What is Risk in Finance? All You Need To Know

Simple Definition of Risk

Simply put, risk is the potential for injury or loss. In the context of finance, risk alludes to the potential for financial loss on investments.

A Short Example of Risk

The most commonly used metric for risk is the standard deviation of portfolio returns. Increasing values of the measure indicate a more unpredictable portfolio, which is seen as negative.

A Deeper Understanding of Risk

Financial risk comes in many forms:

• Market risk: The possibility of loss due to movements in the market, either as a whole or specific investments
• Credit risk: The possibility of loss due to default on a financial obligation
• Model risk: The possibility of loss due to errors in mathematical models, often models of derivatives. Since these models contain parameters, such as volatility, we can also speak of parameter risk, volatility risk, etc.
• Operational risk: The possibility of loss due to people, procedures or systems. This includes human error and fraud
• Legal risk: The possibility of loss due to legal action or the meaning of legal contracts

To understand the mathematics of risk, we must distinguish between risk, randomness, and uncertainty.

Measuring risk in investments often involves using ideas from chance (probability). But to do this, we need to know how likely things are to happen (probability distribution). This can be based on a lot of data or a good guess (model).

The problem is, sometimes we don’t have enough information or we’re dealing with completely new situations. This makes it really hard to say how probable something is, especially for very rare events or things that have never happened before.

For example, we might have a good idea of what might happen during an alien invasion (thanks to movies!), but how likely is it actually to occur? We have no clue!

When you do not know the probabilities then you call it as uncertainty.

Risk vs Uncertainity

1. For risk the probabilities that specified events will occur in the future are measurable and known, i.e.,
   there is randomness but with a known probability distribution. This can be further divided.
   a priori risk, such as the outcome of the roll of a fair die
estimable risk, where the probabilities can be estimated through statistical analysis of the past,
for example, the probability of a one-day fall of ten percent in the S&P index
2. With uncertainty the probabilities of future events cannot be estimated or calculated.

In finance, we focus on estimating risk and using statistical and probability tools to quantify it. Certain financial models attempt to account for uncertainty. Avellaneda et al. (1995) investigated uncertain volatility.

Here, volatility is uncertain, is allowed to lie within a specified range. But the probability of volatility having any value is not given. Instead of working with probabilities we now work with worst-case scenarios. Uncertainty is therefore more associated with the idea of stress testing portfolios. CrashMetrics is another example of worst-case scenarios and uncertainty.

Beyond the Bell Curve: When Standard Deviation Fails

To define risk mathematically, start with standard deviation. The Central Limit Theorem (CLT) states that when a large number of investments are added together, the expected return and standard deviation of individual investments determine the statistical properties of the portfolio, resulting in normally distributed returns. Because the normal distribution is symmetrical around the mean, the standard deviation can be used to quantify possible downsides.

However, this is only applicable if the prerequisites for the CLT are met. Standard deviation may not be meaningful for small, correlated, or non-variable assets.

Focusing on the Downside: Risk with Semi-Variance

Semi variance is a quantitative concept of risk that solely considers downside departures in its calculations. This definition is used in the Sortino performance measurement.
According to Artzner et al. (1997), a risk measure must meet certain qualities to be considered rational. Such risk measures are referred to as coherent.

Related Readings

• Put-Call Parity: All You Need To Know
• Modelling Approaches in Quantitative Finance: All You Need To Know
• Central Limit Theorem In Finance: Power Your Portfolio Now