In Most Markets, Lower Risk Means Higher Reward

[-]Douglas_Knight4y60

Fama-French is not a "model of market efficiency." Honest economists describe it as the best challenge to Fama's theory of efficiency. Sometimes Fama tries to reconcile this model with efficiency by proposing that there is a fat tail of risk correlated with the anomalies, but this is just a hypothesis, a research program, not something that has any evidence beyond the anomaly.

[-]dawangy4y60

I should perhaps clarify that I am talking about weak form efficiency. In a weak-form efficient market, active management through fundamental analysis can still produce excess returns. The three and five factor models attempt to find fundamental factors that can predict excess returns. This contradicts the stronger forms of EMH, but it stands just fine with the weak form. In addition, academic practitioners use the five factor model often in defense of weak EMH.

To your point, perhaps I should edit the original article though. Investopedia says of the FF model, "there is a lot of debate about whether the outperformance tendency is due to market efficiency or market inefficiency."

[-]AaronF4y*50

REMOVED

[-]rossry4y30

Originally the Fama-French model only had 3 fundamental risk factors. If things don't quite work out after the first 3, it seems awfully ad-hoc to just find 2 more and then add them to the back. There also seems to be a belief in academia that getting higher risk adjusted returns through analysis of company fundamentals is more possible than getting them through historical price data.

I'm a bit confused here -- the core Fama-French insight is that if a given segment of the market have a large common correlation, then it'll be under-invested in by investors constrained by a portfolio risk budget. In this framework, I think it's perfectly valid to identify new factors as the research progresses.

(1) As a toy example, say that we discover all the stocks that start with 'A' are secretly perfectly correlated with each other. So, from a financial perspective, they're one huge potential investment with a massive opportunity to deploy many trillions of dollars of capital.

However, every diversified portfolio manager in the world has developed the uncontrollable shakes -- they thought they had a well-diversified portfolio of 2600 companies, but actually they have 100 units of general-A-company and 2500 well-diversified holdings. Assuming that each stock had the same volatility, that general-A position quintuples their portfolio variance! The stock-only managers start thinking about rotating As into Bs through Zs, and both the leveraged managers and the stocks+plus+bonds managers think about how much they'll have to trim stock leverage, and how much is that should be As vs the rest...

Ultimately, when it all shakes out, many people have cut their general-A investments significantly, and most have increased their other investments modestly. A's price has fallen a bit. Because A's opportunities to generate returns are still strong, A now has some persistent excess return. Some funds are all-in on A, but they're hugely outweighed by funds that take 3x leveraged bets on B-Z, and so the relative underinvestment and outperformance persist.

(2) In this case, the correlation between the A stocks is analogous to an extreme French-Fama factor (in the sense the original authors mean the term). It "predicts higher risk-adjusted returns", but not in a practically exploitable way, because the returns go along with a "factor"-wide correlation that limits just how much of it you can take on, as an investor with a risk budget.

If you could pick only one stock in this world, you would make it an A. Sure. But any sophisticated portfolio already has as much A as it wants, and so there's no way for them to trade A to eliminate the excess return.

(3) And in this universe, would it be valid for Fama and French to write their initial model, notice this extra correlation (and that it explains higher risk-adjusted returns for A stocks), and tack it on to the other factors of the model? I think that's perfectly valid.

[-]dawangy4y30

It seems ad hoc to me because they continue to add "fundamental" factors to their model, instead of accepting that the risk-return paradox just existed. Why accept 5 fundamental factors when you could just accept one technical factor?

Suppose that in 20 years we discover that although currently in 2021 we are able to explain the risk-return paradox with 5 factors and transaction costs, the risk-return paradox still exists despite 5 factors in this new out of sample data from the future. What do we do then? Find 2 more factors? Or should we just conclude that the market for the period of time up until then was just not efficient in a weak-form sense?

[-]rossry4y10

I think of the Fama-French thesis as having two mostly-separate claims: (1) correlated factors create under-investment + excess return, and (2) the "right" factors to care about are these three -- oops five -- fundamentally-derived ones.

Like you, I'm pretty skeptical on the way (2) is done by F-F, and I think the practice of hunting for factors could (should) be put on much more principled ground.

It's worth keeping in mind, though, that (1) is not just "these features predict excess returns", but "these features have correlation, and that correlation arrows excess returns". So it's not the same as saying there's a single excess-return factor, because the model has excess return being driven specifically by correlation and portfolio under-investment.

Example: In hypothetical 2031, it feels valid to me to say "oh, the new 'crypto minus fiat' factor explains a bunch of correlated variance, and I predict it will be accompanied by excess returns". The fact that the factor is new doesn't mean its correlation should do anything different (to portfolio weightings, and thus returns) than other correlated factors do.

I also don't think the binary of "the risk-return paradox exists" vs "the market is efficient in a weak-form sense" is a helpful way to divide hypothesis-space. If there's a given observed amount of persistent excess return, F-F ideas might explain some of it but leave the rest looking like inefficiency. The fact that some inefficiency remains doesn't mean that we should ignore the part that is explainable, though.

[-]dawangy4y40

I think I would agree with you that if you could really find the "right" factors to care about because they capture predictable correlated variance in a sensible way, then we should accept those parts as "explainable". I just find that these FF betas are too unstable and arbitrary for my liking, which is a sentiment you seem to understand.

I focus so much on the risk-return paradox because it is such a simple and consistent anomaly. Maybe one day that won't be true anymore, but I'm just more willing to accept that this phenomenon just exists as a quirk of the marketplace than that FF explains "part of it, and the rest looks like inefficiency". FF could just as easily be too bad a way to explain correlated variance to use in any meaningful way.

[-]rossry4y40

Reasonable beliefs! I feel like we're mostly at a point where our perspectives are mainly separated by mood, and I don't know how to make forward progress from here without more data-crunching than I'm up for at this time.

Thanks for discussing!

[-]JenniferRM4y20

Is there any coherent defense for using price volatility as a proxy for risk?

To me, this move just seems... stupid? Like not tracking what matters at all? I've USED this math in practice as a data scientist, when the product manager wanted to see financial statistics, but I didn't BELIEVE it while I was using it. (My own hunch is that "actual risk" is always inherently subjective, and based on what "you" can predict and how precisely you can predict it, and when you know you can't predict something very well you call that thing "risky".)

If we treat this "attempt at a proxy for risk" as a really really terrible proxy for risk, such that its relation to actual risk is essentially random, then it seems like you should expect that doing statistics on "noise vs payout" would show "whatever the average payout is in general" is also "the average payout for each bucket whose members are defined by having a certain random quantity of this essentially noisy variable".

If I understand correctly, this "it is all basically flat and similar" result is the numerical result in search of an explanation... I wonder if there some clever reason that "this is basically just noise" doesn't count as a valid answer?

[-]dawangy4y30

I don't think that gilch answered the question correctly. His two games A and B are both "additive" games (unless I'm misunderstanding him). The wagers are not a percent of bankroll but are instead a constant figure each time. His mention of the Kelly criterion is relevant to questions about the effect of leverage on returns, but is relevant neither to his example games nor to your question of why volatility is used as a "proxy" for risk.

I'd say that to a large extent you are right to be suspicious of this decision to use variance as a proxy for risk. The choice to use volatility as a risk proxy was definitely a mathematical convenience that works almost all of the time, except when it absolutely doesn't. And when it doesn't work out, it does so ways that can negate all the time that it does work out for. The most commonly used model of a stock's movements is Geometric Brownian Motion, which only has two parameters, µ and σ. Since σ is the sole determinant of the standard deviation of the next minute/day/month/year's move, it is used as the "risk" parameter since it determines the magnitude distribution for how much you can expect to make/lose.

But to get to the heart of the matter (i.e. why people accept and use this model despite it's failure to take into account "real" risk), I refer you to this stackexchange post.

[-]gilch4y*00

Suppose I offer you two games:
A) You put up ten dollars. I flip a fair coin. Heads, I give it back and pay you one cent. Tails, I keep it all.
B) You put up $100,000. I flip a fair coin. Heads, I give it back and pay you $100. Tails, I keep it all.
You have the edge, right? Which bet is riskier? The only difference is scale.

What if we iterate? With game A, we trade some tens back and forth, but you accumulate one cent per head. It's a great deal. With game B, I'll probably have to put up some Benjamins, but eventually I'll get a streak of enough tails to wipe you out. Then I keep your money because you can't ante up.

The theoretically optimal investing strategy is Kelly, which accounts for this effect. The amount to invest is a function of your payoff distribution and the current size of your bankroll. Your bankroll size is known, but the payoff distribution is more difficult to calibrate. We could start with the past distribution of returns from the asset. Most of the time this looks like a modified normal distribution with much more kurtosis and negative skew.

The size of your risk isn't the number of dollars you have invested. It's how much you stand to lose and with what probability.

Volatility is much more predictable in practice than price. One can forecast it with much better accuracy than chance using e.g. a GARCH model.

Given these parameters, you can adjust your bet size for the forecast variance from your volatility model.

So volatility is most of what you need to know. There's still some black swan risk unaccounted for. Outliers that are both extreme and rare might not have had time to show up in your past distribution data. But in practice, you can cut off the tail risk using insurance like put options, which cost more the higher the forecast volatility is. So volatility is still the main parameter here.

Given this, for a given edge size, it makes sense to set the bet size based on forecast volatility and to pick assets based on the ratio of expected edge to forecast volatility. So something like a Sharpe ratio.

I have so far neglected the benefits of diversification. The noise for uncorrelated bets will tend to cancel out, i.e. reduce volatility. You can afford to take more risk on a bet, i.e. allocate more dollars to it, if you have other uncorrelated bets that can pay off and make up for your losses when you get unlucky.