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Did Paul Samuelson Support Leveraged Lifecycle Investing?—A Commentary by Ian Ayres ’86 and Barry Nalebuff

The following commentary was posted on newyorktimes.com on July 6, 2010.

Did Paul Samuelson Support Leveraged Lifecycle Investing?
By Ian Ayres ’86 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 <http://www.youtube.com/watch?v=0h9tKy3NA-U%5d> .

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 <http://islandia.law.yale.edu/ayres/samuelsonletter.pdf> .) He suggested that we were, like many before us, falling victim to the “law of large numbers” fallacy <http://web.cenet.org.cn/upfile/74462.pdf> . (We explain why not here <http://islandia.law.yale.edu/ayres/dearreader.pdf> .) 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.