From fate to the black swan
What is risk? Five answers – and not one of them cancelled the previous.
Rolandas Rakštys · Lecturer · Vytautas Magnus University, Agriculture Academy · Faculty of Bioeconomy Development, Department of Business and Rural Development · [email protected] · ORCID 0000-0003-0299-9930
Chapter 3 “Business risk and profitability”, section 3.1.1 · English translation of chapter v1.14.4 (2026-10-31) · set v1.0 · 18 slides, ≈ 30 min
Rakštys, R. (2026). Chapter 3. Business risk and profitability (English translation of v1.14.4, 2026-10-31). Verslo planavimas ir vertinimas [Business planning and evaluation]. Vytautas Magnus University, Agriculture Academy. https://rakstys.eu/studijos/verslo-planavimas-ir-vertinimas/en/skyriai/ch03/ · CC BY-NC-ND 4.0
Two opposite errors – one root
Everything into one number
A manager reduces risk to a standard deviation or a beta coefficient and ignores the psychological and institutional dimensions.
The result is an illusion of “mathematical safety”.
No numbers at all
An entrepreneur rejects any quantitative assessment, “because numbers do not reflect reality anyway”.
The result: the loss of any way to structure decisions and compare alternatives.
Both make the same mistake – they apply one paradigm where several are needed.
Quantitative
the statistical school
Behavioural
the psychological school
Ontological
the philosophical school
The schools did not replace one another in sequence; they coexist in present-day practice. Effective risk assessment is their synthesis: quantitative models, behavioural insights and institutional perspectives do not compete but complement one another.
From fate to instrument
Origin of the word (Bernstein, 1996)
What matters is not the sum but its utility
17th century: Blaise Pascal and Pierre de Fermat created probability theory – an intellectual break.
Expected utility
Bernoulli (1738)Working on the famous St Petersburg paradox, Bernoulli showed that a rational decision maker assesses not the absolute winning but its utility.
Diminishing marginal utility: utility falls as wealth grows.
The first formal model of risk aversion: the choice is
In financial theory the risk–return relationship is inseparable from the assumption of risk aversion (Bernoulli, 1738/1954).
Not all indeterminacy is alike
Risk
probabilities knownThe probabilities of the possible outcomes are known, or can reasonably be calculated from experience.
Uncertainty
probabilities unknownNeither the possible outcomes nor their probabilities are known.
Profit arises from uncertainty, not from risk
Measurable risk can be insured or diversified – and so it yields no long-term economic rent.
The entrepreneur’s function
To take decisions under uncertainty, where others are unwilling or unable to (Knight, 1921).
Models have a zone of validity
First: not all indeterminacy is of the same kind – different situations require different management instruments.
Second: the discounted cash flow model (DCF), Monte Carlo simulations and sensitivity analysis work well in the zone of risk, but in the zone of uncertainty they become deceptively precise – the problem of spurious precision, Chapter 2.
Third: risk cannot always be diversified or insured. A new product in an unknown market, a geopolitical rupture, a regulatory revolution or a technological upheaval is often closer to uncertainty.
Risk becomes a measurable object
1. Risk is variance
Or the standard deviation: the spread of returns around the expected mean.
2. The portfolio effect
Combining assets whose returns are not perfectly correlated reduces risk without reducing the expected return.
3. The efficient frontier
the curve of optimal portfoliosAbove it a higher return is not available without additional risk.
What matters to an investor is not the risk of an individual asset in itself but its contribution to the risk of the whole portfolio – risk depends on correlation too. This is the theoretical foundation of diversification.
The assumptions are disputed, the language remained
1. The normal distribution
Returns are normally distributed.
2. Mean and variance only
Investors assess only these two (mean-variance).
3. Stable correlations
Correlations between assets are stable over time.
Each assumption later became the object of serious academic criticism.
But variance remained the “foundation of the language” of financial theory – it is used even where the assumptions are not strictly satisfied.
The market pays only for systematic risk
Normative
Markowitz’s theory: how a rational investor ought to construct a portfolio.
Positive
How the market prices risk: the Capital Asset Pricing Model (CAPM).
The market compensates only systematic risk. The unsystematic part the investor removes by diversifying, at no cost at all.
The beta coefficient (β)
For business planning: risk that can be reduced by diversifying must be assessed differently from risk arising from the economy as a whole, from interest rates or from geopolitical tension. The application of CAPM to the discount rate and to the Weighted Average Cost of Capital (WACC) is in Chapter 11.
People decide differently from the models
Loss aversion
the loss weighs morePsychologically a loss “weighs” roughly 2–2.5 times more than an equivalent gain. To win or to lose EUR 100 000: the expected value is zero, yet the game is assessed as a losing one.
Reference dependence
the change, not the levelWhat is assessed is not the final position of wealth but the change from a reference point.
The probability weighting function
Small probabilities are overweighted (lottery tickets and insurance against rare disasters), medium and large ones underweighted.
The significance of prospect theory is practical
Forecasts that are too optimistic
Managers systematically forecast revenue too optimistically – overconfidence.
Projects continued for too long
Projects in which losses have already been incurred – the sunk cost fallacy.
Never entirely “objective”
The assessment of risk in an organisation. More on the biases in section 3.1.3 (Kahneman & Tversky, 1979).
Extreme events are more frequent than the normal distribution allows
Markowitz
Mean and variance suffice – normality is convenient but not necessary.
Black-Scholes
A lognormal price distribution, that is, normal log returns.
CAPM
Does not formally require normality, but its empirical tests and risk measures rely on it.
What they share: all of them handle fat tails badly.
Cotton price series: fat tails – extreme events occur far more often than the normal distribution predicts.
Later research found the same regularity in the equity, currency and commodity markets.
Models work between swans, not against them
A black swan is a rare, unpredictable yet powerful event that changes the whole system.
Standard risk management models create a deceptive sense of safety: they work well between black swans but are helpless against the swans themselves (Taleb, 2007).
No single tradition is sufficient on its own
Knight
Reminds us that not all uncertainty is calculable.
Markowitz and CAPM
Give us a quantitative language.
Kahneman and Tversky
Show that people depart systematically from quantitative logic.
Mandelbrot and Taleb
Warn that quantitative logic itself rests on assumptions that can collapse.
A modern business planner has to be able to combine all of these perspectives – that is the central message of Chapter 3.
What is risk? Five answers
They complement, they do not replace
Miller and Reuer (1996) present measures of loss as an alternative to variance – but nothing prevents using them together.
Not a binary distinction
De Groot and Thurik (2018): between risk and uncertainty there is a continuum; in real life uncertainty is met more often than measured risk.
The probabilistic level
Risk as a distribution of possible outcomes; measured by variance or the standard deviation (the Markowitz and CAPM paradigm).
The loss level
The probability and the magnitude of undesirable outcomes: Value at Risk (VaR), Conditional Value at Risk (CVaR), the Sortino ratio.
The systemic level
A relationship with the wider environment: beta, and contagion risk, which cannot be eliminated by diversifying.
The behavioural level
The perception and assessment of decision-makers: reference dependence, loss aversion.
The ontological-organisational level
Structural vulnerability and a constraint on value creation: the managerial decision, the institutional context, the organisational culture.
The five levels explain why the same situation is assessed so differently.
Risk information is always framed
Belonging to a group
Changes risk perception through the availability heuristic: events seen in one’s immediate surroundings are assessed as more likely (Stapel et al., 1994).
Framing
the same object, another frameThe same object of risk is interpreted differently depending on how it is framed. The risk information presented to investors is not “objective” (Vaughan & Seifert, 1992).
“Vivid” and latent
Low-probability, high-impact events are weighted non-linearly – organisations react disproportionately to vivid risks and ignore latent ones (Kahneman & Tversky, 1979).
Risk is not one number but several perspectives
The schools of risk did not replace one anotherThe quantitative, the behavioural and the ontological coexist and complement each other.
Knight’s distinction shows where the models become deceptively preciseThe discounted cash flow model, Monte Carlo simulations and sensitivity analysis work well in the zone of risk.
Risk information is always framedThe risk information presented to investors is not “objective”.
For discussion · question 3.15. Is Knight’s distinction between risk and uncertainty practically useful, or is it merely a philosophical abstraction? Give an example of a business situation in which the distinction changes the decision.
References
Bernoulli, D. (1738/1954). Exposition of a new theory on the measurement of risk. Econometrica, 22(1), 23–36.
Bernstein, P. L. (1996). Against the Gods: The Remarkable Story of Risk. Wiley.
De Groot, K., & Thurik, R. (2018). Disentangling risk and uncertainty: When risk-taking measures are not about risk. Frontiers in Psychology, 9, Article 2194. https://doi.org/10.3389/fpsyg.2018.02194
Kahneman, D., & Tversky, A. (1979). Prospect theory: An analysis of decision under risk. Econometrica, 47(2), 263–291.
Knight, F. H. (1921). Risk, Uncertainty and Profit. Houghton Mifflin.
Lintner, J. (1965). The valuation of risk assets and the selection of risky investments in stock portfolios and capital budgets. The Review of Economics and Statistics, 47(1), 13–37.
Mandelbrot, B. B. (1963). The variation of certain speculative prices. The Journal of Business, 36(4), 394–419.
Markowitz, H. (1952). Portfolio selection. The Journal of Finance, 7(1), 77–91.
Miller, K. D., & Reuer, J. J. (1996). Measuring organizational downside risk. Strategic Management Journal, 17(9), 671–691.
Mossin, J. (1966). Equilibrium in a capital asset market. Econometrica, 34(4), 768–783.
Sharpe, W. F. (1964). Capital asset prices: A theory of market equilibrium under conditions of risk. The Journal of Finance, 19(3), 425–442.
Stapel, D. A., Reicher, S. D., & Spears, R. (1994). Social identity, availability and the perception of risk. Social Cognition, 12(1), 1–17. https://doi.org/10.1521/soco.1994.12.1.1
Taleb, N. N. (2007). The Black Swan: The Impact of the Highly Improbable. Random House.
Vaughan, E., & Seifert, M. (1992). Variability in the framing of risk issues. Journal of Social Issues, 48(4), 119–135. https://doi.org/10.1111/j.1540-4560.1992.tb01948.x
Rakštys, R. (2026). Chapter 3. Business risk and profitability (English translation of v1.14.4, 2026-10-31). Verslo planavimas ir vertinimas [Business planning and evaluation]. Vytautas Magnus University, Agriculture Academy. https://rakstys.eu/studijos/verslo-planavimas-ir-vertinimas/en/skyriai/ch03/ · CC BY-NC-ND 4.0
These slides are based on the textbook Verslo planavimas ir vertinimas [Business planning and evaluation]. The text was translated, structured and visually laid out with the help of artificial intelligence tools (Claude), following the protocol for working with AI and the verification procedures set by the author.