Precise numbers, wrong decisions
A critical analysis: where the model, the person and the organisation go wrong
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 3.1.3 · chapter v1.15.3 (2026-10-31) · set v1.0 · 20 slides, ≈ 30 min
Rakštys, R. (2026). Chapter 3. Business risk and profitability (English translation of v1.15.3, 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
Tidy, but fragile
Mathematically tidy – numbers to the decimal, everything adds up.
…but fragile. The cracks run through three layers:
- the model
- the person
- the organisation
- the model errs
- the person errs
- the organisation errs
- what to do
- how much risk to take
- synthesis
CAPM: an elegant theory, weak evidence
The Capital Asset Pricing Model (CAPM) became the standard for the cost of equity not because its assumptions are realistic, but because it created a disciplined language about systematic risk. Criticism of it has two axes.
The true “market portfolio” would include all the wealth in the world – and it is unobservable. What is tested is therefore not the model itself but the suitability of the market index as an approximation of the market portfolio.
Empirical Fama and French (1992)
The empirical success of CAPM is poor: the beta coefficient alone explains only a small part of the cross-sectional variation in asset returns.
Three anomalies and the Lithuanian market
The size effect
The returns of small-capitalisation firms systematically exceed the predictions of CAPM.
(Banz, 1981)The value effect
Firms with a high book-to-market ratio earn more than CAPM predicts.
(Fama and French, 1992)The momentum effect
Assets that have done well recently tend to keep doing well.
(Jegadeesh and Titman, 1993)A multiscale test of CAPM in three CEE markets: in markets of small capitalisation and low liquidity the explanatory power of the model is smaller still, and pricing is additionally affected by illiquidity, market segmentation and institutional factors (Dajčman et al., 2013).
For a Lithuanian firm the limits of CAPM are not a theoretical remark but an everyday valuation problem. How it is done – section 3.1.5.
A tool for thinking, not a truth
CAPM is not “a truth about the world” but a normative model that allows one to think in a structured way about the relationship between risk and return.
ad hoc additions
In practice CAPM is supplemented by a country premium, a size premium, a liquidity adjustment and other ad hoc additions, which partly compensate for the limitations of a single-factor model (Chapter 11).
The limits of the model show that the ontology of risk cannot be reduced to β alone.
Once in almost 14,000 years
The assumption of a normal (Gaussian) distribution is present in Markowitz’s portfolio theory, in CAPM and in Black–Scholes option pricing – in some directly, in others through empirical tests and risk measures.
● In financial markets such events occur far more often than that. diagram, without numbers
This is not Mandelbrot’s number but a consequence of the assumption of normality: for price changes Mandelbrot (1963) proposed a stable Pareto distribution with infinite variance, in which “five standard deviations” has no meaning at all. The number is not a measure of risk but a test of the assumption.
Model risk
Model risk – an error arising not from reality itself but from the form in which it is represented.
The plan is mathematically tidy yet ontologically fragile: if the model has no place for an extreme scenario, it systematically underestimates the need for:
In 2008 risk management models based on the assumption of a normal distribution showed that banks’ portfolios were safe – for as long as that assumption held.
Quantitative risk models are necessary but not sufficient: they are supplemented by stress testing and scenario analysis covering even the “impossible” scenarios (Chapter 4).
2022: the end of an assumption
Average annual inflation on the harmonised index of consumer prices in 2022 (Bank of Lithuania, 2021, 2023b; Ministry of Finance of the Republic of Lithuania, 2021)
The deviation is not a “five-sigma event” that the model would have classed as impossible, but the end of the assumption on which the model rested. In a business plan an assumption is worth writing down together with the condition whose change makes it void (Chapter 2).
When the person errs
Prospect theory (Kahneman and Tversky, 1979) showed that people’s assessment of risk departs systematically from the rational model. For business planning seven cognitive biases are particularly important.
Overconfidence
“I am 90 % certain.”
Managers’ 90 % confidence intervals contain the true value in only about 50 % of cases (Russo and Schoemaker, 1992).
- overestimation of one’s abilities
- overplacement of one’s position relative to others
- overprecision – which directly produces confidence intervals that are too narrow
In business planning: over-optimistic revenue forecasts and ranges of risk that are too narrow.
The past, vividness and the first number
2Loss aversion and the sunk cost fallacy
Once a project has incurred losses, managers tend to invest further in the hope of “recouping”, even where the rational decision would be to stop. This matters most in long-term investment projects (Chapter 10).
3The availability heuristic
Risks that are more easily recalled – recently experienced, vivid, emotionally affecting – are judged more probable. After a well-known cyber incident the IT security budget may grow disproportionately while latent supply chain risk goes unnoticed.
4Anchoring
Initial information – even when unrelated – influences the final decision disproportionately. In business valuation the first price offered “anchors” the negotiation and shapes the range of expectations (Tversky and Kahneman, 1974).
Groupthink and herd behaviour
Groupthink
The strong unanimity of a group suppresses critical thinking and the consideration of alternatives (Janis, 1972). Conformist boards of directors and investment committees may systematically underestimate strategic risks.
Herd behaviour
Decision-makers follow others in the belief that they have better information – an informational cascade arises (Bikhchandani, Hirshleifer and Welch, 1992): each individually rational decision becomes collectively irrational.
The reputational dimension: it is often safer for managers to be wrong together with everyone else than to be right alone – which reinforces conformity in investment decisions.
The five stages of a bubble
Herd behaviour is the principal mechanism by which bubbles form. In Manias, Panics, and Crashes Kindleberger (1978) described the evolution of bubbles in a five-stage model (Kindleberger and Aliber, 2005).
- 1 · Displacement
A new technological or economic factor creates initial opportunities
accession to the EU in 2004 and a sharp rise in the availability of credit
- 2 · Boom
Prices rise, optimism grows, more and more participants join
the expansion of credit
- 3 · Euphoria
A loss of rationality – “this time it’s different”
the expectation that prices would keep rising
- 4 · Profit taking
Experienced participants begin to sell
the realisation of profit
- 5 · Panic
Mass selling, a collapse in prices
the sudden fall of 2008–2009
Tulip mania (1637), the dot-com bubble (2000), the property bubble (2008): the model recurs, only the object of the bubble changes.
The business plans drawn up during the Baltic cycle rested on the assumption of continued price growth – not because their authors were poor analysts, but because the assumption seemed confirmed by several years of data. A bias enters a plan as an unquestioned assumption.
The planning fallacy
The planning fallacy: the duration and the cost of projects are systematically underestimated because they are assessed from an inside rather than an outside point of view (Kahneman and Lovallo, 1993).
Nine out of ten megaprojects exceed their budget. The average overrun in real terms:
Flyvbjerg (2014, p. 9); IT – Flyvbjerg and Budzier (2011)
One in six IT projects deviates so severely that its costs are exceeded by an average of 200 % (Flyvbjerg, 2014, p. 10).
Spot the bias in the plan
A hypothetical case · section 3.4
“HealthAI”, a private limited company
A Vilnius start-up is preparing a business plan for a venture capital fund. Four observations in that plan deserve a closer reading.
Which bias?
“5 % is not a forecast but an aspiration”: the trace of overconfidence in a plan is not the number itself but the absence of any support for it.
When the organisation errs
The agency problem (Jensen and Meckling, 1976): hired managers and owners have different interests in risk.
Too much risk – when compensation depends on short-term results (bonuses).
Too little risk – when one’s job depends on avoiding “mistakes”.
Organisational optimism (Kahneman and Lovallo, 1993):
- the initiators of projects have a personal interest in presenting optimistic forecasts;
- decision-makers would like projects to succeed;
- organisational culture often punishes “pessimism”.
Risk management must therefore be institutionalised rather than left to an individual manager’s judgement:
Which remedy against what
Structural debiasing strategies:
Problem
Remedy
Choose a problem on the left, then a remedy on the right.
Stress testing matters most for organisations dependent on financing, supply chains and the stability of the regulatory environment; it should cover not only the direct impact of a shock but also its cascading consequences (the cascading of risks – section 3.1.2; the methodology – Chapter 4).
How much risk one may want
Risk appetite
The organisation’s general readiness to assume risk in pursuit of its objectives – a strategic, board-level decision.
Risk tolerance
The acceptable variation of outcomes for a particular objective or process.
Risk capacity
The maximum risk the organisation can assume without facing an existential threat.
The rule: appetite ≤ capacity
Principle 7 of the COSO Enterprise Risk Management (ERM) framework requires the appetite to be defined (COSO, 2017, p. 10), but does not prescribe the form. The examples below are illustrative and are not COSO’s text:
In Lithuanian small and medium-sized enterprises (SMEs) risk appetite is most often not formalised and depends on the owner’s personal position – which gives flexibility but creates the risk of inconsistency and subjectivity.
Two perspectives – one navigation
| Dimension | The objective perspective | The subjective perspective |
|---|---|---|
| The nature of risk | Measured dispersion | Perception and interpretation |
| Principal measures | σ, β, Value at Risk (VaR) | Behavioural biases, the reference point |
| Strength | Formal comparisons, the pricing of capital | A realistic description of decision-making |
| Weakness | The fragility of assumptions, the illusion of precision | Hard to formalise, subjective |
| Field of application | Portfolio management, the discount rate | Risk culture, decision processes |
Quantitative models alone – the psychological and institutional dimensions of risk are missed.
Intuition alone – there is no way of comparing alternatives in a structured way.
Effective risk management is a continuous navigation between the two paradigms: quantitative models as a structural support, behavioural insights as a corrective mechanism.
For discussion · question 3.12. Find a publicly available business plan, identify at least three possible cognitive biases in it and suggest how its authors could reduce them.
References
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Rakštys, R. (2026). Chapter 3. Business risk and profitability (English translation of v1.15.3, 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.