Estimated reading time: 5 minutes

No matter the size of the decision, as humans we are constantly weighting choices. We assess our current situation in the light of previous, comparable situations. In this decision-making process we do not weigh all opportunities equally. Many studies show that we have an aversion to uncertainty, i.e. risk aversion. We also have an aversion to losses, i.e. loss aversion.

Risk aversion is built into our human decision-making mechanism. It is beneficial for us as it helps us to prioritize choices that have a more certain positive outcome and avoid choices that could harm us. It also helps us to search for opportunities that maximize payoff and minimize risk. Risk aversion has a dampening or controlling effect on our decisions. It can result in missed opportunities or make us less entrepreneurial.

As risk aversion is a key factor in our decision-making process, we need to understand the underlying mechanism better. And we want to know how it can help us in optimal decision making.

## A closer look at risk aversion

Risk aversion is generally understood as aversion to volatility. Economic models like CAPM^{1} (Capital Asset Pricing model) take this into account by focusing on the relationship between potential rewards and the uncertainty of those rewards. In other words, people are only willing to take on riskier investments if they expect a bigger payoff to compensate for the increased uncertainty. Therefore, the performance of risky investments is typically measured via the reward-to-volatility ratio, or the Sharpe Ratio.

Closely related to risk aversion is the concept of loss aversion. It means that we weigh losses and gains differently. People in general tend to perceive losses as more significant than gains of the same size^{2}.

## Prospect theory

Using empirical data, Amos Tversky and Daniel Kahneman confirmed the existence of both risk and loss aversion. Based on their experiments they found the loss aversion coefficient for humans to be somewhere between 1.5 and 2.5. This means that losses weight up to 2.5 times more than gains of equal size.

Based on this insight, they developed the Prospect Theory^{3}. Daniel Kahneman later received a Nobel Prize for these findings.

In the graph above we see how risk aversion leads to flattening upper and lower tails, indicating aversion to big moves (or volatility). However, due to loss aversion we see that the slope for the losses is twice as steep as the slope for the gains.

## Implications of risk and loss aversion

These mechanisms have far-reaching implications on our decisions. Those can be observed in the pricing of investments in financial markets. In the CAPM model we already saw that risk aversion makes people require a premium for more volatile investments.

The effect of loss aversion is that it makes market participants react differently in crashing markets than in sideways or rising markets. This leads to faster selloffs and relatively higher volatility in markets trending downwards. We can observe this also from varying implied volatility patterns in the derivatives markets.^{4} This shows us that market participants consistently require additional premium for potential losses. ^{5}

Market activity reflects how all participants feel about risk and potential losses at a specific point in time. Since their perception can change over time due to changing conditions, the risk premium investors demand for taking on risk also fluctuates.^{6} ^{7}

Therefore, a risk model, that is based on historical price-changes, inherently incorporates the risk and loss aversion in the market at specific points in time.

## What about risk-neutral models?

In practice, we also hear about risk-neutral models. These models are used to make risks comparable over time and across multiple use-cases. Therefore, the (varying) risk premiums are excluded. The net present value of an asset or project is then estimated by discounting against the risk free interest rate.

Risk neutrality is assumed in the pricing of financial instruments that are used for hedging, i.e. for covering the risk. The pension sector in The Netherlands for example uses a risk-neutral (Wtp-Q) model alongside a risk averse (Wtp-P) model. The former is used to obtain a risk-neutral corresponding value of a given cashflow of future liabilities^{8} ^{9}. The latter includes the risk and loss-aversion as currently perceived by the market. It is important to note that bothWtp models have completely different risk profiles.

## What is the right level of risk and loss aversion?

In many cases, risk and loss aversion can help us to make better choices. Following the market helps us to obtain a market perceived risk aversion level. However, sometimes we could also opt to deviate from that risk aversion level in the market. For example, if we are faced with choices that could endanger our survival or that of the company, we would be more careful or more risk averse. Or contrarily, if we have enough means to cover potential losses, we could adopt a more risk taking approach. The extent to which we have a different risk aversion than the market is also called ‘relative risk aversion’ or ‘gamma’.

## The importance of proper risk estimations

Risk and loss aversion are key factors in human decision-making. They have substantial impact on the prices and the dynamics of the market.

We can evaluate risks independent of the context by observing the full history of a variable of interest. Alternatively, we can do so in a context-aware fashion. This allows us to capture the varying risk premiums over time and under different situations. Our REGIME models help us to obtain those.

If you want to read more about the principles behind the REGIME method, you can read the article on reference class methodology. An evaluation of the performance of different methods can be found in optimal model selection article.

#### Footnotes

- CAPM: Capital Asset Pricing Model. Developed by Sharpe (1964) and based on Modern Portfolio Theory by Markowitz (1952). ↩︎
- In good periods also ‘fear of missing out’ (FOMO) plays a role which can lead to herding behaviour. In combination with the loss aversion this can lead to more extreme movements and ‘fatter tails’ in the distribution ↩︎
- For more information on the prospect theory see: Daniel Kahneman ‘Thinking, fast and slow’; chapter 26 ‘The prospect theory’. ↩︎
- We can observe this from the ‘implied volatility skew’: out of the money put options are generally more expensive than out of the money call options with the same but oposed ‘moneyness’. The price difference shows the risk surplus by the market. ↩︎
- Valeriy Zakamulin (2023): Can Loss Aversion Explain the Stylized Facts of Implied Volatility? ↩︎
- Baele et al (2018): ‘Cumulative Prospect Theory, option returns and variance premium’. Table 5 shows a CPT model applied for 50% having a time-variant loss aversion coefficient with an average value of 2.42. ↩︎
- Dai and Singleton (2001): ‘Expectation Puzzles, Time-varying Risk Premia, and Affine Models of the Term Structure’. p4: state-dependent affine models or regime-based models with time-varying factors are able to model the term structure. They show time-varying risk premiums. ↩︎
- The previous pension system was based on fixed guaranteed future cashflows, also known as defined benefits (DB). The new pension system instead provides a range of possible outcomes according to the Wtp P model. ↩︎
- See also the wikipedia article aboutvaluation adjustmentsfor more information on the impact of hedging against a risk free rate. ↩︎