Life of Luxury or Life of Crime

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Life of Luxury or Life of Crime

• Yan Li1 and Sean Wilkoff2
• 1Wells College
• 2California University at Berkley

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Introduction

• In the past few decades retirement options have
  become much more complex. Major investment firms
  have started to offer a wide variety of
  investment tools for retiring. People now have
  the choices of investing in different asset
  classes and multiple asset classes. Depending on
  how much risk one wants to take with their
  retirement fund, they can allocate their money
  accordingly. Today the Monte Carlo method helps
  in predicting how one should invest the money.
  The algebraic model is a riskless method of
  calculating the future value of money. A Monte
  Carlo model is a method for including risk which
  gives a distribution of the future value of
  money.

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MODELS

• In the algebraic model there were two models.
  One was Hydes single asset model. The next one
  was an extension of the first into a multiple
  asset model. Give models were considered for the
  Monte Carlo model. The first uses Forsyths. The
  second extends that model to multiple assets.
  After Forsyths model was extended to account for
  multiple assets, we were able to add new
  extensions to answer more questions. The first
  addition to the model was periodic investment.
  The second addition was to rebalance the multiple
  asset model every year. The last model is for
  inflation.

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The Interest Rates and Standard Deviations
Market Historical Interest Rate Historical Average Standard Deviation
SP500 0.125 0.198
Corp. Bond 0.063 0.063
TBill (Cash) 0.031 0.008
Inflation 0.027 0.018

• Table 1 Harvey Historical Perspective
  January 1926- December 2004
• Allocation Rates for Different Assets

Market Allocation Rate
SP500 0.7
Corp. Bond 0.2
TBill (Cash) 0.1
Table 2 Our allocation for testing results unless
otherwise stated
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RESULTS

• The results we got included Algebraic model and
  Monte Carlo model. At the last section, we
  compared the result Monte Carlo model with
  Algebraic Model.

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Monte Carlo Model

• The Graph below shows the portfolio value
  at each time step of a single asset with the same
  starting value but different Standard Deviations.
  This is just one possible outcome of this asset.
  If the model was run again the graph would look
  different.

Figure 1 Possible value for single asset with
different Standard deviations
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The Distribution of Portfolio Values for a single
asset with a standard Deviation of .2.
Figure 2 shows the distribution is not Gaussian
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Figure 3 has a graph of the distribution of
final portfolio values for the multiple asset
model after 10 years.
Figure 3 Possible portfolio value after ten years
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Figure 4 has a graph of the distribution of
final portfolio values for the multiple asset
model after 30 years. If one looks at the final
portfolio value one can see the increase in
expected outcomes from 10 to 30 years.
Figure 4 Possible portfolio values after 30 years
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Algebraic vs. Monte Carlo

• We wanted to solve the problem What percentage
  of ones initial portfolio can be withdrawn
  yearly? We both ran the problem and created a
  table to compare our results. The Monte Carlo
  model says if you take out 13 of your ones
  initial portfolio every year then there is an 80
  chance that one will run out of money in 18
  years. The Algebra model says on can only
  withdraw 10 of ones initial portfolio each year
  in order for the money to last 18 years.

Mean 50 less than 80 are less than Algebraic
4 2891.15 1850 4050 2599.09
6 2168.06 1150 3150 1853.78
8 1481.91 450 2250 1108.48
10 933.20 50 1150 363.19
12 592.54 50 350 -382.11
13 475.94 50 50 -754.76
Table 3 Comparison of how much money one will
have left
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The Value of Money

• This table is to show the time value of money.
  The Table compares starting with 1000 dollars and
  letting the money sit for 10-40 years to
  investing 50 dollars every year.

Time (Years) 1000 50
10 2127.71 820.33
20 4838.97 2532.05
30 11453.16 6529.08
40 27725.54 16132.64
Table 4 Example of the time value of money
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This table is to show the time value of money,
which is similar to above. But the allocation is
different, 30 in cash, and 70 in bonds.
Time (Years) 1000 50
10 1299.82 628.35
20 1718.55 1387.63
30 2304.92 2400.0
40 3127.70 3767.22
Table 5 Example of the
benefits of risk
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CONCLUSION

• Both the Monte Carlo and algebraic models are
  used by financial planners. The Monte Carlo model
  does not by any means say for certain the outcome
  of any investments but can give a probability of
  reaching a goal. The method also only accounts
  for normal deviations and random walks. Market
  shocks are not taken into account by this model.
• The future work will focus on developing the
  Monte Carlo model, which involves risk, and the
  result will be more accurate by comparing to the
  realistic. Furthermore, we will include the
  calculation for tax and transaction fees, so that
  people can use for calculating their investments.