Out On a Limb

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There is something surprisingly useful about broadcasting your own assumptions to other people

There is this concept called “what you see is all there is,” (WYSIATI) discussed extensively in Kahneman’s book Thinking Fast And Slow.

And the point of WYSIATI is that our minds (particularly our intuitive “system”) are extremely biased towards narrative. So if we get a couple of facts we use our amazing powers of association to construct a linear story from the limited data.

What we don’t do is take into account all of the facts that are not at our disposal, or the quality of the facts that are. And this ends up being a frequent source of misjudgment. It is an extremely non-statistical way of thinking, (that we are all quite prone to.)

Which is where this “broadcasting your own assumptions” phenomenon comes in.

When I wrote my recent piece about the role of bonds in a portfolio, my feeling was that I was describing a basic plain-vanilla truth held by most people interested in portfolio theory.

But I found that I was wrong. Which makes me think that my own unconscious patterns of thinking end up being the ultimate example of WYSIATI.

The limited data in this case, was my own filtered perception of the world which is continually and subconsciously molded and engineered to mesh with my own attitudes and biases.

And in some of the polite clashes of disagreement present in the comments section of that particular thread, a central question occurred to me, that at least in my own mind seemed to be at the heart of most of the disagreement.

What is risk?

More particularly, when investing how do we define risk?

Which seems as good of a subject is any, so let’s take a crack at it.

Risk is standard deviation.

I believe that standard deviation, or volatility is the most classic definition of risk when looking at an asset.

The idea here is that the risk of an investment or of a portfolio of investments is represented by the movement up-and-down of the price of that investment.

And this definition ends up being a pretty useful one. It matches up very nicely with our own intuitive sense of risk.

If we think of small companies and big companies we would naturally expect the stock price of small companies to move up and down more violently because they are more susceptible to price shocks and environmental factors than large companies.(Small companies go bankrupt a lot more often than large companies, and also grow much faster when something positive happens to them.)

Or to take another example. Consider countries at varying stages of development. Frontier markets (think Nigeria), emerging markets (think China), and developed markets (think Germany). During times of financial stress we expect the developed markets to do better than the emerging markets and the emerging markets to do better than the frontier markets. Conversely we expect much more rapid rates of growth during good times from the less developed markets.

And when considering the risk of bonds versus stocks, particularly treasuries versus stocks, it is quite intuitive that borrowing money from a company is not as secure as borrowing money from the U.S. Treasury (which in fact prints the world’s reserve currency.)


Volatility is risk.  And Risk leads to return…

And this intuition is what we see when we look at the numbers. The larger the company, the more developed the country, and the more bond like the investment the less volatile its price will be, in general.

One criticism of volatility as a measure of risk is that it treats upward movements of price and downward movements of price identically. And although upward price movement is clearly not risk, it turns out that when you measure downward volatility it ends up measuring the same thing as simple volatility.

Risk is losing all of your money.

This is a good definition of risk, no?

The real life risk of investing your retirement money is losing it all and spending your last days destitute and broken.  (William Bernstein often evokes eating cat food under a bridge to describe this sad outcome.)

And when we think about this type of risk, it is inextricably linked to volatility.

In terms of losing capital, a portfolio of 100% T-bills is much less risky than a portfolio of 100% long-term treasury bonds which is less risky than a portfolio of 100% developed countries stocks, which is less risky than a portfolio of 100% emerging markets stock, Which is less risky than a portfolio of 100% frontier markets stocks.

As your portfolio shifts towards more volatile assets, it’s risk of total loss with financial collapse goes up.  (This is why leveraged investors sometimes kill themselves when financial bubbles burst.  They lose everything…)

(This is not to say you should not own volatile assets. When mixing different volatile assets without perfect correlations you often paradoxically decrease the entire portfolio’s volatility (risk) at the same time you increase its returns. This is the so-called “diversification benefit”.)

This is why, in my view, the less you can afford to risk your capital, the greater the percentage you should own of stable assets like bonds in your portfolio.

One need simply imagine A portfolio of 100% stocks, when compared to a portfolio of 50% stocks and 50% bonds during our most recent financial collapse.

When the 100% stock portfolio was faced with a 50% drop in the value of The stock market, it lost on average 50% of its value. Assuming bonds did not go up or down at the time of the collapse (they usually go up) The 50/50 portfolio would’ve lost only 25% of its value.

But this is not the only risk possible when investing…

Risk is not having enough money in retirement because your investments do not make enough money.

Taking all of your retirement money and putting it under your mattress is actually a very risky thing to do (even if you have 100% guarantee that your house will never be robbed or burn down etc.) This is because your money, instead of compounding, is continually losing buying power to inflation. It is shrinking in value. This makes it very difficult to save enough money for retirement.

Similarly, if you created an entire portfolio of 100% short-term treasuries, your risk of losing all of your money is nearly zero, but your risk of not having enough money during retirement is substantial.

This is why even the most conservative investors should own some equity in their portfolios.

(Another reason is that paradoxically owning somewhere between five and 10% equities in your portfolio actually decreases the volatility ((and risk)) of your entire portfolio.)


Adding risk can decrease risk…..

Risk is losing money to inflation.

When it comes to inflation, cash is more risky than bonds which are more risky than equities and real estate.

So in this definition of risk, volatility is inversely related to risk!

And there are many more risks that I am not  mentioning.  (Please add yours to the comments section.)

But the point is that if your definition of risk as an individual will very much be determined by your own economic situation.

If you are a young worker trying to save for your retirement 30 years down the line, then a bond only portfolio is incredibly risky in terms of you not reaching your goal of a secure retirement.

Conversely if you are a retiree without much Social Security income and all of your portfolio invested in a 401(k), who is counting on withdrawing 4% of your initial portfolio value, adjusted for inflation, going forward, then an 80 or 90% stock portfolio is very risky in terms of you losing a big chunk of your portfolio, and running out of money.

Not to be a damned relativist.  But I have to conclude that risk is very much in the eye of the beholder.

(I still hold that your bond percentage should be determined solely your risk tolerance.   Defining risk is entirely up to you though.)
How would you define investment risk?

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3 Responses to “Out On a Limb”

  1. Robert July 25, 2014 at 12:45 pm #

    Good post, though there are parts I will argue with (you’d expect no less from me!). In fact, I was arguing vehemently as I read the first half, but then you finally got around to how **I** tend to think of risk, and then I relaxed, because of course that part was correct! 

    The problem is that so much financial literature equates volatility (commonly represented by standard deviation) with risk. I see them as related but not the same. Volatility is a subset of risk or class of risk (we agree on that, I think, though you confused me sometimes with your emphasis on standard deviation as a good way to describe risk including risk of losing everything). I think volatility is essentially a time risk—the risk that your investment won’t have the expected value at a given time (when you need it). To me the bigger risk is what you mention near the end of your blog, the risk of not making your investment goals (e.g., by losing your money or not earning an adequate return). i.e., the risk entailed in holding even a low volatility investment that is trending downwards. So, if we can use THAT definition of risk, then I agree that bond percentage should be defined by risk tolerance. And I still contend that for most people, that would lead to them having little or no allocation to bonds, until they are nearing a point where they need to use the money. Unfortunately, I think most people think of risk tolerance in terms of volatility and the ability to stomach a market downturn. Such thinking fails to account for investment time horizon, which if sufficiently long, neutralizes much of volatility risk.

    I’m not sure why there is such emphasis on this. I’m guessing it is that brokers have found their clients to act on a shorter time horizon than they actually have–acting in response to fear. To sell equities, they must first and foremost not lose their clients. Encouraging clients to move between bonds and equities (even via passive rebalancing formulas) increased transactions and commissions, as well. But for most clients, encouraging a much larger percentage of equities would seem to me to make sense, given the long time horizons most investors have.

    I’m curious. Did you think of risk as standard deviation before you read a bunch of investment books that said so? I know I didn’t. I always thought of “risk” as the chance of losing my investment or not achieving my goals. But then I read the books equating risk with standard deviation, and I began to wonder. As a scientist, it seemed a bit odd, since you can have a process in control despite a large standard deviation and a process out of control despite a small standard deviation. Having wondered for awhile, I’m back where I started, almost. I agree that standard deviation does capture one aspect of risk—the dispersion of returns in a given time period—but I don’t think it captures the other aspects of risk that I suspect most of us are more concerned about. Standard deviations (in the stock market context) without defining the time period relative to one’s own investment time horizon may be misleading. And as many commentators, including Mandelbrot, have argued, standard deviation isn’t an appropriate measure for data that isn’t normally distributed, and that is the case with equity returns. They tend to follow a power law, and have “fat tails”, and we end up with “black swans” more often than one would predict from normal distributions and standard deviations.

    You started to discuss alternative definitions of risk mid-way through your blog (“Risk is losing all of your money”, etc.), but I thought you muddied the waters as you stressed the utility of standard deviation even while acknowledging that an investment could have similar volatility while trending up or trending down. You got back on track near the end of your post by noting the time element for different investors. Volatility can be “diversified” by holding an investment long enough that the underlying trend (hopefully upwards, if you picked the right asset class) overwhelms the year-to-year noise (volatility) and you get to your goal, i.e., you don’t end up eating cat food under a bridge. Again, as I argued on your bond blog, bonds make sense if you have a short time horizon but equities give the best return and if you need a high return to achieve your goals, and you have a long enough time horizon, then you will have less “risk” of missing your goal if you are 100% equities.

    Contrary to your statement, T-bills are not less risky than equities as a way of preserving your capital, IF your time horizon is long enough and inflation is present. In a non-inflationary environment, then I agree with you.

    Your efficient frontier curve illustrates the problem Siegel noted (as I mentioned in my response to your earlier post)—such curves typically ignore time horizons. The curves differ depending on an investor’s time horizon! If you have a long time horizon, the most efficient portfolio for you will be different than if you have a short time horizon.

    I don’t agree that more volatile assets have higher risk of total loss when financial collapse occurs. Remember those bond-like mortgage derivatives? Or how about hedge funds? The absolute return trading strategies of LTCM offered low volatility but when the unexpected happened, the meltdown was fast. Almost by definition, hedge funds have lower volatility. But they can be (and demonstrated that they are) vulnerable to “tail” events—repeating the lesson in 2007-08. They are stable until “bad stuff” happens, and then they may suddenly be illiquid, and collapse in value. Ilmanen does a great job highlighting this aspect of risk in his book, “Expected Returns”. It is the inverse of the “lottery” effect; stability for a long time, until disaster happens. A key point, in my view, is that the fat tail nature of these phenomena make it unlikely that volatility/standard deviation will indicate such risks in advance (they may NEVER have cracked, historically, until the ONE time they do). Only by careful analysis might one discover the risk embedded in the investment. (Likewise, who would have predicted that U.S. Treasuries would lose their AAA rating? Especially with all the goings-on in Europe, sovereign debt doesn’t have near the risk-free image it had 10 years ago. Predicting this requires looking at balance sheets, not historical volatility of returns. Likewise, standard deviation wouldn’t have saved you from investing with Madoff or Enron. Risks like the latter can be diversified, but my point here is that volatility doesn’t necessarily predict risk of total loss).

    Likewise, the recent financial crisis illustrated nicely how often negatively correlated asset classes become positively correlated during financial crises. Those mortgage derivatives, for example, which bundled negatively correlated assets to reduce the risk (volatility) of junk debt, fell apart when the correlations changed and liquidity dried up.

    Sharpe Ratio has been developed as a more refined measure of risk. I think you want an investment not just with low standard deviation, but one that has a good return as well. Otherwise, you will risk (in my preferred sense of the word) not meeting your goals. Sharpe Ratio looks at volatility “risk” in relation to returns. Even with SR, however, one needs to also take into consideration investment time horizon and the effects of non-normal distributions/tail events.

    As for small vs. large companies (or countries/economies), the factors you list may be at play. But you can diversify many of those away. For every small company (or several) that goes bankrupt due to environmental factors, another races ahead. You might think of a large company or conglomerate has just a diversified basket of small companies, and you can achieve similar diversification by buying many small companies. But there is another important reason small companies (and economies) are volatile, and I don’t think this can be diversified in the same way. That reason is information. There is more limited information about small companies (or developing economies), which increases investor uncertainty and the chance of surprises. There is also more opportunity for insider trading or manipulation. There is a lot of academic research supporting the relation of information gaps and small company equity volatility (e.g., the pre-earnings announcement anomaly in relation to size).

    (As an aside, it is interesting that the question of whether small cap outperforms large cap is in fact a subject of serious academic debate. There is a strong case to be made that it is other factors that correlate with small vs. big that are at play, not size itself. Thus, I quote Oleg Rytchkov’s chapter, “Size and Value Anomalies,” in L. Zachs, ed., The Handbook of Equity Market Anomalies, p. 275: “Although the size anomaly and the value anomaly played equally important roles in the developing of the Fama-French 3-factor model, now they have a different status in the literature. The value anomaly is shown to be a robust phenomenon, which admits several theoretical explanations. On the contrary, the existence of the size anomaly in the last 20 years has been questioned in the literature. Moreover, it is not obvious whether it is a separate phenomenon requiring a theoretical explanation or a manifestation of other known anomalies.” Some interesting points discussed in that chapter include: that the size anomaly is mostly due to January abnormal returns; that the size premium represents a compensation for illiquidity; that the effect has greatly diminished since the publication of the effect; much of its power is due to microcaps; “Demirtas and Guner (2008) find that the bulk of the size effect is attributable to firms with poor past earnings relative to expectations.”; the size effect varies significantly over time).

    Well, I’ve rambled on enough here and need to turn my attention to preparing for my next vacation (being retired is tough)! Grand Canyon and the Sierras this time. Hopefully there is something useful buried in the above comments! Take care.

    • Miles Dividend M.D. July 26, 2014 at 1:59 pm #

      Robert: good stuff.

      I wrote a long comment yesterday which seemingly disappeared into the ether. So here are Some general responses:

      My initial conception of risk in terms of investing was having my investment lose a lot of value very quickly. That’s what separates investment from Say a savings account. In my opinion standard deviation does an excellent job of capturing this risk.

      I think that investing in T-bills is an excellent hedge against inflation. It is like holding cash with a little bit of interest, and as the interest rates go up every six months you reinvest at the higher interest rate. For long term treasuries, this is clearly not the case. That’s an important distinction I think.

      Because research has shown that there’ve not been any 17 year stretches where bonds outperformed stocks, does not mean that there will not be any such stretches in the future. We may even be in the midst of such a stretch which started in the year 1999. Time will tell.(I.e. could we be just about to get into another bubble?) for the time period from 1999 -2011 larger proportions of bonds returned more in retirement portfolios than aggressive allocation of equities, with much less drawdown. See here.


      I’m not arguing that this recent past is prologue, I’m only raising the possibility that it could be. And in such a scenario if 50-50 portfolio will outperform 100% stock portfolio every time during retirement.

      Using Bernie madoff as an argument that volatility doesn’t equal risk is not a legitimate argument. That was a Ponzi scheme and the volatility figures reported were simply fiction, no more, no less. There was no investment going on. I don’t know enough about long-term capital management to comment on that example. But in general I believe hedge funds are more volatile than broad market funds.

      Although I agree with you that over a long time horizons more equity exposure increases expected returns, my sense is that it decreases efficiency. For example if you move from A 90% stock allocation to 100% stock allocation you gain a little bit of expected return and a lot more expected volatility. This is why the Sharpe ratio goes up as you add bonds to high equity portfolios. So if you want to increase returns at all cost it is always smart to add more equity to your portfolio.

      Actually if you’re after maximum returns and are not concerned with volatility and efficiency, why not just own a completely leveraged portfolio?

      My sense is that this is a spectrum and in general adding bonds decreases your volatility and downside risk of loss of capital and increasing Equity and to an even greater extent leverage increase the probability of big gains and big losses

      The Meb Faber video that I mentioned previously was this one:


      Enjoy and happy camping!

  2. Miles Dividend M.D. July 26, 2014 at 2:55 pm #

    One more point, regarding efficient frontiers. The time horizon in the efficient frontier presented in the blog post is 34 years. In individual human investment terms and by any reasonable metric, that is a long time horizon.

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