Question 4 a. Monte Carlo simulation has its origin in physics. However, it has been used in a variety of fields. Explain why Monte Carlo simulation is widely used in finance. Give one example of an application of Monte Carlo simulation in the field of finance. Frequencies: 21, 22, 23 4.0000 3.0000 2.000 [5 marks -4.0000 160000 0000-0000000 0000 4.0000 3.6000 -4.0000 d. A 65-year old pensioner wants to invest 500,000 for the next 5 years. She is considering to invest in an investment strategy in which she would invest 20% of her assets in a risk-free bond with 5% continuously compounded annual interest and the remaining 80% in a risky asset with 8% mean return and 18% standard deviation The pensioner applied Monte Carlo simulation to decide whether she should invest her money in this investment strategy. The Excel spreadsheet below reports the end-of-year wealth based on one simulation that she conducted. Write down and explain the Excel formula used to calculate the yellowed values in cells E12 and F12, in the Excel spreadsheet below: E F D RETIREMENT PLAN 500,000 5% 80% 1 2 Current wealth 3 Risk-free rate 4 Proportion invested in risky 5 Parameters of risky investment 6 Expected annual return 7 Standard deviation of return 8 9 10 8% 18% Year of year 11 12 13 14 15 16 1 2 3 4 5 Random Wealth at Wealth at Invested in Invested in number, beginning end of risky bonds normally distributed year 500,000 400,000 100,000 -0.0510 534 482 534.482 427,58 106,896 1.2083 688,109 688,109 550,488 137.622 0 2587 769.442 769,442 615,554 153,888 -0.2286 801,722 801,722 641,378 160.344 -0.6405 787.700 C. Consider three randomly generated variables Z1, Z2, and Z3. Explain what the following two figures below show