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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:


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