nisiprius wrote: ↑Mon Oct 19, 2020 6:41 am
Uncorrelated wrote: ↑Mon Oct 19, 2020 3:47 am
...But the effect did show up. Since 1993 DFSVX outperformed total stock market by 0.8% annually, after expenses....

I don't think it did. The important thing is that it didn't on a

**risk-adjusted** basis: Up to 12/31/2019:

Source
If we call that a "tie" (although DVSVX was a smidge lower), then the extra return was just reward for extra risk taken, nothing more.

Why did I cut off at 12/31/2019? Because from inception

*to date*, we don't even have outperformance on raw return.

I was referring to the expected return, which is the average of the distribution of outcomes. Supposing you are an investor that can receive either an investment with the same (past) probability distribution of DFSVX or total stock market, then DFSVX will have higher average returns, and more risk. Therefore, we can say the investments have a different distribution of possible outcomes.

The extent to which investment is preferred depends on the risk aversion of the individuals. There is at least one class of investors that will prefer DFSVX based on this specific period of returns, and those are leverage constrained investors that follow a lifecycle investing strategy. These investors have large human capital relative to their stock allocation, for these investors the arithmetic return determines the expected utility.

CAGR is a measure of risk adjusted return. Specifically, it is the median outcome assuming returns are lognormally distributed, and it is also equal to the expected utility for investors with a logaritmic utility function. For some investors, DFSVX had a more favorable probability distribution of expected returns. For other investors, total stock market had a more favorable distribution. Sharpe ratio is not an useful measure of risk-adjusted performance because it does not correspond to any particular utility function.

If we want to be totally fair, we should add 0.40% to the returns of DFSVX to account for it's high expense ratio compared to factor funds you can buy today.

Anyway, I don't really see how this talk about risk adjusted performance is related to my claim. Markets are random. The purpose of DFSVX is to obtain positive exposure to HmL and SmB. In the last 27 years HmL and SmB were low, but DFSVX did succeed in capturing them. In international HmL returns were less low, and international funds succeeded in capturing them. Of course they are "risk" premium, so this did result in additional risk. Nobody disputes that SCV has additional (multi-dimensional) risks.

Source
Now, how to regard bursty phenomena is a puzzle. But it is what it is, and in my opinion a phenomenon is not robust if twenty-six years of it can be wiped out so easily. And this is not particularly unusual. We've had at least three "bursts" of this general magnitude in the last twenty years. The history is what it is. Maybe the recent drop, which looks a little like 1998, will be followed by three years of going up while the whole stock market goes down, as happened after 1998. How convinced are you that that will happen?

Bill Miller was able to buy not just a yacht, but a superyacht, thanks on his beating the S&P 500 in 1991, 1992, 1993, 1994, 1995, 1996, 1997, 1998, 1999, 2000, 2001, 2002, 2003, 2004, and 2005. I think he was following a martingale-like gambling system, getting very visible seemingly steady small wins, in exchange for rare catastrophes. Who could possibly have anticipated that a roulette wheel would come up red ten times in a row? The global financial crisis? The COVID-19 pandemic?

Miller beat the S&P 500 fifteen years in a row and then lost back all the accumulated outperformance. So I see a bit of the same thing in, at least, the kinds of factor-based portfolios that were published and investable in the late 1990s. Consistent (if bursty) outperformance for two decades, though not literally outperformance every year--and all lost in less than a year.

The bursty performance is not something that is unique to HmL. In the paper "volatility lessons", Fama/French investigated the performance of various factor portfolio's and concluded that the shape of the outcome distribution over long horizons is similar for mkt and HmL. The bursty performance is just random market gyrations.

I ran a 3-factor regression based on Bill Miller's fund in 1991-2005, the statistical significance can be described as weak:

It's nice to have a model that allows us to accurately estimate the confidence in a particular decision. Bill Millers fund is an in-sample 1.5 standard deviation event. US HmL performance (1963-1991 or 1963-2020) is a 3 standard deviation event, and global HmL performance in 1991-2015 is a 4 standard deviation event. The latter of which is out of sample. We can safely say that the evidence that we use here to support an HmL investment would not support an investment in Bill Miller's fund in 2005.

I recognize what you're trying to say, but it's not fair to dismiss a 4-standard deviation

*out-of-sample* anomaly because a previous 1.5 standard deviation

*in-sample* anomaly didn't play out. For reference, the market factor itself is a 2.5 standard deviation anomaly. The market routinely under performs t-bills over multiple decades. That's not a reason to avoid the market, all evidence should be evaluated to determine whether the market is worth investing.

Fama/French investigated the expected return of HmL (i.e. the underlying random variable that generated the sequence of returns) in 1963-1991 and 1991-2019, they state that there is a probability of 87% that the expected return is equal in both periods. That is not even a one standard deviation event.

Based on a model portfolio published by Larry Swedroe in 1998, which I implemented by using the specific DFA funds whose names were an obvious fit for his asset class names.

The time period was constrained by the available data for DFA Enhanced US Large Company I (DFELX) [Aug 1996 - Sep 2020]. The comparison is the three Vanguard "Total" funds, matching percentage allocations for US stocks, international stocks, and bonds.

That's some serious home bias. I ran a similar comparison while writing my previous post, and reached the exact opposite conclusion:

https://www.portfoliovisualizer.com/bac ... tion6_2=30
I opted not to post it previously because I don't think backtest are not a good way to evaluate past performance. The confidence interval on such a backtest is enormous, even if the backtests showed a return differential of 4% per year, I would still consider it weak evidence. The reason I opened this topic in the first place was that some academics use backtest to show time series momentum exists, but it turns out that these backtests can generate an positive alpha for many different reasons, only some are related to time series momentum. Likewise, a backtest between value and non-value can decide in either favor for many reasons which are not related to the expected return of either portfolio, and that's what ultimately matters in portfolio construction.

I appreciate your input but backtests are terribly unsuited for this purpose. The same methods that you use can be used to argue for an overweight allocation in US tech, and we all know that's a terrible idea. If we want to have confidence in our investments, then we need to use a mathematical method that rejects the outperform of US tech as random noise, a backtest is not that method.