Here’s a familiar picture. This is the stock market the past 40 years.

Look how happy someone would have been if they had put all their wealth into the stock market in 1985, and then just kept it there! They would have 30× as much today! As with planting a tree, if the best time to do it was 1985, maybe the next best time is today. Clearly, we should put all our wealth into the stock market and leave it there. Or should we?

But wait: inflation. The darker line in the plot below is the actual inflation-adjusted money our savvy 1985 investor would end up with.1¹ Note that when adjusting for inflation, the stock market did not recover from the dotcom bubble in the 2000s until around 2015!

Not as hot. There’s one more catch still, although a smaller one: holding an entire stock market index is not free.

Back in 1985, we couldn’t just buy an etf – we had to buy and sell the individual stocks that made up that index in order to track it – and retail trading was expensive back then. Today, we have cheap etf​s. Let’s pretend we could hold a stock index for modern low costs also back in 1985. The following plot shows inflation-adjusted index returns compared to the actual returns one would get after initial and holding costs, including tax.2² Costs are modeled on what I experience here in Sweden: the holding costs break down into a rather low annual tax rate of 0.25 % on the total portfolio value – roughly speaking – and management-plus-trading costs of 0.3 %. Initial costs are a minimum commission of $1 and then 0.25 % of the transaction, plus half of an 0.2 % spread for a highly liquid instrument.

This does reduce the gains slightly further, but not so bad. We are not, however, ready to conclude that we should put it all into the stock market. The plot shows a timeline of 40 years – is this really our investment horizon? Most people have a significantly shorter horizon, for example because they’ll want to make a big purchase (house, car, boat, etc.) For the sake of argument, let’s say we might end up needing a significant chunk of our savings five years from now. (This does not change the main conclusions of the article, but the effect will be more pronounced.)

To simulate what can happen on the stock market in half a decade, we’ll draw ten random blocks of six months from the actual post-cost returns.

Okay, not great, but at least we didn’t lose much money, right? What if the future turns out different?

Oh, I like the look of that! Let’s see another future.

Oops. I guess we should have sold off our portfolio back in 2026. We can look at more plots, but it’s more instructive to see a histogram of a large number of possible outcomes.

Amazing! Half the time, we end up with more than +25 % return – the median return is around 6 % per year.3³ The stock market is often quoted as returning 8 % per year, but this is a mistaken calculation for several reasons: it is computed pre-cost, without adjusting for inflation, and it’s taking the arithmetic mean, which is not indicative of what one actually gets with compounding. Then again, around 7 % of the time, we end up with more than a -25 % drawdown. A -25 % drawdown shouldn’t be catastrophic to our life plans, but it comes with a hidden cost due to how money compounds: a -25 % drawdown needs a +33 % gain to recover.

How much an investment wobbles on its way up is known as its volatility. Finance people like to compare how much an investment goes up to its volatility, and this is known as risk-adjusted return. A common measure of risk-adjusted return is the Sharpe ratio, which is the median yearly return divided by the standard deviation of yearly return.4⁴ The Sharpe ratio may not be a great way to measure risk-adjusted return for several reasons (assumes finite variance, symmetric distribution, etc.) but it’s popular enough that it seems to be the way most people think about risk-adjusted return.

The cyborgs among my readers will have already computed the Sharpe ratio of stocks in the data above: 0.62 for the non-adjusted returns, and 0.41 for the post-cost, inflation adjusted returns. These numbers are unrealistic for two reasons:

• First off, the stock market has done unusually well the past forty years. Maybe that will continue for the next forty years, maybe it will not. I don’t know anyone who can tell with any certainty.5⁵ I find it sad when websites aimed at retail investors parade a Sharpe ratio of >2 for whatever equity etf they are peddling – and then explain that it’s calculated just over the past year. That’s a meaningless number. Talk about driving on the highway by looking at the centreline in the rear view mirror.
• Second, this is out of line with the risk-adjusted returns from other investments. We would expect, based on what we know about financial markets, that most widely available investments should have roughly the same risk-adjusted return over the long run.6⁶ Otherwise they would attract investors until their risk-adjusted return is down to the level of everything else.

Both of these arguments point toward a more realistic estimate of the Sharpe ratio of the stock market, which is somewhere around 0.25. If we adjust our model of stock returns to match this more realistic Sharpe ratio, and generate new five-year returns, we get this distribution.

The median return is still in the neighbourhood of 6 %, but under the assumptions that markets are somewhat efficient, there’s now a whopping 16 % risk that we end up with a -25 % drawdown. To reiterate, this is after five years, not just one year. Imagine saving your hard-earned money for five years and then seeing you still have less than you started out with!

So while yes, stocks do go up, they are also risky. Relative to their risk, stocks go up just as much as everything else.

Bonds issued by a government with good credit scores, for example, have a much more modest yearly net return of around 1 %, but their lower volatility means their risk-adjusted return – their Sharpe ratio – is still in the same neighbourhood of 0.25. In fact, the difference between the Sharpe ratio between stocks and bonds7⁷ Using the original stock performance data – not the adjusted one. has the following distribution.

We don’t need any sophisticated mathematical testing to see that this is not statistically different from zero. Relative to their risk, stocks do not go up more than bonds, and this holds true for any other widely available investment.

This might seem like bad news – if stocks don’t go up more than anything else, relative to risk, then what’s the point? But it is also good news: diversification is the name of the game. The way to ensure maximum growth is to include multiple asset classes in the portfolio.8⁸ Note that for diversification to work, correlations must be relatively low. Including 300 stocks in a portfolio does not make it diversified, but a single instrument from ech of 2–3 different asset classes does. A diversified portfolio goes up. A pure stock portfolio, yeah but also no.

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This article obviously skips over a lot of technical details and lacks in motivation for some assumptions. I have started reading about this again and hope to write more about it as time permits. The main thrust of this article depends on two big assumptions:

1. The market invests so as to, on the whole, balance out the risk-adjusted return of popular instruments. We cannot predict future returns better than the market.
2. We reinvest our winnings, i.e. the Kelly criterion applies.

Some readers might read all of the above and think, quite reasonably,

Screw this, I think 0.25 is the wrong Sharpe ratio to expect for the next decade of the stock market. Clearly stocks are better than bonds. Just look at their returns!

Such a reader might be right – we’ll find out 10 years from now. But investment should not be about guessing futures and getting a lucky big success. Sound investment is about making allocations that have the greatest chance of moderate success, because this is what will compound over time.

In that light, we may need a reminder of one of the consequences of the Kelly criterion: making the mistake of underestimating volatility is more dangerous than overestimating it. Overestimating volatility results in a healthy, fractional Kelly bet; underestimating volatility results in overbetting.

In relation to this, someone on the internet wrote that

Oh, I’ve had my portfolio drop 90% once. And drop 50% at other times, and 30% drops. It’s not easy to suppress the panic.

They sound proud over being able to suppress the panic, but a 50 % or 90 % drawdown should trigger a full-on panic, because it means one has been overbetting (taking on too much volatility relative to wealth), and continuing along the same policy, one will eventually go broke.