority of value investing (which has faltered in recent years anyway), and I have little sense of affiliation or identity as a value investor.  It’s not quite that I don’t want to be a member of any club which will have me; rather it’s that that I’m nervous about a club which is now so crowded and where all the members think alike.

The problem with value investing is that it is now a popular and widely followed investment philosophy.  Analytical techniques which historically worked well when used by a small minority of investors will work less well as more investors use them.  This is inherent to the nature of markets: a matter of arithmetic, not opinion.

The misleading header is useful if read as a prompt: are there any ways in which my thinking differs from value investing orthodoxy? Here are a few.

Scepticism about intrinsic value Many value investors place great stress on the concept of intrinsic value – the discounted future cashflows of a company, as distinct from its book value, liquidation value or market value. 

As I explained in a previous post, I seldom write down an estimate of intrinsic value. I think mainly in terms of heuristics. Some heuristics are directly related to value, such as: P/E ratios, dividend yields, and price/sales ratios. Other heuristics have only indirect connections with value, such as: the presence of counterparties with non-investment motivations, director purchases, and patterns of affinity (ie previous associations of the management and advisors to a company).

 Scepticism about deep research I generally do not want to read 20 years of past accounts, visit factories, or conduct interviews with customers, competitors and suppliers. I’m also lukewarm about meetings with management. I don’t deny that such deep research can further your understanding of a company, but I think it is subject to strongly diminishing returns. After a certain point, deeper research doesn’t make the risk sufficiently smaller to be worth the time.  Rather than looking deeper and deeper into one investment (and often, convincing yourself to buy more and more of it), it is better to spend the time looking more broadly for new investments.

 Small bets on large discrepancies, superficially understood When I find a price which looks very wrong for seemingly robust reasons, I sometimes prefer to make a small bet without fully researching the company.  Although I might do deeper research later, the price often corrects before I do. This is fine – I just sell and go on to the next one.   By keeping positions small I keep them easy to sell, that is I preserve options to change my mind as prices and my expectations change. 

Summarising all three points so far: in a noisy information environment with more choices than I can process, I prefer to spend most time looking for new and obvious anomalies, rather than refining my assessment of anomalies I’ve already found.  I aim to maximise the quality of my whole portfolio of insights, not my depth of insight on any particular companies.

 Willingness to look foolish I actively look for investment ideas which are likely to seem silly, embarrassing or trivial to those who think of themselves as “serious” investors (eg value investors!).  Apparent silliness doesn’t necessarily mean that the investment is a good one, but it does mean that fewer “serious” investors will be looking.  One example of a silly investment is ASOS under 5p in 2003 – “a start-up website selling teenage fashion?!”  (I actually bought ASOS in 2003, and I was acutely conscious of both its potential and its silliness at the time. I sold far too early.  The current price is around £50.)

I also look for risks with the following characteristic: if the bad outcome materialises, it will seem obvious with hindsight, making those who took the risk look foolish.  Again this doesn’t necessarily mean the risk is a good one, but it does mean less competition from professional investors with career concerns.

 The Keynesian short-cut By “Keynesian short-cut” I mean the observation in Chapter 12 of Keynes’ General Theory that financial markets operate under a convention that “the existing state of affairs will continue indefinitely, except insofar as we have specific reasons to expect a change.”

  In other words, we expect prices tomorrow and next month and next year to be unchanged (in real terms) from prices today, except where there is relevant new information.  So if I expect some future change when other investors don’t, I can buy at current prices and wait for the change, without thinking much about intrinsic valuation in the current state.

If the current price is already far above intrinsic value – in other words the price is already a bubble – then this approach can lead to trouble.  Implicitly, I do look out for and avoid situations where this might be the case. But my main focus is on looking for early indications of a knowable future change, rather than on intrinsic valuation in the current state.

This mode of thinking is particularly helpful for highly cyclical businesses such as shipping and house-building.  High cyclicality makes discounted cashflow or accounting ratio valuations very difficult, so it may be better not to think about them very much. Better to look for early indications of change, such as freight rates or housing starts increasing.

Avoiding the three R’s Aswath Damodaran critiques value investors with three R’s: rigid, righteous, and ritualistic.  Rigid, because they have firm views and rules about analytical techniques or preferred investment sectors (albeit the rules are different for different value investors). Righteous, because they believe theirs is the only true creed, and that success with other techniques is in some sense inferior or illegitimate.  Ritualistic, because they see value investment education as a sequence of sacred rites: read The Intelligent Investor, read Security Analysis, read all of Buffett’s shareholder letters, attend a Berkshire Hathaway annual meeting, etc. I have followed many of these rites, and I don’t deny their usefulness; but I try not to be too reverent (a fourth “R”!) about them.


Those are some of the ways in which I believe my thinking differs from value investing orthodoxy.  A difficulty with this exercise is that it’s hard to distinguish useful differences from capricious contrarianism or mere idleness.  Some of the points above could be characterised as reflecting my lack of diligence.  Although I worry about this, I don’t think diligence is an end in itself. My aim in investing is to make money, not to burnish a personal narrative or sense of identity as any particular 'type' of investor.

Perhaps a more accurate version of the header is to say that I don’t care whether or not I am a value investor.

Guy Thomas | Monday 07 October 2013 at 12:25 am | | Default | Three comments

On the limits of behavioural finance

Behavioural finance is a fashionable genre of academic research, and a productive strategy for writing academic papers.  But it was not mentioned as a resource by any of the interviewees in Free Capital, and I have never found it much help in my own investing.  There are several reasons for this. 

 Many explanations, few predictions The comprehensive menu of alleged behavioural biases offers an ex-post explanation for almost any decision which hindsight renders sub-optimal. Investors who borrowed money to invest in shares in September 1987 suffer from “over-confidence”; those who failed to do so in March 2009 suffer from “myopic loss aversion.”   Investors who respond quickly to new information overweight “availability”; those who respond slowly are “anchored” by prior beliefs.  And so on for every other ex-post mistake.  

This descriptive charm and versatility is palatable both to academic story-tellers and to casual readers.  But to be scientifically or instrumentally useful, a paradigm needs to make some specific predictions.  Behavioural finance seems more like Freudian psychology: it can be contorted to explain anything ex-post, and therefore predicts nothing ex-ante

 Poorly defined allegations of “irrationality” A common trope in behavioural finance articles is to document some observed behaviour of investors and assign to this the pejorative label “irrational.”  This is an over-used and often unwise epithet, because “irrationality” is usually defined against a narrow normative standard.   On closer examination, all that can usually be said is that large groups of people who follow the observed action indiscriminately over long periods of time will lose money compared with large groups of people who don’t. It does not follow that all (or even most) instances of the action are individually irrational.

Data mining and publication bias Any behaviour which can be labelled “irrational” (often dubiously – see above) against some normative standard is newsworthy and publishable. Null results where people behave “rationally” are less exciting, and more likely to be filed in a drawer. The suspicion of data mining for manifestations of “irrational” behaviour is increased by the disparate and often contradictory nature of the claimed biases.

Signal detection misconstrued as probabilistic judgement Many behavioural finance articles assert that investors make invalid probabilistic judgments. In the archetypal example, it is said to be a “conjunction fallacy” that Linda, a 31 year-old with biographical data suggesting liberal social views, is “more likely” to be (a) a bank teller and a feminist rather than (b) just a bank teller.

But the answer (a) which most people give amy not be a probabilistic judgement; it instead may be a socially appropriate response to cues.  This type of response is learnt both in educational settings (did you ever see an exam question where you were not expected to "use all the information provided"?), and also in everyday life (the social costs of ignoring cues are usually larger than the social costs of over-responding to them). 

The so-called “conjunction fallacy” is generated only because the question is a sort of word-trick: a probability test masquerading as a cue-response test, or a signal detection test.  If the normative standard is signal detection or polite response, the so-called 'wrong' answer is correct. And with a slight change in the question wording to focus attention on numerical frequencies rather than cue-responses, most people give the “correct” probabilistic answer (see Gigerenzer).

Or to put this another way: the "wrong" answer may be correct if I interpret the required probability as one conditional on Linda's liberal social views and the giving of the signal (i.e. the fact that you chose to draw my attention to those views, presumably as a cue). 

Detecting dishonesty is more useful than simulating truth Intuitions about truth and falsehood are often more usefully directed towards detecting liars, rather than simulating causal relations.  For example, apropos the “Linda” example above: when considering reports, it may be a good heuristic to trust the insinuations of people who provide many details - people like Linda's acquaintance - because people who provide many details tend to be truthful witnesses. (This heuristic may invert when considering predictions, where people who provide many details tend to be charlatans.) 

More generally, behavioural finance focuses mainly on failures of cognition and calculation, but largely neglects social phenomena such as trust and deception.  A visiting Martian might expect the title "behavioural finance" to encompass the study of frauds, stock promotions, and pump & dump operations - all endemic behavioural phenomena in financial markets - but in fact the subject never goes there.

Few normative prescriptions Behavioural finance invites us to gawp at all the foolish mistakes other investors make.  This financial freak show is superficially entertaining, but it doesn’t necessarily make us better investors: it doesn’t tell us what to do.  To catalogue all your biases and then do nothing much about them is not humility, it is boasting of your modesty.

 Some emotions are good emotions In the absence of explicit normative prescriptions, the implicit prescription of behavioural finance appears to be that investors should try to suppress all emotion. This is probably neurologically unfeasible, and in any case undesirable. A better aspiration is to aim to have the right emotions : to hope that your delusions are benign, and your compulsions have utility.  A good recent book on this concept is The Emotionally Intelligent Investor.

Update (16 March 2014): How knowing about biases can hurt you.

Update (11 April 2017): John Kay on the weaknesses of behavioural economics.

Guy Thomas | Saturday 10 August 2013 at 8:47 pm | | Default | Three comments

Information asymmetry and the surveillance state

(And now a short break from our normal programming....)

In a comment linked from the Wikileaks Twitter feed on the recent PRISM disclosures, Bernard Keane characterises the surveillance state with the term information asymmetry:

“Information asymmetry is how your government wants to know everything possible about you — where you are, whom you called, what you searched Google for, what was in that gmail you sent, etc etc — while trying to prevent you from knowing about its activities as much as possible by using national security (and other excuses, like “commercial in confidence”) to hide information.”

Whilst the term “information asymmetry” appears highly apt on dictionary definitions, the phenomenon being described is interestingly different from – and wider than – the typical meaning of the term “information asymmetry” in economics. 

In economics “information asymmetry” typically signifies that a seller has better information than a buyer about the quality of the goods being exchanged. 

In the canonical example, the seller of a used car has better information than a potential buyer about the quality of the car (ie whether it is a “lemon”). Similarly an employee – that is a seller of labour – has better information about their productivity than an employer. 

In both these examples – and typically in economics – the information asymmetry is at one level and about one property only, the quality of the goods being exchanged.  This property is exogenous, that is it is not changed by the interaction between the buyer and seller.

State v. subjects: two levels of information asymmetry

In the adversarial context of a surveillance state and a monitored population (call them “subjects”), there are at least two levels of information asymmetry. 

(1)   Knowledge about the state’s thoughts: The first level of asymmetry is knowledge about the state’s thoughts.  This asymmetry is mutual: the state knows more about its own thoughts, and the subjects know more about their own thoughts.

(2)   Knowledge about the state’s knowledge of your thoughts: The second level of asymmetry is knowledge about the state’s knowledge your own thoughts.  In other words, knowledge of the state’s surveillance capabilities.  Again the asymmetry is mutual: the state does not know how much the subjects know about its thoughts, and the subjects do not know how much the state knows about their thoughts.

We can conceive of asymmetry at higher levels: what the state knows you know the state knows about your thoughts, and so on. But at higher levels the significance of asymmetry probably decays (unless the lower levels are exactly symmetric). Two levels are enough to make the following observations.

At both level 1 and level 2 the uncertainty is mutual, that is there is uncertainty in both directions.

At both level 1 and level 2, the uncertainty is endogenous, that is the property to which uncertainty pertains may be changed by the interactions between the parties.

These features – mutuality and endogeneity – make the uncertainty here more subtle than the classical economics set-up, where “asymmetric information” pertains only to the exogenous quality of goods to be exchanged.

Freedom under asymmetric information

The freedom of a society is influenced by the asymmetry of knowledge. To a first approximation, asymmetry in the state’s favour tends towards totalitarianism, and asymmetry in the individual subject’s favour tends towards anarchy (but this is qualified below).

An increase in your level 1 knowledge – your knowledge of the state’s thoughts  – always increases your own freedom.  However the effect of an increase in your level 2 knowledge – your knowledge of the state’s surveillance capabilities – may be less clear, as I explain in a conjecture below.


I conjecture that freedom of subjects as a function of their knowledge of the state’s surveillance (that is level 2 knowledge) follows a U-shaped curve:



If the state’s knowledge of your own thoughts is completely secret, it will not inhibit your actions. Under blissful ignorance, freedom is high (the left hand side of the curve).  However this is not a stable scenario: as soon as the state uses the knowledge against you, its actions betray the knowledge and so the power of surveillance is unlikely to remain completely secret.  

On the other hand if you know everything about the limits of your state’s knowledge of your own thoughts – know all the details of its surveillance capabilities – then you adjust your plans and take steps to avoid the surveillance.  This gives at least a modest amount of freedom, albeit perhaps at great cost in terms of surveillance-avoiding work-arounds (the right hand side of the curve). 

It is in the middle of the curve – where you are acutely aware that the state has surveillance capabilities, but have incomplete knowledge of their workings or extent – that your freedom of thought and action will be most inhibited.

Prescription: create ambiguity about your powers of surveillance (or sousveillance)

Applying these thoughts to the surveillance state and its subjects yields the following prescription. To maximise its freedom of thought and action, each party will maximise uncertainty about its powers of surveillance (or for the subjects, sousveillance).

A surveillance state will not fully detail its surveillance capabilities, because to do so would delineate the subjects’ problem and facilitate their search for surveillance-avoiding tactics.  A surveillance state will instead publicise only vague knowledge of surveillance capabilities coupled with a lack of details, thus maximising the subjects’ inhibition and self-censorship, and hence the state’s power.

A subjects’ leaking platform such as Wikileaks will not fully detail its capabilities in obtaining, anonymising and promulgating leaks, because to do so would delineate the surveillance state’s problem and facilitate the search for leak-plugging tactics. The leaking platform will instead publicise only vague knowledge of its capabilities coupled with a lack of details, thus maximising the surveillance state’s apprehension about what might be disclosed.

The value of a leaking platform is not to reveal all secrets of the surveillance state (an impossible and probably undesirable aim), but rather to increase uncertainty about which secrets may be revealed.  Or in the vernacular: if you keep the bastards guessing, you can keep them honest.

Guy Thomas | Sunday 09 June 2013 at 4:59 pm | | Default | Five comments

Choosing better company names

ADVFN, Interactive Investor, Moneyam, Motley Fool,  Financial website entrepreneurs don’t seem to be very good at choosing names.   This post does some of the thinking for them.  It is not really an investment post, except insofar as a start-up with a good name may have a slightly better chance of success than one with a poor name.

 A good company or product name should be SUMPIER:







and (most distinctively)


The first four criteria SUMP make the name easy.

Short  A short name facilitates word-of-mouth marketing, forestalls unwanted abbreviations (see next point) and generally increases salience. Three or four syllables are good; two are probably better.

 Unique A name should to be unique in two senses: clearly different from all relevant rivals, and not susceptible to unwanted variants, abbreviations or acronyms.  Checks on the first should include a trademark search.  Checks on the second are less easily systematised. One can quickly rule out rule out Celtic Region Aluminium Products or New United Trading Services, but some variants are not so easily anticipated (see the anecdote about Exxon below).

 Memorable This helps salience and word-of-mouth marketing. Memorability is a know-it-when-I-see-it property, but one useful device is alliteration.  Toys for Tots, not Toys for Young Children; Leaping Lizards, not Jumping Reptiles.

Phonetic A name is phonetic if spelling and pronunciation are mutually implicative.  A person who first sees the name in print should be immediately able to say it out loud; a person who first hears the name in speech should be immediately able to write it down. Motley Fool is phonetic; ADVFN and are not.  Odd spellings, capitalisation and even punctuation are quite common nowadays (, flickr, tumblr…), but a phonetic name is always more effective.

The next two criteria IE make the name pleasant.

 Inoffensive A name should have no unhelpful associations for product or the target customers, either in English or any other relevant language. 

Note that this “technical” definition of “inoffensive” does not necessarily exclude risqué names – it depends on the target customers.  There are many risqué names, but also many indications of difficulties with them; I suspect that for most products this game of “niche appeal through offence” isn’t worth the candle.   

Under this “technical” definition, most of the financial website names are OK, but Motley Fool is weirdly offensive to its own users. Yes, I know the etymology: the founders were English majors with a penchant for ironic Shakespearian allusions. But Americans don't do irony. I think the name is weak.

Inoffensiveness can be hard to verify. When Esso and related companies became Exxon in 1973, the new name had been chosen from computer-generated sequences of letters and exhaustively verified as inoffensive in dozens of languages.  Within days Exxon had acquired an alternative moniker throughout the oil industry: it became the double-cross company.

 Euphonious A name should sound pleasant – or at least, not unpleasant.  It should be easy to answer the telephone. Motley Fool is euphonious; ADVFN is not.

The final criterion of resonance makes the name effective. This criterion is more subtle than all those above, and distinguishes great names from merely good ones.

 Resonant A name should resonate with – that is describe, evoke or emphasise – either or both of:

 (a) the benefits of the generic category (product resonance)

(b) the comparative advantages of your specific offering (brand resonance).

Resonance can come either from the name’s literal meaning (denotation) or associations (connotation).

Examples of names with product resonance: eBay, Match, Rightmove, Twitter, uSwitch, Youtube.

Eamples of names with brand resonance: Betfair, Costco, Dulux, Easyjet, Topshop, Valu-mart.  

As these examples show, product resonance tends to be more important when a company is creating an entirely new category, and brand resonance when a company is entering an existing category.  None of the financial website names has either type of resonance.

The ideal is to have both product and brand resonance in one short name, but this is almost unachievable (I find it hard to think of examples, although perhaps Betfair is close). More achievably, a name with product resonance can be supported by a strapline or slogan with brand resonance, and vice versa.


For financial websites, the following table evaluates some extant names against these criteria, and also some hypothetical names (tick = positive, X = negative, ~ = neutral or hard to say).



 Morphological versatility For some products or (especially) services, it helps for the name to satisfy most of the earlier criteria (unambiguous, phonetic, euphonious etc) when used as a verb.  The dominant search engine got this right (“I Googled him”); the ones which fell by the wayside didn’t (I AltaVista’d him”?  “I AskJeeves’d him?”).  Other morphological variations can sometimes be anticipated eg to describe a user of the product or service (“eBayer” for users of eBay works; “tumblrer” for users of tumblr doesn’t.)

Category name versus brand name The category name is the generic description; the brand name (protected by trade-marking) is your specific product. Generally you want these to be clearly different; and so if your product is entirely novel, you may need to invent a distinct category name. 

Vacuum cleaner – Hoover

Personal organiser – Filofax

Betting exchange – Betfair

If you don’t create a distinct category name, customers may create one you don’t like; and your own brand name is at risk of being corrupted by customers to encompass competitor products. (Obvious exception: if you are a latecomer copycat, you may prefer the dominant brand name to be corrupted this way.)

Narrow versus broad names A narrow name alluding to the company’s initial product or geographical location may give good initial resonance, but also act as an obstacle to later expansion.  Think carefully before being too specific.

Domain names The discussion above assumed a unique and hence new name, for which a corresponding domain is likely to be available; but obviously this needs to be checked.  Any similar domains (for example slight misspellings of the name) also need to be checked (and acquired, before somebody else does). 

Book names Similar criteria can be applied to choosing book titles. I think the title Free Capital satisfies the criteria above, except for one drawback: it isn’t resonant – or even comprehensible – until after you’ve read the book.  Hence the sub-title How 12 private investors made millions in the stock market, which I hope gives some prospective resonance.

Finally, I acknowledge that some companies do succeed despite poor names against the above critieria.  Yahoo!, GoDaddy, Digg…these all seem to me to have no resonance, and foolishly indulgent spelling, capitalisation or punctuation.  But a poor name makes life unnecessarily difficult.  Why not try to get it right?

(EDIT 17 Dec 2016) Related: choosing titles for books and articles.

(EDIT 14 May 2018) Related: brand naming guide

(EDIT 21 Nov 2018) Trademarking, an important point which I overlooked.

Guy Thomas | Saturday 25 May 2013 at 3:38 pm | | Default | One comment

Optimal allocation of attention

 “The scarcest resource for successful investors is not money but attention: how to manage the trade-off between time and rationality to best effect. There is not time in life to find out everything about every potential investment. Investment skill consists not in knowing everything, but in judicious neglect: making wise choices about what to overlook.”

...that's the first paragraph of the first profile in Free Capital.  There is nothing casual about this placement: I think allocation of attention is the most fundamental choice an investor has to make.  Some relevant dimensions of attention as follows.


 Acute observation versus judicious neglect In speaking of judicious neglect, the above extract really gives only half of the recipe. You also need acute observation.  The critical inputs to an investment decision are often relatively obscure to an unskilled observer: something in the notes to the accounts, the background of the CEO, recent stakebuilding by an activist, etc.  Investment skill consists of being able to spot these critical points, and neglect much else: a mix of acute observation and judicious neglect. Pay sufficient attention (due diligence). But not too much, because that would waste attention which could better used elsewhere (undue diligence).

 Depth versus breadth Is it better to look very closely at just a few possible investments, or more briefly at a larger number?  My preference is generally the latter.  This doesn’t mean researching all possible London-listed investments: at any time only a minority with some combination of good financial metrics or other idiosyncratic attractions are worth investigating at all. When you do focus in on a particular company, ir's usually more useful to look for more sources of information (another form of breadth), rather than doing more detailed calculations.   If you need a calculator, it’s too close. 

 Local versus global The phrase “London-listed investments” above highlights another dimension for attention. I generally stick to UK-listed companies, which gives the huge advantage of familiarity: I know the parameters of accounting and corporate governance and market dealing.  But I often wonder if I would do better by scouring the world continuously for the cheapest markets – Bolivia one year, Botswana the next, Bangladesh the next, etc.  (All these countries appear to have stock exchanges. I know nothing about any of them.)  

 Defence versus offence This is similar to the depth versus breadth trade-off, but worth highlighting separately.  Defensive attention means keeping up with news about what you already own.  Offensive attention means searching for new ideas.  As the number of investments you hold grows, defensive attention cand easily swell to occupy most of your time.  It takes conscious effort to allocate sufficient time to looking for new ideas.

 Focus versus serendipity  Focus is a self-directed and structured agenda: monitoring news on what you already own, daily checking of new market lows, quantitative screens for new ideas, daily or weekly reading of particular sources, etc.  Serendipity is pursuing an idea suggested by a friend, or an article on another investor’s holdings, or an RNS headline which catches my eye.  I think focus produces better choices most of the time.  But the very best investments are necessarily found through serendipity, because the idiosyncratic features which made them great investments don’t shown up on any quantitative screens. 

First order versus second order thinking Spend a small but non-negligible fraction of your time thinking about how to think: how to allocate attention (eg writing this blog post!), how to make decisions, how to embrace truths which I dislike, and so on.  Almost every chapter in Free Capital says something about the investor’s record-keeping and filing methods – not because they spontaneously talked about this, but because it was of keen interest to me.  (My real interest was how they think, but direct enquiry along those lines invited abstract or flippant responses; asking about filing systems kept the discussion concrete and serious.)


 How can you improve your allocation of attention?  The first step is simply to be consciously aware that attention is your scarcest resource, and that it’s worth thinking about trade-offs such as those above.  Some further suggestions are as follows.

 Develop domain expertise How do you know which elements of a scenario require acute observation, and which can be judiciously neglected?  I think this ability – “good judgment” – flows mainly from domain expertise. 

 For example, I said above that notes to the accounts are often important. This doesn’t mean plod through (or even skim) all the notes.  I skim only the following points (parenthesis gives where they’re usually found):

-         the totals in the remuneration report (usually separate from the notes, in a dedicated section before the income statement and balance sheet);

-         then turn to related parties (towards the end);

-         then pensions, if there’s a defined benefit scheme (3/4 way through);

-         then contingent liabilities (towards the end)

-         and then anything particularly suggested by the company’s line of business or its financial situation.  For example if the company has significant debt I would be very interested in the debt notes – anything on the interest margin, maturity and covenants. 

 Different investors operate in different observational domains. Some (like me) pay attention to the notes to the accounts; others pay attention to what management says in person; others pay attention to price charts.  The important thing is to notice something which is relevant, and preferably not noticed by most investors.

 Seek what is not offered This heuristic is independent of domain knowledge.  It helps to have a predilection to notice what is not said (the dog which does not bark), to seek opinions which are not publicised; and to seek disconfirming evidence.  Things which nobody is discussing often have great value in investment. Companies with no analyst coverage, or little coverage relative to their size, are often good investments.

 Control your own time Investment is an unusually open-ended activity. There is almost nothing you have to do, and no limits on what you could do; this open-endedness is what makes allocation of attention so important.  It helps to keep control of your own time, and to be self-conscious about how you allocate it.

 I prefer not to have a schedule of meetings, or even blocks of time allocated to particular tasks. I just work on whatever seems highest priority at every moment, balancing the trade-off between urgency and importance many times every day.  By not allocating time in advance, I’m relatively free to switch attention, say to a share I was recently buying where the price falls (so I might want to buy more)

Focus on what is knowable Before pursuing a particular line of enquiry, ask yourself whether it is likely to lead to reliable and actionable conclusions. Generally I find that it is not a good use of scarce attention to think about macroeconomics, because such thinking seldom leads to conclusions which are reliable and actionable. Analysis of big banks, insurers and other financially complex businesses falls into the same “unknowable” category, so I generally ignore them.

Guy Thomas | Sunday 16 December 2012 at 6:19 pm | | Default | Three comments