Since a consensus formed on the need to reform the Canada Pension Plan -- from a "pay-as-you-go" plan, financed out of each year's contributions, to a plan funded in part by the returns from investing previous years' surplus contributions in the markets -- the debate has turned to how these savings should be invested. Should they be entrusted to a single, government-run fund, overseen by a quasi-independent CPP Investment Board, as enacted in recent federal legislation? Or should each individual's contributions be directed into his or her own retirement savings plan, similar to the RRSPs many Canadians already hold?

Proponents of the latter scheme emphasize that individuals can choose how to invest their own savings; competition in the marketplace, it is suggested, offers potentially higher returns than if the funds were invested on their behalf by the government. Opponents, on the other hand, stress the risks associated with such investments, as compared to the safety of a government fund in which everyone participates. The Prime Minister, needless to say, is a fervent advocate of the One Big Fund approach, on just these grounds.

"Canadians want a basic retirement pension they can count on, one that does not depend on the fluctuation of the markets," he said in a recent speech.

"Leave it to those who are in a position to take those risks," he went on, rather than exposing "people who want only the security and predictability of a public system," whose operating principle he identified as "pooling risk." In fact, neither side has it quite right. The real case for "personalizing" the CPP is not that individual RRSPs offer higher returns, but that they are less risky than a single fund.

For the average person, competition among investors does not mean the savviest earn systematically higher returns than the rest: it simply beats everyone down to the average. Countless studies have demonstrated the near impossibility of consistently beating the market. All that is achieved in the fervent search for information that might affect stock prices is a sort of collective standoff; whatever temporary advantage one investor might glean is instantly transmitted to millions of others by the very movement of prices.

Hence the popularity of index funds, which simply track the market.

So if it were only a matter of earning the highest return, it might be best to turn the CPP into a giant index fund, and save the outrageous management fees that many private mutual funds charge their customers. But that is to ignore the question of risk. I have already written of the risks of political interference that inevitably arise whenever such a large pool of funds is in government hands: think of the Alberta Heritage Savings Trust Fund, or Quebec's Caisse de Depot. Indeed the CPP itself has been horribly mismanaged, the original contingency fund having been entirely invested in provincial bonds, and at below-market rates.

But even if it were flawlessly managed, the One Big Fund is a poor risk for most folks. The Prime Minister talks about it as if it were an insurance policy. But the risks involved in investing such a fund don't have anything to do with the personal atttributes of individual contributors: they're systemic, tied to the ups and downs of the economy and the markets. You don't pool risk by piling everyone's savings together in this way: you homogenize it.

Everyone, whatever their circumstances -- rich or poor, young or old -- shares in the same mix of investments: stocks, bonds and so on. So everyone is exposed to the same risk.

But what modern portfolio theory teaches us is that different asset mixes are appropriate to different people, depending on their tolerance for risk. A younger person, with a longer time until retirement, should invest more heavily in equities, since stocks earn more than bonds in the long run.

Conversely, a person nearing retirement should have a greater proportion of bonds in their portfolio, since these are safest in the short term.

Mind you, a system based on individual savings plans exposes the government to some additional risk: those who proved particularly unwise or unlucky with their investments would still have to be provided for in their old age. So the government would be well within its rights to regulate an RRSP-style system quite closely. Contributions would be mandatory, of course, and locked in until retirement. But beyond that, the government might even prescribe that each plan must hold a certain minimum proporition of safe investments like bonds, the percentage varying according to how old the plan-holder was.

Indeed, such a system would be just as "public" in its way as the One Big Fund. It would just be a better risk.