57. Consider the following discrete probability distributions of payoffs for 3 securities that are held in a DI's trading portfolio (payoff amounts shown are in $millions): SECURITY Alpha PROBABILITY 0.50 PAYOFF 355 0.49 150 0.01 -300 SECURITY PROBABILITY PAYOFF Beta 0.50 400 0.49 150 0.0025 -300 0.0075 -3.300 SECURITY Gamma PROBABILITY PAYOFF 0.49 400 0.49 150 0.01 -150 0.01 -2.000 What is the one-day, 99% confidence level, value at risk (VAR) of securities Alpha and Beta, respectively (in millions)? A. $3 and $25.50 B. $3 and $0.75 C. $248 and 248 D. $300 and $300 E. 300 and 3,300 Feedback: Recall that the DEAR and particularly VAR is a point on the probability distribution and do not take into account values beyond that point. In this case, the 99 percent level. Alpha: N-day VAR DEAR N = -$3,000,000 1 = $3,000,000 Beta: = N-day VAR DEAR N = $3,000,000 1 = $3,000,000 = 58. Consider the following discrete probability distributions of payoffs for 3 securities that are held in a DI's trading portfolio (payoff amounts shown are in $millions): SECURITY Alpha PROBABILITY 0.50 PAYOFF 355 0.49 150 0.01 -300 SECURITY PROBABILITY PAYOFF Beta 0.50 400 0.49 150 0.0025 -300 0.0075 -3,300 SECURITY PROBABILITY PAYOFF Gamma 0.49 400 0.49 150 0.01 -150 0.01 -2.000 What is the expected shortfall (ES) of securities Alpha and Beta at the 99 percent confidence level, respectively (in millions)? A. -$300 and -$3,300 B. -$3 and -$24.75 C.-$3 and -$25.50 D. -$300 and -$300 E.-S and -$0.75. Feedback: For 99% confidence level, include all values in left tail of distribution until probability is equivalent to one (1): = 0.01 P=0 ES; Probp,j Payp.j f ES Alpha 0.01 x-300=-$3 ESBeta (0.0025x-300) + (0.0075 x -3,300) = -0.75 24.75 = -$25.50