IE2110 Operations Research Optimizing your Fortune Ranvir Malhotra U059386W [email_address] Sharad Madar U059385J [email_a...
1955  (30 years old) Year 1995  (70 years old).  $200,000  3 Options to Grow his $200,000
50  55  60  65  70  Age Premium Paid over 20 years= $ 38,191  20 Year Payment Option for Whole Life Insurance by NTUC Boug...
$100,000 @ Age 70 Least Cost for Term Insurance by NTUC Bought at  30 Years old
S&P 500 Stock Returns at Age 70
<ul><ul><li>30 year old guy, non-smoker who will die at the age of 70 </li></ul></ul><ul><ul><ul><li>Profile of Person to ...
Decision Variable <ul><ul><li>At every 5 year, how much of stocks, whole life and term insurance should he buy? </li></ul>...
<ul><li>Return Coefficients for Objective Function </li></ul><ul><ul><ul><li>Stock </li></ul></ul></ul><ul><ul><ul><ul><li...
No Choice Available Decision Variable to Vary Year Whole Life Stocks Term Start(i) End(j) Cost Return Wij Cost Return Si C...
<ul><li>At age 30, buy $112,640 in Stocks and $87,360 in Term Insurance  </li></ul><ul><li>Return of $1,846,297 when he di...
<ul><li>Flexibility buy and sell stock every 5 years </li></ul><ul><li>Non constant growth in whole life returns </li></ul>
Upcoming SlideShare
Loading in …5
×

Optimizing your Fortune

572 views

Published on

A fortune teller told Madar in 1955 (30 years old) that he is going to die in the year 1995 (when he will be 70 years old). Madar therefore wants to leave behind enough money for his successors after he dies. He has $200,000 savings and he wants to invest in Life Insurance. There are different Life Insurance schemes – Whole Life Insurance and Term Life Insurance. Apart from Life Insurance schemes he can also invest in Stocks.
Madar has three different investment options available to him namely Whole life insurance, Term Insurance and Stock investments.

Published in: Economy & Finance, Business
0 Comments
0 Likes
Statistics
Notes
  • Be the first to comment

  • Be the first to like this

No Downloads
Views
Total views
572
On SlideShare
0
From Embeds
0
Number of Embeds
8
Actions
Shares
0
Downloads
0
Comments
0
Likes
0
Embeds 0
No embeds

No notes for slide
  • Our project revovles around increaseing the wealth of a fictional character who is told that he is going to die at 70
  • Optimizing your Fortune

    1. 1. IE2110 Operations Research Optimizing your Fortune Ranvir Malhotra U059386W [email_address] Sharad Madar U059385J [email_address] Zhou Wenhan U047762M [email_address]
    2. 2. 1955 (30 years old) Year 1995 (70 years old). $200,000 3 Options to Grow his $200,000
    3. 3. 50 55 60 65 70 Age Premium Paid over 20 years= $ 38,191 20 Year Payment Option for Whole Life Insurance by NTUC Bought at 30 Years old
    4. 4. $100,000 @ Age 70 Least Cost for Term Insurance by NTUC Bought at 30 Years old
    5. 5. S&P 500 Stock Returns at Age 70
    6. 6. <ul><ul><li>30 year old guy, non-smoker who will die at the age of 70 </li></ul></ul><ul><ul><ul><li>Profile of Person to base our insurance cost upon </li></ul></ul></ul><ul><ul><li>Income = Expense </li></ul></ul><ul><ul><ul><li>So that he only has 1 lump sum to invest at the start </li></ul></ul></ul><ul><ul><li>Whole Life can only be surrendered after 20 years </li></ul></ul><ul><ul><ul><li>Because we do not have the surrender and death value under 20 years </li></ul></ul></ul><ul><ul><li>He can’t buy any insurance after he is 50 years old </li></ul></ul><ul><ul><ul><li>Because Whole life must be bought for 20 years or more </li></ul></ul></ul><ul><ul><li>He can change his portfolio after every 5 years </li></ul></ul><ul><ul><ul><li>To reduce number of decision variables </li></ul></ul></ul><ul><ul><li>Whole Life non-guaranteed is 5.25% per annum </li></ul></ul><ul><ul><ul><li>Following Projections </li></ul></ul></ul>
    7. 7. Decision Variable <ul><ul><li>At every 5 year, how much of stocks, whole life and term insurance should he buy? </li></ul></ul>W ij  units of $100,000 Whole Life policies taken at year i and surrender at year j T ij  units of $100,000 Term policies taken at year i until year j S i  Dollar amount invested in stocks purchased at year I Objective Function Maximize money at death = age J 70 Maximize Z = Σ (R wij * W ij ) + Σ (R si * S i ) + (Σ T ij (j = 70) * 100,000); Constraints <ul><ul><li>$200,000 of spending maximum </li></ul></ul>Σ (Cost wij * W ij ) + Σ (Cost tij * T ij ) + Σ S i = 200,000 <ul><ul><li>Required at least $400,000 insurance at any time </li></ul></ul>At age i: W ij + T ij ≥=4
    8. 8. <ul><li>Return Coefficients for Objective Function </li></ul><ul><ul><ul><li>Stock </li></ul></ul></ul><ul><ul><ul><ul><li>Historical 5 Year Growth </li></ul></ul></ul></ul><ul><ul><ul><li>Whole Life </li></ul></ul></ul><ul><ul><ul><ul><li>Guaranteed: $100,000 </li></ul></ul></ul></ul><ul><ul><ul><ul><li>Non- Guaranteed: Growth </li></ul></ul></ul></ul><ul><ul><ul><ul><ul><li>= 5.25% Per Annum </li></ul></ul></ul></ul></ul><ul><li>Cost Coefficients for Constraints </li></ul><ul><ul><ul><li>Stock </li></ul></ul></ul><ul><ul><ul><ul><li>-Cost=1 </li></ul></ul></ul></ul><ul><ul><ul><li>Whole Life </li></ul></ul></ul><ul><ul><ul><ul><li>Fixed Monthly Cost for 20 years </li></ul></ul></ul></ul><ul><ul><ul><li>Term </li></ul></ul></ul><ul><ul><ul><ul><li>Least Cost Solution for each starting </li></ul></ul></ul></ul><ul><ul><ul><ul><li>and ending Year </li></ul></ul></ul></ul>
    9. 9. No Choice Available Decision Variable to Vary Year Whole Life Stocks Term Start(i) End(j) Cost Return Wij Cost Return Si Cost Tij 30 35             $540 0   40             $1,200 0   45             $2,220 0   50 $38,191 $58,184 0       $3,120 0   55 $38,191 $67,420 0       $5,100 0   60 $38,191 $79,348 0       $8,160 0   65 $38,191 $94,753 0       $13,260 0   70 $38,191 $114,649 0 $1 4.00 0 $21,840 6 35 40             $660 0   45             $1,680 0   50             $2,940 0   55 $55,817 $85,038 0       $4,560 0   60 $55,817 $98,536 0       $7,620 0   65 $55,817 $115,970 0       $12,720 0   70 $55,817 $138,485 0 $1 8.46 0 $21,660 0 40 45             $1,020 0   50             $2,280 0   55             $4,380 0   60 $85,195 $129,795 0       $6,960 0   65 $85,195 $150,398 0       $12,060 0   70 $85,195 $177,006 0 $1 5.37 0 $21,000 0 Year Whole Life Stocks Term Start(i) End(j) Cost Return Wij Cost Return Si Cost Tij 45 50             $1,440 0   55             $3,360 0   60             $6,840 0   65 $135,137 $205,881 0       $11,040 0   70 $135,137 $238,562 0 $1 5.53 0 $20,160 0 50 55             $2,220 0   60             $5,400 0   65             $14,040 0   70 $229,145 $349,103 0 $1 6.11 0 $18,720 0 55 60                   65                   70       $1 4.61 0     60 65                   70       $1 2.60 0     65 70       $1 1.43 0    
    10. 10. <ul><li>At age 30, buy $112,640 in Stocks and $87,360 in Term Insurance </li></ul><ul><li>Return of $1,846,297 when he dies at the age of 70. </li></ul><ul><li>Only buy stocks at age 30 </li></ul><ul><li>Either buy </li></ul><ul><ul><li>Whole Life only </li></ul></ul><ul><ul><li>Term + Stocks </li></ul></ul><ul><ul><li>Whole Life + Stocks </li></ul></ul>Stock Returns Take stock + term when stock % > 8% <ul><ul><li>Take whole life when </li></ul></ul><ul><ul><li>stock % < 7% </li></ul></ul>Take either when stock return is between 7%and 8%
    11. 11. <ul><li>Flexibility buy and sell stock every 5 years </li></ul><ul><li>Non constant growth in whole life returns </li></ul>

    ×