Tag Archives: Risk


Investing might be considered decision-making under uncertainty. Therefore the following exam.

You must answer BOTH questions correctly to be hired.  You are now in the final pool of candidates to work for a big hedgie fund. Now comes

Question 1:

Imagine playing the following game,  At a casino table is a brass urn containing 100 balls, 50 red and 50 black.  You’re asked to choose a color.  Your choice is recorded but not revealed to anyone, after which the casino attendant draws a ball randomly out of the urn. If the color you chose is the same as the color of the ball, you win $10,000.  If it isn’t, you win nothing-$0.00.

You are only allowed to play once–which color would you prefer, and what is the maximum bid you would pay to play? Why?

Question 2:

Now imagine playing the same game, but with a second urn containing 100 balls in UNKNOWN proportions.  There might be 100 black balls and no red balls, or 100 red balls and no black balls or ANY proportion in between those two extremes.  Suppose we play the exact same game as game 1, but using this urn containing balls of unknown colors.

What is your bid to play this game IF you decide to play?   How does the “risk” in this game (#2) compare to game (#1)?

Take no more than a minute.   So are you hired?!

Answer posted this weekend.

ANSWER (9/10/2017)

A Reader provides a clearer distinction in Question2:

Your second problem is ill-specified for your desired effect . You write that all combinations of red/black balls within the 100 ball population ARE possible; you don’t say they are equally probable. You need to assume them to be equally probable in order for the reader to infer that the expectations are identical between problem 1 and problem 2.

The reason being is that without defined probabilities on the possible ratios the long run frequency of draws from the second bag isn’t calculable. Hence the expected value cannot be computed and therefore cannot be used in comparison to the EV of problem 1 (you need probabilities in a probability weighted average after all).

You could suggest that the offeree has a 50/50 chance of choosing the correct colour (even if the long run frequencies are not known). But this not an argument born from expected value. This is an argument of chance and it assumes the offeree has no additional information from which to make their decision (which is hardly ever the case).

There are 100 possible choices for the proportion of red/black: 100 red balls/0 black balls, 99 red balls/1 black ball etc., 98/2, 97/3     with 100%, 99%, 98%, 97% probability of choosing a black ball all the way………… to 2 black balls/98 red balls, 1/99, 0/100. Put equal weight on them since random.  When computed, the average of the expected payoffs across all these alternative realities, one got an expected value of $5,000, the same as Game 1.

The two games describesthe Ellsberg Paradox, after the example in Ellsberg’s seminal paper.  Thinking isn’t the same as feeling.  You can think the two games have equal odds, but you just don’t feel the same about them.   When there is any uncertainty about those risks, they immediately become more cautious and conservative.  Fear of the unknown is one of the most potent kinds of fear there is, and the natural reaction is to get as far away from it as possible.

So, if you said the two games were exactly similar in probabilities, then A+.  The price you would bid depends upon your margin of safety/comfort.   You would be rational to bid $4,999.99 since that is less than the expected payoff of $5,000.  But the loss of $4,999.99 might not be worth it despite the positive pay-off.  A bid of $3,000 or $1,000 might be rational for you.   The main point is to understand that the two games were similar but didn’t appear to be on the surface.

The Ellsberg paradox is a paradox in decision theory in which people’s choices violate the postulates of subjective expected utility. It is generally taken to be evidence for ambiguity aversion. The paradox was popularized by Daniel Ellsberg, although a version of it was noted considerably earlier by John Maynard Keynes.  READ his paper: ellsberg

Who was fooled?

Anyone not answering correctly or NOT answering has to go on a date with my ex:

The Stock Market: Risk vs. Uncertainty

Life is risky. The future is uncertain. We’ve all heard these statements, but how well do we understand the concepts behind them? More specifically, what do risk and uncertainty imply for stock market investments? Is there any difference in these two terms?

Risk and uncertainty both relate to the same underlying concept—randomness. Risk is randomness in which events have measurable probabilities, wrote economist Frank Knight in 1921 in Meaning of Risk and Uncertainty.1 Probabilities may be attained either by deduction (using theoretical models) or induction (using the observed frequency of events). For example, we can easily deduce the probabilities of the possible outcomes of a game of dice. Similarly, economists can deduce probability distributions for stock market returns based on theoretical models of investor behavior.

On the other hand, induction allows us to calculate probabilities from past observations where theoretical models are unavailable, possibly because of a lack of knowledge about the underlying relation between cause and effect. For instance, we can induce the probability of suffering a head injury when riding a bicycle by observing how frequently it has happened in the past. In a like manner, economists estimate probability distributions for stock market returns from the history of past returns.

Whereas risk is quantifiable randomness, uncertainty isn’t. It applies to situations in which the world is not well-charted. First, our world view might be insufficient from the start. Second, the way the world operates might change so that past observations offer little guidance for the future. Once bicyclists were encouraged to wear helmets, the relation between riding the bicycle—the cause—and the probability of suffering a head injury—the effect—changed. You might simply think that the introduction of helmets would have reduced the number of head injuries. Rather, the opposite happened. The number of head injuries actually increased, possibly because helmet wearing bikers started riding in a more risky manner due to a false perception of safety.2

Typically, in situations of choice, risk and uncertainty both apply. Many situations of choice are unprecedented, and uncertainty about the underlying relation between cause and effect is often present. Given that risk is quantifiable, it is not surprising that academic literature on stock market randomness deals exclusively with stock market risk. On the other hand, ignorance of uncertainty may be hazardous to the investor’s financial health.

Stock market uncertainty relates to imperfect information about how the world behaves. First, how well do we understand the process that generated historical stock market returns? Second, even if we had perfect information about past processes, can we assume that the same relation between cause and effect will apply in the future?

The Highs and Lows of the Market

Warren Buffett, the world’s second-richest man, distinguishes between periods of comparatively high and low stock market valuation. In the early 1920s, stock market valuation was comparatively low, as measured by the inflation-adjusted present value of future dividends. The attractive valuation of stocks relative to bonds became a widely held belief after Edgar Lawrence Smith published a book in 1924 on stock market valuation, Common Stocks as Long Term Investments. Smith argued that stocks not only offer dividends, but also capital appreciation through retained earnings. The book, which was reviewed by John Maynard Keynes in 1925, gave cause to an unprecedented stock market appreciation. The inflation-adjusted annual average growth rate of a buy-and-hold investment in large-company stocks established at the end of 1925 amounted to a staggering 32.13 percent at the end of 1928.

On the other hand, over the next four years, this portfolio depreciated at an average annual rate of 17.28 percent, inflation-adjusted. Taken together, over the entire seven-year period, the inflation-adjusted average annual growth rate of this portfolio came to a meager 1.11 percent. Buy-and-hold portfolios in allegedly unattractive long-term corporate and government bonds, on the other hand, grew at inflation-adjusted average annual rates of 10.18 and 9.83 percent, respectively. This proves Buffett’s point: “What the few bought for the right reason in 1925, the many bought for the wrong reason in 1929.” One conclusion from this episode is that learning about the stock market may feed back into the market and, by changing the behavior of the market, render our “learning” useless or—if we don’t recognize the feedback effect—hazardous.
Is Tomorrow Another Day?

Risk and uncertainty are two concepts that stem from randomness. Neither is fully understood. Although risk is quantifiable, uncertainty is not. Rather, uncertainty arises from imperfect knowledge about the way the world behaves. Most importantly, uncertainty relates to the questions of how to deal with the unprecedented, and whether the world will behave tomorrow in the way as it behaved in the past.

This article was adapted from “The Stock Market: Beyond Risk Lies Uncertainty,” which was written by Frank A. Schmid and appeared in the July 2002 issue of The Regional Economist, a St. Louis Fed publication.

(Source: St Louis Federal Reserve)

RISK/ Aftermath of Trump Election: Independence Revoked!



To the citizens of the United States of America, in light of your failure to elect a competent President of the USA and thus to govern yourselves, we hereby give notice of the revocation of your independence, effective today.

Her Sovereign Majesty Queen Elizabeth II resumes monarchical duties over all states, commonwealths and other territories. Except Utah, which she does not fancy.

Your new prime minister (The Right Honourable Theresa May, MP for the 97.8% of you who have, until now, been unaware there’s a world outside your borders) will appoint a minister for America. Congress and the Senate are disbanded. A questionnaire circulated next year will determine whether any of you noticed.

To aid your transition to a British Crown Dependency, the following rules are introduced with immediate effect:

1. Look up “revocation” in the Oxford English Dictionary. Check “aluminium” in the pronunciation guide. You will be amazed at just how wrongly you pronounce it. The letter ‘U’ will be reinstated in words such as ‘favour’ and ‘neighbour’. Likewise you will learn to spell ‘doughnut’ without skipping half the letters. Generally, you should raise your vocabulary to acceptable levels. Look up “vocabulary.” Using the same twenty seven words interspersed with filler noises such as “like” and “you know” is an unacceptable and inefficient form of communication. Look up “interspersed.” There will be no more ‘bleeps’ in the Jerry Springer show. If you’re not old enough to cope with bad language then you should not have chat shows.

2. There is no such thing as “US English.” We’ll let Microsoft know on your behalf. The Microsoft spell-checker will be adjusted to take account of the reinstated letter ‘u’.

3. You should learn to distinguish English and Australian accents. It really isn’t that hard. English accents are not limited to cockney, upper-class twit or Mancunian (Daphne in Frasier). Scottish dramas such as ‘Taggart’ will no longer be broadcast with subtitles.You must learn that there is no such place as Devonshire in England. The name of the county is “Devon.” If you persist in calling it Devonshire, all American States will become “shires” e.g. Texasshire Floridashire, Louisianashire.

4. You should relearn your original national anthem, “God Save The Queen”, but only after fully carrying out task 1.

5. You should stop playing American “football.” There’s only one kind of football. What you call American “football” is not a very good game. The 2.1% of you aware there is a world outside your borders may have noticed no one else plays “American” football. You should instead play proper football. Initially, it would be best if you played with the girls. Those of you brave enough will, in time, be allowed to play rugby (which is similar to American “football”, but does not involve stopping for a rest every two seconds or wearing full kevlar body armour like nancies) You should stop playing baseball. It’s not reasonable to host event called the ‘World Series’ for a game which is not played outside of America. Instead of baseball, you will be allowed to play a girls’ game called “rounders,” which is baseball without fancy team stripe, oversized gloves, collector cards or hotdogs.

6. You will no longer be allowed to own or carry guns, or anything more dangerous in public than a vegetable peeler. Because you are not sensible enough to handle potentially dangerous items, you need a permit to carry a vegetable peeler.

7. July 4th is no longer a public holiday. November 2nd will be a new national holiday. It will be called “Indecisive Day.”

8. All American cars are hereby banned. They are crap and it is for your own good. When we show you German cars, you will understand what we mean. All road intersections will be replaced with roundabouts, and you will start driving on the left. At the same time, you will go metric without the benefit of conversion tables. Roundabouts and metrication will help you understand the British sense of humour.

9. Learn to make real chips. Those things you call French fries are not real chips. Fries aren’t French, they’re Belgian though 97.8% of you (including the guy who discovered fries while in Europe) are not aware of a country called Belgium. Potato chips are properly called “crisps.” Real chips are thick cut and fried in animal fat. The traditional accompaniment to chips is beer which should be served warm and flat.

10. The cold tasteless stuff you call beer is actually lager. Only proper British Bitter will be referred to as “beer.” Substances once known as “American Beer” will henceforth be referred to as “Near-Frozen Gnat’s Urine,” except for the product of the American Budweiser company which will be called “Weak Near-Frozen Gnat’s Urine.” This will allow true Budweiser (as manufactured for the last 1000 years in Pilsen, Czech Republic) to be sold without risk of confusion.

11. The UK will harmonise petrol prices (or “Gasoline,” as you will be permitted to keep calling it) for those of the former USA, adopting UK petrol prices (roughly $6/US gallon, get used to it).

12. Learn to resolve personal issues without guns, lawyers or therapists. That you need many lawyers and therapists shows you’re not adult enough to be independent. If you’re not adult enough to sort things out without suing someone or speaking to a therapist, you’re not grown up enough to handle a gun.

13. Please tell us who killed JFK. It’s been driving us crazy.

14. Tax collectors from Her Majesty’s Government will be with you shortly to ensure the acquisition of all revenues due (backdated to 1776).

Thank you for your co-operation.

* John Cleese [Basil Fawlty, Fawlty Towers, Sir Lancelot of Camelot (Monty Python & The Quest for the Holy Grail), Torquay, Devon, England]


What is Risk?    A Great Post on Risk


When’s the Crash?

Dow and Q


The cyclicality of markets and risk

I have been sour on a majority of the general “market” since the end of 2013 as anyone following this blog would know, but that doesn’t mean ALL stocks are overvalued, but just that risk in general may be mispriced.   The Q represents for me an arbitrage between buying the asset or selling stock.  I don’t know if a big bear market is coming (no one does) but 20% to 40% declines shouldn’t be surprising when prices are bid up on easy credit (ZIRP and BURP).

Q is high

A Ticking Time Bomb

Certain pundits say a market can be “overvalued for years” but risks rise as market “internals” such as credit spreads widen. Bubble and Bust

Distortions and Time Preference

Note how commodities gain on gold during the boom and decline during the bust phase of the cycle. Proof of gold as money and how extremely distorted cycles have become Boom and Bust Indicator


Have a Good Weekend!

PS: Good example of fracking economics: Oil Markets PZENA

The Stoics and Investing; Volatility and the Prisoner’s Dilemma


The Stoics

Stoics understood that if negative emotions such as anger, envy, greed, fear, and grief plague your life, then soundness and peace of mind will elude you. Serentiy in the midst of adversity–which is hardly the same thing as the modern, Western and secular notion of “happiness”–is a necessary condition of a well-lived life.

nov15_newsletter-1 How the Stoic Philosophers influenced Ben Graham

feb16_newsletter-2 Part 2



Robert Rubin on Decision-Making. Risk vs. Uncertainty






The investment industry deals largely with uncertainty. In contrast, the casino business deals largely with risk. With both uncertainty and risk, outcomes are unknown. But with uncertainty, the underlying distribution of outcomes is undefined, while with risk we know what that distribution looks like. Corporate undulation is uncertain; roulette is risky. (page 11: More Than You Know–Mauboussin

Take the probability of loss times the amount of possible loss from the probability of gain times the amount of possible gain. That is what we’re trying to do. It’s imperfect, but that is what it’s all about.” -Warren Buffett


Treasury Secretary Robert E. Rubin Remarks to the University of Pennsylvania Commencement Philadelphia, PA

As I think back over the years, I have been guided by four principles for decision-making.

  1. First, the only certainty is that there is no certainty.
  2. Second, every decision, as a consequence, is a matter of weighing probabilities.
  3. Third, despite uncertainty we must decide and we must act.
  4. And lastly, we need to judge decisions not only on the results, but on how they were made.

First, uncertainty.

When my father was in college, he too had signed up for a course in philosophy with a renowned professor. On the first day of class, the professor debated the question of whether you could prove that the table at the front of the room existed. My father is very bright and very pragmatic. He went to the front of the room, pounded on the table with his hand, decided it was there — and promptly dropped the course.

My view is quite the opposite. I believe that there are no absolutes.

If there are no absolutes then all decisions become matters of judging the probability of different outcomes, and the costs and benefits of each. Then, on that basis, you can make a good decision.

The business I was in for 26 years was all about making decisions in exactly this way.

I remember once, many years ago, when a securities trader at another firm told me he had purchased a large block of stock. He did this because he was sure — absolutely certain — a particular set of events would occur. I looked, and I agreed that there were no evident roadblocks. He, with his absolute belief, took a very, very large position. I, highly optimistic but recognizing uncertainty, took a large position. Something totally unexpected happened. The projected events did not occur. I caused my firm to lose a lot of money, but not more than it could absorb. He lost an amount way beyond reason — and his job.

A healthy respect for uncertainty, and focus on probability, drives you never to be satisfied with your conclusions. It keeps you moving forward to seek out more information, to question conventional thinking and to continually refine your judgments. And understanding that difference between certainty and likelihood can make all the difference. It might even save your job.

Third, being decisive in the face of uncertainty. In the end, all decisions are based on imperfect or incomplete information. But decisions must be made — and on a timely basis — whether in school, on the trading floor, or in the White House.

I remember one night at Treasury, a group of us were in the Deputy Secretary’s Office, deciding whether or not the U.S. should take the very significant step of moving to shore up the value of another nation’s currency. It was, to say the least, a very complicated situation. As we talked, new information became available and new considerations were raised. The discussion could have gone on indefinitely. But we didn’t have that luxury: markets wait for no one. And, so, as the clocked ticked down and the Asian markets were ready to open, we made the best decision in light of what we knew at the time. The circumstances for decision making may never be ideal. But you must decide nonetheless.

Fourth, and finally, judging decisions. Decisions tend to be judged solely on the results they produce. But I believe the right test should focus heavily on the quality of the decision making itself.

Two examples illustrate my point.

In 1995, the United States put together a financial support program to help Mexico’s economy, which was then in crisis. Mexico stabilized and U.S. taxpayers even made money on the deal. Some said that the Mexico program was a good decision because it worked.

In contrast, last year, the U.S. supported an International Monetary Fund program designed to strengthen the Russian economy. The program was not successful and we were criticized on the grounds the program did not succeed.

I believe that the Mexican decision was right, not only because it worked, but also because of how we made the decision. And I believe the Russian decision was also right. The stakes were high, and the risk was worth taking. It’s not that results don=t matter. They do. But judging solely on results is a serious deterrent to taking the risks that may be necessary to making the right decision. Simply put, the way decisions are evaluated, affects the way decisions are made. I believe the public would be better served, and their elected officials and others in Washington would be able to do a more effective job, if judgments were based on the quality of decision-making instead of focusing solely on outcomes.

Time and again during my tenure as Treasury Secretary and when I was on Wall Street, I have faced difficult decisions. But the lessons is always the same: good decision-making is the key to good outcomes. Reject absolute answers and recognize uncertainty. Weigh the probabilities. Don’t let uncertainty paralyze you. And evaluate decisions not just on the results, but on how they are made.

The other thing I’d like to leave with you is that you will be entering a world of vastly increased interdependence — one in which your lives will be enormously affected by decisions made outside of our borders. We must recognize this reality and reject the voices of withdrawal to face the challenges of interdependence. Then, we can realize the immense potential of the modern era, for our economy and our society.

You’ve just completed an important milestone in developing your ability to deal effectively with the complex choices of the world in which you will live and work. By continuing to build on this foundation throughout your life, you will be well prepared for the great opportunities and challenges of the new century.

Congratulations and good luck.


RISK! A Reader’s Question


The view from Grant’s (Mar. 20th, 2015) is that risk can usually be found where you aren’t looking for it. You get to thinking, for example, that government bonds are perfectly and unconditionally safe. You would so conclude after 33.5 years of a bond bull market. Yet, the same asset struck many as perfectly and unconditionally unsafe at the 33.5 year point in the preceding 1946-81 bond bear market. Nothing in investing is for certain or forever, “Many shall be restored that now are fallen, and many shall fall that are now in honor,” wrote Horace (65 B.C. to 8 B.C.).



A reader asked about the 

sharpe_ratio.asp. I think any metric that uses volatility as risk is absurd. The video below will give you a better understanding of what REAL risk is–permanent loss of life! I know some may disagree–see: FAJ My Top 10 Peeves and a value investor’s view: Risk Revisited


A Reader’s Question

I’m a value investor from Italy, and I’ve been following your blog since a few months ago. I appreciate a lot your work and the way you share your knowledge with the others. I’ve been doing my own research in American stocks, and create a portfolio that I think is doing well.

I’m a retail small value investor with no MBA, or any especial degree in accounting.

How can a “middle class working hero” approach the world of finance? Do you think any money manager be interested in my research, or I’m only wasting my time?

My advice: First, you can post this to the deep-value@googlegroups.com because there are many smart, experienced investors who may offer another perspective.

First, why American stocks (especially now since many are high-priced?) versus Italian or Greek stocks? Can you develop an area of expertise NEAR where you are?  In other words, what makes YOU unique where you can add unique value? Where can you find the biggest edge. Do you have expertise or experience in a particular industry?   Have you spoken to or research Italian Money Managers? Send your write-up to a few of them. The worst that can happen is they give you a thumbs down but you obtain feedback/and learn.

Not having an MBA is no big deal, but you should learn accounting up to the intermediate level so you can translate the financial information into information useful for an investor.  GAAP earning don’t always equal owner’s earnings. Study online for free or attend a class or grind through a textbook but do ALL the problem-sets.

If you know your portfolio is doing well, keep good records that you can show to potential investors or employers. Do you have a clear investment process that you can follow?

Ask further questions in the comment section.

Good luck!

Value Traps; The Dollar Crisis; Depression of 1929


I owe my early success as an investor not to brains or knowledge, because my mind was untrained and my ignorance was colossal, The game taught me the game, And didn’t spare the rod while teaching.  

Whenever I have lost money in the stock market I have always considered that I have learned something; that if I have lost money I have gained experience, so that the money really went for a tuition fee.  –Jessie Livermore

Mark Sellers and PRXI Value Trap

He put over 50% of his fund into MCF:


I added an update to yesterday’s micro-cap post. http://wp.me/p2OaYY-2tX.  The point is to try and understand prior investment successes or failures. Any lessons there?

An excellent book on the inflationary 1970s The-Dollar-Crisis by Percy Greaves

I just like the old photos to capture the spirit of the times: The-Stock-Market-Crash-of-1929

628x471 (1)

I am still in shock over Brazil’s World Cup blow-out.


A fat tail event?

Understanding Bear Markets; Without Comment

Understanding Bear Markets:  http://www.nextbigtrade.com/2014/03/11/learning-from-the-devious-gold-bear/

Charts below from: http://www.alhambrapartners.com/2014/03/11/valuation-bonanza-march-2014/










Speculative Hedge Funds Piling In.



Making the Wrong Move at the Right Time – Cincinnati Kid

The dealer is incredulous. “You’re raising tens on a lousy three flush?” she says to Robinson. Robinson never should have made that bet since he had only the slim makings of a straight flush and he was staring at McQueen’s pair of tens. You don’t often beat two pair, and certainly not a full house.

Lesson for an investor?

Hint: The market is no place for “making the wrong move at the right time.” Stick to your plan. Don’t personalize losses or success–especially success.

The Need to Diversify; Regression to the Mean (Bonds)


Just as another warning, beware of companies and industries that are going to change the world.  They may well do so, but that is no guarantee that they will make money for investors.  In December 1999 I wrote a paper making a fairly compelling parallel between radio in the 1920s and the Internet in the 1990s (“AOL, RCA, and the Shape of History”). Nearly three years later, I was able to publish the following chart, which superimposes the stock prices of RCA and AOL during their booms and busts.  Net-net no money was made in the market, though radio and the Internet did indeed change the world.

The Big Tranisition: A Letter to an Entrepreneur Friend | Tocqueville

Regression to the Mean





Long-term bonds probably should offer a 6% to 6.5% coupon if history is any guide.