Which of the following statements are true?

Which of the following statements are true?

I. The square-root-of-time rule for scaling volatility over time assumes returns on different

days are independent

II. If daily returns are positively correlated, realized volatility will be less than that calculated using the square-root-of time rule

III. If daily returns are negatively correlated, realized volatility will be less than that calculated using the square-root-of-time rule

IV. If stock prices are said to follow a random walk, it means daily returns are independent of each other and have an expected value of zero
A . I, II and IV
B . III and IV
C . I and III
D . All the statements are correct

View Answer

Answer: C

Explanation:

Statement I is correct. If daily returns are not independent, variances cannot simply be added up over the period, and the square root of time rule is not appropriate to use to scale volatility. Statement II is incorrect. Statement III is correct. If daily returns are positively correlated, it means that a high return on one day will likely cause a higher return the next day, and likewise for low or negative returns. Intuitively, it means that a ‘trend’ will be created and volatility will be higher than in a case where daily returns were not correlated. Therefore statement II is not correct. By the same logic, negative correlation between daily returns would mean a higher return on one day would likely be followed by lower returns the next day, ie a reversion to mean will result causing the volatility to be lower than the case when the returns are uncorrelated. (The correlation between the daily returns is called the ‘autocorrelation coefficient’.) Statement IV is false because while the random walk of prices does imply independence, it says nothing about the expected value of returns. It does not imply that the returns will have an expected value of zero (or any other value).Thus Choice ‘c’ is the correct answer and the rest are incorrect.