York University professor Moshe A. Milevsky teaches at the Schulich School of Business. His latest book is The 7 Most Important Equations for Your Retirement: The Fascinating People and Ideas behind Planning Your Retirement Income (Wiley, May 2012).
It is interesting to note that the issue of pensions and the risk involved in planning were thought of over three hundred years ago.
In the 17th century, the state was facing problems not unlike the ones faced by Ford and other companies and governments today. The King awarded pensions for service to the Crown and many members of the clergy, as an example, had been promised lifetime payments.
In 1672, the government established a pension for retired Royal Navy officers and by then British insurance companies were offering annuities to people of all ages, but were charging a flat price, regardless of age.
In 1672, the government established a pension for retired Royal Navy officers and by then British insurance companies were offering annuities to people of all ages, but were charging a flat price, regardless of age.
The City of London was the centre of business in the British Empire and it gradually dawned on the business community that these promise to pay involved risks. But nobody had an accurate idea of exactly how much risk and so they turned to the scientific establishment for help.
The problem made its way to the Royal Society — think of it as a supreme council of scientists — and then to Edmond Halley who spent most of his life gazing at the stars.
He attacked the problem in a careful and novel way. And much to his credit he came up with the first known procedure for properly valuing a pension or lifetime annuity.
He wrote an article which was published in 1693 by the Royal Society’s Philosophical Transactions and provided the equation he had used, along with the first reliable mortality table.
He attacked the problem in a careful and novel way. And much to his credit he came up with the first known procedure for properly valuing a pension or lifetime annuity.
He wrote an article which was published in 1693 by the Royal Society’s Philosophical Transactions and provided the equation he had used, along with the first reliable mortality table.
His equation is still used and taught to insurance actuaries today. More, importantly, it is an equation every Canadian should be aware of as they approach their retirement years.
Halley’s main scientific insight was to combine interest rates, mortality rates and age, to arrive at an equation for the value of a pension annuity.
He properly established that the younger you are — all else being equal — the more valuable and expensive is the corresponding pension annuity. More importantly, the lower the prevailing interest rates — such as they are today — the more valuable is your pension. In fact, you might be surprised to learn how valuable that pension can be.
Think about it. If you can retire on a full pension paying 80 per cent of your salary at the age of 55, the value of your benefit can be in the millions of dollars.
He properly established that the younger you are — all else being equal — the more valuable and expensive is the corresponding pension annuity. More importantly, the lower the prevailing interest rates — such as they are today — the more valuable is your pension. In fact, you might be surprised to learn how valuable that pension can be.
Think about it. If you can retire on a full pension paying 80 per cent of your salary at the age of 55, the value of your benefit can be in the millions of dollars.
Here is yet another application of Halley’s methodology and equation, which is relevant to all Canadians.
Although Old Age Security might only pay $550 per month, its present value at the age of 65 — and in today’s ultra low interest rate environment — might be as high as $115,000. There is much at stake in the debate around reforming OAS.
Although Old Age Security might only pay $550 per month, its present value at the age of 65 — and in today’s ultra low interest rate environment — might be as high as $115,000. There is much at stake in the debate around reforming OAS.
Halley’s equation and methodology for valuing pension annuities is now ubiquitous and intertwined with all retirement decisions. In my opinion, it is one of the seven most important equations for retirement planning.
So, when it comes to the Ford plan (In order to lighten its pension load, the Ford Motor Co. announced recently that it is offering 90,000 retired engineers and office workers the choice of continuing to receive a monthly pension or take a lump-sum buyout from the Ford plan) pensioners, I would suggest that every one of them find an actuary — or at least an astronomer — who is familiar with Halley’s equation, so they can figure out whether the deal is worth it or not.
The other six minds behind calculations for retirement and the questions you need to consider
In addition to Edmund Halley’s equation for valuing pension annuities, here are the people behind six other important retirement calculations.
Present and future value: If I have $1,000,000 in my nest egg, earning 5 per cent per year, for how many years can I afford to withdraw $100,000 before the account is emptied? It’s obviously more than 10 years because of the interest rate, but how much longer?
Italian mathematician Leonardo Fibonacci (circa 1170-1250) derived the equation still in use today. He also wrote the world’s first financial mathematics textbook.
Italian mathematician Leonardo Fibonacci (circa 1170-1250) derived the equation still in use today. He also wrote the world’s first financial mathematics textbook.
How long will I live? The odds of a 75-year-old living to 80 are obviously greater than an 18-year-old living to 80. British actuary Benjamin Gompertz (1779-1865) figured out the exact ratios and the law of mortality underlying this calculation.
Gompertz was a self-taught mathematician, because at that time as a Jew he was not allowed to attend university. He eventually became president of Britain’s prestigious Royal Society.
Gompertz was a self-taught mathematician, because at that time as a Jew he was not allowed to attend university. He eventually became president of Britain’s prestigious Royal Society.
How much can I spend? Yale University economist Irving Fisher (1867-1947) was the first to properly factor inflation into the equation, as well as the notion that you spend less as you age to help answer the question of how much to spend.
How much risk can I take? MIT professor and Nobel laureate Paul Samuelson (1915-2009), whose economics textbook is well known to undergraduates, described the optimal asset allocation between the risky stock market versus safe cash, taking into account all your capital.
What am I worth? Wharton business school insurance scholar Solomon Huebner (1882-1964) pioneered the technique for properly measuring and insuring human life value and he emphasized the role of legacy in financial planning. So, you want to leave $100,000 to the grandkids. How much will that cost you today?
Will my plan work? Russian mathematician Andrei N. Kolmogorov (1903-1987), state hero of the communist Soviet Union, created the mathematical framework that determines the probability your retirement income plan is sustainable.
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