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Do the quality, momentum, low vol, and dividend growth strategies beat the market?

Do the quality, momentum, low vol, and dividend growth strategies beat the market? post image

Few investors would say “no” to beating the market. Even the most passive among us would happily filter-feed a few extra quid – like a financial blue whale – if we didn’t need an ‘edge’ to make it happen.

Last week we looked at one way to potentially do that. The small value strategy has earned a 2% annualised premium versus the market over the long-term. Outside the US, small value has beaten the market by 1.5% annualised since 1990. Which is just as well, because it’s had a torrid time against the S&P 500 these past 20 years.

But other systematic market-beating strategies are available!

The cast of credible candidates includes:

  • Momentum – You buy recent winners, sell recent losers
  • Quality – Firms with high return on equity, low debt, and stable earnings growth
  • Low volatility – Low beta stocks that don’t fizz or fizzle as violently as the market. The draw here is the potential for superior risk-adjusted returns

We can invest in any of these strategies using an ETF, they’re backed by independent research, and the risks are pretty well understood.

But how well do they actually work? If in fact they do…

Are there any diversification benefits to be had if you combine the strategies?

Let’s turn to the data!

While we’re at it, let’s look at the dividend growth / leader / aristocrats strategy, too. Dividend growth is not widely considered to be a market-beating wheeze but we have the numbers, so let’s see.

Investing returns sidebar – All returns quoted are nominal total returns. US data is from the astounding Simba’s backtesting spreadsheet and compiled by members of the Bogleheads to further public knowledge of investing. World data is quoted in GBP and is from the spiffing justETF.

Market beat-’em-up

Which strategies socked it to the market over the longest comparable timeframe?

Here’s our contenders’ annualised returns versus the S&P 500 for the 40 years from 1985-2024:

Strategy Annualised return (%) Sharpe ratio
Broad market (US) 11.7 0.69
Momentum 13.7 0.71
Quality 12.9 0.72
Dividend growth 12.4 0.88
Low volatility 11.1 0.84
Small value 11.1 0.63
Small cap 10.5 0.58

US stocks only. USD returns. Small value and small cap included for comparison purposes.
The Sharpe ratio is a measure of risk-adjusted returns. Higher is better.

On these numbers momentum looks like a must-have.

That’s not too surprising. The long-short version of the momentum strategy stands out as the most profitable of the so-called risk factors in academic literature. And here we can see that a long-only iteration has delivered a 2% premium in the all-important US market.

Moreover, my numbers (not tabulated) show momentum’s volatility is pretty normal for an equity holding. Volatility averages 19.3% across the period.

Also-rans worth running

What about our other belligerents?

Quality also looks good. It beat the market by 1.2% per year on average. That will add up. Again there’s no sign you must endure sickening volatility to snaffle the extras.

The biggest surprise to me is dividend growth. High dividend stocks are routinely found by academics to lack any special sauce. But the strategy has topped the market by a commendable 0.7% over the period we have data for.

Dividend growth also delivered the best risk-adjusted returns. That is, you got more bang for your buck per unit of risk taken (as measured by volatility).

Low volatility1 didn’t beat the market but it isn’t meant to. A low volatility strategy touts superior risk-adjusted returns versus the broad market – and on that score, it delivered.

You might think of low vol as the antacid of equity strategies. It offers relief against stomach-lurching drawdowns without sacrificing too much return.

Finally, small value and small cap were poor over this time horizon. But if that encourages you to write-off small value then I’d urge you to read our recent musings on small caps first.

Time trial

Let’s split apart the 40-year timeframe. Doing so may reveal extra nuance:

Strategy 5yr ann return (%) 10yr ann return (%) 15yr ann return (%) 20yr ann return (%) 25yr ann return (%) 30yr ann return (%)
Broad market 14.5 13.1 13.8 10.3 7.7 10.9
Momentum 11.8 13.2 14.5 11.1 8.6 13.2
Quality 13.6 12.9 13.8 10.8 8 12
Divi growth 11.5 11.4 12.3 9.7 9.6 11.1
Low volatility 8.1 10.2 12.1 9.5 11.1 10.1
Small value 9.9 8.9 11.2 8.5 9.8 10.7
Small cap 9.3 9.1 11.6 9.1 8.7 10.2

Firstly, we can see that none of this lot laid a glove on the S&P 500 these past five years.

Don’t bother with risk factors unless you’re prepared for the long haul. If they beat the market all the time, then they would stop being risk factors. The key word is risk.

With that said I’ve highlighted momentum because it’s the only factor that’s consistently beaten the US market across every timeframe beyond five years.

Quality has been more erratic – while you have to push your view back at least 25 years before dividend growth bests the S&P 500.

Timely reminders

The table shows how considering different time frames can influence our view. For example, low vol and small value would look pretty hot right now, if all we had to go on was 25 years worth of returns.

Is there anything special about this quarter-of-a-century mark?

Well, the broad market nose-dived 38% during the Dotcom Bust (2000-02). But low vol, small value, and dividend growth all climbed during the crash. They hedged your losses at just the right time.

Low volatility and dividend growth also suffered far less than the S&P 500 during the Global Financial Crisis and 2022’s inflationary surge. Meanwhile, small value enjoys a lower correlation with the market than the other strategies across the entire period.

So there is some strategic value in thinking beyond the raw returns, especially if your objective is to limit drawdowns.

For example:

  • Want to curtail your losses in a crisis? Consider low volatility and dividend growth.
  • Want to diversify your returns away from big tech? Think small value.

Incidentally, I find the risk factor framework more convincing than geography as a basis for diversification. Perhaps that’s one we can debate in the comments?

Diversification potential

A correlation matrix can help us assess the diversification benefits of each asset pair. The lower the number the better.

Strategy Broad market Small value Momentum Quality Low volatility Divi growth
Broad market 1.0 0.71 0.90 0.96 0.94 0.87
Small value 0.71 1 0.5 0.59 0.71 0.78
Momentum 0.90 0.5 1 0.91 0.86 0.75
Quality 0.96 0.59 0.91 1 0.90 0.85
Low volatility 0.94 0.71 0.86 0.90 1 0.92
Divi growth 0.87 0.78 0.75 0.85 0.92 1

Small value demonstrates the most diversification potential across the board. It’s the only strategy that’s not highly correlated with the broad market.

Even more intriguing is small value’s relatively low correlation with momentum and quality. That indicates these are likely complementary assets if you’re interested in a diversified multi-factor strategy.

Dividend growth also has some diversification value, so I’d also like to test how well it performs when paired with other strategies…

Multi-factor mash-up

Let’s dial up the fortunes of three equity portfolios:

  • 50/50 momentum/small value (SCV) – best performer + most diversified
  • 50/50 momentum/dividend growth – two strong performers + moderate diversification
  • 50/50 dividend growth/small value – just to see!

Here’s the returns for each portfolio ranged against the market and their component strategies:

Portfolio 10yr ann return (%) 15yr ann return (%) 20yr ann return (%) 25yr ann return (%) 30yr ann return (%) 40yr ann return (%)
50/50 Mom / SCV 11.2 13.1 10 9.5 12.3 12.7
50/50 Mom / Divi 12.4 13.5 10.5 9.3 12.4 13.2
50/50 Divi / SCV 10.1 11.8 9.2 9.8 11 11.9
Broad market 13.1 13.8 10.3 7.7 10.9 11.7
Momentum 13.2 14.5 11.1 8.6 13.2 13.7
Small value 8.9 11.2 8.5 9.8 10.7 11.1
Divi growth 11.4 12.3 9.7 9.6 11.1 12.4

The portfolios are rebalanced annually.

What I’m looking for from my backtest portfolios is only a modest reduction in long-term 40-year returns2 versus the strongest component in the mix.

I’d also like to see strong positive diversification potential at the 25-year mark. That’s the best period for getting a quick bead on the benefit of holding an otherwise weaker seeming asset.

I also want to check if holding two imperfectly correlated assets (for example momentum and small value) essentially delivers the market return. That is, do they just neutralise each other?

Not bad

The good news is that momentum and small value do not cancel each other out.

You still earn a 1% premium versus the market over the long-term, despite SCV’s poor showing overall.

The portfolio result also significantly improves on the performance of the market and momentum over 25 years – the period most affected by the background radiation of the Dotcom Bust.

Yes, you can rightly point out that small value has proved to be a drag overall. But you couldn’t have known that in advance.

Moreover, international3 small value has beaten the international market – even over the past five years. And it’s lagged international momentum by only 0.5% annualised over those last five years, too.

In other words we can’t conclude small value is dead (although it’s clearly resting in the US).

Dividend growth also proves out its diversification chops, while otherwise the numbers show what we already know – the strategy delivered strong returns over 40 years.

Beyond that, I don’t think there’s any point me torturing the data to find some mythical sweet spot involving, say, 17.37% of quality and eye of newt and whatnot.

Essentially, I just wanted to check that choosing moderately correlated factors can produce a diversification uptick without banjaxing the return premium.

If you don’t want to invest in something that hasn’t outperformed for the last ten years then fair enough. Stick to the market, I think that’s a perfectly rational place to be.

Show me the world

We can gain an alternative perspective by checking live fund data. A raft of World risk factor ETFs launched in Europe in 2015, so we can just about scrape up ten years worth of GBP returns by comparing them:

Asset class 5yr ann return (%) 10yr ann return (%) Sharpe ratio
Broad market 12.4 12.6 0.79
Momentum 12.5 14.8 0.82
Quality 11.7 12.9 0.79
Multi-factor 11.6 11 0.69
Low volatility 6.9 9.9 0.76
Small cap 9 9.5 0.56
Small value 12.9 7.8
Dividend growth 8.3 7.2 0.48

Nominal total returns. ETF returns courtesy of justETF. 10-year return is actually 9-years and 9-months due to the youngest ETF’s inception date. Small value is DFA’s Global Targeted Value fund courtesy of Morningstar. Sharpe ratio is based on 10-year returns (not available for small value).

On this view, small value is the best performer over five years but the second worst over ten.

Momentum is the only strategy to beat the market convincingly over ten years.

Dividend growth had a particularly tough time of it.

What does this tell us?

  • It’s been a great time to be a momentum investor
  • Don’t believe small value is dead
  • Don’t count on any strategy beating the market while you happen to hold it
  • Don’t rely exclusively on return comparisons or the experience of a single market to form a view

Personally, before I commit a penny I want to read independent research that can offer:

  • Some confidence the strategy will work in the future
  • A guide to the risks
  • A reason to believe this is more than just an eye-catching pattern in the data or a conveniently arranged backtest

Take it steady,

The Accumulator

  1. Also minimum volatility. []
  2. The maximum comparable timeframe. []
  3. International means ex-US in this context. []
{ 24 comments… add one }
  • 1 big up yourself June 17, 2025, 1:27 pm

    As always, excellent post.

    My approach is to just have a little bit of everything – factors, countries, emerging markets, small cap , large cap, value/ growth etc..

    Ultimately, they all have a positive expected return and you just hope that there is some diversification benefit!

  • 2 ColinThames June 17, 2025, 2:00 pm

    Fascinating article. I’ve been following a momentum investor site called SaltyDogInvestor for about three years which compares fund performances week by week. But the news there might be an ETF that can do it for me, without shelling out a monthly membership is excellent.
    Would you be able to share which ETFs you’ve used in the comparisons please?

  • 3 Martin White June 17, 2025, 4:08 pm

    Are these net of TCosts? If not then largely an illusion as turnover/rebal costs will wipe out the alpha, esp for a high turnover strategy like Momentum.

  • 4 Iain Coward June 17, 2025, 4:31 pm

    Excellent article. Agree with the approach of seeking diversification through different risk factors makes more sense than geographies. Uplift from Shannon’s demon diversification would be a great further discussion. Frank Vasquez on risk parity radio (YouTube / podcast) has a lot of excellent related content if this sort of stuff floats your boat. He’s not for everyone but I personally find him hilarious. Really excellent article from The Accumulator, thank you for that.

  • 5 Howard June 17, 2025, 7:00 pm

    Superb piece. You guys write really well. This is one of the most informative PF/FIRE/investment sites out there. Makes you rethink what you thought you knew.

    Why does multi factor not deliver a bigger rebalancing bonus (5 and 10 yr CAGRs and Sharpes)? It seems an odd outcome. Too many factors in the mix? Other construction issues? Execution costs? Something else?

    Also are the Momentum fig’s WML Long Short academic or Long Only UK ETF? From what you say @TA I’m assuming it’s the former, but could I check please? I think WML L-S only available in US listed Wes Gray / Jack Vogel sponsored vehicle (so can’t hold as an ETF in UK tax wrapper due to MFiD/PRIIPS/ISA reg’s etc).

  • 6 The Accumulator June 17, 2025, 7:12 pm

    @Bigup – Cheers! Yes, in reality I do the same. My tilts are now towards momentum and small value.

    @ColinThames – I’ll just quickly list the ones you can invest in from the UK on the assumption you’re probably a Brit:

    Momentum: IWFM

    Quality: IWFQ

    Low vol: MINV

    Multi-factor: FSWD

    Small cap: WOSC

    Dividend Growth: GBDV

    Small value: AVSG (I used a DFA small value fund for 10-yr returns but only accessible via a DFA advisor)
    https://monevator.com/avantis-global-small-cap-value-etf-review-avsg

    See this link for more momentum choices:
    https://www.justetf.com/uk/search.html?search=ETFS&assetClass=class-equity&equityStrategy=Momentum%2BStrategy

    @Iain – thank you. I would like to understand more about practical approaches to risk parity. Did you see this excellent post by Portfolio Charts a while back?
    https://portfoliocharts.com/2022/04/12/unexpected-returns-shannons-demon-the-rebalancing-bonus/

  • 7 Bob June 17, 2025, 7:32 pm

    What happened to the monkey comparison? Wasn’t there a study that showed monkeys picking investments at random performed better than fund managers?

  • 8 Howard June 17, 2025, 9:25 pm

    #7 @Bob: Arnott et al, Journal of Portfolio Management, Summer 2013 (Summary section): “Many sensible investment beliefs, when translated into portfolio-weighting strategies, result in out performance against the cap-weighted benchmark index. But so do the arguably nonsensical inverses of those weighting strategies. This paradoxical empirical result, which is observed in a large array of long-only strategies globally, is a consequence of the fact that seemingly unrelated strategies that are not based on value or small cap size often have unintended and almost unavoidable value and small-cap tilts, as do their inverse strategies. The resulting factor tilts are the primary sources of outperformance, rather than the underlying investment beliefs. Even Malkiel’s blindfolded monkey throwing darts at the Wall Street Journal would produce a portfolio strategy with a value and size bias that would have out performed historically.”

  • 9 Hariseldon June 17, 2025, 10:54 pm
  • 10 Sparschwein June 18, 2025, 3:52 pm

    Interesting, food for thought. I’m still on the fence, with investing so prone to data mining artefacts. I suppose there is enough research now to trust these factors… Just still wondering, why don’t the factor premiums get arbitraged away when they are common knowledge.

    Ok Small cap and Value have more risk, hence a premium.

    With the other factors, it’s less clear to me.
    Quality and Low vol are arguably *less* risky.
    Some people have an irrational preference for dividend returns and might bid such stocks higher, with lower expected returns.
    Momentum seems to imply nothing about risk.

    (Not saying the factors aren’t real; just struggling to see how they work, from basic principles.)

  • 11 big up myself June 18, 2025, 4:56 pm

    Another interesting point is how the different markets/ factors behave over drawdown periods. Usually, in moments of market distress they move together but over time the picture can be different.

    For example between 2000 and 2012 the S&p 500 was flat. EEM etf was up 5x in that same time period and I think the IWM doubled.

  • 12 The Accumulator June 18, 2025, 9:18 pm

    @Howard – sorry, I missed your earlier question about the numbers: all long only returns.

    USD = index returns (minus hypothetical fund cost) then fund returns once launched in the US. Live fund data varies by factor: early 90s for SCV and small, early to mid noughties for Mom, Qual and Low Vol. I can’t remember off the top of my head for divi growth. I’d guess mid noughties for that too because early trackers were likely just high yield.

    GBP = all ETF data except small value which is DFA’s Global Targeted Value fund.

    The multi-factor ETF was Mom, Qual, Size and Val. (It’s added low vol inside the last year.) It seems to have done ok to me given that size and value are dragging it down. I haven’t checked the split between the factors, though. I’d also note that the rebalancing bonus is an elusive beastie and won’t show up over some periods.

    @Bob – chortle. IIRC the monkey attracted several billion AUM on the strength of his backtest returns. He was subsequently liquidated when his highly leveraged play on Japanese small caps blew up during the Financial Crisis.

    @Sparschwein – from memory, the best explanations for low vol, qual and momentum are behavioural. That said, momentum does look pretty risky to me due to the switchback effects. You can get beaten up pretty badly during periods of negative momentum.

    The argument is that behavioural errors are more easily corrected but then I look at the world around me… 🙂

    @bigup – it’s a good point. Low vol mostly seems to succeed in lowering volatility during market carve-ups. I’m pretty convinced it works, though it’s not offering the kind of exposure I’m looking for personally.

  • 13 Meany June 18, 2025, 11:57 pm

    @TA, re
    >I find the risk factor framework more convincing than geography
    >as a basis for diversification
    I also find the market sector diversification idea pretty intriguing. e.g. I think the S&P P/E is much more “normal” if you drop the tech sector.

    Stepping back on the general method here – these articles are very keen on
    the idea that “the best shot for the future is what worked best for the last 40/125/… years”. Do you have any articles on why that’s probably the best way to look at how to invest (instead of, perhaps, continually assessing which are the strongest companies (=Quality Factor?!); or analyzing where the environment is going to be most shareholder friendly; or looking at which sub-market is likely to have the most net buying in the coming year, etc)?
    This is one of the points as a mathematician I find weirdest about investing – there is no strong inductive principle here. No guaranteed “as before so again”. So a historical study should not be expected to indicate the future. But… There sort-of is a weaker constant isn’t there: human nature remains the same and the rules of money and debt remain the same.
    So businesses across time tend to produce the same return patterns -?

  • 14 Alan S June 19, 2025, 8:26 am

    @Meany (#13)

    While historical data is very good at investigating the past and, for example, comparing the results of different withdrawal strategies, it cannot predict the future but can only be a guide as to possible outcomes.

    I’m a physicist/engineer so not quite a rigorous as a mathematician(!) but having spent at least part of my career looking at ‘random’ data where the underlying physical mechanisms were well known, the problem with return data is that
    1) The mechanism that produces the returns is unknown.
    2) If it is ‘random’ (although if reversion to the mean exists, then it is not completely random) then the exact distribution is not known (there are a number that have been tried in an effort to model the tails).
    3) If the distribution is known, then the mean and standard deviation (if the latter exists) can only be determined from historical measurements which is only an estimate of the ‘true’ value. A question is then how good an estimate is it?

    That question can be tested by generating random data (for simplicity, I’ve used a gaussian with a arithmetic mean of 8% and a standard deviation of 10%*). What range of annualised returns over successive periods of 100 years does this simple model produce? The answer ranges from just over 3% to just under 12%. In other words, if the ‘true’ geometric mean is 7.5% (geometric mean is lower than the arithmetic mean), measuring it over many different 100 year periods could produce an answer anywhere in a range of 3 or percentage points or so either side.

    This means comparing the returns of factors with differences in ‘true’ returns (if such things exist) of 1 percentage point or so is likely to be within the noise.

    *For anyone really interested, you can do this test in octave in two lines of code
    ret=normrnd(1.08,0.1,100,100000);
    ann_retp=100*(prod(ret).^(1/100)-1);

  • 15 Delta Hedge June 19, 2025, 1:27 pm

    Hi @Alan S #14: great illustration of the random walk with an upward slope.

    As I understand it, your example 8% p.a. would correspond to the DMS 5% p.a. total real return to global equities since 1900 (allowing for exchanges which closed, like Russia from 1917 to 1992 and China from 1949 to 1990) plus 3% expected US CPI.

    If that’s right, is the (here 8% nominal) return not explicable (your numbered point 1) from an expectation of 2-3% p a. each for future equilibrium dividend yield (fully reinvested) and real global economic growth, plus 3% inflation?

    And the excess return from value, quality and momentum can then be explained from behavioural biases (investors chasing overpriced lottery ticket stocks; and from first under, and then over, reacting to news)?

    Granted low volatility remains a mystery.

  • 16 ChesterDog June 19, 2025, 4:18 pm

    Thank you, TA for that thorough dive into all of this.

    I’ve always had a little bit of a thing for momentum, caveat being the trading charges if attempting it the traditional way, of course.

    My portfolio actually consists almost entirely of a cheap global index etf, and a small amount in one each for momentum and quality. So it’s very interesting reading for me, even if – as has been ably flagged by Alan – the variations in returns might be really just noise.

    Nevertheless, those two ETFs (for completeness, I also have a similar proportion in gold, thanks to you) make life a little more interesting than just watching the meanderings of FWRG.

  • 17 The Accumulator June 19, 2025, 4:59 pm

    @Meany – “these articles are very keen on the idea that the best shot for the future is what worked best for the last 40/125/… years.”

    That’s not my position. I’ve consistently pushed back against relying on the notion that a thing that’s worked best for the past X years is your best bet for the forthcoming Y years.

    The historical record is interesting to me because if we’re faced with a hypothesis such as:

    “High book-to-market stocks beat the market”

    Or

    “Bonds improve portfolio volatility”

    Or

    “Stocks always produce a positive return beyond 20 years”

    Or whatever… then I think it’s useful to test how far that holds. Or if it’s true under certain conditions then when is it not true?

    I’ve personally learned a great deal from testing those claims.

    But the numbers in isolation mean very little to me if not accompanied by a rational hypothesis that can explain the phenomenon. I also like to see evidence that the hypothesis holds across different markets, different timeframes, and even asset classes.

    I also really want to understand the risks and who the strategy is appropriate for e.g. level of knowledge, capacity for risk, resources, level of safety net, time of life and so on.

    The lack of a strong inductive principle applies beyond investing, as I understand it – for example, in physics. This doesn’t seem weird to me. It reminds me we don’t know – perhaps can never know – all there is to know.

    I’m sorry if I’ve misunderstood your observations. I’m not confident I have followed your line of reasoning 🙂

    @ChesterDog – yes, good point – it’s something of a punt but, hell, sometimes you’ve just got to live a bit. I also can’t prove I’m not living in a computer simulation but I’m not going to worry I could be Crl-Alt-Deleted tomorrow.

  • 18 Sparschwein June 19, 2025, 6:53 pm

    As chemist-turned-biologist I’m far from a proper mathematical understanding. With investing I think it comes down to:
    – you can’t run any experiments to test a hypothesis
    – a myriad of variables, known and unknown
    – a small dataset even if the last 100 years are available (small relative to the complexity
    – economists will disagree on almost anything, to establishing cause-effect is hard
    So in a nutshell, the problem is economics isn’t a proper science 🙂 *

    *) just checking if my partner is secretly reading Monevator

  • 19 Al Cam June 19, 2025, 7:24 pm
  • 20 Howard June 19, 2025, 9:14 pm

    @TA #12: many thanks for clarifying re my #5 Qs.

    @Meany #13, Alan S #14 and Sparschwein #18: would it not be possible to test in and out of sample by splitting the 125 years and then do sensitivity analysis on every rolling 10,15, 20 etc periods (by tweaking parameters) within each? That should give you a standard deviation such that if you were getting IRL results 2 or 3 std dvs out then it would indicate excess returns are noise / result of overfitting. If not, then perhaps one could be a bit more confident in persistence (albeit market regimes change both cyclically and structurally).

  • 21 Meany June 19, 2025, 10:54 pm

    @TA
    >That’s not my position. I’ve consistently pushed back against relying on the >notion that a thing that’s worked best for the past X years is your best bet

    Well you do seem to be favouring mom+scv because (a) it has a strong history and (b) it came through the dotcom (which might have similarity to next year’s AI bust or whatever may come) quite well enough. So your argument does mostly seem to be of the as before / so again kind.

    We could try more of a confidence level / Kelly thing, maybe that’s where @Howard is aiming, like: given that mom+scv has returned 0.8% above the market (which is pushing a 7% outperformance in returns), how much of our pot do we allocate?

  • 22 The Accumulator June 20, 2025, 9:58 am

    I’m interested in momentum, SCV, and the other risk factors because I’d like to know if the academic research, which has been converted into retail investment products, has borne out.

    The reason the investment community at large is interested in the factors is because there’s evidence they can outperform the market, and because they may diversify your sources of return.

    If I was only interested in the thing that’s posted the best returns then, in this article, I’d focus purely on momentum and wouldn’t have bothered looking into low vol, SCV, divi growth etc.

    More generally I’d write endless articles about being 100% US stocks or Big Tech.

    I do like the sound of your ideas around confidence levels and how that might inform asset allocation (which has always felt a bit finger in the air to me). I’ve come across some material lately that made me think it’s possible for an ordinary investor to rustle up a simple risk parity approach. I’m sure it would be flawed but I’d like to look into what’s possible.

    If you can point me towards methods of calculating confidence levels that are simple enough for a layperson to understand (that’s me) then I’m happy to look into it. I’m sure there others who could do much more with that, but who knows, it might add a fresh dimension to Monevator.

  • 23 Alan S June 20, 2025, 10:38 am

    @DH (#15)

    The 8% I chose was arbitrary, but was me vaguely misremembering nominal geometric stock returns in the UK (actually closer to 9%, while arithmetic mean was 10.7%). At 10%, the standard deviation I chose was deliberately much less than for stocks (~20% for the UK).

    However, the point I was making was that if returns are random (which is debatable) and have a fixed underlying mean and standard deviation (whether this is true or not is also debatable) then measuring the mean of the distribution over a period of 100 years does not necessarily measure the true mean of the distribution with errors of about plus/minus 3 percentage points. Provided the assumptions hold, taking measurements over a longer period will increase the confidence in the meaasurement. Of course, the question can be reversed to ‘if I’ve measured a mean of 8%, what range of values could the true mean have?’ – without explicitly doing the calculation, my guess is that it is about the same, i.e., 3 percentage points or so. Note that for a shorter period of 40 years, the range of values is close to plus/minus 7 percentage points. In other words, the difference in returns between the factors over a 40 year period is likely to be much smaller than the statistical errors or confidence in such measurements.

    As for underlying mechanisms, I agree that there are qualitative mechanisms – the basic one being that the price, and returns are driven by supply and demand, i.e. if more people offer to buy than sell then the price goes up and if more people offer to sell than buy then the price goes down. That equation is driven by opportunity (people need spare money to buy) and sentiment (risk, FOMO, panic, response to news etc.). Trying to model those is difficult (at least for me) but there is a large body of published work out there (much of which is beyond my mathematical abilities/interest) – e.g., for the response to news see “The impact of news on measures of undiversifiable risk: evidence from the UK stock market” by Brooks and Henry (there is a downloadable version on the Reading University site) or “How much do UK market interest rates respond to macroeconomic data news?” on the Bank of England site. Of course, even if you can measure the impact of news, you’d then have to model the rate and magnitude of news. Psychohistory awaits!

    As for the effect of GDP, I note that the paper “Stock market returns and GDP growth” by Fichtner
    and Joebges suggests that “Despite strong theoretical arguments, econometric evidence for a long‐term relationship between stocks and real economic activity is mixed”. However, there is a world of published work in that area too!

    @Howard (#20)

    To take UK stocks since 1870, annualised real returns over 10 year rolling periods have ranged from -7.4% to 16.4% with a median of 5.8%, over 20 year periods from -1.3% to 13.6% with a median of 5.6%, and over 30 year periods from 1.1% to 10.5% with a median of 5.3%.

    Annualised returns can vary considerably between adjacent start years – e.g., the 30 year period starting in 1944 had an annualised return of about 5% while the 30 year period starting in 1945 had a return of just under 2% (the stock market crash of 1973 onwards being the cause). In other words, as is well known, start and end years are really important particularly with shorter intervals. For example, if the annualised return over 50 years has been 8.0%, if the stock market crashes by 50% in the following year, the annualised return then drops to about 6.4%.

  • 24 The Accumulator June 21, 2025, 4:11 pm

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