Financial markets, like other markets, are where supply and demand meet and price discovery takes place. And when financial asset prices are discovered, the market fulfills another important function - it prices risk. A price, in turn, can be interpreted as an implied probability-weighted average of all possible outcomes.

It is intuitive, therefore, to approach fundamental valuation by running this logic in reverse; identify possible outcomes, determine their impact and estimate their probabilities. The sum product of all of them represents a 'fair' valuation.

**Risk and uncertainty**

A problem arises when probabilities cannot be estimated and instead have to be guessed.

*When you can make estimates, you are dealing with risk. When you are best-guessing, you are dealing with uncertainty.*

The concepts of risk and uncertainty are quite obviously not exclusive to financial markets. Cambridge University has profiled a series of papers of risk and uncertainty more broadly. Their Professor David Spiegelhalter said "Making important decisions in the face of uncertainty is unsettling and difficult."

Needless to say, "unsettling" is not a pleasant feeling in financial markets. There are a number of examples.

Elections are part risk and part uncertainty. We can use opinion polls and other inputs to try to assign probabilities to various outcomes, but uncertainty remains, well, a certainty. How likely is a gaffe, revelation or external event? Will the politicians actually do what they've promised, and if not, then what instead?

As the number of moving parts increases, so does the difficulty in estimating with confidence and so therefore does uncertainty. Political outcomes are normally harder to predict when different sides are forced to negotiate; between different parties or differently controlled different chambers (as in the US) or to form a government at all (as in most European countries). How will negotiations shape up and what if they don't produce a budget (as in the US) or a fragile coalition government (as in Italy) or no government at all (as in Belgium not so long ago)?

**A sting in the tail**

Tail 'risks' are a special case. Though they are called 'risks', in some cases they are in fact uncertainties. With the US government shutdown and an approaching debt ceiling, what is the probability of the US defaulting, and how severe would be the consequences? The answer to the latter is likely "massive" and, largely as a result, the answer to the former is probably "tiny". But what do you get when you multiply "massive" by "tiny"? Using the 'probability-weighted scenarios' approach above, both the probabilities and the outcomes somehow have to be quantified. And with as many moving parts as either a nation's economy or its government have, such estimation is almost impossible to do with any real confidence.

It's not just politics. Another hot topic at various junctures has been terrorism. What is the probability of a terrorist attack, and (aside from the human consequences) what would be the extent of the economic or market impact? Historical data are useless if you think there has been a structural shift in the world (as after 9/11).

What about natural disasters? Logic dictates than almost all financial markets should price in some chance (however minute) of the 'big one' hitting Tokyo or Los Angeles. When, where exactly, how big and how markets would respond in each case, is anyone's guess.

**Investor decision making in reality**

In practice, uncertainty tends to be viewed in a binary fashion, with market participants considering the extreme scenarios and looking at limit-case payoffs in each.

Tail 'risks' are often priced according to sentiment. For example, when sentiment is positive, a low-probability, high impact negative outcome might be treated as negligible, while when sentiment is bad, its probability might be treated as implausibly high. This can be interpreted as a very significant 'risk' premium, due to the probability of the outcome occurring being unknown or unquantifiable.

Of course, while implying probabilities from prices is useful analytically, it should not be assumed that pricing reflects pure expectations. Aside from the treatment of tail risks mentioned above, there are many other considerations such as carry, positioning, flow, second-guessing of central banks and other policymakers and so on.

And moreover, there is more to consider in markets than valuation alone.

**Where the risk vs uncertainty distinction becomes crucial**

To reiterate: When you can make estimates, you are dealing with risk. When you are best guessing, you are dealing with uncertainty.

You may find that you're asked to discuss the implications of an election, a US government shutdown, the future of the Euro, a natural disaster or a terrorist attack investor decision making, or simply answer a 'logic' question relating to uncertain outcomes. Being able to call upon this type of analysis this in your investment banking interview (especially for a financial markets position) should help you considerably. While you don't need to be able to repeat the entire discussion, understanding and articulating these sorts of concepts is exactly what you should be looking to do.