Is Forecasting BS for your Investments?

x is not always equals to f(x)

In middle school (SMP 2, in particular if you’re Indonesian), our math teacher would have taught us about function. It is a mathematical object, usually represented by a tiny box, that accepts an input and spits out an output. Just like the diagram shown above.

We hopefully have learned (or memorised) the properties of a function whole heartedly. A basic one being a function can accept one or more inputs, but has to spit out only one output. Otherwise, f is no longer a function.

Another basic, yet super important, property of a function is that the output that gets spit out from the function does not have to be the same as the input.

In other words, input x does not have to be the same as f(x).

I don’t think you need to me to prove this do you?

Well let’s prove it because it is easy peasy. Say you have a function that accepts a real number and multiply it by 2.

If I feed in 2 (x=2), then f(x) is x*2 = 4. You can see that x ≠ f(x).

Cool, now that your memory on function is jogged up, let’s talk about what f can represent in finance :)

In the finance world, f can represent your investment payout function. It would depend on your investment strategy. If an event x happens, then x will be inputted to your function and then you will receive a payout in the form of f(x).

As the name of the function suggest, you want to maximise the outcome of the payout function as an investor. Why? Because you want to make more money.

So on one hand, if payout is positive, you make money and on the other hand if the payout is negative, you lose money.

Now this may sound really abstract. What even x and f(x) are you talking about Toby?

Alright, let me give you a concrete example. Suppose you allocate 100% of your portfolio to U.S. treasury bill that gives a yield of 4% in a year (not bad). This is your function that gets applied to your initial capital (money) if U.S. government can service their debt. So if the U.S. government pays their debt, then I can get 0.04 as payout to my investments and I am making money. Hurray!

So event x = U.S. government pays their debt

Payout f(x) = 0.04

In a nutshell, you make money.

But the example above only represents one unit of time

In reality, our investments is a continuous time series that does not rely on just variables at one unit time, but multiple. So in essence, you will have an array of x that describes what happens over multiple periods of time.

Because the value of x is not always certain, we can denote it as a random variable X. So for example, from time 1 to time 7, values of X can be {1, 0, 0, 0, 1, 0, 1}.

Don’t get thrown off by the numbers. Remember, the value in the set above simply means an event that happens at time t. All of them, by the way, will be input to your payout function because the ultimate outcome, whether you make your money or not depends on:

1. The entirety of events that happen, and

2. the payout function that you have.

Let’s run a simple investment simulation

Suppose you have a payout function as follows:

\(f(X) = mean(1-X^2), X \in \N\)

Also, suppose that the non-negative numbers (X) refer to the danger of current economy. The larger the number, the more dangerous the economy is where the smaller the better where 0 is minimum danger.

So X refers to an array of events let’s say denoted as a set of non negative numbers, for e.g. {1, 0, 0, 0, 1, 1, 1}, which represents the level of danger to the economy overtime.

Note: that level of danger of economy is what “financial experts” and gurus and influencers do all the time. Feel free to go to your favourite media site and take a look at the headlines. There will always be a prediction, known as forecast, about what the economy is going to be like in the next quarter, the next year or the next whatever 😄

1st Investment Occasion

Let’s say I am an entrepreneur and I have no clue about predicting the outcome of the economy, let alone a model that helps with my prediction. So I just make a random prediction that the economy will be safe and sound, 0s all the way!

But, reality might be different from what I predict:

1. Time 1: 1 (unemployment level soared)

2. Time 2: 0 (okay, economy is safe and sound)

3. Time 3: 0 (economy is booming)

4. Time 4: 0 (innovation is flourishing)

5. Time 5: 1 (oh no inflation is coming)

6. Time 6: 1 (tech stocks bubble bursting)

7. Time 7: 1 (war in a far away land breakout)

This means my prediction is {0,0,0,0,0,0,0}.

But the reality is {1,0,0,0,1,1,1}.

Based on the events above, I am a terrible forecaster. I am practically wrong more than half of the time.

But what happens to my portfolio?

We could input {1, 0, 0, 0, 1, 1, 1} to the payout function above.

You could calculate as per above and see that my payout is positive! (~0.43)

My bad prediction is giving out positive outcome for my investments. Phew!

2nd Investment Occasion

Then on another occasion, let’s say I am a finance influencer. I use economic model from Keynesian school of economics based on recent AI trends in the tech space, my connections, and my intelligent analysts. I explain my forecast in a word salad and I have super high confidence that economy will be safe and sound. So I predict, again, no danger for the 7 periods.

AI will save the economy! What. a. headline.

Oh boy I am good and I am on a winning streak

1. Time 1: 0

2. Time 2: 0

3. Time 3: 0

4. Time 4: 0

5. Time 5: 0

6. Time 6: 0

No danger to the economy what so ever until the last event…

Time 7: 3

Let’s say the Lehman Brother bank collapse in the last event that’s why it is a 3.

My prediction based on New-Keynesian model, AI, deep learning, churned by ivy-leagues graduates: {0,0,0,0,0,0,0}

Reality: {0,0,0,0,0,0,3}

86% accuracy! Not too shabby!

As a forecaster, I have done a super good job, predicting correctly for more than 80% of the time. A hit rate of 80%+ is better than any fortune teller that I know of.

Also on average, the events that have happened is not as bad as the previous scenario. If you take an average inputs of the second scenario (mean of X), it amounts to 0.43. While the average of the first scenario is 0.57. So the second scenario is less bad than the first scenario in terms of the danger (not the payout).

But what’s the payout to my portfolio?

Well, we can input {0, 0, 0, 0, 0, 0, 3} to our payout function mean(1-X^2) and we get a payout of…

-1.14

So I have lost money!

Now that is a sucker punch. Two observations here:

1. Although my prediction is mostly correct, frequency of accuracy of prediction can mean next to nothing to my investment payout.

2. x ≠ f(x). You can see that the mean of the danger of economy is worse in the first scenario, but my payout is positive. While the second scenario only had one bad event and is better overall, but it is enough to render the payout negative.

   In other words, economy bad can mean make money. And economy less bad can mean lose money.

So how do we tweak the investment payout function?

Well, I don’t know but a simple tweak from

\(f(X) = mean(1-X^2), X \in \N\)

to

\(f(X) = mean(max(1-X^2, -1)), X \in \Nx\)

is already enough from making your -1.14 losses into an astonishing gain of 0.71!

All you have got to do is ask yourselves, if a bad thing happens, how bad will my portfolio be affected? Is there enough “breaks” in my investment portfolio so that I can participate the upside in peace, knowing that the downside will not be so bad.

Forecasting is not important, what’s important is the investment payout function

From the above example, I think it is quite clear that people’s prediction on the outcome might mean very little your investment portfolio. What’s really important is your payout function.

In the example given, our first payout function is bad in handling black swan events. You only need 1 outlandish negative news to trigger your investment portfolio into a death spiral.

But there are two tendencies that I often see people do.

One, people focus too much on what’s going to happen

What if the U.S. increases interest rates?

What if there is no catalyst to economic growth?

What if there is another war that occurs?

And other what ifs that might scare us

However, in reality what affects our investment portfolio more than ever is the payout function that we established earlier.

Do we design our payout function to have a good chance of surviving market crashes? Is our IDX portfolio going to crash if war continues?

Borrowing from David Dredge from Convex Strategies,

Risk is not the bad events that could happen, risk is how much does it hurt you if that bad thing does happen.

Two, people look at the past to eradicate possibilities of what’s going to happen

Yes, we definitely can look at the past as a guideline to see what is the future potential. For example, if a company has been able to sold 100 units of goods the past year, it is likely that the company will be able to sell 100 units or more of goods in the subsequent year, ceteris paribus.

But, the past is not the be all and end all.

A more vivid example that may ring a bell to many people is startup valuations.

If a startup is valued $1mio —> $3.5mio —> $20mio —> $1Bio —> ??

Is the next valuation going to be $100Bio? Past data suggests that it is likely. But present data might paint a different story. In reality, the next day, the startup can declare bankruptcy and lose all of their valuation all at once.

These two tendencies in my opinion is very understandable because while fear and greed usually don’t generate returns, it does generate attention. So if you are in the media business, it might make sense to scare or entice as many people as you can so that you get the attention and the ka-ching from AdSense, endorsement, sponsors, etc. As a bonus, if you get your forecasting correct, you will look cool in front of people. Although you being cool does not necessarily make others richer as investors.

If you are an investor, ignoring fear mongering or greed inducing media isn’t such a bad idea so that you can focus on your investment payout function.

Closing Remarks

Based on errors people make above, we see that worrying about the future through forecasts does not bring investment returns. It rather creates unnecessary bearishness that makes us not invest at all.

On the other extreme, being overly fixated on past performance can make us blind to negative things that adversely impact our portfolio performance. It is unwise to assume that bad future events will never happen because it has never happened before in the observed past time period.

Therefore, I humbly invite people to stop worrying about forecasts and start focusing on what matters most to us, the payout function. Now go and make your middle school teacher proud.