Thursday, January 28, 2010

Identifying Bubbles

In response to the barrage of criticism that has been aimed at the efficient markets hypothesis recently, Robin Hanson makes a plea:
Look, everyone, this game should have rules. EMH (at least the interesting version) says prices are our best estimates, so to deny EMH is to assert that prices are predictably wrong. And for EHM violations to be relevant for regulatory policy, price errors must be so systematic as to allow a government agency to follow some bureaucratic process to identify when prices are too high, vs. too low, and act on that info.
The efficient markets hypothesis makes a stronger claim than just price unpredictability; it identifies prices with fundamental values. So one can indeed question the hypothesis without asserting that "prices are predictably wrong." But Hanson's broader point is surely correct: if the Federal Reserve is charged with reacting to asset price bubbles, then bubbles must be identifiable not just on the basis of hindsight, but in real time, as they occur. Can this be done?
For reasons discussed at length in a previous post, a belief that an asset is overpriced relative to fundamentals is consistent with a broad range of trading strategies, each of which carries significant risks. One cannot therefore deduce an individual's beliefs about the existence of a bubble simply by observing their trades or holdings of the asset in question. However, it might be possible to obtain information about the prevalence of beliefs about an asset bubble by looking at the prices of options.
Specifically, anyone who thinks that they have identified a bubble must also believe that the likelihood of a major correction (such as a crash or bear market) must be higher than would normally be the case. They may also believe that the likelihood of significant short term increases in price is higher than normal. If so, they are predicting greater volatility in the asset price than would arise in the absence of a bubble. And if such expectations are widely held, they should be reflected in the price of options strategies that are especially profitable in the face of major price movements.
In the case of a bubble involving a large class of securities (such as technology stocks) a widespread belief that prices exceed fundamental values should be reflected in higher prices for index straddles: a combination of put and call options with the same expiration date and strike price, written on a market index. The Chicago Board Options Exchange specifically recommends this strategy for investors who are convinced that "a particular index will make a major directional move" and those who anticipate "increased volatility." One possible approach to determining whether bubbles are identifiable as they occur is therefore to ask whether the price of an index straddle is a leading indicator of a crash or bear market.
This basic idea has been used previously in a number of event studies. David Bates, for instance, found that "out-of-the-money puts, which provide crash insurance, were unusually expensive relative to out-of-the-money calls" during the year preceding the 1987 stock market crash. He interprets this as reflecting "a strong perception of downside risk" over this period. Joseph Fung found that implied volatility deduced from the prices of index options rose sharply in May and June of 1997, predicting the Hong Kong stock market crash of October 1997. He concludes that "option implied volatility could be incorporated into an early warning system intended to indicate large market movements or crisis events." There were no index options traded at the time of the 1929 crash, but Rappoport and White used data on brokers' loans collateralized by stock (which they interpret as a option-like contract) to ask whether the crash was predicted. They found that:
During the stock-market boom, "the key attributes of brokers' loan contracts (the interest rate and the initial required margin) rose significantly, suggesting that lenders felt a need for protection from a sharp decline in the value of their collateral... The rise in the margin required and the interest rate charged suggest that those who lent money for investment in the stock market (bankers and brokers) radically revised their opinion of the risks inherent in making brokers' loans as the market climbed and once again when it collapsed.
Event studies such as these are not quite enough to address Hanson's concern, since they do not consider false alarms: situations in which the prices of options signaled an increase in volatility that did not eventually materialize. But it seems that the same approach could be used to determine whether or not bubbles are indeed identifiable: one simply needs to examine a long, uninterrupted time series to see if implied volatility (as reflected in the prices of options) is predictive of major market declines.
If it is, then perhaps the Federal Reserve should respond not only to the inflation rate, output gap, and system-wide leverage, but also to the implied volatility in index options. It is at least conceivable that such a policy might reduce the incidence and severity of asset price bubbles.

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Update (1/29). Even if it were possible to reliably identify bubbles, it is not obvious that the Fed should respond in any systematic way. Bernanke and Gertler (2001) argued firmly that the costs of doing so would outweigh any benefits:
even if the central bank is certain that a bubble is driving the market, once policy performance is averaged over all possible realizations of the bubble process, by any reasonable metric there is no consequential advantage of responding to stock prices.
It would be interesting to know whether Bernanke has softened his position on this. An intriguing possibility is that the willingness of the central bank to intervene could influence asset market behavior in such a manner as to make actual interventions largely unnecessary. As Lucas observed in a hugely influential paper, one cannot assume that structural patterns in the data will persist if policy responses to such patterns are altered.

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Update (1/31). In a comment on this post, Barkley Rosser points out that the clearest examples of bubbles may be found in closed-end funds that are trading at a significant premium over net asset value:
there is one category of assets where the fundamental is very well defined: closed-end funds, although one must account for the ability to buy and sell the underlying assets and must account for management fees and tax effect. Thus, most closed-end funds run single-digit discounts. But if one sees a closed-end fund with a soaring premium of the price over the net asset value, one can be about as sure as one can be that one is observing a bubble.
This is absolutely correct: a closed-end fund selling at a premium is overpriced by definition relative to the value of the underlying assets, and the premium can only be sustained if the overpricing is expected to become even larger at some point.  But how often do such bubbles arise in practice? Barkley directs us to some evidence (links added):
There is an existing [literature] on this that arose in response to the "misspecified fundamentals" arguments about bubbles put forward by Garber and others about 20 years ago. One of those was [by DeLong and Shleifer] in the Journal of Economic History. They noted the 100% premia that appeared on closed-end funds in the US in 1929, arguing that one might not be able to prove that there was a bubble on the stock market, but there most definitely was one on the closed-end funds at that time.

Ahmed, Koppl, Rosser, and White document the bubble on closed-end country funds that hit in 1989-90 (100% premia on the Germany and Spain funds before the crash in Frb. 1990) in "Complex bubble persistence in closed-end country funds" in the Jan. 1997 issue of JEBO.

21 comments:

  1. EMH does not say anything about fundamental values because fundamental values are an undefined term. Fundamental values seem relevant after the fact because we focus on the particular meaning that makes the price appear over valued.

    For example, for stocks, there are many 'fundamental value' criteria. Is it price to earnings, price to dividends, price to sales, price to cash flow, price to free cash flow, Gordon dividend growth model (with what growth rate), discounted cash flow (what growth rate, what discount rate), price to EBIT, price to competitor ratios, breakup value, etc.

    For options, you write, "Event studies such as these are not quite enough to address Hanson's concern, since they do not consider false alarms: situations in which the prices of options signaled an increase in volatility that did not eventually materialize."

    You are saying if I call the fire department everyday, and if one of those days my house is on fire, I have a good strategy. Using implied option volatility that does not lead to a bubble collapse means, the Fed will do the wrong thing many times in order to make sure it does the right thing in a bubble. That is like telling a surgeon to cut into everyone to remove his or her appendix to prevent appendicitis. How many unnecessary recessions and periods of high unemployment are you willing to endure to prevent one bubble?

    EMH says several things, but two important ones are:

    It says past prices and past gains are irrelevant for determining the future gains and prices tomorrow, next week, next year, etc.

    It says public information, including past public information, in addition to price information does not give you any ability to generate a better return than anyone else can or to tell what the price will be in any future time period.

    Hindsight is wonderful. It tells the quarterback (The Fed) what play (money supply, interest rate policy) he should not have done. It does not guarantee that a different action would succeed. Many say Fed's loose money policies caused the housing bubble. Do we know that a tight money policy at that time would stop the housing bubble?

    Even if we can call a bubble as it is happening and the Fed acts and the bubble crashes, is the economy worse or better off than if the bubble crashes without Fed action? Without a bubble, could we put ourselves in a worse economy than we currently are? We do not know. No models or predictors of the bubble crash predicted the severity of this recession. Without the ability to predict this recession from a bubble burst, how do we know it would not have been worse without the bubble?

    How do we know that any Fed action to reduce asset prices in a bubble (housing), will only affect that asset (housing) and not other assets not in a bubble. Could the remedy cause a deflationary spiral across many assets and be worse than the bubble?

    What do we gain and lose by interfering with bubbles? If we had stopped the dotcom bubble, would we have never had companies such as Amazon and EBay, to name two, or Google years later?

    The alternative universe for us to compare economic results does not exist. We will never know if the proposed cure works or does not, or if the economy is better or worse for bursting a bubble.

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  2. Milton, please read the post carefully before you say things like this:

    "You are saying if I call the fire department everyday, and if one of those days my house is on fire, I have a good strategy."

    No, this is the opposite of what I am saying. I am saying that we need to figure out whether implied volatility is a reliable predictor of asset price declines, which the event studies do not do. If I call the fire department every day then my call is not a reliable signal of a fire and should be ignored.

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  3. It depends on HOW the Fed would attack a bubble. It makes sense to use the regulatory scalpel, not the monetary sledge hammer to attack asset bubbles. Bubbles are a relative price problem. It makes no sense to hammer the rest of the economy with tight monetary policy to burst a bubble.

    That leaves an argument over regulation. The Fed has failed to adequately regulate the financial system especially with regard to collateral requirements in each of the crashes. How does one balance the Fed when there is a pervasive anti-regulation bias? Regulatory failure was particularly acute under Greenspan. When an anti-regulation administration is in office, then regulatory failure extends across the board to the SEC, Fannie and Freddie, the energy sector with FERC, and EPA as we saw under Bush.

    Anti-regulatory policies benefit special interests and opportunities for short term profits. However, they do so by increasing risk and injecting a large amount of uncertainty that may stifle investment.

    Efforts to propose coherent regulations get shouted down by the anti-regulation ideologues. Studying positive effects of regulation is not a career path to a high salary. It is difficult to have a conversation about the improving regulatory policy without having to defend the conversation from regulatory minimalists.

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  4. Jon, I agree with you on this point: it makes no sense to use the monetary sledgehammer to deal with asset price bubbles. But this still leaves open the question of whether the regulatory response should be static or dynamic: whether collateral requirements, for instance, should be adjusted regularly in response to market conditions or held fixed for the most part.

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  5. It is not at all clear that even the weakest assertions of EMH--past prices do not contain any information--is even right. Just look at trend following, which has generated positive excess returns for 30 years, probably more.

    BTW, trend following is basically like buying straddles--so its success and Rajiv's suggestion of using option prices to identify bubbles are not inconsistent with each other. (Trend followers are long gamma and not long volatility. So, conceivably you could have a situation where implied volatility increases but the market makes no sustained directional move one way or the other. However, in practice, such occurrences are rare. The stock market is indeed strongly negatively correlated to volatility.)

    On a related note, there is a whole area called systematic trading (not including trend followers), whose models (either fundamental or technical/algorithmic) have consistently generated excess returns. I know, I know, the EMH apologetic's stock response, but the sheer number and the success over diverse market conditions makes me think otherwise.

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  6. I would argue that collateral requirements should be dynamic, and tied to market measures of perceived future volatility like those discussed in your post.

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  7. I supported policy action to combat bubbles in a public forum at the New School in November, 2008. I argued that such a policy must be ad hoc by its very nature, and that more often than not the Fed would probably not be the best policy agent. After all, its obvious tool, moving up interest rates, is a sledgehammer that affects the whole economy, when many bubbles are much more sectorally concentrated. For commodity bubbles, for example, one might use an agency dealing with that commodity to make some sort of regulatory or other change, the USDA or the Department of Energy, or whatever.

    This discussion is all garbled up with the question of identifying EMH failures getting tangled up with that of identifying bubbles. Even though I advocated action, I recognize it is hard. After all, any time you have the government through any agency causing people not to make money, they will get angry and use political levers to resist the action, and that is what is involved in slowing down or stopping a bubble.

    I do think it is possible in many cases to identify bubbles, although not always. Some markets do have fairly well-known and measurable fundamentals, e.g. housing with the price-to-rent and price-to-income ratios. Obvously there is some fuzziness: what if those deviate? Does one look at running averages or current levels? and so on. But one does have something to go on, and when everything is clearly pointing to one conclusion, one can be reasonably certain, which was certainly the case for housing by 2005, if not sometime sooner.

    Nevertheless, one may find it difficult, if not impossible, to do much about any particular bubble, however desirable or undesirable to do so.

    BTW, there is one category of assets where the fundamental is very well defined: closed-end funds, although one must account for the ability to buy and sell the underlying assets and must account for management fees and tax effect. Thus, most closed-end funds run single-digit discounts. But if one sees a closed-end fund with a soaring premium of the price over the net asset value, one can be about as sure as one can be that one is observing a bubble.

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  8. Ravij,

    I understood what you said. I just wrote and posted the comment very quickly. Actually, I was quite pleased to see you mention the false positive effect and I did not mean to make it seem like I disagreed with you on that point. I meant to express my disagreement with those who think there are not risks of economic harm in stopping anticipated bubbles. I expressed myself poorly.

    My apologies for my quick writing, paragraph deletions and repositioning, and a fast trigger on the submit button.

    The recent housing bubble, if you look at real prices versus trend and average, started around 1997. It lasted 8-9 years and was unaffected by the dotcom bubble collapse. House prices averages peaked and started to decline around 2005-6.

    The recession officially began in December 2007, and it is around the 2008 Bear Stearns and the Lehman crises that house prices collapsed and stopped following a gradual decline to the historic mean. Foreclosures also increased at that time.

    If I were either a regulator or a member of the Federal Reserve, I could easily interpret the peak and the decline in home prices in 2005-6 as the end of the bubble. It would be rational at that point in time to think that no further regulatory or monetary action was necessary. Home prices were coming down and I would think that the prices would gradually rejoin the long-term trend line. I would probably have not taken any action in attempts to avoid creating a recession.

    I would be right for 2-3 years until 2008 when the bottom fell out of housing, the stock market and the economy..

    There is an inherent contradiction in trying to control bubbles, as you allude to in Lucas's paper citation. If I am a government agency that can effectively observe and quickly cool bubbles, then if a bubble starts, it immediately ends because the price market for that asset anticipates my reaction and no one wants to be the last one holding an asset at an inflated peak price. Continuing bubbles (and this might be all of them or none) are the ones where I do not have an effective timely response in my tool chest to stop the bubble, or where the bubble is such that I can not observe it as a bubble as it is happening. It is fatalistic. Bubbles cannot happen because I can stop them and if they occur, it is because I cannot stop them.

    Those who say the Fed or regulators should have done such and such at an earlier time to prevent the housing bubble, forget that during the bubble, the information, the models, and the expert opinions were noisy and conflicting. Information about bubbles is probably noisy and contradictory during every bubble as it is happening.

    If the information were clear to the regulators, the Fed and others, they would have responded to end the bubble. As far as I know, neither the Fed nor the regulators saw a bubble and refused to act. They did not see the bubble and they said housing was not in a bubble.

    Continued…

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  9. Continued…

    Every recommendation for improvement relies on an after the fact analysis of weak points in the financial and regulatory system. The assumption is that but for that weakness, the bubble and collapse would not have occurred.

    It is just as logical to think that the factors causing the bubble would have manifested themselves somewhere else, if we had fixed the known weak points earlier.

    As an example, if the crisis resulted from a greater risk tolerances of individual borrowers, then minimizing the risk to the financial system (increase down payments, more collateral, mark to market, etc.), just shifts the risk to another place in the economy.

    Would there have been more buying of stocks on margin, more investing in commodities and foreign currencies, more credit card debt, more borrowing from relatives and friends to purchase first and second homes, more seller finance mortgages, etc. It is unclear to me that the extra risk individuals took on by lower down payments, second homes, adjustable rate mortgages, second mortgages, etc. would go away completely. It could be a case of a gambler who faced with the roulette wheel closing down, decides to play blackjack instead. For every seller there is a buyer and for every lender there is a borrower. Focusing on only one side of the transaction, the lenders, for a fix will not get to the core of the past crisis.

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  10. Srinivas: thanks for the informative comment.

    Andy: there are circumstances in which rules may be better than discretion, but I agree that in this case there seems to be no advantage to tying one's hands.

    Barkley: closed-end funds are interesting for lots of reasons. I understand why they tend to trade at a slight discount to net asset value since the assets held are often not very liquid. But why the initial investors buy at NAV knowing that they will likely soon trade at a discount is a puzzle to me. Why not buy the assets directly?

    Milton: I appreciate the clarification about false alarms. The main point of my post was to suggest a way in which one could try to determine whether or not bubbles can be reliably identified as they occur. If not, then the policy question is moot. If so, then one has to deal with the question of what (if anything) to do about it. But that's a debate for another day...

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  11. Rajiv,

    But this is the very essence of bubbles, people are buying an asset in a bubble because they expect it to go up more and they can make capital gains. As the underlying assets are not moving, there is no expectation that they will move up. Of course, historically buying closed end funds with 100% premia is on average a losing strategy, just as one of those sometimes existing bills on the street is to go around buying funds with discounts greater than 20% and holding them.

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  12. Barkley, yes, I see what you mean... a closed-end fund selling at a premium is overpriced by definition relative to the value of the underlying assets, and its price can only be sustained if the overpricing is expected to become even larger. This is the cleanest example of a bubble, you're absolutely right.

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  13. Bubbles result from two human attributes: greed and wishful thinking. As long as these attributes exist, there will be bubbles.
    Can the Fed identify bubbles? Huh? They CREATED or at least knowingly tolerated the bubbles! Why? Because with the transformation from a productive to a consumption economy based on debt, creating bubbles is the only way to project an ILLUSION of prosperity.

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  14. Anthony, it's not that simple. There are plenty of arbitrageurs out there willing to trade with (and profit from) those whose greed or wishful thinking skews their valuations of assets. The trick is to account for bubbles despite this fact. It's not impossible to do so, but it's not trivial either.

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  15. Rajiv,

    There is an existing lit on this that arose in response to the "misspecified fundamentals" arguments about bubbles put forward by Garber and others about 20 years ago. One of those was "Bull and Bear Markets in the Twentieth Century" by Barsky and DeLong in the Journal of Economic History. They noted the 100% premia that appeared on closed-end funds in the US in 1929, arguing that one might not be able to prove that there was a bubble on the stock market, but there most definitely was one on the closed-end funds at that time.

    Ahmed, Koppl, Rosser, and White document the bubble on closed-end country funds that hit in 1989-90 (100% premia on the Germany and Spain funds before the crash in Frb. 1990) in "Complex bubble persistence in closed-end country funds" in the Jan. 1997 issue of JEBO (prior to when I became editor, btw).

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  16. Excellent, thanks. If time permits, I'll survey this literature in a subsequent post.

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  17. Actually, double checking, the paper that discusses closed-end funds in the 1929 is the 1991 in the JEH by DeLong and Shleifer.

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  18. Barkley, I've corrected the link.

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  19. There are additional factors about closed-end funds to consider before premiums and discounts to NAV will be accurate indicators of the existence of bubbles.

    Closed-end funds have investment advisers who can change the holdings of the fund consistent with the investment strategy.

    Closed-end funds do not regularly redeem shares. Redemption occurs at the termination date of the fund.

    Closed-end funds, because they need not worry about redemption, can buy infrequently traded shares. When a readily available market price is unavailable, funds employ a pricing methodology.

    Closed-end funds pay a dividend, sometimes in excess of the dividends received from the fund's investments. The shortfall comes from the investment capital of the fund.

    Buying a share in a closed end fund is buying the right to the fund's termination value (not to its NAV) and the dividend payouts of the funds. The value of these rights can deviate from NAV without violating efficient markets.

    Suppose a fund is holding $1000 and has 10 shares. Each share's NAV is $100. If the fund will terminate in one year and does not invest in anything other than cash, the fund will trade at a discount to that $100 per share. The fund is giving up an investment opportunity, which let us say is 10 percent. A $1000 payment made one year from now is worth (discounted value) about $909.09 today. Its efficient market price is to trade at a 9.09 percent NAV discount.

    If the fund is paying out a higher dividend (as some close-end funds do) than it can afford from incoming dividends on its investments, the dividend payments will include a return of capital. The return of capital lowers the redemption value. The earlier return of the investment capital can result in a premium to NAV.

    For example (simplified), if the fund chooses to payout $50 more, $150, than it receives in dividends, the extra $50 dollars comes from capital. Suppose the $1000 closed end fund with a 10 percent required return terminates at the end of five years and returns its capital at that time. At the end of five years it has only $750 left in its investments (assuming no appreciation as dividends equal required return) because it paid out 5x$50 ($250) in excess of its incoming dividends. The discounted value of 5 years of $150 per year and a $750 termination value at a 10 percent discount rate is $1034.09. The current NAV is $1000 and the efficient market price is $1034.31. The efficient market price of the fund is a 3.43 percent premium to its NAV.

    If the fund buys illiquid and infrequently traded securities, then the premium or discount to the NAV can reflect a disagreement between the market price and the methodology used to value the underlying investments. During the financial crisis, financial institutions discounted anticipated cash flows and valued CDOs at $X. The market placed a lower value on the CDOs because it anticipated a higher default rate. The market and the financial institutions used different estimates of future payments to derive values, resulting in different valuations of the same CDOs.

    If the investment adviser creates uncertainty about the fund's future investments, the increased risk above the riskiness of the current holdings can result in a discounted market price to NAV.

    Additionally, closed-end funds can borrow and there is increased leverage and loan default risk to consider. There are also tax effects since closed-end funds do not pay taxes and shareholders pay the taxes on the investments, which can have a positive or negative value and can cause funds to trade at premiums or discounts.

    Without valuation adjustments, the information content of the NAV about bubbles is unclear.

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  20. Milton there's something wrong with this example:

    "For example (simplified), if the fund chooses to payout $50 more, $150, than it receives in dividends, the extra $50 dollars comes from capital. Suppose the $1000 closed end fund with a 10 percent required return terminates at the end of five years and returns its capital at that time. At the end of five years it has only $750 left in its investments (assuming no appreciation as dividends equal required return) because it paid out 5x$50 ($250) in excess of its incoming dividends. The discounted value of 5 years of $150 per year and a $750 termination value at a 10 percent discount rate is $1034.09. The current NAV is $1000 and the efficient market price is $1034.31. The efficient market price of the fund is a 3.43 percent premium to its NAV."

    If the fund is paying out 150 a year then it will not have 750 left at the end of five years because its capital will decline by more than $50 a year. You're assuming that it will earn dividends of 100 per year (10% of 1000) but after the first year its capital is already down to 950. It will therefore earn 95 in dividends, not 100. Factor this in for all years and I do not believe that your fund trades at a premium to NAV.

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  21. As I was thinking about 'identifying bubbles' during the last few years, I decided that a regulatory approach might look at things that might accompany system-threatening bubbles, in addition to looking for 'bubbles'.

    I came to the conclusion that if a regulator were to suspect that Old Maid games were being played, whereby people were shedding risk, to others who were notably acquiring huge piles of risk, e.g. AIG, then said regulator might probe deeper to see if there might be bubble-dynamics in play -- e.g. housing markets that were out of kilter. And said Regulator might then also listen to VERY LOUD SCREAMS from interested/soon-to-be-affected bloggers.

    Does such an approach make any sense?

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