Maximizing the Long-Run Returns of Retirement Savings

by FCCC3 min read7th Jul 20207 comments

10

InvestingPolicy Change
Frontpage

Superannuation funds are important and poorly implemented

Australia prepares its people for retirement by requiring them to save a portion of their income in “superannuation funds”, which currently hold about $3 trillion dollars’ worth of citizen wealth. In 2025, the required proportion of income saved will increase to 12 percent. Considering the enormous wealth this system controls, it’s important for the system to work well. It doesn’t. Among the 31 recommendations given in a recent government report, most are regulations that stop the funds from, essentially, stealing money from working people.

If there were no unintended multiple accounts (and the duplicate insurance that goes with them), members would have been collectively better off by about $2.6 billion a year. If members in bottom-quartile of … products had instead been in the median of the top-quartile … they would collectively have gained an additional $1.2 billion a year.

Most people know nothing about investing, nor should they need to—the system should do the hard work of getting them the best deal. To do this, the government report recommends the creation of a committee that would help people choose the best 10 (or fewer) funds to invest in. I don’t like committees and I don’t like round numbers, primarily because they're indicative of poor reasoning. (On what basis do we believe the committee is competent? And why the best 10 or fewer funds and not 9, or 8, or any other number?)

A fundamental overhaul of the system might be a better fix. The goal of my proposed system is to maximize the long-run returns. This is a toy model, so there are obvious issues with it, but I think it could be modified into a system that would work well. If you want to point these issues out, please recommend a fix as well.

The proposed system

Each dollar of forced savings goes up for auction. The highest-bidding fund gets the dollar immediately after the auction (i.e. the present value of the funding is $1):

Then, after a previously agreed-upon period of time, the fund pays the government the second-highest bid (i.e. the future value of the price paid is equal to the second-highest bid):

All of these bets go into one big collective fund, and each citizen’s return is the average return of the fund.

Profit of the fund

The future value of the funding is equal to the present value of the funding, i.e. $1, plus the net return it can generate from that dollar:

The future value of the fund’s profit is equal to future value of the funding it receives minus the future value of the price it pays:

The fund’s profit-maximizing bid

Suppose that funds maximize profits. Thus, the th fund bids its profit-maximizing bid (), which, in a second-price auction with non-colluding bidders, is the bid () that would make its profit zero if it paid its bid:

The profit-maximizing bid can be found by making the relevant substitutions:

Note that each fund’s profit-maximizing bid is independent of the other funds’ bids.

Sufficient criteria to maximize returns

The future value of citizens’ savings is maximized if

1. the fund that can produce the highest net return gets the dollar, and

2. all funds maximize their net return, and

3. the winning fund’s profit approaches zero.

The proposed system satisfies the sufficient criteria

Criterion 1: Best fund gets the money

Fund gets the dollar only if its bid is the highest. We substitute in its profit-maximizing bid, and find that the winning bidder must have the highest net return:

I.e. criterion 1 is satisfied.

Criterion 2: The winner maximizes their net return

Recall that the winning bidder pays the second-highest bid. Recall that, barring collusion, a profit-maximizing fund will bid independently of the bids of any other funds—the winning fund cannot affect the second-highest bid. So, to maximize its profits, the winning fund will maximize the remaining factors, which happen to equal its net return:

I.e. criterion 2 is satisfied.

Criterion 3: The fund’s profit is zero

The winning fund’s profit equals the difference between the total benefit it would provide and that of the second-best fund:

I.e. if the best two funds are equally capable, the profit is zero, and criterion 3 is satisfied.

EDIT: Addressing the main weaknesses of the model

The definition for the future value of profit assumes no bankruptcy

A fund can’t make unbounded negative profits: They'll go bankrupt once their fund’s value goes below zero. So funds could profit by taking high-volatility bets even if the expected value of the bet is below zero. To prevent this, we probably want capital-rich intermediates to underwrite the funds. Or you could have a secondary market that effectively acts as an underwriter.

The problem for underwriters is that the market is risky. To make their optimal bids, funds need to estimate their exact return at an exact time. And that’s not possible.

Making the bidding easier

To make it easier for the funds to estimate their optimal bid, the bids can be stated as whatever the return of the agreed-upon index is (probably a global index) plus some constant.

In other words, when the fund makes its bid, it only gives the value . Recall that the optimal bid also equals . Solving for the constant, we get

Therefore

This allows bidding from index funds (whose excess return over the index is equal to their tracking error, which should be close to zero) to bid the following

So, the only variable they need to estimate is their cost of investment.

Underwriters will only support funds who can estimate their costs well (I'm not sure if this is difficult or not) and have low tracking error. Forcing all bids to be made as an estimate of also leaves the door open for funds that can reliably beat the market (they would make bids with positive values for ).

Why use a global index as a reference point?

The argument for using a global index as a reference point is a bit hand-wavy, but it’s close enough to being true. In the long run, funds can’t exceed the global index by significant amounts. If they did, they’d eventually end up with 100% of market, which would make the index return be whatever the fund’s return is. That fund can’t outperform the market if it is the market. Therefore, matching the return of the global index should be equivalent to maximizing long-run returns. And using that return as a reference point for bidders reduces the cost to investors.

So why have a bidding process at all? What not just put everyone in Vanguard or BlackRock index funds? If, at some point in the future, these funds get worse at matching the index, or they have higher costs, or they’re outperformed by a new competitor, there needs to be a mechanism to switch to the new best fund. Having auctions ensures this transition happens quickly, keeping the market competitive.

10