PROBLEM: PENSION SIMULATION SAVINGS ARE INVESTED IN A RISKY ASSET AND A RISK FREE ASSET INPUT PARAMETERS ARE GIVEN BELOW. EVERY YEAR WEIGHT OF RISKY AND RISK FREE ASSETS ARE RE-SET TO BE AS GIVEN IN TABLE BELOW (I.E., 60% AND 40% RESPECTIVELY) RISKY ASSET FOLLOWS A LOGNORMAL MODEL: THAT IS, S(T) = S(T-1)*EXP((MU-SIG^2/2)*T + SIG*SQRT(T)*NORMAL(0,1)) RISK FREE ASSET UNCORRELATED WITH RISKY ASSET WE ARE INTERESTED TO KNOW THE EXPECTED SAVINGS AT THE FINAL YEAR, 10 YEARS LATER, AND THE PROBABILITY OF SAVINGS > O AS A FUNCTION OF ANNUAL WITHDRAWAL QUESTIONS: * COMPLETE THE INVESTMENT SCHEDULE BELOW * COMPLETE THE TWO-WAY DATATABLE (USE 500 SIMULATIONS) * YOUR OBSERVATIONS $ 10,00,000 INPUTS: Current savings Invested in: Risky asset Risk free asset Annual withdrawal 60.0% 40.0% 1,00,000 $ 4.0% Return parameters Risk free rate Risky asset mean return u Risky asset sigma 11.0% 0 30.0% INVESTMENT SCHEDULE: (YEARLY At end of year At end of year Age Savings at beginning of year 10,00,000 Risk Free Risky asset N et after withdrawal Total Savings at end of Withdrawal at end year of year 1,00,000 1,00,000 1,00,000 1,00,000 1,00,000 1,00,000 1,00,000 1,00,000 1,00,000 1,00,000 83 1.50.000 .. .. .. .. .. .. 7. . . . . . . . .. .. .. .. .. . . . . . . . . . . . . . 1.25.000 n. n. r. n. N. . . . . . . . . . . . . . . . . . . . . . . . . ? 1.00.000 Annual withdrawal 75.000 ? 000 US ? G n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . USING COUNTIE= STDEV= PROB PROBLEM: PENSION SIMULATION SAVINGS ARE INVESTED IN A RISKY ASSET AND A RISK FREE ASSET INPUT PARAMETERS ARE GIVEN BELOW. EVERY YEAR WEIGHT OF RISKY AND RISK FREE ASSETS ARE RE-SET TO BE AS GIVEN IN TABLE BELOW (I.E., 60% AND 40% RESPECTIVELY) RISKY ASSET FOLLOWS A LOGNORMAL MODEL: THAT IS, S(T) = S(T-1)*EXP((MU-SIG^2/2)*T + SIG*SQRT(T)*NORMAL(0,1)) RISK FREE ASSET UNCORRELATED WITH RISKY ASSET WE ARE INTERESTED TO KNOW THE EXPECTED SAVINGS AT THE FINAL YEAR, 10 YEARS LATER, AND THE PROBABILITY OF SAVINGS > O AS A FUNCTION OF ANNUAL WITHDRAWAL QUESTIONS: * COMPLETE THE INVESTMENT SCHEDULE BELOW * COMPLETE THE TWO-WAY DATATABLE (USE 500 SIMULATIONS) * YOUR OBSERVATIONS $ 10,00,000 INPUTS: Current savings Invested in: Risky asset Risk free asset Annual withdrawal 60.0% 40.0% 1,00,000 $ 4.0% Return parameters Risk free rate Risky asset mean return u Risky asset sigma 11.0% 0 30.0% INVESTMENT SCHEDULE: (YEARLY At end of year At end of year Age Savings at beginning of year 10,00,000 Risk Free Risky asset N et after withdrawal Total Savings at end of Withdrawal at end year of year 1,00,000 1,00,000 1,00,000 1,00,000 1,00,000 1,00,000 1,00,000 1,00,000 1,00,000 1,00,000 83 1.50.000 .. .. .. .. .. .. 7. . . . . . . . .. .. .. .. .. . . . . . . . . . . . . . 1.25.000 n. n. r. n. N. . . . . . . . . . . . . . . . . . . . . . . . . ? 1.00.000 Annual withdrawal 75.000 ? 000 US ? G n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . USING COUNTIE= STDEV= PROB
