Did Paul Samuelson Support Leveraged Lifecycle Investing?

Here is a post coauthored with Yale School of Management professor, Barry Nalebuff, regarding?Paul Samuelson‘s criticism of our Lifecycle Investing strategy:

Did Paul Samuelson Support Leveraged Lifecycle Investing?
Ian Ayres and Barry Nalebuff

Those of us old enough to grow up with?Annie Hall keenly remember the scene outside a movie theater in which a Columbia professor pontificating on Marshall McLuhan is confronted by the real Marshall McLuhan, who says “You know nothing of my work.” We feel a bit like that unfortunate professor. In our book, Lifecycle Investing, we characterize the leveraged lifecycle strategy as an elaboration of the ideas published back in 1969 in separate articles written by?Paul Samuelson and?Robert Merton. Our problem is that Samuelson in a speech at Boston University in 2008 explicitly rejected our strategy. His speech was even?captured on video:

According to Samuelson (at about 16 minutes into the clip):

The ideas that I have been criticizing do not shrivel up and die. They always come back…. Just recently as I was preparing this manuscript, I got one of those innumerable abstracts from the National Bureau of Economic Research and I will name no names but a Yale economist [Nalebuff] and a Yale law school professor [Ayres] have advised the world that when you are young and you have many years horizon ahead of you, you should borrow heavily and go on margin, because that’s the way you get the ready money and with that ready money you are going to make a lot of money.

And I have to remind them with well-chosen counterexamples. I always quote from Warren Buffet … And one of the things that he said, this wise, wise man (from Nebraska of all places), was that in order to first succeed you must first survive… People who leverage heavily when they are very young do not realize that the sky is the limit of what they could lose and from that point on they are knocked out of the game.

Yes, we do propose that young investors invest with leverage. But, as we explain below, this is fully in keeping with Samuelson’s own prescriptions. The reason for leverage isn’t that this is a way to double your bets and make quick money. Rather, this is the way to get around a constraint that prevents young investors from getting their desired exposure to equities. To put some numbers on this, take someone whose lifetime wealth is $1,000,000 and who would ideally like to expose half of that wealth, or $500,000, to stocks. The key point, and the source of confusion, is that we aren’t proposing that this person invest double their wealth, or $2,000,000, in stocks. No, we propose that the person invest something like $50,000, with leverage, in order to get exposure of $100,000 to stocks.

That may well seem paradoxical. How can a person with $1 million in wealth have trouble investing $500,000 in stocks? The answer is that for a typical young person in that situation, most of his or her wealth is tied up in his or her human capital. It isn’t easy to borrow against that future income stream. Buying stock with leverage is a way to move closer to the desired asset allocation. Our young investor would like to convert half of her human capital bond to stocks. But those markets don’t exist or charge too much to make this a practical idea. So what she can do is employ leverage. If she has $50,000 to invest, it makes sense to use that $50,000 to get exposure to $100,000 of stocks. Just as most young investors don’t have the capital to buy a house without leverage, they don’t have the capital to buy the desired allocation of stocks without leverage.

The back story here is that in 2008, when we wrote a first draft of an?academic article on the leveraged lifecycle idea, we sent a copy to Samuelson, our former teacher. In our minds, the central idea behind our paper was just the natural implication of what Samuelson and Merton saw back in 1969.

Back in 2008, we weren’t sure if Samuelson-at 93 years old-was still active, but were happy to learn that he was still regularly coming into his office. Before Samuelson gave his speech at Boston University, we corresponded with him back and forth a couple of times. As in his B.U. speech, Samuelson in his letters to us did not accept our analysis.? (Here’s a link to?one of the letters.)? He suggested that we were, like many before us, falling victim to the?“law of large numbers” fallacy. (We explain why not?here.) In our minds, we couldn’t get him to engage with the substance of the theory. He wrote in one letter that he had only read the paper’s abstract. We don’t know if he later read beyond that. In the fall of 2009, we arranged to make a special trip from New Haven to Cambridge just to meet with him in person and see if we could come to agreement.? But his assistant called us the day before we were to meet and told us that, because of Paul’s health, we would need to reschedule. Sadly, Paul Samuelson died a few months later (December 13, 2009) before we ever had a chance to meet.

Notwithstanding Samuelson’s own words at Boston University, we remain convinced that Samuelson’s papers and theories do indeed support our strategy of leveraging investments when young.? In 1994, Samuelson wrote in “The Long-Term Case for Equities“:

If you are a young professional with future [earnings that] cannot be efficiently capitalized or borrowed on, to keep your equities at their proper fraction of?true total wealth, you should early in life put a larger fraction of your liquid wealth in common stocks.

Even stronger evidence that Samuelson would have embraced a leverage-when-young strategy comes from his 1969 classic, “Lifetime Portfolio Selection by Dynamic Stochastic Programing.”? In that article, Samuelson analyzed the optimal investment strategy for a “businessman” in contrast to a “widow” who must live off her inheritance.? Samuelson provided the following prescription:

[The businessman] can look forward to a high salary in the future; and with so high a present discounted value of wealth, it is only prudent for him to put more into common stocks compared to his present tangible wealth,?borrowing if necessary for the purpose (italics added), or accomplishing the same thing by selecting volatile stocks that widows shun.

There is nothing sacred about limiting your investments to 100 percent of your present tangible wealth. You can get more exposure to the market by borrowing or by buying stocks with high beta. The larger point is that prudence calls for you to invest based on your presented discounted value of lifetime wealth. For young investors, the present discounted value of future wealth far exceeds their tangible wealth, and therefore they are constrained in terms of how much they can invest in equities.

Does that mean the young investor who employs leverage is taking inordinate risks? Again, we turn to Samuelson (1969):

[A high salary in the future] does?justify leveraged investment financed by borrowing against future earnings. But it does not really involve any increase in relative risk-taking once we have related what is at risk to the proper larger base. (Admittedly, if market imperfections make loans difficult or costly, recourse to volatile, “leveraged” securities may be a rational procedure.)

This quotation captures the essence of our leveraged lifecycle approach. You should discount your eggs before they hatch, calculating the present discounted value of future savings and exposing a portion of what Samuelson called your “true total wealth” to stock investments today.? Market imperfections make it prohibitively expensive to borrow against future earning, but margin interest or the implied interest of stock index options makes it remarkably cheap to borrow in order to get up to 2:1 leverage on your existing investments.

Indeed, Samuelson’s 1969 analysis answers the 2008 criticism that he himself lodged against our approach. The Boston University speech worried that “People who leverage heavily when they are very young do not realize that the sky is the limit of what they could lose and from that point on they are knocked out of the game.”? But the 1969 quotation shows why this is incorrect-buying stock on margin doesn’t “really involve any increase in relative risk-taking once we have related what is at risk to the proper larger base.” Take, for example, an investor in her late twenties with $50,000 in current retirement savings and $950,000 in the present value of her future retirement savings.? If she follows our strategy and borrows $50,000 to invest $100,000 in stock, it is true that (if there is a market crash) she might lose most of her current investment.? In the short run, the net value of her current portfolio value might fall close to $0.? But the vast bulk of savings are still coming in the future-so counter to the B.U. claim, she will not be knocked out of the game. Indeed, she is really only exposing $100,000 out of $1,000,000, or 10 percent, of her total retirement savings to stocks.

Samuelson’s 1969 analysis is just as true today. His theory is at the very heart of our book. We still proudly claim ourselves mere elaborators of his insights. And we still think it was appropriate to dedicate the book to this greatest of American economists.

The conflicting views of the younger and older Samuelson also suggest a “lifecycle” reason to be leery of?ad hominem argumentation.? The substantive merits should matter far more than whether particular sages support or oppose an idea.? One of the great strengths of economics (say, relative to psychology or philosophy) is that economists spend less time obsessing about “what did Freud or Plato think about this?”? Sure, we have blurbs on the back of the book.? But you should accept our claims only if our arguments and empiricism are compelling, and not because our claims are vouchsafed by venerated sages of the profession.

Michael F. Martin

It seems to me that the same arguments against strict adherence to the Kelly Criterion ought to apply equally against this leveraged life cycle investment strategy.

And if you were to follow something like Half Kelly, you might not be well-advised to take out a loan to invest in equity, even if you had a substantial prospective stream of earnings in the pipeline due to your Yale and Harvard degrees, because of your substantial Yale and Harvard loans.


You and he are both crazy. Leverage is fool's gold.

Marc Robinson

I agree that the younger Paul Samuelson would probably have agreed with your point. I would agree with the older Paul though, particularly in the real world. People's human capital is uncertain, and many are prone to overestimate it. Margin loans can be called at inconvient times, including when your human capital is still illiquid. The costs and benefits of greater beta when young, particularly when the risk premium on margin loans is thrown in, seem highly asymmetric. Moreover, young investors are likely to follow your advice at the worst times, just like young homebuyers did during the bubble. I think your advice is very dangerous.


I understand that the authors' theory makes logical sense, and in the absence of empirical evidence, I might believe it.
But the technique of leveraged stock buying on a large scale has been tried before. It was a major factor in the run-up to the crash of 1929.

If one person can accurately predict their future earnings, and has some reason to believe that stocks will outperform any other asset over the course of their working life, and can find a bank willing to loan money for speculation, then maybe this is a good idea for that person. However, if every young person tries this at once, we already know what will happen: a stock market bubble and crash, wiping out any bank that loaned out this money.

I would also like to point out that if you replace every instance of the word "stock" in this theory with "house," you'll have a lovely description of the mindset of the American consumer circa 2006.


Eileen Wyatt

Of course buying on margin involves more risk than ordinary stock-buying: using margin, it's possible to lose more than the amount invested.

Losing the initial nest egg would call for revising the present value of future retirement savings, as that nest egg would no longer be earning returns. One can't just fiat that a person will be worth $X at time Y: money must somehow be invested to get there. If one's savings drop from $50k to $0, that makes a difference in returns. (Even compound interest can't do much with an investment of zero.)

In any case, if quoting Samuelson was important when he was believed to agree with the authors, I find it disingenuous to dismiss the need for expert support when he turns out to disagree.


I have 2 questions about this approach.

1. Scientists like to express the probabilities of models being incorrect as p and like to be sure that p is less than 0.05 before moving on. I cannot tell what the relevant p values are here. But it would seem prudent to want to have the p for disaster be quite low (is 0.05 low enough??) and to be willing to put up with a fairly low p for being wildly successful, if necessary. What are the "p"s for this approach? Certainly, we don't want to just be assured that, ON AVERAGE (ie, p=0.5), this is the way to go. That seems WAY too risky.

2. When the young investor is calculating his or her future wealth, won't the performance of his or her initial wealth be overwhelmingly important? The nature of compounding interest (or dividends) seems to make this quite obvious. So, whether that first leveraging is successful is more important than the 10% figure implies. If successful, it will likely be less than 10% (because the final wealth will benefit), but, if unsuccessful, it will likely be much more than 10%, because the longest source of that potential compounding will be wiped out. Ah, if only one could see the future!


Sasha Berman

One problem always overlooked by investment advice-givers, is the limited pool of sound investments. The amount of money seeking a good return on investment greatly exceeds the sound investments that exist. That is what fuels bubbles and all kinds of speculative behavior -- too much money chasing after returns that just don't exist.

bob sallamack

No, we propose that the person invest something like $50,000, with leverage, in order to get exposure of $100,000 to stocks.
This is a 50 percent margin call where the investor has a possible worst case loss of $100,000 if the investor makes margin calls and 50,000 if the investor fails to make margin calls. Think the magic word ENRON.

Imagine buying your stock on margin at the height of market and having daily margin calls when the stock goes down.

Where do you get the cash for these margin calls. The only sure way is to have 50,000 in the bank where you can immediately make up the margin. The alternative is to the stock covered by the original 50,000 sold to make up the margin call. It is always great to be selling stock when it is falling in value.

So if you intend to make margin calls you have to have 50,000 in the bank or take the chance that you have to get the money from another investment where cashing out might mean a loss. Is not it great to take a loss to just cover another loss.

It is very conceivable that in a bad market the stock of your original investment because of missing the margin call might be go down to S10,000 since the leverage is going to double any market loss of the stock. So now you own less stock by not making leverage calls and you will make less money if stock goes up.

Leverage as these clever people suggest is great in a down market where you have to risk more money or see your investment having double the market loss because of leverage.

Of course if you did not meet the margin call you can never recover the investment lost because of failure to meet margin. Imaging losing 60 percent of your investment in a few days and then getting back very little when the the market suddenly rises.

Of course besides picking the wrong stock there is also the possibility of even picking the right stock at the wrong time when the market crashes.

Hey why go through all this trouble and daily margin calls. Take the $50,000 to a casinos. Hey you are young and you might be lucky.



This sort of advice, which admits that the future is unknown, but assumes a return to an average CAGR over a long enough time period sound like a perfect contrarian indicator to several lost decades in the stock market. See Japan, for an example.

Drill-Baby-Drill Drill Team

Why ask for a second hand or third hand opinion?

If Samuelson is still alive, is he not the ultimate authority on his own opinion?

Rob Meredith

Isn't his point that risk is intrinsically linked with future earnings potential?

Michael Radosevich

Excellent. Leverage your money to the max, & invest in tech stocks in 1998. Then, leverage again, & invest in real estate in 2006. By this time, even if you're LeBron James, you'll be in debt for the rest of your life.

And by all means borrow every penny you have today & sink it in the market today. When the sheriff sells your property at auction, I'll take pictures for your photo album.

Are you nuts? Or just pretending.

Michael Radosevich


Ian, as a young actuary who has studied and worked a great deal with present values, asset/liability matching and market risk analysis, I find that your proposal makes complete sense. It's one of those things that seems obvious in retrospect. I had already been allocating 100% of my 401k to stocks because at such a young age it simply felt like a waste to have anything in a conservative "safe" investment, but I never formally understood why until I first read about your idea here on this blog.

I am disappointed to see people getting distracted by unrelated ideas such as bubbles, or not understanding the mechanics of calculating a present value of future income. Don't worry, despite the reactions you seem to get, there are some of us out here who understand it :-). Keep up the good work. This type of post, exposing "common sense" that turns out to be wrong and supporting it with facts and analysis, is exactly why I love everything Freakonomics!



Sasha: in a normal free market, interest rates shift in response to how much money is seeking investment versus borrowing, and that controls the balance. The more people that want to invest, the lower the returns will be, which will discourage some of them. The interest rate stabilizes at the point where the supply of investors is the same as the demand for loans.

A bubble will form if this equilibrium is broken, such as through a government ceiling on the cost of borrowing. As any econ student knows, a price ceiling causes excess demand. Normally this would just result in shortages, but instead the government steps in to make up the excess supply. The result is pretty obvious: excess borrowing/consumption. (Since Keynesian economists use consumption as a proxy for economic health, this looks like a Boom. Great news!) This excess borrowing has to get repaid at some point, causing a corresponding period of underconsumption. (A Bust, which somehow very few people see coming.)

Bringing it back to lifecycle investing, leveraged investing is okay as long as the lenders are actually forgoing consumption in order to give you their money, because then your extra demand is matched by their reduction. Bubbles come when the government (or anyone else) lends money from nothing, so that there is no reduction on anyone's part to balance out the increased consumption of the borrowers!



Humans are naturally risk averse, it seems fairly apparent to me that a lot of people wouldn't countenance leveraging. The problem I have is not with leveraging per se -- I'm fairly confident about my future earnings and am willing to bet based on them. The problem right now is I might not have enough assets to cover a margin call should there be one, and the consequences of personal bankruptcy are pretty bad. I would leverage, but probably not to the degree recommended.

People pontificating against leverage probably don't understand discounting and net present value, and/or are applying their own personal circumstances to a general issue. In the abstract, leveraging is fine. But there are real world complexities which may make it hard to leverage your present investments. That doesn't mean leveraging should never be an option.


Leveraging as a policy is absolutely a wrong policy.

Not leveraging when the opportunity knocks is a sin!

Not getting out of the market after making a bundle is a foolish greed.



You are casting pearls before swine.

We have seen recently the peril of highly leveraged real estate. Do the critics of your brilliantly simple strategy advise against home mortgages?

I expect muddle-headed analysis from the average Freakonomics reader, but I am disappointed that Samuelson didn't take the time to understand your strategy before publicly denouncing it.


First you must survive. Good advice.


"leverage' is very different from "having a high proportion of your assets in stocks". It seems to me that the latter is what was originally suggested and the former was your mis-understood extrapolation.

Having 100% of your assets in equity compared to say a more balanced approach of 50%, is what samuelson suggested for young people, because it targets to make higher returns taking higher risk in early years, WHILE STILL STAYING IN THE GAME NO MATTER HOW BRUTAL THE MARKET GYRATIONS. the leverage that you are suggesting will take the poor youngster out of the game altogether if there is a big draw-down as he will lose all his investment without any chance of recovering with the market. That is stupid and nothing else.

The only exception is the scenario where that leveraged investment is not marked to market (and hence no margin calls) + one can continue to pay interest or other required payments while maintining the loan for a long time. That can be true for property loans in some cases, but it is never possible for stock loans....



You folks just don't get it. Even if a "youngster" loses his entire leveraged equity portfolio in a "brutal market gyration" he is most certainly not out of the game. He still has his human capital which will be converted into a stream of future earnings over his working career.