Friday, December 24, 2010

More Criticisms of Index Futures Convertibility

Lawrence White and Roger Garrison criticized a version of index futures convertibility. (Can Monetary Stabilization Policy Be Improved by CPI Futures Targeting? Roger W. Garrison, Lawrence H. White; Journal of Money, Credit & Banking, Vol. 29, 1997) Sumner had proposed that the Fed buy and sell CPI index futures during the month proceeding the date the futures contract matures. For example, during May, the Fed would buy and sell CPI index futures contracts for June.

Like Woodford and Bernanke, White and Garrison claim that if Sumner's system works, then there will be no incentive for anyone to trade the contracts. If the CPI remains on target, the contracts mature without any payments being made.

In truth, the actual trades of the contracts depend on the dispersion of market expectations about the value of the targeted macroeconomic variable. Those who expect the variable to be above target buy and those who expect it to be below target sell.

Consider three traders, Smith, Jones, and Davis. All expect that the CPI will be 1% above target. Because they ignore the operation of the system, they all buy futures from the Fed, leaving the Fed short three contracts. The Fed contracts the quantity of money. Suppose that all three traders revise their expectations and now expect the CPI to be on target. They all sell contracts to close out their positions. (They have no reason to take a risky position on the contract with no expected profit.) Now, the Fed has no position the contract and is hedged. However, the traders incurred transactions costs and received no benefit. Why would they do that?

Now, suppose that the expectations are heterogeneous. Smith expects that the CPI will be 5% above target, and Jones expects it will be 1% above target. Davis expects that it will be 1% below target. Smith and Jones buy and Davis sells. The Fed is short one contract. The Fed contracts the quantity of money. Suppose everyone expects the CPI to be 1% lower than before. Jones expects the CPI to be 4% above target. He stays long. Jones expects the CPI to be on target and sells a contract to close his position. Davis now expects the CPI to be 2% below target, and remains short. The Fed is hedged.

If Jones expects the operation of the system, (a heroic assumption,) then he bears transactions costs for no benefit. However, even if Smith expects this, he will still buy a contract. He is buying a contract to make money from Davis, not from the Fed.

However, suppose Davis understands the system too. Won't he sell a contract as well? Won't Smith buy a contract and Davis sell, leaving the Fed hedged? Jones expects the CPI to be 1% above target, but he fails to purchase a contract, because if he does, the quantity of money will fall until it closes his position.

But let's add a fourth trader, Brown, who initially expects the CPI to be on target, and didn't trade at all. When the Fed contracts, he began to expect the CPI be below target, and he sells a contract. Davis and Brown are now short, Smith and Davis are long, and all of them expect to make money on the contract.

Of course, if everyone expects this outcome, then why don't they all trade immediately? As explained in the previous post, if everyone knows that everyone knows, then what is the problem? The Fed just undertakes the appropriate monetary policy. If the rule prohibits the Fed from taking any action unless it first has short or long on the contract, the chairman of the Fed can just call a public spirited individual and ask him to take the needed position. And then the Fed sets monetary policy at the level that everyone knows is appropriate. In the real world, no one has all of this knowledge.

The example, however, is instructive because it illustrates White and Garrison's other criticism of Sumner's proposal. Why don't the speculators all wait until the very last minute to trade? White and Garrison emphasized how such last minutes trades would leave little or no time for the Fed to engineer a change in the quantity of money much less impact the price level. Keep in mind that they were criticizing Sumner's proposal to have the Fed trade the June CPI contract through the end of May. Trades on May 31 would be very late for even heroic Fed actions to have much impact on the June CPI.

Superficially, the late trade problem isn't too hard to correct. If all of the trades come in late in the day on May 31, and Fed policy that night cannot impact the June price level, then stop trading the June contract on May 15. Perhaps trading for the June contract can be from May 1 to May 15. Or, perhaps it can be from April 15 to May 15. And, perhaps, the June contract can be traded in April. (A proposal to trade first quarter 2012 NGDP index futures contracts in the first quarter of 2011 makes the "too late" complaint a bit less pressing.)

Sumner (and I) have often argued that ordinary open market operations should be made in parallel with trades of the index futures contracts. If the trades of the futures contracts are bunched up at the end of the trading period, it would be possible that the Fed could not complete the matching open market operations before trade in the future contract closes. However, that isn't really a problem. The futures trading desk reports to the open market trading desk its position on the contract, and then the open market operations trading desk completes the trades as promptly as possible. If there is a backlog of needed security trades when the futures trading closes, then the trades of the securities can be completed as time permits.

For passive and automatic versions of the system, where the Fed makes open market operations with securities in response to its net position on the futures contract, the compression of all trades to the end of the period makes little difference. Trading closes on the futures contract, and the Fed is left with a short or long position. The Fed sells or purchases securities in an equal amount after trading on the futures contract is complete.

The implications for the constrained discretion version of the system, (which I favor,) are more troubling. The Fed is supposed to adjust monetary policy subject to the constraint that it remains hedged on the futures contract. If all the trading come at the end of the period, the constraint would not be binding during most of the period because no one is trading. Then, with the end of the period rush, simultaneous changes in monetary policy could be insufficient to generate sufficient trades to leave the Fed fully hedged before it ceases its trades of the futures contract.

With the constrained discretion version of the system, the Fed can continue to adjust monetary policy after it stops trading the futures contracts. It will, of course, be trading the next period's future contract, but if trading in that contract will also be concentrated at the end of the next period, the Fed would be free to respond to its short or long position from the last period.
I believe that some of the intuition behind White and Garrison's argument is that speculators would be motivated to game the system by sticking the Fed with an unfavorable position on the contract at the last minute. If the Fed is able to respond by adjusting monetary policy after trading ceases, the joke might be on those speculators. They have left themselves open to exploitation by the Fed! Of course, such a possibility is not a benefit of the system. For the Fed to engineer a recession because it was left with a short position on the contract would be very undesirable. However, this reasoning does provide a reason for speculators to give the Fed plenty of time to hedge, and to understand that they are speculating against the rest of the market rather than the Fed.

Finally, when considering the possibility of an end of the period rush, what happens if congestion prevents some trades from being completed? How much should be invested to make sure everyone can record desired trades at the last instant before close of business (right before midnight?) on the last day the Fed is trading the contract? People did have all month (or quarter) to trade.

Another modification that would help the Fed (and others) hedge would be to end trading with a close out period. For example, during the last month of the quarter, if the Fed is short, it will not sell any more contracts, but it will buy to close out its position. Similarly, if the Fed is long, it won't buy any more contracts, but it will sell to close out its position.

Sumner has proposed shortening the contracts to a single day. For example, on December 24, 2010, a contract for December 24, 2011 should be traded. The target value would be based upon a weighted average of the targets for third quarter and fourth quarter 2011 NGDP. The settlement value would be a similarly weighted average of the actual values of third and fourth quarter 2011 NGDP.

In my view, this modification creates an additional incentive to trade on the last day of the quarter. For example, suppose it is October 2010. A speculator determines that 4th quarter NGDP in 2011 will be above target, but that third quarter NGDP will remain on target. The greatest difference between the weighted average and the target will be on December 31, 2011. Without the daily contracts and the weighting, the payoff will be the same regardless of when the contract is traded during the quarter.

Perhaps the answer is to charge lower (like zero) "brokerage" fees at the beginning of the quarter and higher ones at the end. Keeping zero brokerage fees for those closing their positions, or even those helping the Fed to close its position might help solve the problem of last minute trading.

White and Garrison claim that index futures convertibility can't avoid the time inconsistency because the Fed can print currency to cover any losses. There is some truth to their argument, however, no monetary system is free from the threat of blatant repudiation. With index futures convertibility, an independent monetary authority will book growing accounting losses as it fails to meet its nominal target. And since each failure will involve substantial rewards to more and more "speculators," these losses can hardly be kept secret. Any repudiation of the nominal target will be at least as spectacular as a gold devaluation.


  1. You say your critics (from the Fed chairman down to random idiots like me) "claim that if Sumner's system works, then there will be no incentive for anyone to trade the contracts. If the CPI remains on target, the contracts mature without any payments being made." And your response is that "In truth, the actual trades of the contracts depend on the dispersion of market expectations about the value of the targeted macroeconomic variable. Those who expect the variable to be above target buy ..."

    Well, yes. Those who actually buy/sell will be those who expect the variable to be above/below target, i.e. they think they know that the Fed will fail in a particular direction. And you describe this "dispersion of market expectations" as if it were an exogenous variable.

    In other asset markets, I believe the dispersion of market expectations is substantially exogenous, e.g. the value of a stock coming from anticipated future revenue. And if enough people's expectations are exogenous then you've broken the circularity -- Yay! My question is, who are these people? Who are Smith, Jones, Davis and Brown? For myself, I would edit the critic-claim very slightly: if Sumner's system works, then there will be no rational incentive to trade the contracts as described, because the Fed's final effort to target the target variable will be as likely to wind up slightly high as slightly low. So at least some of the people who keep the stock market going, learning fundamentals about specific industries and corporations, will learn that this market doesn't pay. Call them the Buffetts, and Buffett wanna-bes. They're gone. (Unless the system doesn't work.) Then we have technical analysts who will watch the market go up and down and try to outguess each other -- they don't actually have opinions about whether NGDP will be high or low in the end, so I see no reason for them to converge on an answer. They might stay in, but they don't help the system work. Imagine a financial columnist getting a column out of predicting the over-under, encouraging investors...I don't see it. Do you? Or maybe something else altogether. Something to make me believe in Smith, Jones, Davis and Brown, each of whom "expects" a specific final high/low outcome even though he knows that if everybody agreed with him then the final outcome would be low/high, and in that sense they are betting only on each others' psychology.
    This bothers me mainly because I'm afraid that arguments about the specific form of the market may keep NGDP-level-targeting from happening, and you've certainly sold me on the basic idea here. I want it to happen. I'd personally be happy with a policy that worked only on the Fed incentives; give them each a Christmas bonus every year, equal to 10x their salaries if they've hit the target, 0 if they're more than 2% from it, linear-interpolation in between. Or something like that. There's no circularity there.
    If we need a market to aggregate information about needed further stimulus, then we want incentives for rational investors to collect information about current Fed policy. We can do that; if you believe that $100 billion is the Right Answer for the Fed to provide as stimulus to reach 5% growth, and I believe that it should be $200 billion, but both of us believe (as we will, after the system works well for a while) that the Fed will do approximately the right thing, then we can buy/sell contracts on the net stimulus amount (and there will be regulations keeping the Fed board from involvement with this market.) This also would break the circularity. Some circles are good, especially on Christmas morning... my daughters are here, two of my sons will arrive in a few minutes, we'll see the other (and his wife and kids) this afternoon -- Merry Christmas, and may the details of some targeting regime work out convincingly.

  2. If you put hedgers (which I mentioned in "Sumner and DeLong" entry comment) into the picture, I suppose there would be constant selling pressure, because hedgers would like to hedge against downside risk. Maybe there are hedgers who want to hedge against NGDP overshooting, but I suppose they are very few, if any.
    I also wonder what happens if we introduce option trading for NGDP futures. Perhaps it won't change the basic scheme, but I expect that it would add the liquidity to the futures market.