What is the mean and the standard deviation of the ACCUMULATION

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(This assignment is based on Problem 13.23 (edition 4) which you can find at the bottom. Do not do 13.23)

Jennifer just had her 4th birthday and her parents have decided to save money to pay for her college education. They will invest $24,000 right now, and $8,000 each year on her future birthdays for the next 13 years (i.e. $8,000 when she turns 5, 6, 7, … 16, 17). They are bullish on America and have a 75% Stock / 25% Bond Asset Allocation strategy. (i.e. 75% of each investment is in a tax exempt Stock Fund and 25% is in a tax exempt Bond Fund.) The principal and returns of each fund are allowed to accumulate (i.e. are reinvested) in the same fund and no redistribution will be done before Jennifer starts college. Assume that the returns of each fund are normally distributed and are independent of each other and past years. See the table;

REQUIRED – Jennifer is planning to go to college starting on her 18th birthday; hence it is important for the parents to know how much money will have accumulated in her College Fund at that time (Call this the ACCUMULATION of the College Fund). Construct a Monte-Carlo simulation model in EXCEL or CRYSTAL BALL (EXCEL add-on) to model the problem. Run the simulation for at least 1,000 trials to answer the following questions:

a. What is the mean and the standard deviation of the ACCUMULATION?

b. What is the probability that the ACCUMULATION is over $240,000? over $300,000? over $360,000?

c. What is the ACCUMULATION if the standard deviations are both zero. (Fixed return)

d. Can you compute a 95% confidence interval estimate of ACCUMULATION? If so, what is it? If not, why not?

e. Can this problem be solved without using simulation? If so, how?

EXTRA CREDIT – Now consider the case where the funds are re-balanced every year. (i.e. The money is moved at the beginning of the year between the Stock Fund and the Bond Fund so that the Asset Allocation ratio is satisfied. At the beginning of each year 75% of the College Fund is in Stocks, 25% in Bonds.)

f. Modify your initial model and answer questions “a”, “b”, and “c”.

g. How do the results of this model compare with the original model? Are they what you might have expected? Comment.

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OPR 3450 – Fall 2018 Assignment 6 page 1 of 1

Problem 13.23 (ed. 4); Problem 13.22 (ed. 3)

Assign 8 - part A

C:\Users\RBlau\Desktop\Fall 2012\OPR 9721 - Fall 2012\Assignments\Assignment 08 - Simulation\Problem from text\Assign 8 - part B.tif

AllocationMean (

µ)

Standard Deviation (

σ

)

Stock Fund75%9%12%

Bond Fund25%3%5%

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