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The 7 Most Important Equations for Your Retirement: The Fascinating People and Ideas Behind Planning Your Retirement Income Hardcover – May 8 2012


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The 7 Most Important Equations for Your Retirement: The Fascinating People and Ideas Behind Planning Your Retirement Income + Pensionize Your Nest Egg: How to Use Product Allocation to Create a Guaranteed Income for Life + Your Money Milestones: A Guide to Making the 9 Most Important Financial Decisions of Your Life (paperback)
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Product Details

  • Hardcover: 224 pages
  • Publisher: Wiley (May 8 2012)
  • Language: English
  • ISBN-10: 1118291530
  • ISBN-13: 978-1118291535
  • Product Dimensions: 14.5 x 2.2 x 22.4 cm
  • Shipping Weight: 458 g
  • Average Customer Review: 3.5 out of 5 stars  See all reviews (2 customer reviews)
  • Amazon Bestsellers Rank: #136,258 in Books (See Top 100 in Books)
  • See Complete Table of Contents

Product Description

From the Inside Flap

Where do all these numbers come from?

If you have spent any time at all planning for retirement, you have probably come across an assorted collection of numbers. Some of these numbers are very large, like how long you might live, or how much money you will need to retire comfortably. And, some of these numbers are very small, like the interest you are earning in the bank, or how long your money will last if the stock market takes a tumble at the wrong time. But, have you ever stopped and asked yourself: Where do all these numbers come from? Who created the underlying calculations? When were they discovered and how long have they been around? Do they have a proven track record? Well, you might be surprised to learn that the stories behind your numbers may be a lot more interesting than the numbers themselves.

For example, did you know that:

  • The value of a pension was first discovered by a comet-chasing astronomer following his father's suspicious death and a plot to kill the King of England?

  • The first calculation for how long your retirement nest egg will last was conceived over 800 years ago by an Italian merchant traveler best known for an obsession with rabbits?

  • The most famous mathematical model of human mortality was formulated by an Englishman who wasn't allowed to attend university?

  • Your stockbroker's very capitalistic plan to help you retire rich is based on an algorithm designed by the greatest Russian mathematician ever, who was a communist and Soviet hero?

Moshe Milevsky, bestselling author and internationally-renowned retirement quant, explains to the rest of us the work of seven scholars—summarized by seven equations—who shaped all modern retirement calculations. He tells the stories of Leonardo Fibonacci the Italian businessman; Benjamin Gompertz the gentleman actuary; Edmund Halley the astronomer; Irving Fisher the doomed stock picker; Paul Samuelson the economic guru; Solomon Huebner the insurance visionary, and Andrey Kolmogorov the Russian mathematical genius—all giants in their respective fields who collectively laid the foundations for modern retirement income planning.

With remarkable narratives that span several continents and 800 years of history, The 7 Most Important Equations for Your Retirement focuses on universal concepts and big-picture concerns, which help you first appreciate and then figure out how to retire while you can still enjoy your money.

From the Back Cover

From the introduction: An equation can't predict your future . . . But it can help you plan for it

Most books about retirement planning are written as guides, instruction manuals or "how-to" books. The authors tell you what to do, when to do it, and what to expect. I know this quite well because I have authored many such tomes myself.

Rest assured, this is not one of those books.

This book tells stories which I hope will lead into conversations. It is a narrative involving seven people, their discoveries and the conceptual innovations that made it possible for you to stop working and enjoy the money you have accumulated, one day. These protagonists—or scientific heroes—didn't achieve their breakthroughs while hunched over a laboratory workbench, peering through a microscope or trekking through jungles. They made their discoveries sitting in front of a blank sheet of paper, but while thinking very carefully about life and money. And, like the greatest thinker of them all, Albert Einstein, they too expressed their discoveries using a very beautiful language called mathematics. Alas, the seven equations profiled in this book aren't as famous or as elegant as the simplicity of E = MC 2, but they are far more practical for your retirement.

Yes, I know from many years of teaching experience that financial conversations are often dry and humorless. So I promise to do my best to lighten up the topic by keeping the technicalities to a minimum and focusing on the art.

"Art," you say?

Yes. In my mind, famous equations are like beautiful Picassos. Even if I don't quite understand the painting or the mathematics I can certainly appreciate the beauty and genius behind it. The seven equations presented in this book typify, at least for me, the conciseness, elegance and beauty that the best of the best equations demonstrate. By the end of this book, if you're not already inclined to appreciate mathematical equations for what they are, I hope you'll agree about the beauty.


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4 of 4 people found the following review helpful By G. Poirier TOP 50 REVIEWER on July 18 2012
Format: Hardcover
Reading books on finance can be a harrowing experience for the uninitiated. This is certainly not the case for this book. The author, an expert in the field, gently guides the reader through seven equations that can have a most illuminating effect on anyone's retirement plan. Each factor/variable in each equation is carefully explained; then plenty of useful examples are given for illustrative purposes. As a bonus, the author provides brief overviews of the lives of the individuals responsible for the subject equations - individuals whose collective work was done over a period spanning from the thirteenth century to the twentieth.

The author's prose is exemplary as far as clarity and friendliness are concerned. It is also lively, authoritative and, yes, even quite captivating at times for a book on finance. This is a book that can not only be enjoyed but carefully studied and used by anyone planning a happy, financially worry-free retirement.
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Format: Hardcover Verified Purchase
This book may be a great read for a mathematician or a historian, but it is over the head of the average person planning their retirement.
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Most Helpful Customer Reviews on Amazon.com (beta)

Amazon.com: 24 reviews
17 of 18 people found the following review helpful
A playful Milevsky looks at the history of retirement planning May 29 2012
By Robert Kirchner - Published on Amazon.com
Format: Hardcover Verified Purchase
I believe this is an interesting read if you are interested in financial planning, but it is definitely not a how-to-invest for retirement book. Instead it's a playful Milevsky telling the stories of some of the historical figures who helped shape modern retirement planning with their break thru contributions to finance. The seven equations aren't exactly as the seven original thinkers wrote them, but how Milevsky thinks the equations would be written if these visionaries were writing today.

The book begins with Fibonacci in Italy 800 years ago introducing present value calculations into financial math. Fibonacci, we also learn, tried to convince those dealing with math calculations in commerce in 13th century Italy to switch from using Roman numerals when doing calculations to the Hindu-Arabic numeral system. Milevsky reports that rivals of Fibonacci did not take kindly to his radical idea of switching from Roman numerals, and had the new number system banned. Even 300 years later in the mid 1500s merchants in Frankfurt, Germany, introduced legislation to have the radical new number system banned.

The book then moves to Gompertz in England in the early 1800s and the Gompertz function and the law of mortality. What Gompertz discovered was that the mortality rate for populations increases year by year by an average of about 9% over a wide range of years. So for instance if a population has a 10% chance of dying at age 65, the survivors will have about a 10.9% chance of dying at age 66, and those survivors will have about about 11.8% chance of dying at age 67, and so on and so forth. There is apparently a careful script the Grim Reaper follows. We also learn that at very advanced ages this breaks down. Beyond age 100 you have a chance of surviving that's about 50% every year - life becomes an annual fair coin toss. This implies that the aging process stops at about age 100 and, according to Milevsky, there is some evidence that at age 105 or so the aging process actually reverses a little bit - this possible reverse process even has a name, negative senescence.

The book then moves back in time to the astronomer Edmond Halley. Yes the Halley the comet is named after. Halley was the first to come up with an equation to value a pension or an annuity.

Next is American economist Irving Fisher and his 1930 equation that is the foundation of life-cycle finance, that is, how to spend our resources over our entire life-cycle. We also learn that Fisher invented the Rolodex and wrote best selling books on how to stay in good health in the early decades of the 20th century.

Next up is economist Paul Samuelson and his equation concerning about how much to invest in risky stocks and how much to invest in safe assets. Samuelson argued that if an investment was risky over one year, additional time didn't make it any safer. Time alone is not an excuse to hold more stocks. Time does not diversify risk and time is not on your side.

The story about Samuelson is personal for Milevsky. In 1997 a then young Milevsky published a finance paper claiming time was on your side and if investing for the long-term you should invest heavily in stocks. Milevsky was stunned to receive a letter from the then retired Samuelson scolding Milevsky for publishing a paper that was both misguided and erroneous. Receiving a personal scolding from one of the world's greatest economic scholars thoroughly shook up Moshe. It also got him to see the error of his ways. In 2008 Samuelson attended his last economic conference. Milevsky also attended that conference and shook Samuelson's hand and thanked him for pointing out the errors in Moshe's thinking in 1997 that seemed so obvious to the older and wiser Milevsky of 2008.

The last two chapters are about Huebner and life insurance, including life insurance in retirement, and the great Russian mathematician Kolmogorav and his differential equation, which can be used as a check to see if your retirement plan is sustainable.

Altogether, this is an interesting and fun read, if you really like thinking about retirement planning. But it is definitely not a how-to-book. The playful tone of the writing continues to the very end. The last two pages of the book is a poem about the stories and individuals in the book written by Milevsky's 11 year old daughter.
8 of 8 people found the following review helpful
Retirement Finances Clearly Explained July 18 2012
By G. Poirier - Published on Amazon.com
Format: Hardcover
Reading books on finance can be a harrowing experience for the uninitiated. This is certainly not the case for this book. The author, an expert in the field, gently guides the reader through seven equations that can have a most illuminating effect on anyone's retirement plan. Each factor/variable in each equation is carefully explained; then plenty of useful examples are given for illustrative purposes. As a bonus, the author provides brief overviews of the lives of the individuals responsible for the subject equations - individuals whose collective work was done over a period spanning from the thirteenth century to the twentieth.

The author's prose is exemplary as far as clarity and friendliness are concerned. It is also lively, authoritative and, yes, even quite captivating at times for a book on finance. This is a book that can not only be enjoyed but carefully studied and used by anyone planning a happy, financially worry-free retirement.
7 of 8 people found the following review helpful
Less than I hoped for Aug. 18 2012
By D. Clarke - Published on Amazon.com
Format: Hardcover Verified Purchase
Milevsky writes clearly and entertainingly but the book falls short in each of its three major areas. As biography and history of major figures in mathematics and finance the material amounts only to a few pages for each individual which will not be nearly enough for those interested in history.

For those looking for information to help plan their retirement finances, the equations are relevant and interesting but their presentation is sometimes flawed. For example, the Samuelson chapter does not provide enough information to fully support an idea that is contrary to prevailing wisdom. The usual concept is that the decline in volatility of stock market returns when stocks are held for longer periods of time justifies holding more stock when you have a long time horizon. Samuelson's notion is that this benefit of reduced volatility over time is canceled if you are risk averse. Samuelson's equation for this produces some numbers that even Milevsky describes as "insane" and needs more justification and explanation. Milevsky also mentions the key concept of the impact of an up vs down stock market early in your retirement but never elaborates on this essential point.

As a math book the text is more successful but the Kolmogorov chapter is flawed by departing from the straightforward high school math of the earlier chapters. It would be challenging to implement the Kolmogorov equation on a spreadsheet.

The book tries to blend history/biography, finance/retirement and mathematics but 180 pages of main text is too short to do them justice.
5 of 5 people found the following review helpful
An Entertaining Intellectual History June 26 2012
By Wade D Pfau - Published on Amazon.com
Format: Hardcover
With The 7 Most Important Equations for Your Retirement, Moshe Milevsky has written in the style of my favorite genre of book about my favorite research topic. It's fertile ground for me to like the book.

About the genre, I like reading about the history of people and ideas who've shaped our modern world. You can see this approach in books such as Robert Heilbroner's The World Philosophers, Peter Bernstein's Capital Ideas, Justin Fox's The Myth of the Rational Market, Niall Ferguson's The Ascent of Money, countless books by Bill Bryson including, in particular, A Short History of Nearly Everything, as well as television series such as James Burke's Connections. I really have a soft spot for these sorts of works.

Though it would be nice to see what Bill Bryson could have done with the same source material, and comparing the biographical sketches about Irving Fisher presented by Justin Fox and Moshe Milevsky shows the some of the missing potential for really helping us to feel a connection to life and times of the thinker, I do think that Moshe Milevsky pulled off a really difficult feat. That is, he wrote in an entertaining manner about these historical figures in a respectable way. This is an extra special feat for Milevsky, because he is really showing his versatility by branching off to a new style of writing. Even if it hadn't worked, he can always fall back on being the world's leading researcher and authority on retirement income strategies.

The book works very well, building up the intuition behind key results, and culminating in a chapter which essentially provides the intuition for one of Milevsky's important research papers, "A Sustainable Spending Rate without Simulation," from a 2005 issue of Financial Analysts Journal. We learn about present value analysis and calculating sustainable spending with a fixed return from Leonardo Fibonacci, and then about adding in the randomness and uncertainty about our remaining lifespan, but how that randomness follows a predictable pattern observed by Benjamin Gompertz. Andrei Kolmogorov further teaches us about what to do in the case that market returns are also volatile and random. We learn how to calculate the value of a lifetime of annuity payments with the work by Edmond Halley, and how to calculate the current cash value of a life insurance policy with the work of Solomon Huebner (who also brought us the idea that life insurance should be used to protect the value of our human capital). Paul Samuelson teaches us how to determine our stock allocation, and then answer depends on our holdings of human and financial capital, our expectations about future market returns and volatility, and how we feel at a gut level about fluctuating market returns.

Milevsky also has a chapter on the proper spending rate based on the work of Irving Fisher, which is of special interest to me as this is where I am personally doing research these days. Just a note, Milevsky must have ran out of sugar for his Cheerios (and I don't mean the honey nut kind) the morning he wrote this chapter, as he is none too kind to the Journal of Financial Planning, referring to it first as a "trade magazine" (page 81) and then as a "rather obscure journal" (page 82). I don't think that's fair. Certainly, the JFP has aspects of a trade magazine, but it's "Contributions" section at the end does provide proper peer-reviewed research articles. The journal may not have much reputation with academics, but it provides an outlet for quality works and is a widely read and influential publication. Milevsky published several articles there as well, including an influential 2003 article with Peng Chen on allocating between annuities and mutual funds. This section also has typos, as unless Milevsky is back from the future, Bill Bengen didn't write his article more than 20 years ago (it was 1994), and at the end of 30 years you'd be left with zero in the worst case scenario, not on average.

Back to the story, though. I've said before that Milevsky is The Simpsons of retirement income research, as any idea you can think of has already been investigated by Milevsky. With Fisher, he describes his idea of longevity risk aversion, which provides a good explanation for why the 4% rule is not a good baseline retirement income strategy. Working with Michael Finke and Duncan Williams, I like to call this same idea "spending flexibility." We wrote an article about that in... naturally... the Journal of Financial Planning. I also wrote a blog post "Is it Optimal for Retirees to Plan for Reduced Spending with Age" which provides a discussion of these issues.

To make a long story short, you have to be extremely inflexible with your spending or extremely averse to outliving your wealth to prefer a strategy of constant spending over retirement. Generally, constant spending will force you to make too much cutbacks on spending in early retirement to allow for the same spending much later on when the probability of survival is quite low. As Milevsky adds, if you are really so inflexible then you should probably use an immediate annuity. That eliminates your longevity risk.

Milevsky's book provides fresh insights about these and a host of other issues, and I think it makes for good summertime reading for those interested in retirement income. It is a pretty short book. Maybe I'm finally learning how to read faster or something, because I got through the book in a couple of hours despite thinking that I did pay pretty close attention to what I was reading.
2 of 2 people found the following review helpful
A real eye opener Dec 23 2012
By Jerry O - Published on Amazon.com
Format: Hardcover Verified Purchase
This book exposed me to realities I had not considered particularly the odds of living a very long life. This was an eye opener for me as I felt that I was in such great health.


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