Getting average returns right - The Merchant of St Petersburg

Many, even those that think they know mathematics, will do this simple but misleading mistake.

We've even seen experienced investment people getting this wrong.

The mistake of mixing up what kind of average to use. 

If you're interested in estimating growth, historical growth, comparing performance of different strategies (and we all are interested in those things) - then avoiding this mistake become supremely important.

Let's go through three examples: The Merchant of St Petersburg, Chekov's gun (an easy example), and an Investment Portfolio. 

We will see that the arithmetic average is misleading for evaluating an investment, and yet, this is a prevalent measure that is commonly presented with investment advice, and as we will see, the arithmetic average brushes risk under the carpet of miscalculation.

1.  Slightly trickier example: The Merchant of St Petersburg

A paradox borrowed from Mark Spitznagel that in turned borrowed the example from Daniel Bernoulli.

Here's an adapted version of Bernoulli's paradox.

A 18th century merchant wants to ship merchandise from Amsterdam to St Petersburg, over a pirate-infested Baltic sea. 

Wrong century, but still seems looks like a very savvy merchant. 
Jan Gossaert, Portrait of a Merchant, c. 1530

Our merchant has 11 000 florins, buys merchandise and pays shipment costs for 8000 florins, and sell the merchandise in St Petersburg for 13000 florins, making a 18% gain on the trade.

Unfortunately, every 20 ship is lost to pirates, which means that all the invested 8000 florins are lost, and the merchant is left with 3000 florins. Our merchant makes a -73% loss. So, there is a 95% possibility of making a 18% gain, and a 5% risk of making a 73% loss.

The arithmetic average of this trade would be 95% * 18% + 5% * (-73%) = 13.45%

But pirates are frustrating. Is there a way to get around these infrequent setbacks? The Merchant ponders his options, and finds an insurance company that can insure his cargo for 800 florins.

This would change his expected gain to only 12200 florins each time the ship arrives in St Petersburg, changing the profit to only 10.9%. When the ship is captured by pirates, he only loses his insurance money, that is, 800 florins, which, on that trade, limit the loss to 7,3% instead of 73%.

Let's do the arithmetic average once more: 95% * 10,9% + 5% * (-7.3%) = 9,9%

So the expected average outcome is lower than going without the insurance. 

What should our rational merchant do? 

The insurance seems expensive, but is it really?

The crux here is that one can't add percentages. A loss of -10% is not the same as a win of +10%. It's not meaningful to add them together. What our Merchant is really after is how his wealth is expected to grow.

So if he does the trade between Amsterdam and St Petersburg a hundred times, reinvesting what he earned, he could expect, without insurance, a growth of 1.18 of his wealth if the ship arrives, and otherwise a setback to only 0.27 (=100%-73%) of what his wealth was when he sent that unfortunate shipment.

To evaluate the uninsured case then, we need to look the trade occuring again and again, multiplying the trade to the power of 95, and the negative pirate-outcome to the power of 5: 1.18^95 * 0.27^5, which corresponds to a growth of 9674 times his initial investment after 100 shiptments. 

As this corresponds to 100 times the trip, we need to take the 100th root out of 9674 to see what it would correspond to as growth per shipment if there were no pirates. The 100th root of of 9674 is 1.096, which is called an geometric (not arithmetic) average, which is then 9.6% per shipment.

This is clearly lower than the initial 13.45% we calculated!  

There's something going on here!

If we evaluate the insured case, the return is 1.109 in the 95 shipments when things go well, and 0.927 in the 5 shipments when things go bad. So his wealth will increase with 12498 after 100 shipments, corresponding to an expected 9.99% growth per trade (close, but not exact to the arithmetic average). 

That's a 30% higher return in the end for our Merchant. 

So our Merchant will be a lot more wealth over time with the insured alternative, in stark contrast to the first simplistic calculation using averages as we learned to calculate them in, well, kindergarden? 

It seems that, especially for large losses, the arithmetic average gets things dangerously wrong and underestimate the risks. 

Interesting. 

2. Easy example: Chekov's gun

Another example.

Three russian frenemies, Alexei, Boris and Chekov, play russian roulette (with a three barrel gun, to make it simpler). They all put 100 roubles on the table, and after the game, Chekov ends up dead. 

Their average outcome on the investment of this would be (+50% + 50% - 100% ) / 3 = 0 %

A zero sum game when it comes to wealth distribution, so no surprises so far. 

So there would be, on average, no expected change in wealth playing this game, but would Chekov agree? 

Let's look close at what happens. 

Once again the arithmetic average shows up. As in our Merchant example, it assumes - almost always erroneously for the kind of questions that we want to study - that units can be compared one-per-one, that is that 1% up is the same as 1% down, so they can be added together and divided to create an average.

But of course, that is not the case, especially not for our frenemy Chekov. He will suffer an even more dire fate than our Merchant from St Petersburg.

Because what he, Alexei and Boris have in common, is that they are interested in the growth of their investment (and perhaps the sudden exit of one of their competitors). 

So, what is interesting for the individual is the growth one can expect from playing the game, and especially playing the game several times. 

Let's say that Chekov, while still alive, decides to play the game three times, always with three players that always match what Chekov puts on the table, and, unfortunately, our friend Chekov dies the third time he pulls the trigger.

His growth will be: 150% the first game, then 150% the second game, and 0% the fatal final round. He's wiped out.

So the growth of his investment here would be 1.5 * 1.5 * 0 = 0, with a complete loss of wealth and no possibility to rejoin the game. 

The total expected growth to do Chekov's little game would thus be 0, even if he earns 50% on the first two games.  

The worse the outcome of a single game, the more misleading the arithmetic average becomes.

3. Stock market example

A final example. 

Let's take the US stock index for the years 1970 - 2022. The arithmetic, inflation adjusted average, is around 7.5% - a number that we have seen many times, and that is being touted as the expected inflation adjusted return from the US stock market. 

This inflation adjusted expected average of 7.5%, we're sorry to say, is wrong.

As we see above, it's really growth we are concerned with, and the geometric inflation adjusted average is only 6% of the US stock market. So if one invested those 52 years, one would earn 6% per year, on average, known as the cumulative average growth rate (shorted CAGR) - inflation adjusted.

It's just harder to get up when one has been fallen down, and this is more accurately reflected in the geometric average.

The very common number that is floated around is unfortunately wrong, if one wants to stay invested over time and consider one's growth.

Growth is hard. 

Can we hedge?

Yes. We can hedge. If one mixes 20% gold into the mix and rebalance annually, we actually - and very counterintuitively from most investment advice out there, get 6.3% geometric average return.

So actually slightly better, and this is more astonishing and counterintuitive than one might think. 

And we probably sleep better, because the swings are smaller with this 80/20 portfolio.

So adding gold doesn't cost us as the common thinking might have it - it has actually given us a higher return - just like the insurance for the St Petersburg Merchant above.

We earn more money over time. There's no other way to put it. 

Another way to hedge is using options, though this requires serious expertise. Options can give insurance that is quite similar to our Merchant of St Petersburg above. If we buy an option that costs us 2% of our capital each year, but has a payoff that offset the loss each time the loss is more than 15%, we get a geometric average return of 7.3% for those 52 years. 

There are actually ways to hedge an investment, that makes it less volatile, and gives it higher return over time. 

What's going on?

There are three common ways to calculate means. 

Arithmetic, geometric and harmonic.

Arithmetic concerns what can be added and subtracted linearly (such as adding or removing apples in the shopping cart), geometric concerns growth, and harmonic concerns velocity. 

For any given set of changes, the arithmetic average will be the highest, the harmonic the lowest, and the geometric will be in between. 

Almost everywhere we look we see how this is presented wrong when we see assumptions on return. 

We are concerned with growth, not apples and oranges.

This has misleading consequences when making assumptions about the performance of different portfolios, the true cost and impact of downswings and risk, and what numbers people unfortunately put in when trying to calculate different "rich-by-Excel"-numbers, and misleadingly indicates especially high volatility or large drawdowns as less dangerous than they are. 

Geometric averages more correctly assess the impact of growth.

And the risk of ruin and the impact of large drawdowns are very dangerous risks with big impacts, that the arithmetic average gets very wrong as we saw with our friend Chekov and Merchant above.

Still, one should not only rely on geometric averages. 

One still need to be prepared for the black swans, ergodicity - ensuring that one can live through and recover also from the very bad scenarios - and understand that a close shave with an absorbing barrier is more common, likely to hit at some point during a lifetime, and hard to get out of. 

Never put your life savings at unacceptable risk, thinking that the barrell will always be empty when  playing russian roulette.

Remove hope out of the equation. Look at scenarios. Simulate. Be careful when seeing an average being presented. What will happen in the worst and the bleak scenario. Do you get stuck in an absorbing barrier?

And will you be able to get up again? 

Farewell,

//antinous&lucilius

Cash - The Strangest Asset Class

As we write this, inflation sores, markets tank, even hedges against inflation such as gold stay back.

We see our savings slashed as measured in euros and dollars, 

Day-to-day prices fall and fall.

Yet. There is one asset that behaves strangely. 

If another asset is down 50%, that means that cash is up 200% compared to that asset. 

 Le Radeau de La Méduse, sailing through strange waters
(Théodore Géricault, 1819)

And suddenly, cash - a perfect hedge when markets plummet - step out of the shadows with a quite impressive value explosion. 

Even when inflation rages through the economy.

These are months for cash.

How do you measure your wealth?

Farewell

//antinous&lucilius

Other Asset Classes, and a Fun Sex-life

Where might conventions limit us?

What is there, that we might not see or understand, because we stay limited in our thinking? 

For those with a more open mind there are deeper ideas to explore. 

'Scandalous' but beautiful, reminding us that there is more to this world than just convention
(The Warren Cup, 5-15 AD)

Like the conventional stock market and the stock-picking, there are more, broad and well-acknowledged asset classes, but they are out of the main stream and probably nothing you will hear of if you only attend a conservative congregation.

So of course this is taking things a little over the top. But being gay we sometimes marvel how purple around us seem to be locked in conventional thinking in not only who you could live and have fun with in bed, but also do much more; as if there's an built in value to studying conventional.

When you're not so straight at all, one really needs to consider that what's normal might not be what's good for you.

Who knows, other ways might be something to consider.

And with finance, the real beauty is that we can bet on all at the same time. 

Let's consider some alternatives.

Long term government bonds.

Long term bonds are bonds that promise a fixed payment far off into the future, as far as 25 years from now. 

The price today is the market's valuation of what that future promise is worth today. 

That means that the value of a long term bond today contains the markets consensus of long-term expectations on inflation, monetary policy and interest.

Small changes in those expectations has a large impact on the current price of the bond.

Why do we prefer government bonds? Well, because governments - and we're talking governments from stable countries here - are rather reliable when it comes to paying back their debts. At least, they own the money printing press. 

And hence, the price of bonds are dictated by something very different than stocks.

It's a hedge out of the conventional.

Cash.

Cash? Can that be an asset class? 

Yes. But many are blind to cash as an asset class, because of convention; almost an illusion - that keeps it the asset characteristics of cash out of sight. 

Let's make a thought experiment to see the blind spot.

We usually measure wealth in a currency, that is, as if it was cash. 

And so, when the portfolio drops in value, we have a hard time to see the situation from the other way around.

The drop of value in prices is exactly the same thing as the cash increasing in value.

Stocks falling 50%? That's one perspective. 

Another perspective is that cash just increased 200% in value against stocks. 80% drop in the stock market? Or was it the other way around, and cash just increased 500%?

What about an option that is guaranteed to raise 500% in value if the stock market drops 80%? An asset that is guaranteed by the money printing press. And an asset that will be lovely to go on a shopping spree with when prices are low. 

Don't underestimate the value of cash as an asset. Available cash when there is blood on the streets will build a vast fortune. 

Gold

Why does governments keep gold in their reserves? 

Gold is a value storage through space and time. 

It keeps a piece of the long-term increase of value and production of all humanity, and it's much independent on political whims, short term booms and busts of stocks and unreliable monetary policy. It's even anonymous, if it is melted down.

And we know that we will always keep a reliably exchangeable piece of value with gold, and, when political turmoil and trust in the economy is low, it's more than unlikely that gold will have lost its value - quite the opposite, in most cases - and we will be in for a good deal. 

The states know this. 

When trust is low, gold might still trade.

Bet on everything: The Art of Re-Balancing.

As with all good things, there is balance to be found.

By doing a little bit of all, one also always have what the market wants. 

Are you into Gold? We've got gold aplenty. Cash? A credit crunch and you need a bail out? We got you covered, just hand us some of those stocks in exchange.

Are you crazy about stocks? We've earned a lot while the markets went up and you realized you want some of the fever. We will sell of ours to you.

By knowing more asset classes than the most common kind of love, we're on a sure, steady spiral upwards.

For a better experience: mix it up

And just like life might be better by broadening the perspectives; the financial life might benefit, even find a new stability and security, if one mix in more dimensions.

Farewell,

//lucilius&antinous

More to read:

- What is asset allocation? Some thoughts here: How we dared to start investing

- Our thoughts on portfolios.

Why stock index investing is probably wrong for you

Stock index investing is a common recommendation on the journey to financial freedom.

And sure, it looks like there could seemingly be advantages to stock index investing. 

Are we sure which chimpanzee is picking the stocks here?

In stock index investing, there is no smartassing around with what stocks should be in the index. 

Hence, a stock index is less risky than certain other high-risk-behaviors, such as running around in a cage of chimpanzees armed with guns, sky diving in a squirrel suit, picking stocks, etc.

An index has the advantage that we don't need to bring our small and far too proud and easily tricked brains into how to pick out individual stocks. No guns, no squirrel-suits, no fragile ego complex in the equation.

Just a mathematical, simple rule, behind the index.

That's good, in the exceedingly likely event that we do something stupid when we try to 'think'.

Another important advantage: it's easy to start investing in a stock index. 

Investing in an index can very easily be set up to be automatic. 

Yet, does that automatically make the index the right choice for you?

Obviously, index investing is - over the very, very long time - probably better than not investing (but that's not entirely true, as we will see below, and that's a helluva important nuance). 

"It's better to start early" as they say.  "Good for you that you are still young if something happens", is what they actually mean.

Why stock index investing is not good for you

So one way or the other, we're talking about our life's savings.

Even if it takes a few hours more of effort, we think that given all the tens of thousands of hours one has potentially spent earning one's life savings, one might be able to stomach a few more hours to understand some more nuances than just blindly following the stock index investing-recommendation.

Let's say that we're not complete investing newbies and have understood that we need to invest, and that it's better to avoid the squirrel suit-bunch and chimpanzees with guns, yet we're still ready to spend some hours to think a little deeper, after all. 

So is there something hiding immediately beyond stock index investing? Is the recomendation, well, really good?

Let's start with what "good" could mean.  

Good could mean 'good' as in efficient; as in there is no other obvious alternative that, with reasonable ease, provides a better price for the risk one is taking on. 

Unfortunately, it doesn't seem that stock index investing is efficient; however we measure risk, as long as we stay within some minimal boundaries of what 'rational' can mean; there are simple yet better variants. 

Here's a trivial example: balancing in just 20% of a very different asset class (we propose gold) makes the resulting two-asset portfolios much, much less volatile. 

And that has a tremendous impact. Less volatility means a higher probability to reach the destination in a comfortable time even in a bleak scenario. Less volatility means a higher safe withdrawal rate when living off one's investments, which directly translates into higher material standard. 

Less volatility means sleeping better at night.

Why wouldn't one go with that?

Well, you're right. Why wouldn't one. 

A rule such as the 80/20-split is so simple that one can easily stay rule-based, applying yearly rebalancing back to the asset split. Such a rule is so straightforward that only someone with severe cognitive deficits would say that the the portfolio suggested above is not, to the minimally interested investor, just as trivial as investing in an index. 

There are other alternatives; investigate and find a composition that suits you, instead of assuming the one-size-fits-all-recommendation of pure stock index investing.

A quick summary from previous articles here on the blog:

• Stock index investing can have up towards the double time needed to recover back to +/-0 (often more than 10 years) than a simple modification with another asset class. 
• A stock index is a very dangerous place to be. 10+ years of severe underperformance is common. Life is long enough for most of us, and everything that can happen should be assumed to happen during our investment lives.
• Even worse: catastrophic setbacks of 20+-25 years have happened in recorded history. What, then, promises that such setbacks, or worse, might not happen again in our lifetimes? 
• Because of the risk of decade-long setbacks, one is much more likely to try to time the market with stock index investing even if one is 'supposed' not to. This will destroy the average return that was the motivation in the first place.
• One doesn't get fair compensation of a better average return for the wild swings of a stock index compared to easy adjustments to a much safer portfolio. 

Let's leave the serious reservation concerning the lack of efficiency with that. Because that's not the most important objection.

Most importantly: where are we in the assumption?

We're concerned if one doesn't feel that one shouldn't even consider one's own risk tolerance when investing one's life savings. 

Serious downside protection is very cheap, like house insurance. 

One-size-fits-all is a non-sequitur; a deceptive misuse of logic. The conclusion (that it's right for us) don't follow on the premise (that stock index investing is easy and hopefully gives some kind of average return after a few decades).  

Yes, a stock index buys a certain basket of stocks. But that doesn't mean that the risk implied in that basket is acceptable for us. 

We have our own plans, goals, appetites, emotions, journeys and ambitions.

Why should a certain portfolio by default match an acceptable investing profile for us? Why assume that we are not ready to 'pay' with less chance of the most rosy best scenarios, to be able to stay out of seeing or investments devaluated for decades until they reach the same level again, if we're even there to see it?

Not to mention a higher withdrawal rate, that just plain simply translates into a higher material standard when living off one's investments. 

The 'one-size-fit-all' assumption of the stock market, and stock market index investing, is, we think, a dangerous one.

For us, for instance, it has been more important to arrive at financial freedom within a reasonable time, also in a hypothetical bleak scenario, rather than arrive a tiny little bit quicker on average. 

The assumption that all our hopes and dreams fit automatically in the strategy of stock index investing is a hole in the deceptive conclusion of stock index investing as a universal recipe for everyone. 

Examples of misalignment 

- Importance to reach the goal: There are better ways when it's more important to reach the goal within a reasonable time, than to reach the goal quickly.

-High and stable withdrawal: There are better ways when it's more important to be able to withdraw a high, sweet amount to live of. Risk efficient returns it's the cherry on financial freedom, and stock index investing doesn't have it as we saw above. 

- Fear might derail the plans: In the beginning of one's investment career, contrary to common wisdom, one might be so discouraged by a long setback that it's worth to trade a slightly lower expected return and have serious and robust protection of the downside. The same fear might get hold of experienced investors as well, when they realize how long a downturn might turn out to be.

A side-note on cost averaging

It's at this point that proponents of blind stock index investing might throw in the argument of cost-averaging. Of course we don't mean that you should invest everything you own tomorrow, they say. The risk of regret would be to high, they try to comfort the nervous investor. 

Cost-averaging, we're afraid to say, is a fallacy. Let's see what we mean. 

The problem lies in the answer to this question: If one feels that one can't go all in with a large sum due to fear of regretting the timing, well, why should one be comfortable with the risk profile in a year? Or in two years? 

There's a never-ending recursion behind the argument. 

Two years down the line when one is entirely in the stock index; should one sit awake every night and wonder if we should "cost average" in (or out) of the investment? 

No. The obvious conclusion is that the risk profile of the investment is wrong for that investor from the outset.

A tragic recommendation

The most tragic (almost criminal) aspect with recommending stock index investing as a cure for everything, is perhaps to recommend it for complete newcomers, perhaps especially those with some savings already. 

Many are the examples of a newcomer that are emotionally attached to their savings ("I worked a lifetime!") or perhaps sudden wealth ("I inherited my mother!").

These newcomers are then scared and overwhelmed when the market eventually drops (as it always does), and sells at a low point, misses the bounce upwards and might be set back for decades, if they even ever gets back in ("I destroyed my life savings", "I lost not only my mother, but also the sum of money she left me").

Think about your risk profile first, if someone recommends that you should cost-average into an investment. If you can't stomach to own a certain portfolio today, why should you be able to stomach that in a year from now? 

Once more, volatility is more dangerous than one might think from the armchair, until one starts to face real prospects of financial ruin, however minute they are.  

So why would you assume that stock index investing is right for you? 

Farewell

//antinous&lucilius

Hope is not a good strategy

When we started to think about investing, one of our reservations - and a reason that we avoided investing - was that we felt that there was, well, far too much hope involved.

And hope felt like speculation.

Who would like to put one's hard-earned money up for something as fickle as that?

Hope is not a strategy

Yet, if one can make a decent return again and again, consistently, even if one doesn't end up on top every year, as time accumulates, one will have a very good return over one's investment lifetime.

John William Waterhouse, Pandora, 1896.
According to Hesiod, Elpis - the Goddess of Hope - was hiding as the last item in the box.

When thinking through a strategy, as we felt intuitively when we were young, the best path is to try to figure out a way to remove hope. 

If we can look at the strategy without hope for any particular scenario over another, then we're on to something.

Removing hope

For a small-guys investor, there are some ways of removing hope.

• Long-run. One strategy is to go for the long run (read: Welcome to the 1825 day-year)
  
  - If you don't need the money for 20+ years: invest in the stock market (but we have some reservations)
  - If you don't need the money for 5-10 years, invest in some kind of asset allocation

• Creating a well-devised money machine (read about our pathfinder portfolio, or the permanent portfolio), put the money there, and trust the mechanics that a certain withdrawal rate (3% or 4%) should work in the future as well. 

The stomach and the trade-off

The trade-off here is: will one stomach the lower returns when other assets are booming? When the less prudent investors chase hope and gets the fickle rewards as fortune sails in their waters?

Betting on both

The mistake in our youth was to think that there was no other strategy than hope.

But there is, call it the Kelly-criterion, the safer bet, or winning the war - not the battle.

Bleed a little, and win a little, all the time.

Yes, a strategy contains an element that bets on a good outcome.

But it also bets on protection, so even a bad outcome becomes good.

Don't chase the risky bet.

Or as Howard Marks has it: Take care of the downside, and the upside will take care of itself. 

Farewell.

//antinous&lucilius

More reads:

- Amor fati. The art (and Stoic habit) of loving whatever fate has in store for us. 

- Don't predict. The ego-defending little-sister of Hope is the Fortune Teller. 

- How long is the long run? Read: The speed and the destination

- What is asset allocation? Some thoughts here: How we dared to start investing

When the knifes are falling

It has been a rough spring for our open societies, not to mention the people in Ukraine where we have friends and acquaintances that have caused many a white night for us. 

A stress-free portfolio

Despite all that, we have not been particularly anxious about our portfolio. Sure, it has fallen somewhat, but not with more than we can brush it off. We also remember all the simulations and back-tests for the "bouncing back factor" of our portfolio, which is one of the reasons we've chosen it. 

Over a three-year period the portfolio has been back where it began in all cases, during the last 52 years. 

So it's more bombs falling than the portfolio falling that keep us up at night. 

In short: we felt prepared when the financial world started to seemingly fall apart during this spring.

,
In Ciceros original telling of the story, there were boys (twinks?) at Democeles' party. Just saying. But a debauched same-sex orgy (with additional food and wine to satiate all appetites) was a little too much in 1812 when Richard Westhall imagined the impeding fall of the sword and gory end of the party, so the twinks became ladies instead. 

The markets price everything in

In the last few weeks, we've read doomsday forecasts for all asset classes we own. 

Allegedly, Putin would be sitting like an old dragon on a ton of gold, and what happens with that pile, one way or the other, might completely perturbate the price of the shiny metal. We'll soon see kitchenware in pure gold instead of steal at Ikea, according to the most negative predictions.

Inflation eats bond yields, and it's going rampant and then central banks and governments will not able to control inflation, or so it goes, so treasury bonds and toilet paper are soon to be equivalent investments. Actually, toilet paper might be an investment with a better outcome if the wars in Europe get severe enough. 

And the world economy will never be the same, with supply chain disruptions, a scared populace that refuses to consume and shrinks demand, and shortages of all kinds. 

Perhaps. Perhaps not.

Don't forecast. And with enough time, everything happens. 

What these fortune tellers seem to forget is, in our opinion, a very fundamental thing. 

All assets above correspond to financial contracts, traded on open markets in anonymous transactions, by intelligent agents - mostly institutions - with access to much information, and much more than the alluring stories presented above. 

Which means that all ideas about what will happen in the future is already priced into the current asset prices. There's no "natural laws" or "safe bets" that haven't already been baked into a (very refined) average assessment of the situation - an assessment that we normally call the current price.

For instance, bond prices already anticipate what the future payment stream (coupons) will be worth today, in today's money, inflation and all, with expected real returns, in the net present value in relation to existing bonds, buy backs, expectations of future quantitative measures, money printing and issues of new treasuries. It's all there, in the price, already.

So what one is saying when trying to see anything as "doomed", is that one is more intelligent than the market, or perhaps that one has figured out a bias that no-one else is exploiting. But beware. Markets are learning machines, and they are smart. 

As good stoics, we prefer to lean back instead of trying to outsmart people that, truth be told, probably are much more intelligent than us. 

We rely on the method, and we have pre-meditated that the sword may fall.

Come year's end, we will follow our strategy, and as usual pour our hard-earned money into the worst performing asset of the year (whichever that might be). That is probably then the lowest priced bet possible between long term treasuries, gold and stocks, and hence, also the bet with most upside if the market expectations are surprised.

So yes, we bet, but according to a pre-meditated and simple plan.

And the markets are always surprised, but not in ways that the stories above indicate - but genuinely surprised and one, at least not we, will not be able to predict why, when or how. 

For instance, in our own risk assessments for our future FIRE-life, we hadn't even really written out war explicitly (it was implicitly there, but more like "Sweden becomes impossible to live in"). 

Once more: with enough time, everything that can happen will happen, and now war is raging in Europe, despite (at least) us not foreseeing it. 

The best is to be aware that the knives might be falling at any time, and take precautions in advance and not hope that one will be able to do a last millisecond rescue when the unforseen actually happens. 

Be prepared in advance, prepare for all eventualities, consider a strategy that works for the human you are and not the hero you wish to be, so you are able to stick to the plan when the party ends.  

Farewell,

//antinous&lucilius. 

More reading:

Ergodicity - everything that can happen, will eventually happen.

Amor fati - love what destiny has in store for you.

Our portfolio - the pathfinder, bringing us to our goal. 

The speed and the destination

When we want to go somewhere, is the speed we can arrive at the destination the only factor to consider?

Let's say that we are to go and visit some friends in a remote area in northern Sweden. 

The winter roads through the forests are full of moose, reindeer, bears, polar bears, and what-not.

What kind of driver (and car) would we prefer for the journey?

Let's make a thought experiment with obvious hints to a financial journey.

One driver promises to keep a good, high average speed, with the performance one can expect of a good, new car, let's say around 120 km/h (80 mph).

Another driver wants to arrive as quickly as possible. This driver proposes a new kind of car (untested on arctic winter roads) that he thinks could go really fast, let's say 160 km/h  (100 mph). We will reach the destination in no time, or so he promises us. All other alternatives seem unnecessarily slow to this driver.

The third driver seems, in comparison, dull and boring, but quite stable from a temperamental perspective, and proposes to drive in 80 km/h. Just in case.

There might also be this guy from the local bank who tells us to walk the whole way.

Quick? Or safer but slightly slower?

Speed might not be the only factor to consider when aiming for a given destination (that doesn't include a dead moose in one's lap).

To arrive at all, in an acceptable time, is for many much more important than being the first to arrive.  

Let's end with the analogy there. 

Many seem to focus on optimizing for just one parameter when considering one's financial journey.

• Insane returns. Including untested assets, which could be anything that is new. New is the definition of tech stocks. Or exotic assets that didn't exist 20 or 50 or 100 years ago. Might be quick, yes. Will it always work? Who knows? And what happens at an unexpected turn?
  
  
• Average speed, known car. Buy the index, or pick value stocks and reinvest the dividends. This is less insane and it's far from impossible to reach our destination. Yet, if one is not that familiar with the conditions of winter roads in northern Sweden, then do we really understand what risks we are exposing ourselves to? And what makes the assumption true, that high average speed is the only factor that is interesting for our journey? Is the assumption that average speed automatically also has a decent reward for the risk? Or that the risk matches our journey and appetite to arrive also if conditions or events are less than optimal?

• Slow yet steady. Even a sharp turn becomes much less challenging with slower speed and higher safety. The big swings, so to speak, of the road  becomes less dangerous, and we can both handle sudden ice and even the odd moose on the road. We might get to our goal in a slightly longer time. But in most scenarios we will get there, alive. 

We have given the question which vehicle will bring us to our destination some thought, and for us, slow and steady might not be so bad, as we prefer to arrive in most scenarios rather than being quick in the average scenario. 

You can read our thoughts on portfolios here, and our thoughts on volatility here.

How about you? Are you mostly considering your speed in your portfolio? Or is arriving at the destination even if the unexpected moose shows up behind a curve also in your equations?

Farewell,

antinous&lucilius

How we dared to start investing

Our investment journey started with that we both went through crisis at work; where we realized that our financial future shouldn't rely on the paycheck alone.

Yet we had too much fear of the total stock market, and of stocks, to go all in on stocks.

Looking back we had some investments, mostly in mutual funds with corporate bonds that had a return of 4%. So very weak returns for the accumulation phase. And we really didn't pay attention to it. 

At some point, Antinous said that if we put our brains to it, we should be able to get at least a 7% return, still with reasonable risk. 

Sunrise for Antinous & Lucilius Financial Freedom Journey

Enter Asset Allocation

That's when we came across the permanent portfolio. We soaked up and read everything about it, we got the books of which we would especially recommend Craig Rowland's The Permanent Portfolio from 2012 that goes into more depth and answers some of the questions otherwise left unanswered. 

Compared to the advice one would get from one's bank, this is a wildly different approach.

It allocates 25% in four completely different asset classes (cash, long term government bonds, gold and the domestic stock market via a broad index fund).

Why? If we don't know anything about the future, then we bet equally on what's going to happen. And then the asset balance each other out, providing a radically different risk approach than anything one has heard from the old bank's investment advisors.

Why we dared going all-in

We already had a bunch of money when we started to be interested in investing. But it didn't feel good to go all in in the stock market, as many seemed to recommend in the financial independence-sphere.

Basically, it was the table below that made us dare to put our hard-earned money in a portfolio. The data below sums all periods from 1970 to now, with yearly re-balancing. We added US and France below just as a reference, with the US stock market as a benchmark. 

	PP SE	PP US	PP FR	Stocks (US)
Deepest Drawdown	-12%	-14%	-13%	−49%
Longest Drawdown	5y	5y	5y	13y
Average Return*	5.9%	5.2%	4.9%	8.2%
Short Term 3y Bad Case*	1.1%	1.6%	1.6%	-2.3%
Long Term 10y Bad Case*	3.2%	3.9%	3.6%	1.4%
Min Time to FI**	4y	7y	6y	3y
Max Time to FI**	10y	10y	10y	14

* Returns here are per year without inflation. So one needs to add one's expectation on inflation to see the same returns one would see in a brokerage account. The bad case is at the 15% percentile. 

** We assumed a 50% savings rate and 8 years expenses already saved. But this is 

When we started, we didn't really find online numbers for Sweden, so we crunched the numbers ourselves. It would show that the permanent portfolio is even better in Sweden than we first thought. Now there's portfoliocharts that is excellent for getting better ideas about different asset allocation strategies. 

So the higher average return in the stock market has also a very high price of 4 red boxes in our table, where each and one of the red box represent a very unnerving result for us. 

In short: the idea of asset allocation and perhaps the permanent portfolio might be worth checking out. 

So we did go slightly slower, but preferred to avoid the red trapdoors. Can you go more aggressive? Yes. Did we dare go more aggressive? No. So better to have something to start with rather then bring scared into doing nothing at all, or to pretend to be an ideal stoic sage that will be unaffected whatever happens just to discover that it might not be true. 

Farewell,

//antinous&lucilius

Amor fati

Mark Spitznagel of Universa, the guy that did a 2000% return on the start of the pandemic, has an interesting thought experiment, that he attributes to Fredrich Nietzsche. 

It's about a curse (and a lion).

The curse is that we will freeze in a time-loop, being 5 years long (yes, there are a Hollywood clichés on this theme).

And the loop is there forever and contrary to the Hollywood clichés, there's no hope of escape. And we wouldn't know what would happen during those 5 years that would repeat forever.

What would be a wise strategy going into the time-loop, before we know the results?

In Nietsche's writing the answer to that question is represented by a lion, what else. And the lion turns "thou shalt" spend an eternity into "thus I willed it and thus I willed it for eternity".

Because, well, a lion doesn't much care what happens. 

Would we be able to say, whatever fate has in store for us; "thus I willed it"?

Medici lion, reasonably calm about the future.

sammydavisdog CC BY 2.0 

We do plan to live longer than 5 years. But we are also interested in what will happen during the next 5 years. It's a liberating thought-experiment to try to look oneself in the mirror and think about one's own strategy for the next half-decade. 

Is it a strategy that gives the confidence of a lion?

Are we so calm and confident with our strategy so we are able to, like Nietzsche's lion, say "Thus I willed it and this I willed it for eternity", whatever happens?

Or is something meeker looking back at us from the mirror?

Farewell,

//antinous&lucilius

Where to go now?

Try: Ergodicity: Anything that can hit us will, eventually, hit us

What's meant with 'all seasons' in investing?

There is more to what happens in the markets, than what happens in the stock market alone.

And that can be very useful. 

When looking broader than thinking if the stock market will go up and down, one can start try to understand the financial markets in scenarios of what might happen, and how one can profit with different asset classes in these scenarios.

Scenario thinking

Let's move outside of the stock market, and for a few minutes think about what can happen with an economy at large. 

First, let's face it. Some of the things that might very well happen during one's life time, due to ergodicity, will be quite severe. 

The country we're in might cease to exist. Property might be confiscated, which happens in most parts of the world at least a few times per century; remember gold in the US, not to mention Europe after the second world war. New regulation might be introduced that creates havoc with private enterprise, and so on. 

This is why hardcore financial planners recommend having part of one's investments entirely abroad. And the bags packed.

Financial Seasons

But before we start to save up on the tin cans and buy a gun, let's think about what can happen before the tanks come rolling in. 

The proponents (Brown, Dalio and others) that recommend asset allocations often have a model to understand what might happen in the economy, short of war on the streets. 

Such a model can, for instance, break down the investment climate into fundamental dimensions. 

What are those dimensions that can reasonably encompass a whole economy, we hear you ask?

One is what happens to the values produced by the economy. Does the economy fundamentally produce more goods or services that society value? Or is the economy shrinking? So the (local) economy itself is one such dimension that can either grow or shrink.

So what's left when we've considered everything in the economy? What could possibly be left? The other dimension is that which we use to trade these values that the economy produces. 

When I give you something, I trust that you will pay me back, and that token of trust is often expressed as the currency used in the local economy where I have an expectation that the token will work in my next transaction with someone else. So this consists of all kind of short promises, that is, short debt that can be turned into exchangeable tokens in the economy. In broad terms, let's call this dimension the credit available in the local economy.

So now we have two dimensions:

• The Economy consisting of everything we value and we can potentially access, 
• Available Credit, that can trade those values.

With the above said, let's not fool ourselves that the mental model is everything that can happen. It's a model, not the rules of the game. In the real world there are few games that really bend to rules, as the ludic fallacy reminds us.

Economy: increase or decrease

So the economy can both increase or decrease. For instance, if trade increases, or we invent new sweet things that we enjoy, or we proposer and just value new or subtle things more, then the economy increases. 

If we instead screw up trade, we destroy what we value or we get depressed and don't value anything anymore, the economy decreases.  

Credit: increase or decrease

All that we value in the economy, for a monetary civilization, is traded using some kind of credit. 

Credit is multiplied via different mechanisms by the level of trust that currently prevails, through one kind or another of fractional banking; as money itself, or through credit cards, interbank lending, consumer credits and so on, and the basis of that multiplication is that short term promises will be honored. 

When trust is high, a lot of credit can be created, far exceeding what the central banks actually puts out in the shape of money. 

And on the other hand, if trust disappears or the central bank decides to remove money from circulation, the credit in the economy can evaporate rapidly, leaving only true, liquid, accessible hard cash in it's wake, and nothing much else.

Beware of theories

Now, this of course opens up tons of questions. But we are not academics. And we're wary of overly much theory, especially for theory's sake, not to mention what theory is currently in fashion. We try to stay away from that. 

We know that this is a model, and not the rules of the game. And we're not going to use it to predict (don't predict!), or speculate about cause-and-effect. 

It's much more like four different boxes that the economy is likely to end up in, because there are few other scenarios to go to (except war and confiscation, as said above). 

The economy shrinking or growing, credit increasing or decreasing create four "seasons" and the economy will be in one or another of these seasons. 

Winter is coming,

Caspar David Friedrich 1811

Now the important question. If we have these four fundamental seasons in an economy; how can we profit from them?

Well, different assets have different characteristics depending on the season. Let's flesh out a little more what might be going on.

1. Increasing economy, increasing credit. 

This is the way "everybody" wants things to be; what we normally call growth. The stock market chums along, sometimes very impressively, and credit that can trade the values that are being created chums along with the economy. 

Stocks can perform extremely well during the growth season, and long term bonds (25y+) are expected to perform very good as well. 

Cash and gold are both probably at bargain prices. 

A side note on cash in this season, which is a little difficult to observe because we're not used to think about cash in that way, as an investment asset: What does it mean that cash is at a bargain price? Well, price goes both ways. Something is almost always available at a bargain if one knows how to look for it. 

In this season, it's precisely cash that is at a bargain price. And what should we do with an asset that we can obtain at a bargain price? Well, get it, for the bargain price of course. 

2. Increasing economy, decreasing credit. 

Increasing economy and decreasing credit is a season that happens when the economy grows, but a lunatic in the central bank might constrict monetary policy, or a politician might interrupt interbank-trade, or any hick-up in trust might happen, which means that credit evaporates like dry tinder in a wildfire. 

This triggers the onset of a crisis. Flash sales occur. 

We might be in for a quick devaluation of stock and bond values. Anyone with real cash or long term bonds in the local currency might expect to benefit, and gold sometimes also perform.

But often, if the trust evaporates quick enough, it's only cash that will work, and one can suck up tons of stocks, and also gold and bonds with the cash that one got cheaply earlier. Anyone with liquid, real, accessible cash at hand in the immediate has the opportunity to go on a shopping spree and build the fortunes of their lives in 6 or 12 months, when the other asset classes start to bounce back.

Now, the crisis can either bounce back or turn into a full-blown, protracted depression.

3. Decreasing economy, increasing credit. 

Another alternative might be that the economy decreases, but someone in the government might get the good idea to solve the issue of a decreasing economy by printing more money, by calling it modern monetary theory, quantitative easing and what not. It might work if the economy is actually increasing beneath the credit. But if the economy is truly decreasing, we're in for another ride that will trigger inflation and an even worse crisis.

It might also be a a high point in the economy, and the growth has started to flatten out, but this is obscured by the trust that is still there and keeps credit expanding.

Now inflation looms, and when it strikes, then very hard assets will perform well. And the hardest asset of all is what nation states put in their vaults for bad times, the most trusted asset since Seneca's time and well before that.

Gold. 

And when inflation strikes, everyone suddenly rushes after the hardest of assets, and gold prices turn explosive.

Decreasing economy, decreasing credit.

And the last season, the winter, is a protracted depression. Both credits and the economy are decreasing. The sudden fall in trust and credit has now spread and infected the whole economy. 

Anyone that needs cash will be forced to sell inventory and assets at low prices, which will be reflected in the daily prices in the stock market that will spiral downwards. 

The newspapers will call this a crisis and disaster with black headlines, and some bank directors (central or otherwise) will jump from skyscrapers. The newspapers will continue to call it an ongoing crisis, and as usual the news will be blind for the opportunities that now open up for those with the right assets on their books.

Cash will be useful. And perhaps even better, when there's no real trust not even in cash, gold will allow us to do the shopping.

Conclusion

By having different assets in a portfolio, one can always have at hand what the market wants. 

Oh, so you're ready to sell your stocks really cheap to get cash? Lucky you, I've got cash, so just hand over some of those stocks for a really low price. 

Or you value stocks at crazy levels? Sweet, I bought some a few years ago when they were at a bargain. So here you go, I can by some gold or keep some cash instead. 

Oh, so you don't trust anything anymore? Lucky you, I've got some gold saved for a rainy day.

This is the beauty of having an asset allocation and rebalance from time to time, as the gentlemen Mr Dalio and Mr Brown discovered.

And if one mixes the assets in good proportions, one can build a quite powerful portfolio that will sail one's portfolio safely through any storm.

Farewell,

//lucilius&antinous

More: Can this thinking really perform and create reasonable returns? we hear you ask. And how can one mix the assets? Keep on reading about Our Crawling Road: A portfolio for accumulation part 2 or our current portfolio.

Don't predict

We want to avoid speculation. To avoid speculation, we need to avoid predicting. But how can we earn a good return and not predict?

It's really hard not to make a prediction. News, twitter and much commentary in general are predictions. Prediction creeps into our thinking whatever we seem to do, even if we actively try to avoid it. 

• "Let's hope this will be a good year"
• "Small cap, investment trusts or tech stock are overvalued. The P/E ratio seems high, don't you think?"
• "Inflation will destroy all returns in the next decade!"
• "Interest rates can't go down more"
• "I'm sure this stock is undervalued"

Why shouldn't we predict? Because there is no reliable crystal ball for the future. Predicting has a notorious bad track-record, obscured by winner bias.

The price on the market is the average prediction of all the market's participants. For us, the best model of the market is that it follows an entirely random process - it's perhaps not always true but it's the best approximation for how the market behaves for, we dare say, any small investor, like us.

The Oracle of Delphi, perhaps reading the financial news. 
Delphic Sibyl, fresco painted by Michelangelo, Sistine Chapel Ceiling (1508-1512) 

But what should one do if we don't want to predict?

First, we should refrain from predictive narratives that sound logical. Because that's what narratives do (sound logical) but it doesn't make those narratives into better predictions.

Examples:

• Reached the bottom? Perhaps we, or the 'experts', are sure that we're at the bottom of a stock market cycle - but in reality it's very hard to say when and how fast the recovery will come. And when prices are low, developments can be very quick. One can loose 50% or 90% of one's money in a day going in or out of the market when it moves around the bottom of a boom- and bust cycle. So it's better not to predict and stay the course with a strategy that was thought-through before the stock market cycle went downhill. 
  
  
• Reached the top? Perhaps we are sure that the stock market will stop going up, because any number of good-sounding reasons. Yet - when will that happen? Over time the market goes up, and that means that it beats its all time high again and again. And whatever theory one picks to predict the top, there are nuances that the theory will not encompass. The markets are a learning-machine, that already contains all known theories. For instance, a simple point: there's a denominator in the P/E-equation.
  
  
• Cash and gold. Perhaps we think that "only productive assets" will survive, and discover that market price appreciation for other assets also delivers real money, especially when those productive assets are at bargain prices. Who realizes that cash increased 500% in value between 2001-2003 instead of seeing the other (but same) picture - that the stock market went down 80%?
  
  
• Interests are low or high. Perhaps we think that "interests can't go down more" and discover that long term interest is powerfully controlled by the long-term expectations on inflation and interest rates by the markets. And as the central banks and politicians discover, markets are much more adaptable learning machines that are much more powerful then what a 'sovereign' state wants to admit or can fully control. 

We might hear what we want to hear when we think we should rely on a prediction. The easiest person to fool is ourselves, with our desire to hear what we want, and avoid to hear what we don't want to know. We're prisoners to our own delusions. 

Temet nosce as it was said in Delphi. Know thyself before you try to understand a prediction about the future; and the ancients knew with many a cautionary tale how a prediction tend to fool the listener.

We've tried as well. We've been rock sure that we're at the bottom of a stock cycle. And just as sure that gold can't go up. What we've learned is that we are usually 180 degrees wrong when we try to guess what is going to happen. 

Perhaps you are better than us; which shouldn't be too hard, but to really outperform the market one needs to be better than average, which doesn't mean better than any average Joe, but better than professional investors.

It's a tough game to play.

So what could one do?

A solution to not predicting

Well, build a strategy that doesn't predict. 

One popular way is just to buy the stock market on average, by buying an index fund.

We don't think this gives a good price on the risk one is taking on, but it's a strategy with less prediction. 

Another closely related strategy is to focus on dividends, not stock market prices.

Betting on many futures at once

Our way is to combine assets that performs well for most scenarios of an economic and credit expansion and contraction. 

The idea behind asset allocation is to buy into different likely scenarios and have assets that perform well in different futures and hence not bet on any future in particular.

What we started our journey with, was the hardcore solution of strategies like this and when it comes to erring on the safe side: the permanent portfolio, which has much better returns and performance than most newbie investors think.

Read more here: A-well kept secret: Our portfolio for accumulation.

Not even we are that hardcore as the permanent portfolio anymore. But it's worth knowing that it exists and how it behaves, and also ponder using it. We did so for many years.

The bottom line is: we still pay extreme attention to avoid trying to foresee the future.

Farewell.

//antinous&lucilius

Where to go next? Perhaps some thoughts of why it's not overly wise to rely on an expert. 

Time for rebalancing and avoiding the herd

We rebalance at 6 month intervals now, as we are still in the accumulation phase, so we never have too much cash laying aroundd.

And as it will take some days to move the money around we started today.

It's been a good 6 months. The portfolio is up 6 percent since the beginning of the year, so slightly above expectations, perhaps driven by some inflation also in SEK. Let's remember that any real return will need to have the inflation deducted at the end of the year.

Herd

Swedish small cap and investment companies are up 20+.  US stock market is not quite as impressive with + 13 percent from a SEK vantage point.

Gold is right plus minus zero in SEK.

Long term bonds are down much, around 20 down.

And as usual we bet on every future climate. Except that we don't bet. We behave more like robots.

So most of our money will go into long term bonds and gold. Feels strange to buy into a losing asset. But that's part of our strategy.

That is what it is to have a contrarian strategy and not follow the herd.

Volatility from a 5 year perspective: Welcome to the 1825 days year

Once upon a time, at the birth of our solar system, the time for the earth to spin around the sun became the 365 1/4 days we are used to.

It was a God given, a necessity, perhaps, and of course entirely out of human control.

Those 365 days has some impacts on our life, and certainly our evolution. For the two of us, the arctic summer and winter are a stark reminder of the solar year, on other places closer to the equator the climate will be more stable year round. 

The Arctic Sun

In the heated, air-conditioned, civilized life of today, the impact of earth's rotation on everyday life is smaller. The time it takes for earth to orbit the sun would seem even more arbitrary if one lived outside our frame of reference, let's say on one of the moons of Jupiter. 

From a more elevated perspective, an earth year is a seemingly randomly set constant.

Yet, we tend to give this period an out-of-proportion importance. We count our age in it, we celebrate the summer and winter solstice and equinoxes with rites and feasts. 

In finance the year has significance as well; as if the returns of our investments where a crop to be harvested every year. The year is the basis for what we understand with returns; if we see the number 7% it's assumed that it's the annual return that is meant. 

What is the impact of this metaphor on our thinking about investments? Investments that might not really care about the arctic sun, the moons of Jupiter or the passing of midsummer? 

What if we measured returns in another constant? 

Let's say that we just as arbitrarily instead measured a new unit that we set at 43 800 earth hours, or 1825 earth days, corresponding to 5 earth years. 

A unit, as if earth was spinning five years slower than we are used to. Or as if one only can be bothered to have a look at the planet every five year and wouldn't notice that it's actually spinning faster. Or as if we saw that grand red dot in the clouds of the gas giant Jupiter from our moon every five years, and measured the passing of time in red-dot-revolutions and not earth years.

What would we think of our investments then? How would volatility look with our new, more relaxed, slower 1825 days year's perspective? What decisions would we make?

Let's plot our pathfinder portfolio's return excluding inflation in a logarithmic diagram, with our normal earth years and our new, 1825-days-years. 

A thin red thread that always strives upwards

And voilà. An almost straight, red line that always marshes on upwards and never ever turns the other way. It's the same return, just with a lower resolution.

Our way of looking at things are bound by conventions that might be out of place. This hints on what volatility looks like for the Gods. 

And perhaps, it could for us too.

Farewell,

//antinous&lucilius

Portfolio Stability And A Good Night's Sleep

If one goes to a place like portfoliocharts (strongly recommended for the interested asset allocator), there's a concept that we have struggled with.

It's the idea of Start Date Sensitivity.

For us, this is not at all intuitive, so let's try to go all the way to see where we are now in our understanding. We have discovered that it's key to quite a lot of insights around investment portfolios.

It's a funny and unusual measure. It took us quite some time to start to understand this way of looking at a portfolio. 

One way to define it is as a measure of how good a guide the 10 years last history has been for the 10 years that lay ahead. By pointing out when this difference is as large as possible (both in the postive and negative sense), it focuses on the year when the previous time period was as maximally misleading for the upcoming time period, and how big that effect was. 

Is history a good guide for the future?
(Reconstruction of the West Pediments of the Parthenon, CC BY-SA 2.0 Tilemahos Efthimiadis)

Going with one asset class

Let's look at some examples:

• Total US Stock Market: Luckiest 10 years = 14.9 percent points better, per year, than the preceding 10 years, Unluckiest 10 years = -18.1 percent points worse per year then what the preceding 10 years annual average return hinted at.

So this mean that a happy US investor could sit and look at the stock market and think that: well, this is sure looking good. And at some point, the investor would say that, what the heck, the last 10 years have been going really, really well. Let's jump in and put my savings in the stock market.

The most unlucky the investor could have been when doing that decision, was the period when the stock market performed on a yearly average -18.1 percent points worse per year, for 10 years, than it had done the last 10 year period.

So that's a measure of how bad a guide for the future the last decade was.

For the US stock market, that would have happened in 1999, back when we were in our teens. The market had had a return on around 14 percent per year for ten years, but that would not continue. The average yearly return for the next 10 years would be -4 annually. This gives us the most unluckiest start date sensitivity for 1999, with those 18 percent points .

As both of us experienced and at least vaguely remember 1999, this negative experience colored our view of the stock market and probably at least partly explains why we treat it with caution. 

Of course, time would have partly fixed it for our unlucky investor, but it would take a very long time indeed. Still today, that 1999 investor would have got only a modest 5% return per year from that initial decision, and a lot of volatility on the way. Not that much of an issue if one is a teen and just started to accumulate money. More nerve-wracking if one is deeper into one's career and accumulation, and put substantial money on the table.

On the other hand: the luckiest investor would have jumped onboard the stock market in 2009 and then been in for ten tremendously good years, a lucky strike we're still part of.

Just for fun, let's have a look on a much more volatile asset class. No, not bitcoin. Gold, of course. 

• Gold (USD): Luckiest 10 years = 21.0p.p. , Unluckiest 10 years = -30,7p.p.

One would probably be close to insane to put a significant part of one's money in an asset class that is as volatile as gold, but let's play with the idea. 

In that case, an investor, after witnessing a terrible performance for gold during 10 years and then by some miraculous inspiration buying into it anyway, could be 21 percent points better off, per year, for the upcoming ten years. 

So the start date sensitivity goes both ways, and the bigger it is, the less guidance we seem to get from the last ten year period.

What happens if we mix two assets?

Let's instead mix a healthy portion of the stock market with a substantial amount of gold. Let's say by using our hypothetical 80/20 split.

• TSM (80%), Gold (20%), looking on performance in USD:  Luckiest 10y= 10.6 percent points, Unluckiest 10y = -11.3 percent points difference per year

What does that mean? Well, our investor would still be in for a surprise if she hit the unluckiest year, but after yearly rebalancing in and out of that gold, she could comfort herself that she would be much better of than with going totally into the stock market, and she would have come out quite ok 10 years later and would be back in black numbers much quicker.

Good for her.

Several asset classes

What happens if we go to our more conservative portfolios that we've been using ourselves, where we mix gold, long term bonds in different currencies, cash and small and large cap stocks, both domestically and abroad?

• Permanent portfolio, our take on it, in SEK: Luckiest = 5.1 p.p. , Unluckiest = -4.9 percent points difference per year.

The results are roughly the same for the US market, but with even smaller sensitivity. You can read more about our take on the portfolios here, here and here.

What does this mean? Well, there was a  year, where the last 10 years had an annual average return of 10%. If our unlucky investor jumps in that year, she would be in for 10 years where the average annual return would be 5.1%, or 4.9 percent points worse than indicated by the preceding 10 year period. All this after inflation.

And that was the most unlucky difference that ever happened during the last 50 years.

So in the worst case it would be roughly the same as for the stock market, but with much lesser volatility. And the permanent portfolio is back in black much quicker.

That's a glimpse of why we, who both were into our careers and had a bunch of money, decided to start our investment journey with the permanent portfolio. 

The permanent portfolio with its more narrow start date sensitivity, in contrast to the stock heavy alternatives, almost entirely avoids the question of 'is this the right time'? 

That's an important, stress-inducing question that can be avoided.

Finding our path

But of course, one pays a price with the permanent portfolio when it comes to where return. So now the fun part. 

• Our Pathfinder Portfolio, our take on it, in SEK: Luckiest= 6.5 percent points, Unluckiest= -7.3 percent points difference annually
• Our Pathfinder Portfolio, our take on it, in USD: Luckiest = 4,1 p.p. , Unluckiest = -4,2 p.p.

Our pathfinder portfolio of course has a higher start date sensitivity, measured as the difference between the luckiest and unluckiest points, than the permanent portfolio.

But still, it's much, much lower than the stock market. For our domestic set-up, the average return for the pathfinder portfolio was 9.2%, and a US adaptation was 7.3%. 

The total US stock market for the same period had an average return of 8.3%. 

So by mixing a combination of individually high volatility assets, one gets a lot more safety, quite small sensitivity in regards to when to buy into the portfolio, and an average return on par or even higher than the stock market. 

Just saying.

A Good Night's Sleep

That could be the end of this article. But it's not. 

What we then slowly realized was that the question if one should put all one's money in this or that portfolio is not only a question about start date.

It's not a one-time question.

It's a question that comes up all the time, nagging with these little thoughts that can keep anyone who is not a Stoic God awake at night.

• Have the last years been booming? How much could we realistically loose by sitting still?
• For how long should we accept that the portfolio is lagging behind? 
• Should we sell tonight? Or should we sit still and hope that the boom continues for a little longer?
• Do we dare to buy into an asset that has been lagging for a long time?

All investors take the decision if we should stay in an asset allocation or leave it every night, irregardless of if we try to pretend that we don't. There's no real way of avoiding this, as taking no decision is still a decision.

At the bottom of it, start date sensitivity is about the stability of an asset mix. Having a good stability in the mix of assets means that one has to think much less about time periods, paradigms, bull and bear markets and timing in general, and all those little nagging questions that timing entails.

Because the effect of being lucky or unlucky with timing has much less impact on the performance of the portfolio.

The decision to stick with the portfolio can then truly become permanent, with less second-guessing, and better sleep at night. 

Farewell,

//antinous&lucilius

Where to go now?

• Go over to portfoliocharts.com and play around for yourself.
•  Read about the Pathfinder Portfolio
• ... or the Permanent Portfolio: A Portfolio for Accumulation Part 1 and Part 2.

Note on the numbers: As usual, this is back-testing from 1970, cumulative annual growth rate, with inflation removed.