1. An investor wants to invest $300,000 in a portfolio of three mutual funds, one with a short-term focus (S), one with a medium-term focus (M) and one with a long-term focus (L). The annual fund returns are normally distributed with means and standard deviations as shown in the table below. Fund type Short-term Medium-term Long-term Mean Return 2.00% 5.00% 6.25% Std.Dev. Return 0.30% 2.50% 5.50% An initial plan for the investment allocation is 45% in the short-term fund, 35% in the intermediate-term fund, and 20% in the long-term fund. a. Use R with a seed of 1 to develop a Monte Carlo simulation with 1,000 trials.¹ Estimate (i) the mean ending balance at the end of the year, (ii) the risk level of the proposed investment allocation, and (iii) the probability that the ending balance is at least $320,000. (15 pts) b. For each measure estimated in part (a), write a short statement indicating whether it can be easily calculated without simulation. If it can, briefly (in 1 short sentence) describe how; if it cannot, briefly (in 1 short sentence) describe why it is difficult to calculate analytically. (15 pts)

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