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One of the most common questions I have heard during the course my PhD studies is - what is the point of ambiguity?
The short answer is - to encourage one be more cautious (and realistic about ex-ante analytics).
In Bodie, Kane & Marcus (2019), the authors highlight the importance of quantifying risk on both the probability and size of potential losses. This is different from ambiguity, which is conditional only on the probabilities of outcomes. Therefore, risk is outcome dependent, whereas ambiguity is outcome independent (Brenner & Izhakian, 2018). This implies that probability-based analytics should be taken with a pinch of salt.
In my research on ambiguity, I have observed that periods of low (high) volatility are often accompanied with high (low) ambiguity. This leads me to conclude that financial markets are more unpredictable than expected during calm regimes. However, when the market is in a crisis (proxied with high volatility), one can be sure that the current volatility estimates provide a more accurate picture of distributional outcomes.
A picture speaks a thousand words. Can you show me a figure to illustrate how ambiguity works?
In Kahneman & Tversky (1979), or more recently - Thinking, Fast and Slow (2011), the authors explained how people exhibit risk-seeking preferences under loss aversion. For example, between two choices - the first being a sure loss of $100 and the second being a 50-50 chance of losing $200 and nothing, most people would opt for the second choice.
Under the same conditions, people would similarly exhibit ambiguity-seeking behaviour, which is better represented in the figure. As people become more ambiguity-seeking, they desired to be exposed to a greater set of probability distributions for the same set of outcomes that is represented by the sub-figure at the bottom right of the figure.
I provide empirical evidence using data on European index options to illustrate how investors exhibit probability-contingent ambiguity attitudes on the average daily probability of favorable returns in my first working paper "A Forward-Looking Index on Investor-Perceived Ambiguity".
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