Nobody likes to lose money (Like I just very likely did on Kuetzal). I

*particularly dislike*losing money. If you invest however, you're bound to lose money at some point.

It's inevitable. You will lose money. Accept it.

I'm trying my best to embrace loss, despite my utter dislike for it. To avoid loss at all costs means to avoid wins too.

It doesn't mean you can do whatever though! But remember, people will always ridicule those who take risks they don't dare to take.

It's still on you to asses what's too much risk for you.

## Math of a random loss

Imagine you have an investment A. On a normal year it produces a 15% return. However, there's annually a 5% chance it will go to 0.

Should you invest in it?

Investing just one year is a gamble. A pretty safe gamble, but a gamble still. Either you get a nice 15% return, or 1 out of 20 you go to zero.

Mathematically the gamble makes sense. The expected return is 9.25% (95% x 115% - 100%), so it makes sense, right?

Not quite. There's a 5% chance of total failure. That's pretty troubling. What if you put

__all your savings__on the one gamble? That would be pretty scary, right?
If you put all your eggs in the same basket, here's what the expected value over time looks like, and the likelihood of total failure.

The blue is the exciting exponential curve of compounding interest, but the red - that one is the likelihood of you being at

**zero**at that point in time.
In fact, at just year 14, the

**likelihood of you having no money is higher than having any money at all**. An yet, the mathematical**expected value**keeps on growing. Ok the term might confuse you.
The expected value is simply the

**sum product of outcome value and their likelihoods**. In the case of year 14, it is:1.15^14 * 0.95^14 + 0 * (1-0,95^14) = 3,45This means +245% return.

But actually, there are only two alternatives. Either you've gained a +608% return at year 14 (1,15^14), OR you've suffered a catastrophic -100% total loss. The blue bars deceive you.

If you run a test with e.g. 20 portfolios that follow roughly this mechanism, then here's what that can look like (I've added a little randomness to separate the otherwise overlapping lines)

As you can see, only one out of 20 survived in my sample over 40 years.

So would anyone be dumb enough to put all their capital in the one investment? Of course not. You diversify.

### Adding more investments

What would happen if you added another investment? One that was in no way dependent on the other. Let's call it B. Instead of having 100% allocation on A, you have a 50%/50% split between A and B. For the point of this exercise, I'm assuming

**the portfolio is re-balanced every year**.
Things get much more interesting now. The likelihood of a total loss at any given year becomes very small (5% x 5% = 0.25%). The likelihood of suffering

__some loss__increases of course, since now there are two investments of which either one could go to 0.
But the good thing is you'd still be left with half of your investment. Let's see what this looks like.

Woah! This time, only 2 out of 20 are at 0, but there are a few that have performed quite poorly. If we look at the histogram for the end value, it becomes even more clear how many portfolios haven't really compounded well over the 40 years.

5 portfolios out of 20 are either only doubled in value or less (including the zeros).

It's an improvement over the portfolio with everything in the same basket, but still quite far from being optimal. But before we go to the obvious choice to increasing our distribution, I want to point out a non-intuitive conclusion.

5 portfolios out of 20 are either only doubled in value or less (including the zeros).

It's an improvement over the portfolio with everything in the same basket, but still quite far from being optimal. But before we go to the obvious choice to increasing our distribution, I want to point out a non-intuitive conclusion.

### Having "worse" investments is still good for long-term returns

Many investors I've seen try to find the

**one best thing**and put everything they have on that.
If it's the best thing they've found, isn't it sub-optimal to have

**anything**on another investment? Shouldn't you just find the**best**and bet everything on that? If you**know an alternative is worse**, what's the point in investing anything on it?
Here's why:

- You don't know what you don't know.
- What you don't know, might cause catastrophic losses.

Therefore, even if I am

**sure**something is a winner, I still diversify. Even if it means for lower-yielding investments.
For example, our investment B had the same expected return as A (95% x 115% - 100%). In a normal world, you usually don't have access to two identical

**yet completely independent**investments. So, what if Investment C is significantly worse than A? What if it has a return of only 10% and still having a 5% likelihood to default, leading to an expected return of just 4.5%. Are you better off betting everything on A, or splitting 50/50 to A and C?
Those of you who are gamblers will go with 100% allocation on A and end up broke along the way.

Those who went with A and C, ended up with a lot more at the end. Again remember that the portfolio is re-balanced yearly.

This is an important lesson to take to heart.

**Diversification in itself is valuable**, even if it means diversifying to worse investments.
Now let's increase our diversification.

### A widely diversified portfolio is more predictable

When you increase your diversification, the likelihood of

**some**of your investments going to zero increases, since you have more of them. However, at the same time the distribution hedges from a total portfolio-wide loss, since the likelihood of**each of your investments imploding simultaneously**goes to practically zero.
Yay! Diversified portfolios for the win! 🤘

The worst portfolio has 18-folded. Looking at the histograms, returns are much tighter.

Adding more will of course narrow the spread even more, but growing the diversification to e.g. 50 could be over-doing it. Doesn't hurt though,

**if it doesn't feel like a lot of work**.## What to learn from Kuetzal

It was obvious that there's risk involved with Kuetzal. The returns gave that away.

However, I didn't think it could go to zero. All of it gone. I didn't consider a scam could be possible like that.

Sure, I thought the projects could be overly optimistic and even if my investments were all in buyback guaranteed loans, I figured there should always be a way to salvage

*something.*

Luckily, I'm diversified and I lost a very small share of my portfolio. I am pissed that I got scammed, but when I look at the long-term overall performance, it's not a catastrophe.

However, what

*was*the likelihood of something like this happening? Is it 5%? Or is it more?
There are some forces that have a very correlated impact on P2P/P2B platforms, the biggest being regulation. If EU decides to put a stop to this, it might drive through legislation that could completely kill the industry in Europe.

This would take a bit of time though and investors should have a heads-up before blood fills the street, but it's a good example of a systemic risk. Another is economic environment. A recession can impact everything.

In the beginning of this article I casually suggested that our investment has a 5% likelihood of total loss. What is the likelihood of total loss for each investments you have in your portfolio?

How likely is it that my projects on Agrikaab default?

It's definitely more than 1%. Could it be 10%? Maybe. It could be 15% too. If it's more than that, then the investment doesn't make sense any more.

The likelihood of total loss has a drastic impact on the long-term portfolio performance. At 5% total loss likelihood and 15% return otherwise, the twenty 40-year portfolios returned at median about 35-fold returns. At

**9.3%**per annum that's unsurprisingly very close to the expected annual return of 9.25%.
In the world of buyback guarantees, some returns are very binary. Take Fast Invest, PeerBerry, RoboCash or Swaper for example. They all are very narrowly in the roughly 12% interest rate space, all providing buyback guarantees. Interestingly, all of these platforms to an extent provide the buyback guarantee themselves. It's not all that on/off but you could have a mental exercise to evaluate the individual likelihoods of those platforms imploding.

If the likelihood for default is 5% or more, then check the math what it does to your expected returns. 😉

The same thinking applies to individual loan originators. It doesn't make economical sense to include high-risk loan originators if the interest rate doesn't justify it.

So the thing I learned from Kuetzal is that assessing total loss likelihood is something I should put more thinking into. Even with a widely diversified portfolio, assessing total loss is important, since we're in a space where things like that can happen. Startups fail, often.

And when the likelihood for a total loss is too high, it's wise to pull out, go somewhere else.

But always keep it diversified.

## Total portfolio performance matters

Back to the Kuetzal case.

A single mistake is not a catastrophe if I learn from it.

Losing money on Kuetzal is not fun but manageable, since I'm diversified. I cannot afford doing something like this every year though. But as long as I am diversified and learn from mistakes, my portfolio will be able to take it.

I've beat myself a little bit for being dumb with Kuetzal. I should have known better. But, on the other hand, my total portfolio over multiple years is still over 12% measured by internal rate of return. That's what matters to me.

Stay diversified.