## DImensions of investment risk.

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bertilak
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### DImensions of investment risk.

Think for a moment about a sine wave. It has two attributes: Amplitude and Frequency, each with its own measurement.

Note than risk is often given as a single number that is represented as one axis on a risk vs. expected return graph, but, does risk really have TWO dimensions similar to a sine wave's amplitude and frequency:
• Amplitude: What's the worst (or best) that is likely to happen? (Is likelihood measured in standard deviations?)
Frequency: How often is it likely to happen?
I bring this up because it is how I picture risk and why I think some risks are riskier than others, fully realizing the circularity of that statement exposes the weakness of my understanding. I think somehow planning horizon (i.e. "wavelength," the inverse of frequency) needs to be factored in to more fully express the overall concept of risk.

Can anyone help me with this little nagging thought? It is essentially why I reject an SCV tilt, not rejecting it as a valuable investing tool, but as not understanding what SCV risk means to me, personally. Does it increase risk's equivalent to wavelength?
May neither drought nor rain nor blizzard disturb the joy juice in your gizzard. -- Squire Omar Barker, the Cowboy Poet

alex_686
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### Re: DImensions of investment risk.

bertilak wrote:...does risk really have TWO dimensions similar to a sine wave's amplitude and frequency..
I might be missing something, but are you not talking about standard deviations? A standard deviation is based on a bell curve, a nice little curve where 50% of the possibilities lay to the left of the peak and the other 50% lay on the other side. Most of the risk measurement tools are based on this.

Even the faults of standard derivation are well know. The is Skewness, or the fact that the curve is not symmetric. There is Kurtosis, or fat tails - the fact that very low probability events turn up in real life more frequently than expected.

Everybody more or less agrees on this model, it answers 99% of the questions around risk. Of course the danger in risk is that last 1%. We can guess at the skewness or kurtosis but we can never be sure.

bertilak
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### Re: DImensions of investment risk.

alex_686 wrote:
bertilak wrote:...does risk really have TWO dimensions similar to a sine wave's amplitude and frequency..
I might be missing something, but are you not talking about standard deviations? A standard deviation is based on a bell curve, a nice little curve where 50% of the possibilities lay to the left of the peak and the other 50% lay on the other side. Most of the risk measurement tools are based on this.
I don't think that bell curve represents two dimensions of risk, but only what I called the likelihood of the size of outcomes. It would not address the "how often" aspect. Of course I could be misreading the bell curve, thus the reason for my post.
May neither drought nor rain nor blizzard disturb the joy juice in your gizzard. -- Squire Omar Barker, the Cowboy Poet

NPT
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### Re: DImensions of investment risk.

alex_686 wrote: I might be missing something, but are you not talking about standard deviations? (...)

Everybody more or less agrees on this model, it answers 99% of the questions around risk. (...)
Some disagree. For example, Warren Buffett famously wrote in one of his letters to shareholders:

“(...) That lesson has not customarily been taught in business schools, where volatility is almost universally used as a proxy for risk. Though this pedagogic assumption makes for easy teaching, it is dead wrong: Volatility is far from synonymous with risk. Popular formulas that equate the two terms lead students, investors and CEOs astray.”

alex_686
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### Re: DImensions of investment risk.

bertilak wrote:I don't think that bell curve represents two dimensions of risk, but only what I called the likelihood of the size of outcomes. It would not address the "how often" aspect. Of course I could be misreading the bell curve, thus the reason for my post.
It encompasses both time and level of risk.

As a example I am going to throw up Yahoo's option page for the S&P 500 For December 2017.
https://finance.yahoo.com/quote/SPY/opt ... 1513296000
Find the calls that are right at the money. Find the "implied volatility" column. You should find something around 10%

This is saying that it has a standard deviation of 10%, which is the level of risk. This value is annualized, which is the time dimension.

In theory risk is constant. No skewing and no tails. In theory should be getting a annualized 10% risk no matter which set of options we looked at. 1 month, 1 year, 3 years. Of course we don't. If you start looking at the tails, if you start looking out, you will see the implied volatility increasing. This is called the "volatility smile"

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### Re: DImensions of investment risk.

bertilak wrote:I don't think that bell curve represents two dimensions of risk, but only what I called the likelihood of the size of outcomes. It would not address the "how often" aspect. Of course I could be misreading the bell curve, thus the reason for my post.
What you’re describing in your mind’s eye is reminiscent of the long-term volatility charts I’ve seen (second chart below). Volatility measured over long periods includes both the dimension of degree and the dimension of frequency.

• NOTE: Horizontal time scales are not exactly aligned.
Source: JP Morgan
Even so, as has been so often discussed on the Forum, volatility is only one aspect of total portfolio risk.
Last edited by SimpleGift on Sun Jul 16, 2017 7:35 pm, edited 1 time in total.
Cordially, Todd

alex_686
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### Re: DImensions of investment risk.

NPT wrote:
alex_686 wrote: Everybody more or less agrees on this model, it answers 99% of the questions around risk. (...)
Some disagree. For example, Warren Buffett famously wrote in one of his letters to shareholders:

“(...) That lesson has not customarily been taught in business schools, where volatility is almost universally used as a proxy for risk. Though this pedagogic assumption makes for easy teaching, it is dead wrong: Volatility is far from synonymous with risk. Popular formulas that equate the two terms lead students, investors and CEOs astray.”
2 points.

The first is that the standard deviation model fits what the OP was asking about. There is a rich set of literature and research that the OP can draw from, both for and against.

Second, if not the standard deviation model than what? A popular book is Nassim Nicholas Taleb's The Black Swan. It lays out some excellent criticism against using standard deviaiton as a measure of risk. The problem that I have with the book is that Taleb's recommend solution is to rely on heuristics, which is not much of a recommendation in my opinion.

The choice comes down to using a tool that is 99% accurate with well know flaws or one's gut instinct.

Longdog
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### Re: DImensions of investment risk.

To me, risk is a possible adverse outcome. It has a likelihood and a magnitude, like you said. Multiply the likelihood by the magnitude of the adverse outcome, and you have its expected value.

There are many types of investment risks, each with its own likelihood and magnitude.
Steve

bertilak
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### Re: DImensions of investment risk.

alex_686 wrote:
bertilak wrote:I don't think that bell curve represents two dimensions of risk, but only what I called the likelihood of the size of outcomes. It would not address the "how often" aspect. Of course I could be misreading the bell curve, thus the reason for my post.
It encompasses both time and level of risk.

As a example I am going to throw up Yahoo's option page for the S&P 500 For December 2017.
https://finance.yahoo.com/quote/SPY/opt ... 1513296000
Find the calls that are right at the money. Find the "implied volatility" column. You should find something around 10%

This is saying that it has a standard deviation of 10%, which is the level of risk. This value is annualized, which is the time dimension.

In theory risk is constant. No skewing and no tails. In theory should be getting a annualized 10% risk no matter which set of options we looked at. 1 month, 1 year, 3 years. Of course we don't. If you start looking at the tails, if you start looking out, you will see the implied volatility increasing. This is called the "volatility smile"
OK, I found approx 10% where the strie price is about the current price. But, if this is annualized and represents 1 year, what does it mean for 5, 10, 20 years?
May neither drought nor rain nor blizzard disturb the joy juice in your gizzard. -- Squire Omar Barker, the Cowboy Poet

pkcrafter
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Contact:

### Re: DImensions of investment risk.

bertilak wrote:Think for a moment about a sine wave. It has two attributes: Amplitude and Frequency, each with its own measurement.

Note than risk is often given as a single number that is represented as one axis on a risk vs. expected return graph, but, does risk really have TWO dimensions similar to a sine wave's amplitude and frequency:
• Amplitude: What's the worst (or best) that is likely to happen? (Is likelihood measured in standard deviations?)
Frequency: How often is it likely to happen?
I bring this up because it is how I picture risk and why I think some risks are riskier than others, fully realizing the circularity of that statement exposes the weakness of my understanding. I think somehow planning horizon (i.e. "wavelength," the inverse of frequency) needs to be factored in to more fully express the overall concept of risk.

Can anyone help me with this little nagging thought? It is essentially why I reject an SCV tilt, not rejecting it as a valuable investing tool, but as not understanding what SCV risk means to me, personally. Does it increase risk's equivalent to wavelength?
Well, I think you are on to something.

The problem with small caps isn't necessarily volatility, it's their tendency to underperform large caps for long periods of time. During those times the volatility is lower. These extended periods of underperformance are one reason the premium still exists. If planning horizon is wavelength, then the peculiarities of small cap performance can interfere.

Paul
When times are good, investors tend to forget about risk and focus on opportunity. When times are bad, investors tend to forget about opportunity and focus on risk.

bertilak
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### Re: DImensions of investment risk.

pkcrafter wrote: Well, I think you are on to something.

The problem with small caps isn't necessarily volatility, it's their tendency to underperform large caps for long periods of time. During those times the volatility is lower. These extended periods of underperformance are one reason the premium still exists. If planning horizon is wavelength, then the peculiarities of small cap performance can interfere.

Paul
Paul, you have absolutely understood my concern. Perhaps some risk needs to be paid for in acceptance of the magnitude of volatility (what is called risk tolerance?) and some needs to be paid for in patience (planning horizon). Not everyone has the same amount of currency in each of those accounts.
May neither drought nor rain nor blizzard disturb the joy juice in your gizzard. -- Squire Omar Barker, the Cowboy Poet

alex_686
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### Re: DImensions of investment risk.

bertilak wrote:OK, I found approx 10% where the strie price is about the current price. But, if this is annualized and represents 1 year, what does it mean for 5, 10, 20 years?
This is off the top of my head but:
std for your period = std * sqrt (time)

so 5 years would be 10% * (5 Years ^.5) or 10% * 2.25 or 22.5%

NPT
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### Re: DImensions of investment risk.

alex_686 wrote:Second, if not the standard deviation model than what? (...)

The choice comes down to using a tool that is 99% accurate with well know flaws or one's gut instinct.
Perhaps the prudent answer to the above question is to admit that it is entirely possible that the models we have are not very good. Clearly those models are useful, but my gut instinct tells me that "99% accurate" is wishful thinking and that both Buffett's and Taleb's criticisms are very insightful.

rnitz
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### Re: DImensions of investment risk.

I think the problem with your proposition is that risk is multi-dimensional. And by that I don't mean two or three dimensions, I mean hundreds or thousands of dimensions.

Risk of what? Interest rate increase? Many companies have different exposure to interest rates (if they actually increase). Inflation risk (related to interest rate risk, but not identical) - many companies, bonds, investors have different exposure to this risk. Geopolitical risk - if Russia invades Ukraine that's a different risk exposure. If there's political instability in the US, a different set of risk exposures. If there's a reduction in US corporate tax rates, a different selection of risks. AI/robot risk of eliminating employees? You can go on forever.

I'm not a slice and dicer, but the the thing that made the Fama/French model make sense to me was that equity risk was not best explained by a single dimension of "volatility" but better explained by a multidimensional model (in the original case, three).

Ask yourself the follow-on question: risk of what?

nisiprius
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### Re: DImensions of investment risk.

Yes, I share something like your point of view.

I'd like to see some kind of model of the "power spectrum" of the stock market. I'm not clear on why we don't see frequency-domain plots of the stock market "signal" in addition to time-domain plots.

I can caricature the "stocks for the long run" point of view by saying that it is the idea that almost all the power in the signal is at frequencies of 0.05 cycles per year or more... that is to say, periods of 20 years or less... and that the power in the spectrum at longer periods is negligible.

I can caricature what is either Mandelbrot's point of view or my own by saying that stock market signals are amazingly self-similar at different magnifications, and the power is very evenly distributed, does not roll off below 0.05 cycles per year, and has significant signal power (=standard deviation = volatility = risk) no matter how low the frequency or how long the period.
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alex_686
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### Re: DImensions of investment risk.

nisiprius wrote:I'd like to see some kind of model of the "power spectrum" of the stock market. I'm not clear on why we don't see frequency-domain plots of the stock market "signal" in addition to time-domain plots.
Have you done any research on volatility surfaces? It is a very technical area but it might be what you are looking for.

Benoît Mandelbrot (of fractal fame) wrote a good laymen book on how to measure risk. The (Mis)Behavior of Markets: A Fractal View of Risk, Ruin, and Reward