It's safe to say that the most difficult job in finance is to estimate and manage **risk,** which drives the discount rates and therefore the valuation of any asset that would generate cash flows in the future — however distant it is.

A more difficult job, however, is to distinguish **risk** from **uncertainty**.

For most people the two terms mean the same thing: something that is not known for sure in advance. For financiers the two are very different animals: risk could be measured and managed while uncertainty is completely out of the hands of any moral being.

Or in financial jargon: **risk has a known (or presumed) distribution; uncertainty does not.**

In the strictest sense, there is actually nothing in our life that is 100% certain. Unpredictability is so fundamental a part of our life that it's actually surprising how most people choose to ignore it or believe otherwise.

Take the **Bus 68** that I use everyday to go from my little apartment in the 6th arrondissement (Saint-Germain-des-Prés) to our office close to l'Opéra for example.

The one-way trip seldom takes more than 20 minutes. A normal citizen with the same commute would psychologically assume a 30-minute trip to be unusual — "There must be an accident!" — and take pride when the bus finally passes by a seemingly broke-down Monoprix truck on the road side.

On the contrary if the trip is less than 10 minutes, he would consider himself "lucky" and spend an extra 5 minutes in the café nearby the office where he usually has his morning *croissant* and *café au lait*, maybe tweetting about his **luck** along the way.

In other words, most of the mini-tasks we accomplish in our everyday life, we see them through a pair of **binary** lenses — we only care whether the mini-tasks are accomplished at acceptable cost (both in time and money). We seldom analyze the distribution of the outcomes.

By ignoring the distribution of random outcomes (in our example it would be the time it takes to go to my office from my apartment), we human beings therefore develop a **false sense of confidence** regarding our understanding of the world.

**A tale of risk and uncertainty**

Using my daily trip on Bus 68 as an example, if one takes time to analyze enough samples, one might form a different opinion toward this seemingly simple thing.

For example, in the rush-hour window of 7am-9am, during the week days and in April, the **researcher** might find out that the time it takes for Bus 68 to complete this commute for the energetic young VC (origin: Taiwan) is actually very close to a normal distribution with **a mean of 15 minutes and a sigma of 2 minutes**, after analyzing the 450-something samples collectible given the criteria.

Such researcher could then develop a more advanced understanding of this simple subject, equipped with the powerful statistics. He would be able to tell me that in this season — he has confidently generalized the month of April to a full season — the probability for me to spend more than 19 minutes on Bus 68 would be less than 2.5%.

If punctuality is absolutely important for my job, I could then buy an insurance from him, who had decided to quit his stable job at INSEE (Institut national de la statistique et des études économiques) and started his own startup selling insurances to young VCs living in Paris — *such a huge market that no startup should miss.*

As a diligent person I've always strived to hop on the bus before 8:30am while my first meetings of the day usually start at 9:00am. The payout of the insurance would be used to cover the loss due to my spending more than 30 minutes on the bus — which is 7.5 sigmas from the mean — therefore missing an important meeting that could generate an expected *carried* in long-term startup investments with an NPV (net present value) of $2M. I will then pay a weekly premium in exchange for this insurance.

This is risk measurement and management. The financial structure of this vehicle is such that it allows an unknown future with a certain distribution to be "smoothed out" at least financially. The input variables for all parties are expected loss and the distribution of the commute time.

Initially the statistician-turned-insurer labelled the payout as at a fixed amount of $2M. Given that the event is 7.5 sigmas from the mean, he figured that there's very little chance for him to ever need to doll out the $2M. After enjoying my premium payments for a year without having to pay anything, he decided to propose a new package that was more tailored to the target market (young VCs living in Paris).

After carefully analyzing all historical French VC return numbers, he offered to cover the bonus that I could have earned if I had not missed the meetings and therefore the chance to invest. He would follow up the missed investments until its exit — assuming there is one — and pay me out accordingly. In exchange he wanted a much higher premium.

"You could have scored a real unicorn, my friend." He smiled and said, knowing very well that there has been very few unicorns in the recent history in France.

I took the deal and started paying him a much higher premium.

On a beautiful May day, a *Collège Stanislas* student who just got dumped by his girlfriend decided to throw himself in front of Bus 68, right in front of his ex and her friends waiting outside the school for the chime. I was on that particular bus — in fact, I have been on the same bus for years which arrives usually around 8:25-8:30am. The police officer that came insisted on interviewing all 10 passengers (and therefore witnesses) before letting us go. I was the 3rd in line and I managed to cut short my time by faking a Chinese accent in my French.

I arrived at the office 20 minutes late for my 9:00am meeting, which is 17.5 sigmas away from the mean. The entrepreneurs had left. I called my insurer, registered the process. He put it into his system.

5 years later, the startup that I missed went IPO on Nasdaq and became the first ever lean startup in French to break $10B market cap — a *decacorn*. I quickly calculated the carried interest I could have earned and it racked up, even on a conservative side, to $100M.

I made a call to my now good friend through my years of paying high premia. His voice trembled, telling me that his startup, now a registered insurance company, had only $20M in cash and marketable securities.

He declared bankruptcy in the following week.

**Confusing uncertainty with risk**

In the 2nd half of the story, there were a couple of confusions regarding risk and uncertainty.

The commute time with Bus 68 is very likely a genuine normally distributed random process. Paris is a city that changes very slowly. All the events that could happen on the route that could slow down (or speed up) Bus 68 are reasonably uncorrelated. Therefore Central Limit theorem works out here by giving Bus 68 commute time a normal distribution.

The insurer and I added in our own buffer by stretching the sigma multiple to 7.5 — I don't expect to collect the payout because I would rather have made it to the meetings and earned the carried interest that could come from the investments. And given the original deal of fixed $2M payout, the only unknown here is the bus commute time, which is normally distributed. Even at an outlier event, e.g. a poor Collège Stanislav student killed himself on that particular day, the payout would still have been covered nicely as that's the only unknown.

This is a good example of risk management through insurance, from both the insurer's side and my side.

Then the insurer got "smart" and incorporated his analysis on the expected carried interest of the French VC industry into our deal.

Big mistake.

VC returns are highly skewed, with a handful of super VCs making most of the profit of the industry. France historically fell into "the rest of the pack". The mean value — however sophisticated the estimation is — of French VC returns was surely a relatively low value that he believed that he could handle.

But I was not a French VC and I invested globally. In other words, I was an outlier VC that invested in the game of true outliers.

Then the meteor hit. The little pony I missed that morning grew up to become a *decacorn*. By incorporating the highly uncertain VC returns (with no valid distribution globally) into the insurance policy, the insurer turned a sure **risk** into an unsure **uncertainty**.

Instead of managing the **risk**, he turned his business into managing the **uncertainty**, which is impossible since the distribution is unknown or unstable.

On my side I committed a serious mistake as well.

I underestimated **the default risk** of the then startup founded by the former INSEE statistician. When it's time for me to collect the payout, after years of premium payment, the insurer went down and I ended with nothing, after all legal processes were done.

Would I have been able to estimate the default risk of the firm? It's probably unlikely since it was another startup and therefore highly **risky** — or shall we say highly **uncertain**? — by itself.

I was just as naïf as the statistician-turned-insurer, if not more.

### Mapping the tale to the history

The above might sound like a pure narrative in itself. However, if you map the players to those during the last financial crisis with the insurance being the infamous CDS (Credit Default Swap), you'll be able to see how dangerous it is to mistake one's knowledge about risks with his (false) knowledge about uncertainties.

For readers that are interested in the topics of **risk v.s. uncertainty**, do not miss out on Nassim Taleb's books.