Why should Investors care about Risk? An investor’s goal is to make money. If you’re a smart investor, you also know that the best way to do that is to compound your money over a long period of time. The main rule to do so is to never lose money. Buffett once said:
In 'Elements of Successful Trading', Robert Rotella described risk as being a function of the amount of loss and the probability of experiencing that loss. So that means an asymmetric bet is not necessarily one involving unlimited upside and limited downside, but one where the probability-adjusted reward-to-risk is in one's favour. This is a more realistic approach.
Another consideration - note in Howard Mark's version of the reward-to-risk graph, the line corresponding to the mean of each distribution of outcomes is placed on the reward-to-risk line. This reflects the effect of the central tendency measure, which is influenced by the frequency of outcomes at the mean.
In a normal distribution, which is the one being represented in the graph, the greatest frequency of outcomes is at the mean. But in finance, most market distributions are not normal; they are leptokurtic, meaning they have excess kurtosis, which may or may not be to a degree that's significantly different than normal.
And they tend to be skewed. Both of these moments imply greater frequency than normal of outcomes in the 'tails' and on one side of the distribution, respectively. And skew may or may not be to a degree that is significantly different than normal. But if a distribution is significantly different than normal, the 'Z' scores corresponding to probable outcomes loses its effectiveness.
Thus, while standard deviation is a decent measure of volatility it's a lousy measure of potential risk, which is better defined by the moments of skew and kurtosis (especially). Hence the increasing adoption of measuring for the risk of 'fat tails' and awareness of skewness.
A good example of risk mis-underestimation is in the shares of AI darling, Nvidia.
Going into its late May'23 earnings release, various popular measures of risk ranged from about +/-6-7% using ATM straddle options implied move to -9-11% using parametric and historical Value-at-Risk or VaR (even at the 99%, one-tailed confidence interval).
In the event, shares popped 25% on the day, equivalent to if I recall correctly without checking, a nearly 7 standard deviation move encompassing daily returns data since the company's public listing inception in 1999.
What made this particularly tragic was, in my opinion, that the stock had just recently before its earnings completed a textbook upwards measured move out of a bullish (inverted) head and shoulders pattern on its weekly chart, likely prompting many bears to position short, whether in shares or options.
If you were short, and were only expecting what these measures suggested, the pain was palpable.
You might say, 'Right then; there's no value in attempting to measure risk at all'. But that would be a mistake. Rather, you have to make sure you understand what the measure of risk you're using is actually doing. And try to get a picture of as much data as possible.
Looking at a distribution of the entirety of Nvidia's actual daily returns going into its earnings revealed positive skew, albeit not significantly different than normal; but excess kurtosis that was significantly different than normal. So - there was fat tail risk, and it was to the upside.
Visually inspecting the distribution and a graph of past actual daily returns prior to the earnings revealed that Nvidia indeed had some extreme upside days in its past, at least one if not two exceeding its 25 May'23, +25% percentage change. They just hadn't occurred in close time proximity, which reveals yet another weakness with typical risk estimation - recency bias.
We humans tend to conceptualise around only the previous five years (at best). And that recency bias is reflected in the typical lookbacks used in summary statistics. For example, within the Portfolio Risk function on even the vaunted Bloomberg Professional terminal, VaR tab, estimates for historical (non-parametric) VaR using confidence intervals of 95%, 97.5% and 99% are calculated for only 1, 2 or 3-year lookbacks.
The old saying goes, 'Anything's possible, but not everything is probable'. And it is on this maxim that most risk estimation leans. But knowing what's possible is perhaps more important than knowing what's probable, especially if the returns profile of an asset reduces the relevance of the probability values associated with that asset's distribution. This is especially so as even knowing what's possible from past data is at best a sample, as you point out in the article.
The reality is that the most nimble, consistently profitable operators in the markets are using proprietary models that are far more sophisticated than the ones in the public domain, with most of the public not even using those, and this is what differentiates their performance versus the public's results.
While sobering, that's not reason alone to abstain completely from trading or investing, but rather to realise that the models you're leaning on have flaws. One way of minimising the potential shortcomings is to not use summary statistics in isolation, but augment them with visual inspection of the data and adjust exposures to levels commensurate with what's really possible.
This reckoning will de facto result in being more selective in choosing opportunities and cautious in the size and directional bias of positioning, hopefully improving overall outcomes over time.
Looking at your 'About', I must say it is rare to see a college student with your level of enthusiasm for the markets and all things investing/trading, as embodied in this blog. Something tells me, you'll be going far. ;-)
Fantastic, illuminating and enlightening piece.
In 'Elements of Successful Trading', Robert Rotella described risk as being a function of the amount of loss and the probability of experiencing that loss. So that means an asymmetric bet is not necessarily one involving unlimited upside and limited downside, but one where the probability-adjusted reward-to-risk is in one's favour. This is a more realistic approach.
Another consideration - note in Howard Mark's version of the reward-to-risk graph, the line corresponding to the mean of each distribution of outcomes is placed on the reward-to-risk line. This reflects the effect of the central tendency measure, which is influenced by the frequency of outcomes at the mean.
In a normal distribution, which is the one being represented in the graph, the greatest frequency of outcomes is at the mean. But in finance, most market distributions are not normal; they are leptokurtic, meaning they have excess kurtosis, which may or may not be to a degree that's significantly different than normal.
And they tend to be skewed. Both of these moments imply greater frequency than normal of outcomes in the 'tails' and on one side of the distribution, respectively. And skew may or may not be to a degree that is significantly different than normal. But if a distribution is significantly different than normal, the 'Z' scores corresponding to probable outcomes loses its effectiveness.
Thus, while standard deviation is a decent measure of volatility it's a lousy measure of potential risk, which is better defined by the moments of skew and kurtosis (especially). Hence the increasing adoption of measuring for the risk of 'fat tails' and awareness of skewness.
A good example of risk mis-underestimation is in the shares of AI darling, Nvidia.
Going into its late May'23 earnings release, various popular measures of risk ranged from about +/-6-7% using ATM straddle options implied move to -9-11% using parametric and historical Value-at-Risk or VaR (even at the 99%, one-tailed confidence interval).
In the event, shares popped 25% on the day, equivalent to if I recall correctly without checking, a nearly 7 standard deviation move encompassing daily returns data since the company's public listing inception in 1999.
What made this particularly tragic was, in my opinion, that the stock had just recently before its earnings completed a textbook upwards measured move out of a bullish (inverted) head and shoulders pattern on its weekly chart, likely prompting many bears to position short, whether in shares or options.
If you were short, and were only expecting what these measures suggested, the pain was palpable.
You might say, 'Right then; there's no value in attempting to measure risk at all'. But that would be a mistake. Rather, you have to make sure you understand what the measure of risk you're using is actually doing. And try to get a picture of as much data as possible.
Looking at a distribution of the entirety of Nvidia's actual daily returns going into its earnings revealed positive skew, albeit not significantly different than normal; but excess kurtosis that was significantly different than normal. So - there was fat tail risk, and it was to the upside.
Visually inspecting the distribution and a graph of past actual daily returns prior to the earnings revealed that Nvidia indeed had some extreme upside days in its past, at least one if not two exceeding its 25 May'23, +25% percentage change. They just hadn't occurred in close time proximity, which reveals yet another weakness with typical risk estimation - recency bias.
We humans tend to conceptualise around only the previous five years (at best). And that recency bias is reflected in the typical lookbacks used in summary statistics. For example, within the Portfolio Risk function on even the vaunted Bloomberg Professional terminal, VaR tab, estimates for historical (non-parametric) VaR using confidence intervals of 95%, 97.5% and 99% are calculated for only 1, 2 or 3-year lookbacks.
The old saying goes, 'Anything's possible, but not everything is probable'. And it is on this maxim that most risk estimation leans. But knowing what's possible is perhaps more important than knowing what's probable, especially if the returns profile of an asset reduces the relevance of the probability values associated with that asset's distribution. This is especially so as even knowing what's possible from past data is at best a sample, as you point out in the article.
The reality is that the most nimble, consistently profitable operators in the markets are using proprietary models that are far more sophisticated than the ones in the public domain, with most of the public not even using those, and this is what differentiates their performance versus the public's results.
While sobering, that's not reason alone to abstain completely from trading or investing, but rather to realise that the models you're leaning on have flaws. One way of minimising the potential shortcomings is to not use summary statistics in isolation, but augment them with visual inspection of the data and adjust exposures to levels commensurate with what's really possible.
This reckoning will de facto result in being more selective in choosing opportunities and cautious in the size and directional bias of positioning, hopefully improving overall outcomes over time.
Looking at your 'About', I must say it is rare to see a college student with your level of enthusiasm for the markets and all things investing/trading, as embodied in this blog. Something tells me, you'll be going far. ;-)