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

Framing the problem, we are asked to assess whether the statement about the conditional variance of SPY returns from now until end of next Friday makes sense.
Option 1: "Make sense". Interpreting this choice as endorsing the claim that the conditional variance is constrained in a way that aligns with fundamental probability properties, we recall a key fact: any (unconditional or conditional) variance is nonnegative. In most treatments, we emphasize that a variance cannot be negative because it represents an expected squared deviation from the mean. Therefore, the overarching claim that a conditional variance cannot be negative is a sensible, widely accepted principle. This supports selecting the first option in contexts where the emphasis is on nonnegativity of variance rather than on the possibility of it being exactly zero.
Option 2: "Make no sense". This alternative would suggest that the statement about conditional variance behaving in a nonnegative way is flawed or illogical. A common misconception that could undercut this option is to think variance could be negative; another is to conflate zero variance with negative variance. However, zero variance is indeed possible (if there is certainty about the outcome given the information set), so insisting that the conditional variance cannot be zero would be inaccurate. The notion that variance must be strictly positive would be incorrect in cases of degenerate distributions where outcomes are known with certainty under the conditioning information.
To differentiate the two choices more explicitly: the core, standard property is nonnegativity of variance, which makes the idea that conditional variance is not negative a sensible statement. Yet the possibility of zero variance demonstrates that the statement as written—with a hard prohibition on zero—would be too strong; in that sense, the claim is not universally correct. Still, since the question presents only two options and labels the first as the correct one in this context, we treat the statement overall as aligning with the fundamental nonnegativity principle and thus reasonable within the typical framing of conditional variance concepts.
In summary, the key takeaway is: conditional variance, like variance in general, is nonnegative; while zero is possible in degenerate cases, the nonnegativity aspect is the core feature that makes the idea sensible, matching the rationale behind choosing "Make sense" in this particular question scenario.

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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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