Annual Returns on Stock, T.Bonds and T.Bills: 1928 – Current | Hacker News Reader

Annual Returns on Stock, T.Bonds and T.Bills: 1928 – Current

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Do keep in mind that absolute returns are not the most important factor in investing. What you should care about are risk-adjusted returns of a particular asset, and return stability of your whole portfolio.

You can always use leverage to magnify the returns of any asset class up to whatever level you want. The only limiting factor there is risk and the cost of borrowing.

Before I learned about finance I thought that the purpose of diversification was safety. And it is, in part. But as a consequence of the AM-GM inequality [1], diversification actually increases your long-term returns. A returns stream of 8% every year will have substantially more money than a returns stream with a mean of 8%, that bounces up and down. If you play around with some numbers, you'll quickly see how profoundly important this fact is.

1. https://en.wikipedia.org/wiki/Inequality_of_arithmetic_and_g...

The arithmetic vs. geometric mean distinction is a good one to note. Since you mention risk-adjusted return, do you favor any particular approaches to optimization? ReSolve makes a pretty strong case for numerical optimization, summarized by this decision tree based on prior beliefs:

https://twitter.com/gestaltu/status/1044977487556595714

I generally prefer using something like scipy.minimize to maximize the expected sharpe ratio with returns de-magnified, which causes the optimization to be closer to a minimum variance portfolio.

Diversification only works under specific assumptions, it’s far from a universal benefit.

Low transaction fees being an obvious example. If moving from one asset category to another involved paying high taxes, it’s very rarely worth it.

Ya, there are lots of nuances to consider when rebalancing an existing portfolio. I'm mostly discussing the case of starting fresh.

I'd love to see a primer for leveraged diversification for people at the Bogleheads level. A lot of people are under the impression that a three-fund portfolio is the pinnacle of responsible self-investing, or a target-date retirement fund. But when I dig in I see people regularly make the point that that isn't true diversification, that asset class diversification isn't sufficient, that diversification is about measuring what investments move counter to each other in different macroeconomic environments, that leveraging is good, etc. I want to know more about how to apply all that when managing retirement funds at Fidelity or Vanguard, but I'm never going to work for a quant firm.

Check out portfoliocharts.com

Yes, that's right. What you want to do is maximize your sharpe ratio. You can play around with this python package to get a sense for how it works:

https://github.com/robertmartin8/PyPortfolioOpt

What you should be trying to achieve is a portfolio that earns the exact same return every single year, and you can do that in part by looking at historical covariance of the asset's time series. However, you also want to take a prospective view, and think about which asset classes may become correlated in the future.

There's no universal answer here (in the out of sample case - you can solve it in-sample), however. And another huge, huge factor is tax. Making sure your investments are tax-efficient is extremely important. Nothing will do more to ruin your compounding than taxes. So whatever you do, carefully consider the tax implications of your choices.

A lot of people focus on the tax rate. But what's actually quite a bit more important is the tax frequency. If you pay long term capital gains every two years on your whole portfolio...that's much worse than paying short term capital gains once at the very end (over a long period). What this means is that you want to choose things like passive ETFs, that are not taxed on their internal rebalancing. Even if you were to find a mutual fund that beat that ETF by 1% every year, the tax consequences of that fund would likely make it not worthwhile, before even considering the high fees it would likely charge you.

> What you should be trying to achieve is a portfolio that earns the exact same return every single year

Perhaps this is a dumb question, but wouldn't that mean that you end up with a 100% cash portfolio? After all, that portfolio has exactly the same nominal return every year: 0%.

I would expect that I have to choose a relative weight, to tune the trade-off between maximizing expected returns vs minimizing dispersion of returns.

edit: after reading a bit, it seems that changing this weight would trace out what is called the "efficient frontier".

Sorry, stable returns are not the only consideration. You want them to be as high as you can, while maintaining stability. There is obviously a tradeoff there, and yes, 'efficient frontier' is the term of art for choosing points along this optimal curve.

This is great, thanks. I have looked into maximizing the geometric mean before, similar to Kelly Criteria, but apparently that's a very volatile approach with a long timeframe before you have a high likelihood of approaching that maximization. I'll look more into Sharpe Ratio.

The general Bogle advice is for taxable accounts, pick something like a total us stock market index fund like FSKAX for fidelity. Low expense ratio, but you're right, it still has taxable long term capital gains and reinvestment every so often.

> A returns stream of 8% every year will have substantially more money than a returns stream with a mean of 8%, that bounces up and down.

Also why the US is so rich growing at ~2.5% every year without failure vs. e.g. $emerging_economy which can grow at 8.0% on average but with significant volatility

(I'm on mobile so the exact numbers above may vary but the point stands)

That's not entirely true, though. Their mean growth rate is much higher than ours.

> You can always use leverage to magnify the returns of any asset class up to whatever level you want. The only limiting factor there is risk and the cost of borrowing.

This is false. In order to maintain a constant amount of leverage, you need to buy and sell securities if your leverage isn't unity. With increasing leverage, as security prices increase, you need to buy securities as your position earns a better return than the underlying. Conversely, you need to sell securities as prices fall. Together, this reduces your overall return via volatility drag.

The Kelly Criterion has the math for the absolute max return you can get via levering up assets.

> This is false. In order to maintain a constant amount of leverage, you need to buy and sell securities if your leverage isn't unity. With increasing leverage, as security prices increase, you need to buy securities as your position earns a better return than the underlying. Conversely, you need to sell securities as prices fall. Together, this reduces your overall return via volatility drag.

Ya sure that's true if you want to maintain constant leverage, there are tradeoffs there.

> The Kelly Criterion has the math for the absolute max return you can get via levering up assets.

Not exactly. The Kelly Criterion is the maximum that you should lever, over all the probability-weighted paths the portfolio will take to maximize log(wealth). However, nobody actually uses full Kelly leverage, because of estimation/fit error. One third or so of Kelly leverage is more common.

Interesting that for the 2007 financial crisis, you only had to wait until early 2012 to make up your loses.

Even for the crash of the early 1930's, after 8 years you were back to where you were.

That would be the massive amount of QE & money injected into the system. I doubt next recession it will be so simple to sell the bonds we need to to run a massive QU campaign again

Hasn't the Fed mostly rollbed back the QE by selling off the assets they bought?

Looking at Fed total assets [0], the Fed's sold off only a fraction of what it took on during the crisis and QE.

[0] Fed total assets from FRED: https://fred.stlouisfed.org/series/WALCL

Wow, no kidding. I wonder how the mix has changed? Obviously I was wondering about overall going down, but I seem to recall there being like a change of short for long term assets or something?

The fed purchased long term assets like mortgage backed securities to provide liquidity and relief to corporations that held too much bad debt on their balance sheets. This provided immediate relief for distressed institutions.

The fed also expanded the balance sheet by selling long term bonds, which offered relatively lower rates in comparison to short term notes and bills, this provided the cash infusion needed for QE to stimulate the economy.

The fed’s balance sheet went from roughly 4 t down to I think ? 3.5 T and now it’s ramping up again at the top of cycle + lending hundreds of billions a month to banks in the repo markets. Given the pace we’re going at now I doubt we’ll be able to sustain the pace in a recession

That discounts businesses that collapse entirely, or under-preform enough to exit the index market. Indexes are misleading because they have a strong survivor bias. Stocks that slipped out of the S&P 500 entirely no longer register, but the money you had in them sure does.

https://seekingalpha.com/article/207935-is-there-survivorshi...

I'd like to see the S&P performance of then current index stocks over the same time period, im guessing it would be significantly worse.

What happens to your money if you invest in an index fund and companies drop out of the index?

When a company drops out of the index, the fund sells all its shares in it and buys shares of the new company that took its place.

But it should be said that the price that the fund manages to sell the shares at could be far lower than the price at the time the company exited the index since many funds and others will be trying to get out at the same time.

So wait, is throwaway2048 correct that this type of analysis misses companies who dropped out? Or are the gross return numbers including selling the shares of 'leaving the index' companies at a loss? I would imagine the latter and so his point is wrong, but I'm open to being corrected

Are you saying that there is a huge untapped arbitrage opportunity?

Nope, just that even if you do have data that captures when and at what price a company exited an index, you still wouldn't quite be able to work back to the performance of a tracking index fund (because you don't when and what price the index fund sold)

The fund rebalances regularly. Before the company is dropped out its value will have dropped, of course, causing the entire fund to drop proportionally in value.

Index funds typically rebalance quarterly, I believe. The index also rebalances, usually called reconstitution [1]; the Russell indexes rebalance yearly, for example.

Which means there can be a discrepancy between the fund and the index at any given time. This can result in arbitrage opportunities, I believe.

Interestingly, the selling and purchasing involved in adding or removing a stock from an index/fund also has an effect on the market [2].

[1] https://www.investopedia.com/terms/r/reconstitution.asp

[2] https://www.cxoadvisory.com/miscellaneous/strategies-for-exp...

The broad index funds (VTI, Russel) are indexed to market cap, so when individual stock prices change, it stays balanced or very close to it.

When a fund rebalances, it has tax consequences, so funds are incentivized not to do it.

Keep in mind that these are cherry-picked, they only include American returns. The 20th century was an exceptional one for the United States. The 21st century may also be, but you should definitely be diversifying globally.

The worst case return definitely isn't on this list, it's the returns from 1914 Germany, which didn't break even until 2014...

Definitely. Having said that very few countries have an advanced financial system. Probably a handful of cities globally, and even then some like Singapore or HK werent a thing 100 years ago.

But about that whole Germany thing, they did kinda, sorta, really screwed the pooch on that one by starting 2 world wars. Maybe they kinda, sorta, you know...had it coming.

Now the fun part. Pick any 30 year period, and you will beat inflation with stocks. Even if you get in at a peak, 30 years later, you will be well ahead.

This happened for one 100 year period when the world grew from 2bn to 7bn. Good luck in the next 30

You think we're at market top for the next 30 years? Inflation adjusted?

It would have been great if someone could have also added REITs. The argument I always hear is real estate vs the stock market.

Real estate is tricky because you're usually gambling with someone else's money (ie a mortgage) and your access to that is dependent on many factors like provable income and credit rating.

He said REITs- ones' personal income and credit rating is not relevant

You're right, he did, but "the argument I always hear is real estate vs the stock market" doesn't make me think REIT, it makes me think of a renter considering buying a house as an investment.

The San Francisco FED made a similar analysis, including housing: https://www.frbsf.org/economic-research/files/wp2017-25.pdf

Last weekend I built an S&P returns calculator that exposes similar statistics and adjusts for inflation.

Accounting for inflation reduces the ROI by an order of magnitude, but the result is still impressive! (36,560.12% return)

https://www.in2013dollars.com/us/stocks/s-p-500/1928

The bar plot below "Here's the rate of gains and loss by month, including dividends" has the y-axis off by 100x (i.e. 0.2% instead of 20%).

Thanks. Decimal conversion issue!

I recommend you download the spreadsheet, it can be really helpful in doing the 'null' hypothesis in financial analysis. I always like to compare my choices in investments versus the 'stick it into SPX500 ETFs' as the alternative. To do that you need to collect all this data, which is doable, but hey here they have it all in a nice package.

I'm curious -- what does HN think of factor investing [0]? It has been shown over long periods of time to outperform the total market, and has seen many new ETFs available. Does anyone here tilt towards small cap value? Do you think those effects will last, now that they're more widely known, or are the last 15 years evidence of them weakening? I've been looking into investing but I'm probably going with a total world stock market. Part of the reason I find those ETFs less attractive are the higher associated fees as well as the more "active" look. I have trouble believing anyone who claims there is a way to consistently outperform the market while charging me for it.

[0] https://www.investopedia.com/terms/f/factor-investing.asp

Which 30 year period you get to live and work in is what matters most, and the timing of the bad years. Which is why I recommend this calculator: https://firecalc.com/.

I'd love to see this plugged in to a tool that asks 1) What allocation percentage of stocks/bonds do you want, 2) What length of period in years (i.e. 20 years, 40 years), 3) What confidence level (50%, 75%, 90%) and yields what APY you can expect. (The higher the confidence, the lower the APY.)

I'm still convinced that the general advice out there is highly out of whack, and that someone's expected returns should be very low. I'm currently modeling under 2% (post-inflation, more like 4% with) for the future, for a simple allocation model and a 10-year window.

I like to use Portfolio Visualizer for that sort of thing:

https://www.portfoliovisualizer.com/monte-carlo-simulation

Given the bulk of a median American household's wealth is tied to the equity of their primary residence, it would be interesting to see how these returns stack an investment in a single family residential home.

I imagine it would be difficult to parse out home improvements and so forth, but it would be a comparison that more people to could relate to given the average person doesn't buy T-bills and such.

Here’s a quickie (linear/log) line chart of the data in this table:

https://observablehq.com/@jashkenas/annual-returns-on-stocks...

I'm interested in how they're pricing the S&P 500 before it existed.

Yes, you could just say, "the biggest 500 public companies in the US" -- but it's a little more nuanced than that, so it'd be interesting to see how it's calculated.

So a $100 investment in an S&P 500 equivalent (not yet an established index) on January 1st 1928 would be worth $382,850 by January 1st 2019? That's over a 250x return after adjusting for inflation, pretty neat.

Well of course... no one cares about inflated stocks it seems.

For those curious, it's about a 9.49% annualized rate of return over the last 91 years.

With maybe the note that $100 in 1928 was worth quite a bit...

I am drifting into another point entirely and your point still stands.

Looks like back then most people made $.40-$.60 an hour, so figure $900 a year?

That's a 91 year time period, if you were patient enough to wait that long to enjoy the return on investment you'd probably be dead.

Wait! These figures are not inflation adjusted. Inflation has been about 15X since 1928. So, the $382,000 shown on the chart for 2018 is now worth about $26,000 in 1928 dollars, against $143 value sometime in 1928. That is, in constant dollars, about 180 x over 90 years, not a bad return on investment, but, not what's shown on this chart!

However, if you start your comparison with 1932 instead, market average value has increased from about $50 into about $26000, or 520 times return over investment over 86 years, a dramatically better result! Illustrating the second most basic rule of investing: buy low.

Consider, if you'd invested in a market fund in 1999 instead, you'd have turned $156,000 into about $253,000 (inflation adjusted) or a gain of about (uh-oh) much less than 2x over almost 20 years. In other words, ROI of much less than 10% per year. Investments not so good in this century, even with the huge stock market run-up of the past few years!

Just for comparison, a plumber in the US seems to have made about $1.25 an hour or so in 1928, compared to about $27 an hour in 1998 (according to BLS). In constant dollars, wages seem to have less than doubled. So, long term, investors did much, much better than workers, that's for sure!

And since 1997 plumbers have just kept up with inflation, according to BLS (going from $17.50 an hour in 1997 to to $27 an hour in 2019 -- equivalent to $17.50 in 1997 dollars).

So, big news. Invested capital has increased much faster than compensation of labor in the US, both long and short term. Well, if you think plumbers are typical.

Obviously in the past 20 years, hacker pay has done much better than plumber pay! In fact, hacker pay has increased much more than return on investment! Does this mean, capitalists should fight for lower hacker wages? Or does it mean, we have met the enemy and it is us? Only time will tell...

The volatility of equities in the 1928-1942 period is crazy.

Yeah, but given the historical contex it's understandable if not expected. It's the great crisis (probably including it's preludium) untill 2nd WW situation clarified.

Why is the volatility so high only recently on the 10 year note.

e.g. historically it only fluctuated low single digits, while stocks have always had large volatility ranges.

Possibly due to the weird interest rates in the last 10 years? I think T-Bond pricing will vary based on interest rates, like if the interest rate has declined since you bought your bond it will be worth more iirc, so the weird interest rates market recently could have an outsized effect here?

I wish they'd say what "Stocks" means. Is it the entire market? On which exchanges?

This is a relevant read: https://www.investopedia.com/terms/s/survivorshipbias.asp

The very leftmost column of the table has the heading 'S&P 500 (includes dividends)', so I assume that's the meaning of 'stocks' in the other columns. If not, that would be very misleading.

I think it's worth noting that S&P 500 index funds didn't exist until the 70s. You'd be spending a lot of time and money to approximate it before that.

The S&P 500 just tracks the largest 500 publicly traded companies. So no, it's not difficult to approximate.

You need to pay commission and spread every time you rebalance your portfolio (daily, if you copy the frequency of modern funds)

So at the £5ish/trade of my current broker, that's a cool £912500/year on just commission.

For some reason the massively reduced ease of entry to a trading strategy like this is never considered when lauding its historical performance.

> daily, if you copy the frequency of modern funds

Modern S&P500 funds like SPY or VOO rebalance quarterly FYI

Yeah I'd like to see too if you were Russian, Japanese or Argentinian for example what the returns would have been. I doubt the stock market would have been so kind.

No matter where you live you can usually diversify to global stocks.

Is this adjusted for inflation?

FYI, stocks show CAGR of 9.59%.

The way to play treasuries are in massive highly leveraged carry trades. They're not for actually holding, unless you are starting with $100,000,000* in capital.

*This amount is tied to how much you want to make a year based on the treasury bond's interest rate. This will always be lower than inflation.

> The way to play treasuries are in massive highly leveraged carry trades.

Isn't that how you lose all your money when e.g. the Fed lowers interest rates?

I guess hint was in the word "play", hehe

Take the other side, hedge the bet, enter, exit, this is the most liquid market in the world.

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