Loved this insight on Risk from the esteemed Terence Tao
In times of great uncertainty, the relative advantage of "playing it safe" diminishes because no option can completely eliminate risk. Paradoxically, in such situations, taking bold actions can become more rational, as decisions should align with the level of external risk in the system. This highlights that uncertainty fundamentally reshapes the balance between safe and bold choices, requiring a more nuanced approach to decision-making.
Many decisions in life involve the tradeoff between risk and reward. Perhaps one has to choose between a "low risk, low reward" course of action that plays it safe but does not achieve any big wins, or a "high risk, high reward" choice that could potentially give greater benefits but also greater downsides.
Risk management is a complex task, but it can initially be explored with very simplified models, always keeping in mind George Box's dictum that "all models are wrong, but some are useful." For this simple model, one can assume that each course of action comes with two numbers: the "reward," representing the average positive net gain, and the "risk," interpreted here as the standard deviation from the mean. A "safe" action might have a reward of 5 and a risk of 3, written as 5±3, while a "bold" action might have a reward of 9 and a risk of 10, written as 9±10.
Given the general preference for risk aversion, one strategy is to minimize "value at risk"—the value one might lose in a bad scenario. For the safe action (5±3), the value at risk is 3-5 = -2, indicating that even in bad luck, a small gain is likely. For the bold action (9±10), the value at risk is 10-9 = 1, suggesting possible losses. This favors the safe action.
When external shocks are introduced, the analysis changes. Suppose a fixed shock of -5 uniformly affects outcomes. While this lowers rewards, it does not alter relative decision-making. However, with uncertain shocks (e.g., -5±10), risk is recalculated using the law of additivity of variance. For uncorrelated risks, the safe action moves from 5±3 to 0±√(10²+3²)=0±10.44, while the bold action moves from 9±10 to 4±√(10²+10²)=4±14.14. This reduces the relative value of "playing it safe."
In times of great uncertainty, no option remains truly safe. Paradoxically, bold actions can become more rational as personal risk tolerance aligns with systemic risk. However, this conclusion depends on the assumption that external shocks add to risks rather than multiply them. If risks are multiplied (e.g., converting 5±3 to 5±6), the safer option becomes preferable again.
Behavioral economics highlights how human decisions deviate from models, as external shocks psychologically distort decisions. Nevertheless, there is a rational basis for altering choices when shocks themselves carry risk. The broader insight remains: uncertainty reshapes the value of safe versus bold decisions.
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