Answer all questions with detailed explanation

Suppose today's volatility were estimated to be o, and the realized return was u=2%. Which of the following values of U would yield the highest likelihood? Assume that the probability distribution of returns conditional on the volatility is normal, expected daily return is zero. 0 a. 5% O b. 4% O c. 2% 0d. 3% Suppose that a oneday 915% 'v'aR is estimated as $10 million from 500 observations. The oneday changes are approximately normal with mean zero and standard deviation 4.5 million. What is the 99% confidence interval for the VaR estimate? 0 a. {16,124} 0 b. {5.6,11.4} O '5' {7.2, 10.3) 0 d. {8.6, 11.4} Suppose that the change in a portfolio value for a onebasispoint shift in the 1, 2, 3, 4, 5, 7, 10, and 30year rate (in $ millions) +5, 3, 1, +2, +5, +7, +8, +1, respectively. Estimate the delta of the portfolio with respect to the second factor given the following factor loadings. O a. 8.6 O b. 0.4 O c. 3.8 0 d. D.2