I said earlier that small caps.as part of the higher-risk lower-quality part of the market, is more prone to do well when the market does well. Yuval’s remarks above are correct and expand on what I said.
Essentially, whatever we’re doing, we’re all looking for anomalies. And because small caps are small, they are in fact easier to grasp and analyze. But nowadays, fewer and fewer people are into serious company analysis so one who does analyze small caps probably has better chances of finding situations where Mr. Market missed the boat . . . maybe underestimating growth, or maybe over-estimating risk (this happens a lot - a risky company priced as if it were twice as risky as it really is makes for an opportunity). The world is so primed by gurus to look for great things, many fail to appreciate how stocks can move if a company goes from ridiculously in the red to just plain in the red, and if they start to get within hailing distance of breakeven, you’ll probably get to take nice profits selling to latecomers bidding the stock up to excessively optimistic levels.
So there’s really nothing wrong with small cap investing, as long as we understand what it is. We’re not naively assuming there’s a “small cap effect” that automatically boosts returns and driving ourselves crazy at times when it seems to vanish. We’re looking for the usual set of V-G/S -Q anomalies and looking in a place where a particular pattern of these anomalies is apt to happen a lot.
A lot of you are already doing this V-S/G-Q type of strategizing it so what I’ve bene writing isn’t meant to get you to change. For folks like you, it’s meant to put some intellectual armor around what you’re doing and helping you stay the course and resist so much nonsense that’s out there.
My mathematical “abilities” limit me to small parts of this, but I do know that although the normal distribution is assumed for just about everything that has come out of financial research, it’s now pretty well acknowledged that in the real world, none of the observed distributions are normal. Third and fourth moments tend to be high, and often the forth moment can be especially notable. I saw that a lot some years ago when I studied many of the factors we use here.
I don’t have the mathematical vocabulary to explain myself, but the Merton model comes from a completely different theoretical heritage.
FWIW, for your own personal use you are likely to be okay using a normal distribution as the central limit theorem saves you most of the time. If you use longer holding periods you are better off using the natural log of the returns. This gives a nice bell shaped, pretty symmetrical curve (usually), that is considered (or assumed to be) lognormal. However, the tails may (or may not) be fatter than a normal distribution.
Merton (Black-Scholes) assumes a lognormal distribution, I think. And again this does work for a big part of what we do—fat tails or not–because of the central limit theorem.
Fat-tails and non-normal distributions are important for leverage, as we all know. We don’t need to read “The Black Swan” buy Nassim Taleb to know this. You know the history and experience where the CAPM has failed (especially with excess leverage) better than I do. Nassim Taleb (and others) have used Long-Term Capital Management as an example—to the point of literally advocating the rescinding some Nobel Prizes. I would be interest in your experience and take on this.
But assuming a fat-tail does not cause you to go broke, over a long period your average returns will be part of a lognormal sampling distribution (central limit theorem).
And as you say it is a different topic. The DDM is, as you suggest, pretty universal. No one gives up money without expecting more money in return. And the sooner they get the money the better (time discounting). The riskier things are (or if they can get almost as much return risk free) the less likely they are to give up their money. The way you present it you successfully extend the theory into discounted cash flow analysis.
That may be the canonical view, but the two are linked by the time value of money principle. The difference is that the Merton model supposes the investor receives a one-time terminal payout of the expected Max(0, FV_Assets - FV_Debt) at maturity where FV_assets is a diffusion process determined by the expected PV of cash flows (or earnings). DCF presupposes that the investor receives NPV of equity over regularly spaced intervals (or continuously) with no diffusion taking place. The chief advantage of DCF is the presumption that earnings accrue discretely, which is a more realistic way of modeling how things work in the real world.
While most DCFs presume no diffusion, it can be shown that the randomness vanishes in the case of DCFs under some unconditional probability measure,
(as this example shows). But conditionally, as in the real world, equity investors actually expect to receive payout Max(0, FV_Assets - FV_Debt) due to the limited liability clause of equity. This would explain why markets assign negatively earning companies positive values… not necessarily because of positive future expectations, but because losses are limited to principal invested. One could think about this residual value as “extrinsic value”.
Not to get lost in weeds, I just was wondering if anyone had though about to how deal with uncertainty of cash flows and how this could affect NPV. As I think I have shown, the embedded “optionality” of equity ensures that equity NPV is at least equal to the unconditional expectation given by DCF. Instead of looking at this uncertainty problem holistically, conventional financial analysis has devised a multitude of ways to price around actual cash flows by evaluating companies by EBITDA, sales, book value, all sorts of variations around interest rates, and more. Not that these are necessarily wrong, but just really rough approximations. Merton-like models are a step the right direction, but are ultimately worse at predicting returns than much simpler cash flows and earnings based perpetuity models (such as what Marc proposes) or structured annuity models (such as what Jim has outlined) since they assume only a one-time payout at maturity (furthermore… what maturity? What drift? What variance? What initial value? etc.).
Anyway, my intuition strongly tells me that an ability to model the conditionality of equity would in turn allow us to more price things under a single framework, meaning fewer assumptions and thus more robust estimates.
There are people who do research in areas like this. You may want to go to web sites for “Journal of Finance,” “Journal of Portfolio Management,” “Financial Analyst’s Journal,” etc. and look at the indexes of published artices (these will be academic research papers). If you see something that catches your attention, Google the name of the article; someone somewhere may have uloaded a opdf you can easily retrieve. If not, you can see how muchb the publication charges for individual-articile access . . . Or try to communicate directyl with the author, who can usually be traced via his or her academic affiliation.
My problem in using sentiment as a factor is one of implementation.
The only effective use, that I have seen, is to look at changes in estimates over the last four to eight weeks. (As used in the Basic ranking system.)
I find using this to give very high high turnover with losses caused by slippage and commissions.
I have played around with other rules that use estimates but none seem to have much effect.
Anyone have any sentiment rules that are effective in lower turnover systems (say 100-300%/yr?)
I like P123’s Basic Sentiment rankings a lot, and use them, but you’re right, that’s for high-turnover systems. For lower turnover systems, try a combination of SI%ShsOut, compared to industry, lower numbers better, and Pr52W%ChgInd, compared to universe, higher numbers better.
David, I don’t know if this counts as sentiment, but there may be a use for longer term comparisons comparing the current analyst estimate to estimates that came before it. For example: CurQEPSMean vs. EPSActual(3,QTR) and permutations of that idea. That would give a longer window of comparison anyway that might be a bit more stable.
I think there’s some effectiveness in various comparisons of that nature and that’s one branch of a new growth model I’m working on. But I’m not sure if it’s strong enough to survive combination with other factors. I’m not to that point yet.
The paper is a high-level description of the Vacicek-Kealhofer model, which is Moody’s proprietary extension to the Merton model. A few years old, but I think it’s a nice conceptual overview.
I am reading now. It does offer a wonderful overview. Thank you.
But I still find the Merton framework circuitous (a chicken and egg ordeal).
How does it value assets? By inverting the market value of debt and equity…
How does it value equity? Through the imputed value of assets…
It assumes that assets are a diffusion process (which is just a modeling assumption), but it does not directly estimate any values provided that their is a market for them. This of course presumes semi-strong form market efficiency – i.e., the market gives the right values for equity and debt. This might be useful to ratings people who guess at credit worthiness or credit portfolio managers, but it says nothing about future equity returns which is what we care about. Also the veracity of this model seems to be antithetical to the existence of risk takers and arbitrageurs such as ourselves.
DCFs, on the other hand, directly impute generic asset values, which is much more strongly aligned to our incentives. Even if markets are usually right, it pays to find out when/where they are wrong. I just keep finding that the existing literature on real options involving DCFs is incredibly lackluster.
Again, the two are linked by time value, but Merton/KVM assumes only a terminal payoff. This is true even if we were to adapt Merton for estimated asset values and (American style) early exercise.
I agree. That’s what it’s commonly used for. The motivation is that corporate debt (even for large, publicly traded corporations) is so illiquid that prices are almost always stale. When you are looking to value a particular corporate bond, it may be days or even weeks since it has last traded. And even then, it wasn’t sold in an “open market transaction”. So you use a model that uses the highly liquid stock price, to come up with a “mark to model” fix for the inability to mark bonds to market.
I don’t see a way to turn this around to value equity.