Explanation

Let's analyze each option:

I. Normal Distribution - NO

• Normal distribution is symmetric (skewness = 0)
• Not positively skewed

II. Lognormal Distribution - YES

• Lognormal distribution is positively skewed by definition
• It has a long right tail
• Commonly used for asset prices which cannot be negative

III. The Returns of Being Short a Put Option - NO

• Short put position has limited upside (premium received) and large downside risk
• This creates negative skewness
• Maximum gain = premium, maximum loss = strike price - premium

IV. The Returns of Being Long a Call Option - YES

• Long call position has limited downside (premium paid) and unlimited upside
• This creates positive skewness
• Maximum loss = premium, unlimited gain potential

Conclusion: Only II (Lognormal Distribution) and IV (Long Call Option) exhibit positively skewed distributions.