Saturday, November 23, 2019

The Seven Most Important Equations for Your Retirement


Book: The Seven Most Important Equations for Your Retirement
Basic Information : Synopsis :  Expectations : Thoughts : Evaluation : Book References : Good Quotes : Table of Contents : References

Basic Information:
Author: Moshe A. Milvesky
Edition: ePub on Overdrive from the Fresno County Library
Publisher: Wiley
ISBN: 1118291530 (ISBN13: 9781118291535
Start Date: November 13, 2019
Read Date: November 23, 2019
210 pages
Genre: Personal Growth, Retirement
Language Warning: None
Rated Overall: 3 out of 5


Synopsis (Caution: Spoiler Alert-Jump to Thoughts):
Milvesky has seven equations which he is interested in sharing concerning retirement preparedness and living it. These are all financial. He goes through and talks about the uses of each, explains their origins, and talks about the background authority of each one-not necessarily the one who came up with the equation.

  • How long will my money last (Fibonacci)
  • How long will I spend in retirement (Gompertz)
  • Is a pension annuity worth it? (Halley)
  • What is a proper spending rate? (Fisher)
  • How much in risky stocks versus safe cash? (Samuelson)
  • What is your financial legacy today? (Huebner)
  • Is my current plan sustainable? (Kolmogorov)

Expectations:
  • Date Became Aware of Book: November 13, 2019
  • How come do I want to read this book: I was skimming through the Fresno’s library for something to read and came across this title sounded interesting
  • What do I think I will get out of it? Maybe some quantitative means to meaure how I am doing in my retirement, financially.


Thoughts:

Notations used in equations:


Notation Meaning Formula’s Used
ax
The value of a $1 per year for life pension annuity for a person x years old
 III
b
the dispersion coefficient of human life in years, usually 9.5 years
 II
c
the amount you would like to spend or consume above and beyond any retirement pension you might receive
I
FC
Financial Capital accumalated (dollars)
 V
HC
value of Human Capital, i.e., expected is how much you expect to earn until retirement. It should be in terms of present value.
 V
i

III, VI
iPx
survival probability (from chaper 2)
 III, VI
ln(px)
survival probability for one year, where x=the age
 IV
m
modal value of human life. Usually 87.5 years. Given your group, the most like age you will die.
 II
p Probability that you will live to a given age II
P
Prbability of ruin (spending will outrun the money
 VII
qx
Probability of dying
 III(?), VI
r
interest rate your nest egg is earning while being depleted. Need to assume a flat line interest.
IV-should be after inflation
V-interest rates from safest investments, such as savings, ... (I show this mistakenly as ρ-rho)
 I, IV, V, VI
R
Periodic interest rate
 III, VI
t Years nest egg will last I
T Retirement time VII
t
the number of years you might still live in years
 II
W
size of the nest egg
I
w
Amount of money relative to what you are planning on spending (Money/spending)
 VII
x
current age in years
 II, III
γ
risk aversion-how long do you think you really are going to live. The higher the value, the less risk you are willing to take on.
 IV, V
λ
Instantaneous force of mortality. When it is over time , it is λt
 VII
μ
rate at which you/experts think stocks will grow over time. This is in percent. Historically it is 7%
 V, VII
ρ
subjective discount rate-how patient you are to spend
 IV
σ
volatility pf stocks. For a well diversified portfolio, it has been historically around 20%
 V
ψ
The amount in dollars is about how much you should risk
 V



Introduction: An Equation Can't Predict Your Future . . .But It Can Help You Plan for It


Chapter 1: How Long Will My Number Last? Equation #1: Leonardo Fibonacci (1170–1250)

  • This formula is not concerned with preserving principal, only when using the principal for living expenses-high long will it last?
  • Milvesky notes that you can solve for any of the three variable, not just how long it will last. Such as, if you live 30 years and want $5,000 income from a 3% interest rate, you can see how big of an amount you would need to start with.
  • See the seventh equation for a more robust solution than this first one.


Chapter 2: How Long Will I Spend in Retirement? Equation #2: Benjamin Gompertz (1779–1865)


Wikipedia's version of Gompertz' equation
  • Gompertz law of mortality – gives an idea of how long a person will probably live given their current age. From Wikipedia, it states The Gompertz–Makeham law states that the human death rate is the sum of an age-dependent component (the Gompertz function, named after Benjamin Gompertz),[1] which increases exponentially with age[2] and an age-independent component (the Makeham term, named after William Makeham).[3] In a protected environment where external causes of death are rare (laboratory conditions, low mortality countries, etc.), the age-independent mortality component is often negligible. In this case the formula simplifies to a Gompertz law of mortality. In 1825, Benjamin Gompertz proposed an exponential increase in death rates with age.
  • This formula, allows a person to plan for his financial future for as long as his expected life span is.
  • For mortaily figures, you can look at www.mortality.org


Chapter 3: Is a Pension Annuity Worth It? Equation #3: Edmond Halley (1656–1742)

DB=Defined Benefit Plan-where a set amount will be paid for your pension
DC=Defined Contribution-offeres projections, hopes and expectations, no pomises.

  • The above equation will tell you what a DB/pension is worth and how much it should cost to aquire one which is an equavalent. From this you can tell if it is better to take a lump sum or take the DB.
  • People who take out life insurance have a tendency to live longer
  • When it comes to which is right, an equation or the market, the market is always right.


Chapter 4: What Is a Proper Spending Rate? Equation #4: Irving Fisher (1867–1947)

  • Left side of the equation is telling us how to change our buying behavior as we age.
  • The right side is what affcts our buying behavior.
  • How do rational consumers formulate a spending plan? That is the thrurst of this equation.
  • Fisher was no infalliable. Even when the Great Crash of 1929 occurred, he was saying the stock market would rebound quickly. Also he was a fan of Eugenics to correct the problems of society.


Chapter 5: How Much in Risky Stocks versus Safe Cash? Equation #5: Paul Samuelson (1915–2009)


  • It is not time per se which is a factor in this equation, but a person’s preferences/attitude towards risk.


Chapter 6: What Is Your Financial Legacy Today? Equation #6: Solomon S. Huebner (1882–1964)

  • The idea here is that while people are dependent on you how much is a good amount to leave for those who are left behind. Once you’ve retired, should you-and can you actually afford to-leave them anything by still paying for an expensive life insurance policy?
  • Should you have term or whole life? Along that lines, does it make sense to have life annuities?


Chapter 7: Is My Current Plan Sustainable? Equation #7: Andrei N. Kolmogorov (1903–1987)

He starts out summarizing what was covered:
  • Chp 1: linking the fixed spending rate with a fixed interest to figure out how long your money will last
  • Chp 2: Life expectancy is somewhat randomn. What is the probable age of passing?
  • Chp 3: Value of pension annuity
  • Chp 4: Quantifying the effects of patience in spending at a constant rate vs some longevity risks
  • Chp 5: Hw to think about assest allocation as age and time
  • Chp 6: What is the value of a death benefit?
  • Chp 7: What is the probablility that your retirement plan can be sustained

  • dollar-vauled withdrawl rate
  • The assumption with probability is that there is a smooth line, not discrete stages of change.
  • Gambler’s ruin problem

Conclusion: Controversies, Omissions and Concluding Thoughts 175
Appendix: Crash Course on Natural and Unnatural Logarithms 179



Evaluation:
This is not a book for everybody. It is for those who want to quantify what their financial retirement will look like. Even then, these are not easy formulas. Stephen Hawking said that for each equation in a book, you halve its sales. With seven of them, Milvesky may have troubles having this book be profitable,

Milvesky gives seven formulas ranging from a good algebra level formula to calculus. He examines probabilities on life expectancy, how much of my assets can I spend and when, as well as how should my assests be invested. On the later it is more conservatively vs aggressively, This is not a book you pick up to plan your retirement, but a book to help you understand if you are on the right track. It also is a book of probabilities than definites. It gives you the tools to say that things look like you are coming out OK vs you are going to be OK-it is important to know that distinction.

Milvesky does a good job of giving examples of how to use the forumlas. He also goes through the people behind them as well. But I you really do need to be the type of person who enjoys equations in order to get through the book.

 
Book References:
  • Liber Abaci by Leondardo Pisano Fibonacci (2003 translation from Latin by Laurence Sigler)
  • The Nunmber by Lee Eisenberg
  • Principles by Isaac Newton (Halley assisted in getting this book published)
  • Sense and Sensibility by Jane Austen
  • The History of Fish (De Historia Piscium) by Francis Willughby
  • The Theory of Interest: As Determined by Impatience to Spend Income and Opportunity to Invest It by Irving Fisher
  • The Theory of Interest by Irving Fisher
  • Stocks for the Long Run by Jeremy Siegel
  • Economics by Paul Samuelson
  • General Theory by John Maynard Keynes
  • The Teacher Who Changed an Industry by Mildred Stone
  • War and Peave by Leo Tolstoy
  • Aryabhatiya by Aryabhata
  • The Improbable Origins of Modern Wall Street by Peter Bernstein

Good Quotes:
  • First Line: Most books about retirement planning are written as guides, instruction manuals or “how-to” books.
  • Last Line: It [e] truly is a remarkable number, and justifiably embedded in the DNA of the most important equations for retirement.
Table of Contents:
  • Introduction: An Equation Can't Predict Your Future . . .But It Can Help You Plan for It
  • Chapter 1: How Long Will My Number Last? Equation #1: Leonardo Fibonacci (1170–1250)
  • Chapter 2: How Long Will I Spend in Retirement? Equation #2: Benjamin Gompertz (1779–1865)
  • Chapter 3: Is a Pension Annuity Worth It? Equation #3: Edmond Halley (1656–1742)
  • Chapter 4: What Is a Proper Spending Rate? Equation #4: Irving Fisher (1867–1947)
  • Chapter 5: How Much in Risky Stocks versus Safe Cash? Equation #5: Paul Samuelson (1915–2009)
  • Chapter 6: What Is Your Financial Legacy Today? Equation #6: Solomon S. Huebner (1882–1964)
  • Chapter 7: Is My Current Plan Sustainable? Equation #7: Andrei N. Kolmogorov (1903–1987)
  • Conclusion: Controversies, Omissions and Concluding Thoughts
  • Appendix: Crash Course on Natural and Unnatural Logarithms
  • References and Sources
  • Acknowledgments
  • About the Author
  • Short Poem by Maya Milevsky (age 11)
  • Index


References:
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