What is risk?

I was recently asked how I managed risk in my own stock holdings, on a portfolio level. And I must admit that I was stumped for a moment. Because, you see, I don't manage risk on a portfolio level per say.

I am, at heart, a stock picker. And I manage risk by picking stocks/companies that I know the value of and which I know possess attractive risk/reward propositions. The logic behind that is that, if my individual holdings are attractive on a risk/reward basis, then my portfolio as a whole should enjoy the same characteristic.

A counter argument to this view is that there may be correlations amongst stock positions that may make the portfolio seem riskier than it appears. But clearly, there are two issues here - 1) how does correlation affect risk here on a portfolio level?; 2) is that an unsolvable issue?

On the latter, simple common sense will guide a reasonably prudent man to not hold all its positions in one sector for instance (e.g. real estate). So by construct, a reasonable man would naturally source for attractive ideas across a number of sectors, rather than just one.

So I do not set out to have a concentration in one sector (or not) for my portfolio. The construction of my portfolio is just a product of the ideas I have, at any point in time. If it so turns out that I am heavily weighted towards one, it is not necessarily a bad thing, as long as I have conviction that my individual ideas are good. But of course, I do consciously avoid betting my house on 1 single sector/factor exposure. Plain old common sense is what guides me here.

On the first point about correlation and risk, my reply is that it is largely an academic exercise. First, how do you measure correlations, other than stock price correlations. Is one able to realistically, with precision, break down each position into the factors that drive it and draw correlations across positions? That seems rather hard and way too many assumptions involved. The more assumptions you make, the more likely you will be wrong.

If so, then we are down to price movements as our last bastion of hope in measuring correlations and the implied assumption there is price movement - i.e. volatility - is risk. Risk is bad and as such, price volatility is evil.

And this is the juncture which I evoke the brilliance of Buffett, and which I absolutely agree with.

"I think volatility as a measure of risk is nuts. You should really try to understand the business instead, and try to understand the volatility of the business instead. Risk should be measured in terms of the quality of the business and the risk of permanent capital loss. That makes far more sense to me. It has nothing to do with volatility." - Buffett

As such, to manage risk, all you have to do is understand what you own and assess what your downside is (i.e. risk of permanent capital loss).

The open secret: why does value investing still works

Why does value investing still work despite being such an open secret? To answer that, I quote Professor George Athanassakos in the extract below.

The short answer, for those who desire instant gratification is this - the stock market is dominated by i) humans which are fallible and ii) fund managers who act in ways that serve their self interest rather than their clients and in doing so lead to irrational outcomes. This causes mispricing in the market which allow value investors to come out ahead.

Note that I did not quote the entire article because I do not necessarily agree with it in its entirety, especially the point that value investors are contrarian. Nonetheless, you could access the article, in its entirety, in the link below.

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http://www.ftadviser.com/2013/08/12/investments/global/the-human-psychology-behind-value-investing-QaFquIhxGCx7eyXvI1QORL/article.html

"If the evidence in favour of value investing is so overwhelming, why isn’t everyone a value investor? Why does a value premium (that value, on average, beats growth investing) still exist? Shouldn’t it be eliminated? Not necessarily, because the forces behind the value premium are psychology and institutional biases
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Human and institutional behaviour bias stock prices in such a way that give rise to the value premium. Individuals are subject to irrational behaviour. They are overly optimistic, they overreact and most importantly they herd. They herd to protect their jobs. If the group loses and a portfolio manager is in the losing group, his job is protected as he lost as everyone else – but if he is wrong and others win while he loses, then his job and reputation are at stake.

At the same time, individuals working for institutions have their own agendas that may conflict with those of their clients or investors. They act on these agendas to benefit themselves, rather than those who hired them. They rebalance their portfolios throughout the year to earn their Christmas bonus, they window dress to look better than they are to their clients.

Weaknesses of human nature and institutional biases are not going to go away – just as portfolio managers do poorly not due to lack of stockpicking abilities, but rather due to institutional factors that encourage them to over-diversify to protect their jobs and assets under management, investors will also continue to believe the promises that growth (glamorous) stocks make, overbidding them, and giving rise to the value premium."

Is Education the Great Equalizer?

Some say that education is the Great Equalizer that will provide social mobility to the poor. Our parents believe in that, which is why they told us all to study hard.

But times have changed. That bastion of hope is getting eroded as branded tuition centres serve to extend the rich-poor gap from a young age, amongst other things that erode the Great Equalizer.

Plus, even as it is, many young graduates have since learnt that their years of studies is only getting them a meager $2 - 4k starting pay. How do you close the income gap with that sort of salary? A $2k salary, even if you saved it all for 40yrs, barely gets you to S$1mn!

Nonetheless, I continue to believe that education is the way to go. Because frankly, there are not many pathways to success. But the substance of said education is where I differ. 

How many have left school and continue to apply quadratic equations and the principles of thermodynamics in their daily life? Shall we compare this to the number of people who grapple with their finances? 

The truth is that some of the things we learnt in school are important, some make us a more well-rounded person, and some are just plain useless. And some really important skills such as simple budgeting and investing are not being sufficiently emphasized.

I would go one step further to argue that the stock market is the Great Equalizer that allows a transfer of wealth from the incapable to the capable and potentially from the rich to the poor. The stock market is agnostic. It does not judge or discriminate against who you are, but just whether you are capable or not. A true meritocracy is what we have here.

Everyone has a good chance of making $ and profiting from Mr. Market, as long as you have the right skills. Skills that you would pick up if you bother to learn. (No ten year series textbook here though)

Some may argue that the stock market is manipulated by the rich and in doing so, the rich get richer. Fair enough, the world is not perfect. But with the right knowledge, you would know when to avoid situations like those and when to take advantage of it.

One of the worst things in life is ignorance. Ignorance is not bliss. It has consequences. To invest without learning how to do so is no different from jumping into the sea without knowing how to swim. 

In short, education is important. Being educated in the right things is even more important.

P.S. I am planning to do some pro-bono financial literacy courses for students. Appreciate any feedback/ideas on course content/delivery and contacts within education institutions.

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How did US market behave in periods of rising interest rates?

Let's not mistake correlation with causation. But still an interesting data set that shows stock market returns in periods of rising interest rates. Some of the annualised returns are quite pathetic and unclear whether it is inclusive of dividends. But at least it is positive.

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http://www.businessinsider.com/liz-ann-sonders-market-snapshot-2013-12#heres-a-look-at-what-rising-rates-have-meant-for-the-markets-and-the-economy-12

 

SMRT raising fares of some taxis

Taxi fares are increasing as expected. Will we see more? Will owing transport companies be a good hedge against transport cost inflation?

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A Straits Times Article (12 Dec 2013)

TAKING a ride in an SMRT taxi could cost a third more from Monday.

In the latest series of taxi fare changes, SMRT Corp is upping the flagdown fares of all its Chevrolet Epica cabs to $3.60.

Distance fares of its Mercedes-Benz, London, Hyundai Starex and Ssangyong Rodius cabs go up to 30 cents for every 400m travelled for up to 10km, every 350m after 10km and 45 seconds of waiting time.

Previous rates were $3.40 and 22 cents respectively.

The changes take effect from Monday and could mean the cost of trips in these cabs being around 30 per cent costlier compared to existing fares and also what some competitors charge.

Besides Mercedes and multi-seater taxis, the rate for most other cabs is 22 cents per 400m.

SMRT, the third largest taxi operator, last posted new rates when it launched its fleet of Toyota Prius hybrid cabs in October.

Its petrol-electric cabs have a flagdown fare of $3.80, higher than the $3.50 to $3.70 competitors charge for similar taxis.

A company spokesman said the changes were to "keep pace with current rates in the industry".

There are about 30 types of cabs in Singapore, with more than 10 different flagdown fares, three different metered fare structures, more than 10 different types of surcharges and eight types of phone booking charges.

Fares, deregulated since 1998, have been rising in recent years on the back of higher taxi rental rates, which operators attribute to higher certificate of entitlement (COE) prices.

But an industry source said that rises in COE premiums - which have climbed from around $50,000 two years ago to around $73,000 today - are not a valid reason.

"The increase in COE translates to only about $10 per day per cab over its seven-year lifespan," he said. "Rental rates for many cabs have gone up from less than $120, to $135 or more per day - even for cabs bought with much lower premiums."

With SMRT's hike, other firms are poised to follow, although no operator would admit it.

Market leader ComfortDelGro Corp, which runs Comfort and CityCab taxis, said it does not comment on taxi fare changes until they take place.

Trans-Cab and Premier Taxi said they had no plans to adjust fares at the moment.

Prime Taxi, the smallest player, said there had been discussions about raising fares, but "we are watching the situation" before deciding.

Commuter H.Y. Loh said that she will now take cabs "sparingly".

 

"Now that bus services have improved, I will take cabs only when it rains, I have lots of shopping or am travelling to a faraway place that I'm not familiar with," the 58-year-old professional said.

Relationship between businesses, castles and moats

Warren Buffett on competitive moats

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Q: You were the first person to use the term “moats” as competitive advantage. Morningstar has built on this. What do you think about Morningstar’s work on moats?

WB: I think they’re doing a great job. I came up with this term 40+ years ago because in capitalism, you have these economic castles. Apple, Microsoft, etc. Some have smaller castles. If you have a castle in capitalism, people are going to try to capture it.

You need 2 things – a moat around the castle, and you need a knight in the castle who is trying to widen the moat around the castle.

How did Coca-Cola build their moat? They deepened the thought in people’s minds that Coca-Cola is where happiness is. The moat is what’s in your mind. Railroad moats are barriers to entry. Geico’s moat is low prices. Every day we try to widen the moat.  See’s Candies creates a moat in the minds of consumers.  It is a more effective gift on Valentine’s Day than Russell Stover.  See’s Candies has raised its price every year on December 26 for 41 years.  BRK bought See’s Candies for $25 million in 1972.  Today it earns $80 million.  Richard Branson failed 10 years ago with Virgin Cola.  Snickers has been the number one candy bar for 40 years.

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How did you fare in the ovarian lottery?

How did you fare in the ovarian lottery? I think I did ok. At least I am healthy (for now). Be thankful for what you have.

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http://www.businessinsider.com/warren-buffett-on-the-ovarian-lottery-2013-12

Warren Buffett recently met with a group of MBA students.

A student asked him what shaped his political views (Buffett is a Democrat). The famous investor offered a great through experiment, which helped him think through the kind of world he wants to live in. In it he characterizes something he calls the 'Ovarian Lottery':

 

My political views were formed by this process. Just imagine that it is 24 hours before you are born. A genie comes and says to you in the womb, “You look like an extraordinarily responsible, intelligent, potential human being. Going to emerge in 24 hours and it is an enormous responsibility I am going to assign to you – determination of the political, economic and social system into which you are going to emerge. You set the rules, any political system, democracy, parliamentary, anything you wish, can set the economic structure, communistic, capitalistic, set anything in motion and I guarantee you that when you emerge this world will exist for you, your children and grandchildren.

 

What’s the catch? One catch – just before you emerge you have to go through a huge bucket with 7 billion slips, one for each human. Dip your hand in and that is what you get – you could be born intelligent or not intelligent, born healthy or disabled, born black or white, born in the US or in Bangladesh, etc. You have no idea which slip you will get. Not knowing which slip you are going to get, how would you design the world? Do you want men to push around females? It’s a 50/50 chance you get female. If you think about the political world, you want a system that gets what people want. You want more and more output because you’ll have more wealth to share around.

 

The US is a great system, turns out $50,000 GDP per capita, 6 times the amount when I was born in just one lifetime. But not knowing what slip you get, you want a system that once it produces output, you don’t want anyone to be left behind. You want to incentivize the top performers, don’t want equality in results, but do want something that those who get the bad tickets still have a decent life. You also don’t want fear in people’s minds – fear of lack of money in old age, fear of cost of health care. I call this the “Ovarian Lottery”.

 

My sisters didn’t get the same ticket. Expectations for them were that they would marry well, or if they work, would work as a nurse, teacher, etc. If you are designing the world knowing 50/50 male or female, you don’t want this type of world for women – you could get female. Design your world this way; this should be your philosophy. 

 

I look at Forbes 400, look at their figures and see how it’s gone up in the last 30 years. Americans at the bottom are also improving, and that is great, but we don’t want that degree of inequality. Only governments can correct that. Right way to look at it is the standpoint of how you would view the world if you didn’t know who you would be. If you’re not willing to gamble with your slip out of 100 random slips, you are lucky! The top 1% of 7 billion people. Everyone is wired differently. You can’t say you do everything yourself. We all have teachers, and people before us who led us to where we are. We can’t let people fall too far behind. You all definitely got good slips.

Even if you don't buy Buffett's idea that only government can alleviate certain forms of inequality, one thing that's great about Buffett is his appreciation of luck, and the realization that he won a lottery ticket by dint of his birth. So many of our elites can't stop talking about how hard they worked, or the importance of taking risk and all that. Buffett readily acknowledges that he had incredible fortune from the moment he was born.

At the same event, Warren Buffett also explained why he thought George W. Bush said the greatest economic statement of all time.

F&N: Is minority interest at risk?

For those who own shares in F&N, it appears that there was a married trade of ~61mn shares or ~4.2% of total share base today.

It is assumed that this placement is done by K. Charoen for the free float requirement. But we will have to wait till the official SGX annoucement to confirm that, which is not out at time of writing.

The crucial question now is this, imo - what % of MI is currently in the hands of parties that may be friendly to K. Charoen?

This is a crucial question as the original MI, prior to the married trades, were able to control the outcome of any (potentially) damaging related party transactions. And in doing so, protect their interest.

With the introduction of more MI that are potentially friendly to K. Charoen, the rules of the game may have changed. For those who are not friends with K. Charoen, can you still protect your interest?

Food for thought.

P.S. Do not forget that allies of K. Charoen could potentially have taken out some of the original MI since the time trading halt was lifted post-takeover. The original MI can be assumed to be non-allies since they did not take up his original exit offer. Hence, the MI friendly to K. Charoen could potentially be more than the free float placement.

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Climbing the Ladder of Inference: The unfortunate incident of Little India

This blog is not meant to be political or in any way, to express any views on what society should or should not be.

But this article written by a mediator on the Little India incident, raises very valid considerations that any thinking individual should consider. And the points raised are cross-applicable to the field of investing, in my opinion.

The key message of the article is that different individuals can reach entirely different conclusions based off the same set of facts, because people have a tendency to climb the Ladder of Inference.

Same facts. Different observations. Different interpretation. Vastly different conclusions. All because people tend to introduce their own assumptions & emotions into the equation, as they climb the Ladder of Inference, rather than focusing on facts

We see this in the stock market as well, where we have countless professionals offering their opinions and views, which are oftentimes laden with (faulty) presumptions. Perhaps we can all be better investors by focusing on the facts and by leaving our presumptions behind.

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http://harmonymediation.com.sg/the-little-india-riot-and-the-ladder-of-inference/

As the situation in Little India unfolds, I cannot help but feel a sense of dread, but also a sliver of hope for what is to come.

Dread arises from the fast and furious poisonous arrows that have been shot from the members of the public. People have a habit of looking at a limited set of data, interpreting this limited data from their beliefs, assumptions and experiences; and drawing from them conclusions that they verbalise. This is widely known as the “Ladder of Inference”, which is used to describe how people can draw vastly different conclusions from different, limited, or even the same set of data.

I have seen comments online to the tune of, “We should not condone such behaviour… If we do, they will get more brazen… and I’ll say good luck to you and our future generation”. The author of this comment made observations hours after the event, interpreted that the actions were unacceptable and concluded that the the future of the country was at stake. He has climbed his ladder of inference. 

Contrast this with a different comment, “It is easy to hate. But these guys are human beings too. I wonder if they feel they’re not given any respect at all because of their job scope”. This person has seen data from the event, but included data external to this singular event, and made a tentative interpretation, where he then expressed reluctance to draw a conclusion.

After some time, as more news came in, a number who watched online footage of the mob overturning police cars left comments along the lines of “The video shows it all….the police are a disgrace to their uniform and their oath…Moral of the story – the police will not be there to protect anyone of us.” 

Contrast this with a comment from someone else who has watched the same video, “the riot police should be congratulated for showing restraint and not deploying tear gas and cannons.” Same video. Different observations. Different interpretations. Vastly different conclusions.

As conflict resolution professionals, we often see parties perch themselves at the top of the ladder, adamant that their conclusion is the only valid one. And if they look hard enough, they will often find others who have climbed that exact ladder to commiserate with (and vice-versa, leading to different camps and power struggles). Our job is never to judge, but to alert warring parties that they have, inadvertently or not, climbed their individual ladders of inference.

For people who seek genuine solutions to their disputes, what we endeavour to do is to assist them to climb down their ladders of inference – leave the perch for a minute with a neutral, examine the facts again, and in a safe place, question one’s assumptions. Not because the facts can be so easily verified, nor that truth can ever be so easily ascertained, nor that basic beliefs and assumptions well-honed from past experiences can be so easily eradicated. But simply because the willingness and the process of CLIMBING DOWN the Ladder of Inference is that critical turning point at which parties can even begin to ask themselves what they really want out of the dispute.

To those uninitiated to my profession, some may wonder, ’Who cares about this Ladder of Inference?’ It is just an academic exercise that is irrelevant to the real world. In the real world, people have different thoughts, feelings and opinions. Why analyse this to death? 

Well, I started off this post with what I described as a feeling of dread, because I have seen how words when verbalised and dosed with heightened emotions, can take on a life of their own. Words linger long after they have been uttered. Their intent may be forgotten, but their effects continue to multiply. What starts out as a single event, because of the shocking halt to the daily routine of a peaceful nation, has the potential to escalate if people do not take care to examine their own as well as others’ responses.

What I pray and hope for is that Singaporeans will take care to examine the Little India riot carefully before they speak. What data have you have observed versus what other facts might you not know about? Which are facts and which are assumptions and feelings? Reflect on your own interpretation – is it with one set of facts or a hypothetical set of facts? Consider if someone else would interpret this differently. Go through a thorough exercise before you draw your own conclusion and take care to consider the effect on others when you verbalise these conclusions.

Researchers in this field have observed that the exercise of repeatedly climbing down and up the ladder of inference is an act of self-mastery observed in mature and successful individuals. As a relatively young nation, our collective response will show if we have a measured, well-considered, and even a gracious response to this incident. As in many disputes I’ve had the privilege to attempt to resolve, events like the Little India riot (and other national incidents) will strip us down to our very core and exhibit to the world our true maturity, a maturity that is not necessarily measured in years.

Which brings me to the sliver of hope. The heart of a mediator is a peacemaking heart. What drives us is the ideal that we should always strive for a better way to resolve differences. While I am not naive about the competition for scarce resources, the need for the rule of law and the dignity of the country, I also choose to believe in the best of human nature. In all things, I hope and pray that as a nation, we will have the good sense and gracious hearts to speak only if it is constructive, and to do unto others what we would have them do unto us. This incident will reveal what we are made of.

Conversations with a real estate broker

Just had coffee with an institutional real estate broker. It appears that deals are currently hard to close as buyers remain cautious and unwilling to pay up, while sellers have yet to capitulate and are not moving their prices down.  Financing is not an issue, but a mismatch in pricing and risk expectations is.

It thus appears that risk tolerance remains low and investors have yet to throw caution to the wind, IMO. As such, this reduces the probability that we are in bubble territory on the real estate front. Having said that, questions remain as to how much upside remains on the table for real estate.

It is similarly important to figure out the downside, which nobody has a good answer to. What is only clear though is that people currently still have funds on the sideline and an intention to buy at a lower price, which may provide support on the downside.

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Are we already in bubble territory?

Recently, someone asked me if the US market is in bubble territory, given that stock prices have risen so sharply. She read it from the papers, she said.

My short answer is that it is too presumptuous to assume that we are in bubble territory. Even more so, if you consider your source from a journalist who may or may not be qualified to judge whether we are in a bubble - an assessment which ten thousand other brilliant minds could not conclude on.

Clearly, such an assessment need to be more thorough and well thought through. And thankfully, we have the clairty of thought from Howard Marks, Chairman of Oaktree Capital, to guide us along in this topic.

Note that Howard Marks is merely human and he may be wrong. But on average, he has been more right than wrong.

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Extract from Howard Marks' Nov 26 2013 memo:

No, I don’t think it’s time to bail out of the markets. Prices and valuation parameters are higher than they were a few years ago, and riskier behavior is observed. But what matters is the degree, and I don’t think it has reached the danger zone yet.

First, as mentioned above, the absolute quantum of risk doesn’t seem as high as in 2006-07. The modern miracles of finance aren’t seen as often (or touted as highly), and the use of leverage isn’t as high.

Second, prices and valuations aren’t highly extended (the p/e ratio on the S&P 500 is around 16, the post-war average, while in 2000 it was in the low 30s: now that’s extended).

A rise in risk tolerance is something that should get your attention and focus your concentration. But for it to be highly worrisome, it has to be accompanied by extended valuations. I don’t think we’re there yet. I think most asset classes are priced fully – in many cases on the high side of fair – but not at bubble-type highs. Of course the exception is bonds in general, which the central banks are supporting at yields near all-time lows, meaning prices near all-time highs. But I don’t find them scary (unless their duration is long), since – if the issuers prove to be money-good – they’ll eventually pay off at par, erasing the interim mark-downs that will come when interest rates rise.

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In the 1950s, when I was a kid, I watched old movies on TV when I got home from school. One from the 1940s was called It Happened Tomorrow. In it, a struggling young journalist made a deal with the devil to be given a peek at the next day’s news. His scoops brought him huge success, and everything ran smoothly until he received a newspaper headlined “Reporter Shot Dead at Racetrack.” He tried all he could to avoid it, but as a result of some very clever plot devices, he of course ended up at the track (where he learned that the headline had resulted from a case of mistaken identity).

I go through all of the above to explain that – try as I might to avoid it – my memos on excessive risk bearing and what to do about it invariably end up back at the same place: my favorite Buffettism:

. . . the less the prudence with which others conduct their affairs, the greater the prudence with which we should conduct our own affairs.

I repeat Warren’s injunction for the simple reason that you just can’t put it any better. When others are acting imprudently, making the world a riskier place, our caution level should rise in response. (It’s equally true that when others become overly cautious and run from risk, assets get so cheap that we should turn aggressive.)

Over the last 2-3 years, my motto for Oaktree has been consistent: “move forward, but with caution.” I feel the outlook is not so bad, and asset prices are not so high, that it’s time to apply maximum caution (or, as they said in The Godfather, “go to the mattresses”). But by the same token, the outlook is not so good, and asset prices are not so low, that we should be aggressive. That’s the reason for my middling stance.

Having said that, however, there’s no doubt in my mind that the trend is in the direction of increased risk, and I see no reason to think that trend will be arrested anytime soon. Risk is likely to reach extreme levels someday – it always does, eventually – and great caution will be called for. Just not yet.

Here’s my conclusion from The Race to the Bottom. I’ll let it stand – another case of “ditto.”

. . . there’s a race to the bottom going on, reflecting a widespread reduction in the level of prudence on the part of investors and capital providers. No one can prove at this point that those who participate will be punished, or that their long-run performance won’t exceed that of the naysayers. But that is the usual pattern.

Speculators vs Investors

Not all people in the stock market are investors. Benjamin Graham, the father of value investing, believed it was crucial for people to determine whether they were investors or speculators.

The difference is simple: an investor looks at a stock as a business and as an owner of the business, while the speculators views himself as playing expensive pieces of paper. For the speculator, value is only determined by what someone will pay for the piece of paper.

To paraphrase Graham, there is intelligent speculating as well as intelligent investing. In short, multiple ways to skin the cat and make money. Just be sure you understand what you are doing and what you are good at.

P.S. I dont hate cats, so dont hate me with my cat metaphor!

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Warren Buffett market-beating skills revealed - A Bloomberg Businessweek article

As it turns out,surprise surprise (not), investing in quality companies is the way to go. See below for a Bloomberg Businessweek article which touches on research done by the National Bureau of Economic Research.

The article nonetheless over-simplifies the Warren Buffett's approach, where it alludes that he buys cheap companies, and that a low P/B is taken to be cheap. A low P/B is a good starting point but is not the be all that ends all as there are multiple other factors to consider.

Plus, there is a slight technical issue here - how low should P/B be to be considered cheap? Whether it is cheap or not requires a yardstick to measure against and that yardstick should be in the form of a company's intrinsic value.

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http://www.businessweek.com/news/2013-12-05/warren-buffett-market-beating-skills-revealed-cutting-research

Warren Buffett isn’t just a great investor. He’s the best investor, an economic study has found.
An index measuring returns adjusted by price fluctuations shows the billionaire chairman and chief executive officer of Berkshire Hathaway Inc. (A:US) has done better than every long-lived U.S. stock and mutual fund.

Looking at all U.S. stocks from 1926 to 2011 that have been traded for more than 30 years, a paper published this week by the National Bureau of Economic Research calculated that Buffett’s so-called Sharpe ratio is 0.76 since 1976. That was about twice the stock market’s 0.39.

The ratio is also larger than all 196 U.S. mutual funds that have been around for 30 years. The median Sharpe ratio for them is 0.37.

The review of Buffett’s investments concluded he has been rewarded for his use of leverage, coupled with a focus on cheap, safe, quality shares.

The study said Buffett is willing to take on borrowing to finance investment, then picks stocks that have low volatility, are cheap -- with low price-to-book ratios -- and are high quality, meaning they are profitable and have high payouts.

By breaking down Berkshire Hathaway’s portfolio into ownership of publicly traded stocks versus wholly owned private companies, the authors also found the tradable equities performed best. That suggested to them that Buffett’s returns are due more to stock selection than to the pressure he puts on companies he has stakes in to improve their management.

“Buffett’s performance appears not to be luck, but an expression that value and quality investing can be implemented,” said Andrea Frazzini and David Kabiller of AQR Capital Management LLC and Lasse H. Pedersen of Copenhagen Business School. “If you travel back in time and pick one stock in 1976, Berkshire would be your pick.”