10. Currently, shares of MJ Corp. trade at $100. The probability of the price increasing by $10 in one day is 30% and the probability of the price decreasing by $10 in one day is 70%. Let R2 denote log-return on the asset over two days, i.e. with Sd denoting the stock price at day (:1. Given that Sc- : 100, what is the volatility of R2? Choose the best answer. (a) 12.96% (b) 13.09% c) 7.69% (d) 20.90% IT. A risk manager would like to simulate the prioe of a stock using the disoretized GEM, where St+nt = St + #313: + 0V AtStEt with p. and 0 denote, respectively, the stock annual mean return and annual volatility. The data suggest that the weekly mean return on the stock is 0.3% and the weekly volatility is 3%. Assuming a weekly time step of At = 1/52 (in terms of annual units), what is the appropriate estimate of 1.1? (a) a = 15.61% [b] a = 15.34% (o) 11 = D 3% (d) a = 17.94% 18. Suppose that the price of an asset obeys to geometric Brownian motion (GEM) with an annual mean return of p. = 0.02 and an annual volatility of o" = 0.2. If today's price is $100, what is the probability that the price two years from now will drop below $80? Hint: Recall that under GEM1 the future price at T, i.e. ST, given today's spot price, 3:, is 0.2 ST=SgXBXp [pE]xr+xax.e withT=Ttand~N(0,1). (a) 21.51% (b) 35.48% (c) 51.1% (d) 6.2% 20. 1Which of the following statements best describe a disadvantage of the simulation approach to nancial problem solving? (a) In practice, with the use of an initial seed for the start of random draws, it is not possible to replicate results from previous experiments. (b) If alternate assumptions are made in the data generating process the results may be very similar. (c) Imprecise results may be present even with a very large number of simulation iterations when the assumptions of model inputs or the data generating process are unrealistic. (d) The complexity of markets and issues that are examined have also become increasingly com- plex, leading to low computation costs. 25. An investor has a bond portfolio worth USD 20,000 with a duration of 8. How can the position be hedged with a bond that has a duration of 10'? Note: By hedged, the question refers to attaining a zero-duration target. [a] Short USD 20,000 of the bond with duration of ten (1)] Short USD 16,000 of the bond with duration of ten [:3] Long USD 20,000 of the bond 1with duration of ten (d) Short USD 12,000 of the bond with duration of 10