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 which statement about the conditional variance of the SPY weekly return from now to the end of next Friday makes sense.
Option 1: 'Make sense' — This would assert that the conditional variance cannot be 0 or negative. In general, conditional variance given information up to now is nonnegative, since variance is defined as an expectation of squared deviations. However, it is possible for the conditional variance to be exactly 0 in degenerate cases where the future outcome is known with certainty given the current information, i.e., there is no remaining uncertainty about the weekly return. Therefore, claiming it cannot be 0 is too strong and not universally true, even though negative values are impossible. This makes the statement questionable and not universally correct.
Option 2: 'Make no sense' — This asserts that the claim that the conditional variance cannot be 0 or negative is not appropriate. Since conditional variance is always nonnegative and can be 0 in certain scenarios (when the outcome is almost surely determined by the conditioning information), the broad claim that it cannot be 0 is indeed incorrect. Thus, this option aligns more closely with the correct understanding that while negative variances are impossible, zero variance can occur under certainty given the information set.
In summary, the intuition hinges on two facts: (a) variance cannot be negative by mathematical definition, and (b) conditional variance can be zero when the future is known with certainty given the information available today. The first option’s blanket exclusion of 0 is the core flaw, while the second option correctly flags that the initial statement does not generally make sense. The analysis highlights the subtle distinction between impossibility of negativity and the possibility of zero under degenerate conditions.

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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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