FRM Part I · FRM Exam Part I · Measuring Return, Volatility, and Correlation
A risk analyst estimates that the daily log-return volatility of an equity index is 1.20%. Assuming returns are independent and identically distributed with 252 trading days per year, what is the annualized volatility (to two decimals)?
Annualized volatility is 19.05%. With independent, identically distributed returns, variance grows in proportion to time, so daily volatility is multiplied by the square root of 252, about 15.87, giving 1.20% times 15.87, or roughly 19.05%.
- A19.05%Correct
- B14.40%
- C302.40%
- D1.20%
Explanation
Under i.i.d. returns, variance scales linearly with time, so volatility scales with the square root of time. Annualized volatility = 1.20% x sqrt(252) = 1.20% x 15.8745 = 19.05%. Multiplying by 252 directly (302.4%) wrongly scales volatility linearly; 14.40% uses 12 as the factor.
Did you get it right without looking?
One question tells you little. A timed set on Measuring Return, Volatility, and Correlation shows your real accuracy, how long you take and where you lose marks.
More Measuring Return, Volatility, and Correlation questions
- A stock trades at USD 50 and pays a dividend of USD 1 at month-end, when the price is USD 54. A risk analyst computes the total simple retur…
- An analyst computes the correlation between the daily returns of two assets using a window containing a few extreme, same-direction outlier …
- Returns on assets A and B have variances 0.09 and 0.16 and correlation -1. What weight in A (with the remainder in B, weights summing to 1) …
- A stock rises from 80 to 88 over one month, with no dividends. What is the continuously compounded (log) return for the month?
- Over five periods, the returns of asset X (in %) are 2, 4, 6, 8, 10 and the returns of asset Y (in %) are 1, 3, 2, 5, 4. Using the sample co…
- A stock is priced at USD 80.00 at the start of the month and USD 88.00 at the end of the month, with no dividends paid. What is the continuo…