A fundamental derivation is only useful to the extent it can be tested. For example, CAPM (capital asset pricing model) is a very fundamental and theoretical model that follows from very simple assumptions, but it's not a very good one because economics have difficulty showing market beta is related to return, which is a result of CAPM.JackoC wrote: ↑Tue Dec 08, 2020 9:37 am1. Again you speak strictly in terms of a regression analysis of past CAPE v subsequent past return. You do not address the fundamental derivation whereby earnings yield=expected return, at all. And then you assume the allocation would be changed according to CAPE which I very specifically said am I not proposing. It really seems you have a certain hammer, and see all counter arguments as nails, so to speak.Uncorrelated wrote: ↑Mon Dec 07, 2020 4:14 pm1. I believe there is enough evidence to think that the 1/CAPE is colossally wrong. This can be easily observed by performing a regression of 1/CAPE and observing that the intercept is not 0. An more neutral question is: if we want to determine μ, does CAPE contain any signal of economical significance? If the conclusion is that the signal is too weak or not economically significant, the natural choice is to fall back on a constant estimate for μ, which is what I suggested as the default option. Dynamically adjusting μ over time based on CAPE *is* an attempt to raise risk/return and should be met with the same skepticism as all other forms of market timing.JackoC wrote: ↑Mon Dec 07, 2020 2:32 pmYou are interested in 'optimal allocation' and perhaps a 'CAPE timing strategy'. Fine, and perhaps even some 'pro CAPE' posters are also. But the post you just responded to is not talking about that as I read it. I've definitely not been talking about that.Uncorrelated wrote: ↑Mon Dec 07, 2020 11:18 amI have seen no evidence that 1/CAPE or CAPE linear regression outperforms a constant allocation. I have seen some evidence (from papers) that a constant allocation is extremely hard to beat, and that a simple regression on P/E ratio's does not beat a constant allocation by anything that can be considered significant. The expected gains of "optimally" using CAPE in your investment strategy have not been examined yet by any source linked to in this thread. You seem to believe the opposite, could you link to a few papers that investigate the certainty equivalent gains for using a CAPE timing strategy?
Starting from zero in a financial plan I need some indicator of expected return, even if it's going to be quasi-fixed (age dependent) % stock/bond. People who say they don't need this are confusing themselves IMO, I see no way around it. Dealing in 'actual' past returns inevitably means assuming implicitly that the expected return now is the average of past returns. Because in fact you must assume something, even be it a range, but any range has a midpoint, which is basically (not necessarily mathematically exactly) what the expected return is.
The earnings yield is a fundamental estimator of expected return per the derivation linked above, standard.
https://docfinder.is.bnpparibas-ip.com/ ... 07E654E5AE
To reject the 'paper airplane' of 1/CAPE=real expected return for basic planning, not dynamic asset allocation, purposes I believe you must explain why it's systematically biased in one direction or another (how the real world violates the assumptions of the derivation in a way which makes 1/CAPE systematically under/overstate expected return), and show why another estimate is better*.
'Active long vol' or factors can only refer to a strategy neither is itself an estimate of expected return, whereas bond yield can be a measure of expected return but not a strategy. The term 'CAPE' used loosely might refer to either an estimate of expected return or a strategy to use a regression of past CAPE v past subsequent return to vary allocation attempting to raise risk v return performance. So it's perhaps in part a semantic problem, but seems you also would rather talk about 'optimal allocation' only partly depending whether other people are talking about it.
2. My experience tells me it's fairly hard to beat a constant allocation, even if there is some signal in the indicator. For example, VIX is an ok-ish estimator of future volatility (R^2 of 30% on a monthly timescale, IIRC). But actually trading on that in the optimal way (or at least, the way that theory suggests is optimal) results in a lower certainty equivalent return than a simple constant allocation. Therefore, if 1/CAPE has a nonzero amount of signal, it doesn't imply that it will be better than a constant estimate.
The reason the regression analysis is not the only or even necessarily central issue actually a reason you've pointed out yourself. The regression is heavily influenced by change in CAPE over what's actually a pretty small sample. It is not a good evaluation of whether there are flaws in the fundamental derivation which says earnings yield=expected return. The argument against that must be made in terms of that derivation and its assumptions: which ones result in the measure being systematically biased up or down? Which is the question at hand in my contention that the 'paper airplane' of 1/CAPE is the best easy estimate of expected return *for planning purposes*. To address my point, I believe you must drop regressions and t-statistics and tell me the flaws in the derivation which make some other easy estimate of expected return a better one.
Again, current risk free rate + historical average ERP is not as bad as just assuming past return period as the best indicator of future return. But it has the obvious mismatch that it assumes we have 100% ability to derive the expected return of the 'rfa' from current market prices, but 0% ability to derive the expected equity return from current market prices, rather instead have to take an average of the difference in past realized equity and bond return over a past period part or all of which may bear little fundamental resemblance to now. When we just rejected that same method for the rfa itself...and for good reason.
2. Again a strange response to my post I think clearly saying 'let's assume a quasi fixed (perhaps age, but not market dependent) % stock/bond, more than once.
Even if 1/CAPE doesn't systematically over or under-estimate the expected return, it doesn't mean it's a good estimate. That is something to be determined with empirical research. All models are wrong, but some are useful. I believe it's up to you to show this model is useful, or more useful than others.
If you accept that CAPE is useful for planning purposes, then you must also accept it can be used for market timing. Intuitively, if CAPE10 has impact on your asset allocation, then it must be true that next month's CAPE10 figure contains more information than the last. Changing your asset allocation as soon as next months CAPE10 figure comes in must result in higher expected utility. If you don't do this, you'll end a path dependent asset allocation, which is always suboptimal (wikipedia has some more info, but it's quite hard to read if this is outside your area of expertise...). rf + ERP doesn't have this problem, the ERP is assumed to be constant, and if the rf changes or is mis-estimated then it does not affect the asset allocation at all. (see the solution to merton's portfolio problem).
I understand you want a quasi fixed stock/bond allocation, but that is simply not where CAPE will lead you. CAPE will lead you either to an asset allocation that changes as often as monthly, or to a contradiction of the bellman equation. You don't seem to want the former and the latter is clearly very, very bad.