For 1-year SPX options, we observe that the 25-delta put implied volatility is at 45%, the 50-delta call implied volatility is at 30%, the 25-delta call implied volatility is at 35%. These observations suggest that the option-implied SPX 1-year return risk-neutral distribution is (a) normally distributed, (b) positively skewed, (c) thin tailed, (d) negatively skewed

Option B, positively skewed, is the right answer.

Explanation:

A positive-skewed distribution generally has a long right or positive tail. The positive-skew distributions are also known as the Right-skewed distribution. The main reason behind calling this a positive-skew is that this skew has a long tail in the positive direction on the number line.

In the given question, positively-skewed implies to one-year return risk-neutral distribution, as the delta put raises, the volatility decreases but not in the same proportion. In such a condition, the median will be less than the mean. Therefore, it will be Right-Skewed or Positively Skewed Distribution.