It is Friday evening now, you want to know the conditional variance of the weekly SPY return from now to the end of next Friday. Which of the following statements makes sense?

The conditional variance cannot be 0 or negative.

Question

It is Friday evening now, you want to know the conditional variance of the weekly SPY return from now to the end of next Friday. Which of the following statements makes sense?

The conditional variance cannot be 0 or negative.

BlackTom AI · Accepted Answer

The question asks us to evaluate the plausibility of the statement about the conditional variance of the weekly SPY return from now to the end of next Friday.
Option 1: 'Make sense'.
To judge this, recall a fundamental property: a variance, whether unconditional or conditional on information, cannot be negative. However, it is not necessary that the conditional variance must be strictly positive; if the future return were determined exactly given the information at Friday evening, the conditional variance would be zero. Therefore, claiming that the conditional variance cannot be 0 or negative is too strong, because zero is a valid value for a conditional variance in degenerate or certain models. This makes the statement questionable and generally not accurate in all modeling contexts.
Option 2: 'Make no sense'.
This option prompts us to consider that the previous claim is not correct in general. Since conditional variance is nonnegative by definition, it cannot be negative, but it can equal zero under certain conditions when there is no remaining randomness conditional on the information set. Hence, a blanket claim that it cannot be 0 or negative misstates the reality that zero is possible in some scenarios. The phrasing 'Make no sense' captures the idea that the statement is not universally valid because of the possibility of zeroconditional variance.
In terms of subtlety, one could argue about the likelihood of zero conditional variance in practice for financial returns, which are typically uncertain, but the mathematical possibility remains, undermining the universal assertion that it cannot be 0. Also, the timeframe from now to end of next Friday leaves room for randomness, yet the conditional variance could collapse to zero only if the model or information set implies a deterministic outcome, which is unusual but theoretically possible.
Overall, evaluating the intuition about conditional variance being strictly positive in all cases reveals that the claim is not universally valid, so this option aligns with the idea that the statement does not make sense in general.

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It is Friday evening now, you want to know the conditional variance of the weekly SPY return from now to the end of next Friday. Which of the following statements makes sense? The conditional variance cannot be 0 or negative.

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