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

Question restatement: The problem asks about the plausibility of the statement that 'The conditional variance cannot be 0 or negative' for the conditional variance of the weekly SPY return from now to the end of next Friday.
Option A: Make sense. This would claim that the conditional variance cannot be 0 and cannot be negative in this context. Remember that by definition variance, including conditional variance, is a nonnegative quantity. However, it is possible in degenerate or special modeling scenarios for the conditional variance to be exactly 0 if the future return is known with certainty given the information available (i.e., there is no uncertainty left conditional on the information set). Therefore the blanket claim that conditional variance cannot be 0 is not universally true. This makes Option A incorrect as a general statement.
Option B: Make no sense. This option asserts that the stated claim is not reasonable. Since conditional variance is inherently nonnegative but can indeed be exactly 0 in a degenerate case where future outcomes are perfectly predicted with certainty given the conditioning information, the statement 'The conditional variance cannot be 0 or negative' is false in general. The proper interpretation is that the conditional variance is nonnegative and can be zero under certain conditions, so the original claim does not make sense as a universal rule. Hence Option B aligns with the correct understanding in probabilistic terms.
In summary, the core idea is that variance measures dispersion and is always nonnegative, but zero is possible when there is no remaining uncertainty conditional on the information available. The assertion that it cannot be 0 or negative contradicts that possibility, so it fails as a sensible universal statement. The second option correctly identifies that nuance, while the first overstates the restriction and mischaracterizes when zero variance can occur.

BU.230.730.81.SP25 Final Exam- Requires Respondus LockDown Browser

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.

View Explanation

Log in for full answers

Similar Questions