Investors Chronicle by Alistair Blair. Extracts:

*"...a compelling read..."*

*"You could learn a lot from this dazzling dozen..."*

*"...definitely the best investment book that has crossed my desk for some time."*

Full text of review here.

Stockopedia Extracts:

*"At last,a true to life account of UK investing..."*

*"...highly recommended reading..."*

Full text of review here.

Andrew Howe (longer version of an Amazon review). Extracts:

*"Free Capital is excellent storytelling..."*

*"...has both impact and depth..."*

*"...If it's not worth £10 of your money I don’t know what is."*

Full text of review here.

Financial World Extracts:

*"...fascinating...above all an unusually compelling self-help title."*

*"This book answers its market extremely well."*

Full text of review here.

*(Last update: 19 Nov 2011)*

### A strategy, not an omission

From the concluding chapter of *Free Capital*:

*“A consensus of expert opinion is often not useful in finance, because of its self-negating property: if something is widely anticipated, it is already in the price. But the investors’ antipathy towards the concept of taking advice sometimes seemed to go beyond recognition of this point. John expressed the view that “authorised investment advice is a bit of a con”; Sushil said that he placed “almost no reliance on advisors”; Peter remarked that a small company where the management relied heavily on advisors displayed “a typical big-company mentality” (which was not a compliment).” *

I’ve written a longer article developing this idea...

**On The Value of Not Taking Advice**

**SUMMARY** Conventional wisdom commonly exhorts non-experts to take expert advice when dealing with specialist fields. This works well in relation to the physical or biological world, because theories of these worlds are generally neutral: popular acceptance of a theory does not change the phenomena it describes. In contrast, theories of social phenomena such as finance are often reflexive: popular acceptance of a theory does change the phenomena it describes. Reflexive theories can be either self-fulfilling or self-negating. Advice based on self-negating theories is not likely to be useful. Expert advice is therefore less useful in fields such as investment, which are dominated by self-negating theories. Full article here

### If you need to, you shouldn’t hold the stock

The investors in *Free Capital* have divergent views on the value of meeting company management.

Bill (Chapter 3) : *“I never visit companies, hardly ever go to an AGM, and speak to hardly anyone.”*

Sushil (Chapter 5*) *:* “…the relevant question for me is whether, say, six hours spent on a meeting with one company I already own …is more useful than, say, half an hour looking at each of 12 possible new investments.”*

Eric (Chapter 8) :* “…social interactions with company directors and other investors and contacts are the primary source of [his] edge.”*

There’s a succinct rationalisation of Bill’s “no meetings” philosophy in a recent CNBC interview with Warren Buffett:

*“In fact, they call me - some of the things we own, they call me and they want to come from thousands of miles away to talk to me. And I say listen, ***if I need to talk to you, I shouldn't own your stock.** I mean, I don't - I don't need to be schmoozed, you know?”

Above a certain level, not very important. IQ is a hygiene factor, not a discriminating factor: it helps to be reasonably smart, but above a certain threshold, further increments help less than in some other fields. The two PhD’s in the book specifically commented on this…

Sushil, Chapter 5*: “…for anyone in the top few percent of the population, IQ points are not the limiting factor in investment – other qualities such as recognising your ignorance matter more.” *

Vernon, Chapter 7: *” Compared to his mathematics degree and his doctoral work in computer science , he thinks investing is not technically difficult, but it does require some mental habits which are possibly unusual, although not difficult…”*

Emanuel Derman gives another version of this: *"I once said to one of our equity traders that I thought, on average, fixed-income traders seem to be smarter than equity traders. He agreed, adding ‘That’s because ***there’s no competitive advantage to being that smart in equity trading’**."

I think it helps to distinguish between mental strength and mental characteristics.

**Mental strength** refers to raw processing power, IQ, analytical ability.

**Mental characteristics** means things like

- Actively seeking information from dis-confirming sources
- Adjusting for one’s biases
- Accepting uncertainty for long periods
- Deferring decisions for as long as possible
- Calibrating your certainty to the weight of evidence
- Responding unemotionally to new information
- Indifference to group affiliation. (Buffett in 1965
*: “We derive no comfort because important people, vocal people, or great numbers of people agree with us. Nor do we derive comfort if they don't.” *)

For intelligence above a certain level, **mental characteristics are related only weakly, if at all, to IQ.**

By the way, the mental characteristics listed above are not universally positive. There are many occupations and endeavours which require the protagonists to maintain habitual biases (*eg* politics), reduce or deny uncertainty (*eg* leadership), and affirm group affiliation (*eg* almost any role in any organisation). **The mental characteristics which are helpful for investing may not be much use for anything else. **

**Update (1 Nov 2011):** some psychologists characterise the distinction above as intelligence versus rationality.

From Vernon, Chapter 7:

*"He drew a distinction between activities with ‘positive scoring’, where success is defined by gaining wins, and activities with ’negative scoring’, where success is defined by avoiding faults.*

*Positively scored activities include selling, leadership, and most sports. In these activities bravery, ‘having a go’ and risk-taking give a better chance of success than careful deliberation, and the downside of making errors is low. Negatively scored activities include driving a car, piloting an aircraft, and anaesthetics in medicine. The successful driver, pilot or anaesthetist is not the brave one who always ‘has a go’, but rather one who never makes any big mistakes."*

Here's a more succinct, more mathematical way of putting this. For any activity, **what's your payoff function - the max, the min or the average?**

**Max payoffs** *(Vernon's "positively scored" activities) *Your payoff is your highest result. Failure has no lasting consequences. High energy, irrational optimism and persistence are optimal traits. Don't worry about failure, just get on and "have a go."

Examples: selling, most sports, writing books(!).

**Min payoffs** *(Vernon's "negatively scored" activities)* Your payoff is your lowest result. A single failure may have lasting consequences. Meticulous care, good judgment and respecting your limitations are optimal traits. **Don't** "have a go" unless you're sure you know what you're doing.

Examples: flying a plane, driving a car, anaesthetics.

**(Weighted) average payoffs** These are somewhere in-between.

Investment is an activity with weighted average payoffs. But it helps - both because of the maths of compound growth (see earlier posts) and for psychological reasons - to place particular weight on the **min** payoffs. **A lot of success in investing comes from just avoiding mistakes. **

Another metaphor for this idea is **winner's games** and **losers' games. ** Tennis played between expert professionals is a winner's game: the winner is the player who hits the most winning shots. Tennis played between mediocre amateurs is a loser's game: the winner is the player who makes the fewest unforced errors.** In this sense, investment is probably a loser's game.**

Chapter 5, Sushil, talks about optimal leverage and compound growth. The main takeaway is that investors are better off maximising **expected logarithmic return** (*not expected return*), and this often means lower leverage than you think.

In my view expected return (the mean) is often a poor objective, because the distribution of terminal wealth from any long period of compounding is likely to be very positively skew – a small number of very high outcomes contribute a lot to the mean. **Median** terminal wealth – found by *summing the logarithmic returns, and then taking the anti-logarithm* – seems a better measure of ‘typical’ results than the mean.

For example, consider an investment which either doubles or falls 60%, each with probability 50% in each period, over a time horizon of 3 periods. This gives eight equi-probable outcomes for terminal wealth levels: 0.064, 0.32 (three times), 1.6 (three times), 8. Taking the mean of these, we find mean terminal wealth as 1.728 (=1.2^{3}). If you used the mean as your objective, the investment looks good. ** But 7 of 8 possible outcomes are below this. ** The median terminal wealth of exp –{0.11x3} = 0.72 seems a better measure of 'typical' results.

If we extend the scale of the graph in the book, we can show the expected compound growth (the blue line) as well as median compound growth (the red line). Adding leverage always increases the expected (the blue line slopes upwards), but increases the median only up to a certain point* L** (the red line has a maximum). And with too much leverage, the red line eventually goes negative - which means that in the long term, you almost surely go broke.

We can also draw a graph for the example Sushil talks about: an investment which rises 25% or falls 20% in each period. With no leverage (*L *= 1), the expected compound growth is +2.5% per period (blue line intercept on the y-axis), but median compound growth is zero (red line). The optimal leverage in this case is *L** = 0.5, that is, invest only half your bankroll, keeping the other half in cash (assumed nil return here, for simplicity).

Of course, these examples – repeated trials of investments with only two equi-probable outcomes in each period - don’t correspond to any real-world problem. The value of the examples is to highlight the following points.

- mean return is what casual intuition leads to, but this is not the same as median return, which is usually lower
- median return is the best measure of 'typical' results over long periods
- if we want to maximise median return, we need to maximise expected logarithmic return.

Looking up logarithms is inconvenient for mental arithmetic, so it helps to have a simpler approximation. Suppose *E* is the expected return of the investment, and *V* is the variance of return. For short periods *E *will typically be small, so *LE *will be small, and log(1+*LE*) ≈ *LE, *and (1+* LE)*^{2} ≈1; and if we use these approximations for the first and second terms of the Taylor expansion of log (1+*LE*), the errors in the two approximations are of opposite sign. A quick mental arithmetic approximation of the expected log return of a leveraged investor is then

** ***LE * – *L*^{2 }*V* / 2 .

This expression is maximised when *L* = *E / V*. For example, suppose you invest in equities with an expected return (net of any charges) of 6%pa and standard deviation of return of 20%pa (ie *V* = 0.2^{2} = 0.04). The theoretically optimal leverage is 0.06/0.04 = 1.5x. In practice I would halve the leverage above 100% for safety, ie maximum 1.25x, (partly because I don't know if my estimates of *E* and V are correct). Leverage of *L* > 3x gives **negative** expected log return, ie you would almost surely go broke in the long run. Quite a few hedge funds operate with leverage > 3x !

This quick estimate *(LE * – *L*^{2 }*V* / 2) for the expected log return is often enough to highlight the lack of safety in common financial structures, including some cases of hedge funds, spread betting and CFD leverage, and split capital investment trusts.

This is another angle on the “how many shares” question.

Over the years I have observed many successful private and professional investors. There have been a very few – including some, but not all, of the investors in *Free Capital* – about whom I’ve thought *“If I ever get bored of investing, I'd be happy for them to manage my money.” *

Most of these people have eventually disappointed me. The disappointments have tended to arise because they got stuck with concentrated positions – 10% of one small company, 20% of another – and were unable to react when the world changed against the businesses to which they had made large commitments.

This affects even the very greatest investors. Look at Warren Buffett: large positions in the *Washington Post* and other print newspapers, businesses which now look a lot like manufacturers of horse-drawn carriages, circa 1900.

Having seen many people whom I greatly admired come a cropper with concentrated positions, I’ve become less enamoured of extreme concentration. Nothing grows forever; most investors come a cropper eventually; and concentrated positions in illiquid shares make it hard to escape from your mistakes.

### (2) Some practicalities

My last post discussed how many shares one should hold in a relatively abstract way. Another angle is to ask how many shares it is practical to follow.

There is clearly some sort of **trade-off between number of shares held and your quality of knowledge**. Many experienced private investors are surprised (and often derisory) about the fact that that I hold around 50 shares. Surely I must know far less about many of them than if I held only 10 or 15 shares?

Well, perhaps. But this is diamonds versus flower bulbs again. If I held 10 or 15 shares, I would want them all to be diamonds. I find diamonds very hard to recognise, and most of the time, I can't find 10 or 15 of them. A lot of the time, I can't find any of them.

Flower bulbs much easier to find. At most times I can find some shares on P/E ratios around 5, shares trading below net cash, shares where there’s been a failed bid but the bidder looks likely to return, or shares with some other idiosyncratic cheapness. The quality of these businesses is often low (they aren’t diamonds). But there are plentiful, and easy to recognise.

My portfolio of 50 flower bulbs comprises **businesses of lower average quality** than if I held 10 diamonds. But the **certainty of my insight** about the 50 flower bulbs is relatively high. This is because my insights about flower bulbs tend to be (a) simple and (b) short-term. For example: "*it's trading 25% below net cash, and something is likely to happen to make it trade at net cash."*

Insights about diamonds tend to be more complex, long-term and nebulous. *"It has long-term comparative advantage and it's going to be a bigger business in 5, 10 and 20 years' time."* So you say. *But how do you know? * Generally, I don't.

Or to put it another way: to identify diamonds, you need long-term foresight about their durability - market position, susceptibility to technological changes, etc etc. I've always found this very difficult. But you don’t need long-term foresight to identify flower bulbs.

A final point in favour of diversification is that even if a very few shares is the optimal policy in theory, many highly concentrated investors eventually come a cropper in practice.

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