1) The S&P 500 index mean yearly return is 9.42% and the standard deviation of the yearly return is 19.74%. On October 19, 1987, the S&P 500 index dropped more than 20%. How many standard deviations is -20% one day return away from the mean?

It locates at______ standard deviations below the mean return (rounding your answer to the integer)

Hint: you need to convert the mean and the std of the yearly returns to daily measurement by

r_daily= r _yearly/365 ; Std_daily= Std_yearly/sqrt(365)

2) Based on your calculations for previous question. Which of the following descriptions is correct?

a) The return distribution of S&P 500 is normal.

b) The return distribution of S&P 500 skewed to the right.

c) The return distribution of S&P 500 has long tail on the left.

d) The return distribution of S&P 500 has fat tails on both sides.

3) Which of the following statements is not correct?

a) Suppose the fifth percentile return of an investment asset is -30%. Its 10th percentile return must be greater than -30%.

b) Suppose the fifth percentile return of an investment asset is -30%. There is 5% chance that the investment return will be -30%.

c) Suppose the fifth percentile return of an investment asset is -30%. The investment return will be better than -30% for 95% of the time.

d) If the fifth percentile return of an investment asset is -30%, its 5% VaR is -30%.

4) Suppose a portfolio's daily return is normally distributed with mean return of 0.04% and std. of 0.8%. What is the 10% VaR of the portfolio in a day? (use excel if needed)

a) 0.985%

b) -9.855

c) -0.985%

d) -0.75%

5) The S&P 500 index yearly return is 9.42% and the standard deviation of the yearly return is 19.74%. The probability of losing -20% or worse for investing in the S&P 500 index fund in a given year is _______ % (rounded to two decimals).