A friend offers you to invest all your savings, 100,000, in...

A friend offers you to invest all your savings, $$\$ 100,000$$, in his dot com company. You find it very hard to understand the business plan he presents to you, but your friend tells you that your $$\$ 100,000$$ will 'certainly' be worth at least $$\$ 10 \mathrm{M}$$ within two years. Naturally, your friend may be right, but he may also be wrong - you feel that you cannot estimate the probabilities for this. Consider the decision matrix below. What is wrong with this formalisation? $$ \begin{array}{lll} \hline & \text { Friend is right } & \text { Friend is wrong } \\ \hline \text { Invest } & \$ 10 \mathrm{M} & \$ 0 \\ \text { Do not } & \$ 100,000 & \$ 100,000 \\ \hline \end{array} $$

A friend offers you to invest all your savings, $$\$ 100,000$$, in his dot com company. You find it very hard to understand the business plan he presents to you, but your friend tells you that your $$\$ 100,000$$ will 'certainly' be worth at least $$\$ 10 \mathrm{M}$$ within two years. Naturally, your friend may be right, but he may also be wrong - you feel that you cannot estimate the probabilities for this. Consider the decision matrix below. What is wrong with this formalisation?
$$
\begin{array}{lll}
\hline & \text { Friend is right } & \text { Friend is wrong } \\
\hline \text { Invest } & \$ 10 \mathrm{M} & \$ 0 \\
\text { Do not } & \$ 100,000 & \$ 100,000 \\
\hline
\end{array}
$$

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Key Concepts

Decision Matrix

A decision matrix is a tool used in decision theory to list actions and their possible outcomes, paired with the states of the world. It helps to organize potential payoffs for each combination of decision and state. However, a proper decision matrix should also incorporate the likelihood of each state, or at least acknowledge the uncertainty involved if those probabilities are not known.

Uncertainty and Ambiguity

The problem illustrates a case of uncertainty—often referred to as Knightian uncertainty—where the probabilities of the outcomes are not known or cannot be reliably estimated. This ambiguity means that simply assigning monetary outcomes without accounting for uncertain probabilities can lead to a deceptive representation of the decision situation.

Expected Utility and Risk Preferences

When making investment decisions, it's important to recognize that outcomes are typically evaluated based on expected utility rather than raw monetary values. Investors have different risk preferences and might value a guaranteed outcome more than a gamble with high returns but significant uncertainty. Ignoring the decision-maker's utility function can lead to an oversimplified and possibly misleading analysis.

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