Note to Self: On Konstantin Magin's Social Security Privatization Project

Konstantin Magin strongly believes that the existence of the equity premium implies that large chunks of the Social Security system should be invested in equities in order that the poorer half of America's population can reap some of the extraordinary long run returns that follow equity ownership. (I agree.) He goes further than I do, however, and believes, for political economy reasons, that such investments should be made through the form of regulated, individual, private accounts.

The counterargument is that individual, private accounts are too risky to be a proper vehicle for the Social Security tranche of people's retirement savings. What if people misinvest--churn their accounts or fail to diversify or take on inappropriate systematic risks? Magin grants this point--such accounts would have to be regulated, and invested in a properly-diversified buy-and-hold portfolio. But there is a second bowstring to the counterargument: even if private accounts are invested in a diversified buy-and-hold portfolio, there is still the risk that the stock market will tank over the next generation--and that risk is inappropriate for the Social Security tranche of people's retirement portfolio.

Konstantin Magin's current project is to try to quantify this risk. How big a risk is a 35 year old running by placing the money he or she wishes to use to fund consumption at 75 in a unit beta diversified buy-and-hold stock market portfolio? The way that he quantitatively evaluates this risk is by running the obvious thought experiment: Suppose that the investor wants to insure him or herself against real declines in the value of the portfolio--wants to guarantee a real return of at least zero--by purchasing a put option on the portfolio that expires in 40 years with a strike price of the porfolio's current real value. What would be the value today of such a put option as a fraction of the value of today's initial portfolio investment?

The approach Konstantin Magin has taken has been to use Black-Scholes and the historical distribution of stock returns plus an assumed 1% or 2%$ per year riskless rate to value the cost of such a put: what would an insurance company that was going to then construct a dynamic hedge charge an investor who sought to insure his or her portfolio? There is, however, a second approach that he has started to explore: what would be the most that an investor with a specified coefficient of relative risk aversion would be willing to pay for such a put option?

The answer to Konstantin Magin's first question was that the cost of the put was small: about a nickel or a dime for each dollar invested. I think the answer to his second question is going to be much smaller for reasonable value of the coefficient of relative risk aversion--less than, say, five. I think this because the insurance company making the dynamic hedge is implicitly buying insurance from a market whose representative agent has a very high risk aversion--on the order of twenty or so. And so the willingness to pay for the put of an agent with a reasonable coefficient of relative risk aversion has to be a lot less than the cost someone would charge to write the put and then dynamically hedge it, which is what the value as calculated by Black-Scholes really is.

Here's a spreadsheet to do some preliminary finger exercises on this. The answers are--for historical returns and permanent components of variances--indeed smaller: mills rather than cents:

http://spreadsheets.google.com/pub?key=p_zylRhg4tozhBJyXhfclKw&output=xls
http://spreadsheets.google.com/ccc?key=p_zylRhg4tozhBJyXhfclKw&hl=en_US

This document at:

http://delong.typepad.com/sdj/2007/03/note_to_self_on.html

Comments

[anne]

Agreed; but look to Sweden in proposing a model for change and modification and correction:

http://www.nytimes.com/2004/02/05/business/05scene.html?ex=1391403600&en=784ee58cfda79063&ei=5007&partner=USERLAND

February 5, 2004

Retirement Lessons From Sweden
By ALAN B. KRUEGER

YOUNGER workers," President Bush said in his State of the Union address, "should have the opportunity to build a nest egg by saving part of their Social Security taxes in a personal retirement account."

According to former Treasury Secretary Paul H. O'Neill, the president believes that the reason he was elected was his bold - some would say risky - stance on replacing part of Social Security with personal accounts. If the president holds onto office in November and his party continues to hold Congress, the creation of some sort of personal retirement accounts as part of Social Security seems likely.

Although it is impossible to know what form such accounts might take, in 2000 Sweden instituted a system of personal accounts that holds many lessons for any country seeking to reform its retirement system.

Sweden now has a blended system, an approach Mr. Bush apparently favors. Employers and employees contribute a combined 16 percent of payroll toward a "pay as you go'' retirement system like Social Security, and an additional 2.5 percent toward individual retirement accounts. Those born after 1954 are fully in the new system, while older workers are phased in.

The reform process began in 1991, when a center-right coalition came to power. At the time, Sweden's generous retirement system was expected to exhaust its "buffer" funds in about 20 years, a more dire situation than what now confronts the United States; Social Security will not exhaust its trust fund until 2042, according to the latest projections.

To address its problems, Sweden set up a committee with representatives from all parties in Parliament. Because the reforms were expected to last for decades, there was pressure to devise a plan with broad support, said Annika Sunden, an expert on pensions at Stockholm University. There was agreement back in 1994 that reform would include individual accounts, so beginning in 1995 the government began tucking away 2.5 percent of payroll for employees to invest once the system was set up.

Personal investment accounts were not established until 2000, with a bewildering array of funds to choose from. Some 456 funds participated initially, and the number has since grown to around 600. Most funds invested in stocks, with a quarter primarily in Swedish stocks. Workers could choose up to five funds.

Anyone who did not choose a fund was automatically assigned to the default fund, which was set up by the government. The default fund must invest 80 to 90 percent of its assets in stocks....

[steve]

The results depend very much on which historical time series you use to extract parameters such as the vol in your random walk. If you use US equities you get a radically different result than, say, European equities over the last hundred years. (In some cases the extracted equity risk premia are close to zero.) It's very hard to quantify the risk associated with this uncertainty ("model parameter risk" or "model risk"?), and hard to find a way to ensure against it. 40 years is long enough for completely unforseen rare events (war, revolution, global depression) to intercede.

An insurance company itself would be rolling dice if it offers you a quote on something like this. They can't really hedge out all the risk. (Remember, real vols are time-dependent!)

BTW, Sweden, as a smaller country, is in a very different situation than the US. If the US govt suddenly allocates 2.5% of payroll into equities that may have serious distortionary effects on global markets. (The supply demand relationship for equities suddenly shifts: demand increases, but it takes a long time for supply to catch up -- you can't create new public companies -- i.e., earnings -- overnight.)

[wcw]

One word: nationalize.

Me, I am all for it.

You?

[Bruce Webb]

Two words: administrative cost

What would be the cost of setting up and managing individual trading accounts?

I am all for asset diversification in the Trust Fund but it doesn't follow that that has to be accompanied by individual accounts. And frankly most of the arguments for the latter are specious moves in a campaign to kill the program outright.

The Swedish blended system seems okay to me. I just don't think it is anything like Cato has in mind.

[Michael J. McIntyre]

Our current social security system (SS)is Pay-As-You-Go. The current generation of workers has some obligation (strong, weak, whatever) to pay taxes to support the pensions of the retired generation, just as that generation did for their retired generation. For this system, it is beside the point to even discuss "investment" and how it might be managed. There is no investment --- just transfer payments from one generation to the other (but those with aged parent do benefit, and big time).

So, what is Magin discussing? Is he saying that the informal covenant underlying SS should be broken? Or is he discussing what the USA should have done in 1938, when families devastated by the Great Depression has no savings for their retirement years? Well, those two trains have left the station and are not worth the time to discuss. Breaking the covenant is for evil people with no heart, and having dreams about what might have been in 1938 if poor people had not been poor is beyond silly.

Or is Magin suggesting some additional retirement system, over and above SS? Is so, the debate changes. In that event, we are not talking about taking money out of a system already short of money (the Bush plan that Magin appears to support) but rather about having some supplemental pension system. The question is whether there is a useful role for government in this new system.

The reason, if there is a reason, for a supplemental pension system (an add-on to SS) is that poor and middle class people will not save a lot without government compulsion. If THAT is what the debate is about, then the terms of reference have to change. We do not care so much about risk because we have SS as the safety net. We mostly care about getting a good return, balancing the return and the risk. My guess is that we are led to invest in foreign stocks, probably some indexed fund. That form of investment protects against the main doomsday risk for retirees --- a bad US economy that leaves workers unwilling to pay SS benefits.

Anyway, it is nonsensical for Liberals to support IRA-style pension accounts if they are a replacement, even in part, for SS. If they are an add-on to SS, then Liberals should want a system that eliminates the huge bias in favor of the wealthy from an IRA-type arrangement, since the tax benefit to the rich is far greater than the tax benefit to the poor and middle class.

SS, it must be remembered, is specifically structured to give extra benefits to the poor and low-income classes. IRA-type accounts are structured to give the opposite result. Magin's focus on risk is substituting a 4th order concern for several 1st order concerns.