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Interesting. Never thought about it that way before in relation to options. You see this near-term uncertainty problem talked about in the business press.

It started with the inconsistent pattern of bailouts. The big one everyone talked about was of course Lehman, but more, you saw it with the FDIC which adopted a very ad hoc to bank solvency. Suddenly no one knew which banks, when... and if the bank was seized which creditors would get paid. The FDIC scrambled long-standing rules of pecking order, and refused to describe any unifying theory.

Meanwhile, even before the 'crisis' took root, credit regulations were getting rewritten. We already went through student loan reform (in the space of three years, the entire student loan industry was squeezed into non-existence), then consumer credit, then the general financial sector.

Spent several months with radically varied 'deal-clinching' proposals for the financial reform bill. Weekly stories about how these firms or those firms would become insolvent with the passage of this language or that language. Frantic lobbying by Warren Buffet after one provision got incorporated (finally removed) that would have necessitated tens-of-billions of charges for Berkshire.

FASB guidance on mark-to-market vacillating every few months.

The health-care bill: complete and total chaos as to whether and how much of the economy would be nationalized outright. Who would pay what, when, and how much.

Wild vacillations about changes to income tax rates, capital gains rates, the estate tax. Periodic muting of a big new VAT regime.

Finally, just a month ago, the Business Roundtable, long-standing supporters of the administration finally joined the Chamber of Commerce and screamed, 'stop! all these changes make planning impossible'

I really enjoyed this text, Nick, but I do not know if I agree to the final 100%. I mean, you can also think of a long period of preference for liquidity, if people believe that there will be inflation (or that prices will fall). Perhaps that uncertainty is not (it's pretty low expectations), but money is still the cornerstone.
But your article is great ... and very clear.
I Believe that money is what allows us to speak of macroeconomics. Those who think that markets are always empty should clarify that they are talking about a barter economy. Money is the fundamental piece when speaking about market, "it is the commodity that is present in all them" whereas its value is determined into its own market, a financial market connected with all other financial markets. It is therefore not neutral, as imbalances of demand and supply of money affects all markets (and are determined by them).
I am therefore skeptical about fiscal policy not complemented with some monetary policy. Can you imagine a fiscal policy in a barter economy?
I do not know if this is NK, K, or M

Great post.

But you need to add the real yield on "cash."

Of course, negative real yields are especially interesting when there is this general desire to wait to see if uncertainty will be resolved.

Also, who is issuing the cash? If it is inside money, what do they do with the funds raised? Then it is the holder gets to wait for uncertainty to get resolved, but the issuer bears it instead, right?

Jon: Yep. I've been half-aware of businesses talking about the effect of political uncertainty on investment. And the recent blog debate about why firms are hording their profits as cash. But as I said towards the end (and I just woke up and added that little bit about crystal balls near the end to emphasise it more strongly), it's not *high* uncertainty that causes low investment. It's expected falling uncertainty that's the problem.

Luis: Thanks. Things like interest rates, expected inflation/deflation, and the expected return on investment, also matter, of course. I'm just adding the option value of doing nothing as something else that could also affect the demand for money and aggregate demand.

I like to think of what you and I are talking about as that narrow intersection between the two sets of: Keynesian economics, with it's emphasis on disequilibrium: and Monetarism, with it's emphasis on the excess demand for money an monetary exchange. Bill Woolsey belongs right there in that narrow intersection too. Actually, all true Keynesians (and New Keynesians) should recognise that their theories are logical nonsense except in a monetary exchange economy. Fiscal policy is a continuation of monetary policy by other means.

You gotta be a little bit careful though when you say that money cannot be "neutral". The "neutrality of money" has a well-defined meaning, and it's not the same as saying that money doesn't matter. It's taken as meaning that a change in the money supply doesn't affect any real (as opposed to nominal) variables, in equilibrium. And that can only happen if prices are fully flexible, so that an initial excess demand/supply for money eliminates itself by all prices falling/rising to a new lower/higher level, increasing/decreasing the real supply of money to eliminate the excess.

Bill: Good to see you back! Taking time out from the Mayoral race?
Thanks! Yes, I ignored real yields on cash, and expected rates of return generally. They all matter of course. But I wanted to focus on the things that weren't certainty-equivalent.

Yes, I totally ducked the question of what "cash" is. I was getting tired, and my brain can only focus on one question at a time.

Here's one thought: it might be that the firm postponing making an investment isn't holding cash; it's just waiting before borrowing cash. You could say that it is holding zero cash rather than holding negative cash. So the option value of doing nothing increases that firm's demand for cash from a negative value to zero. But then, as you say, what about the lender, or the issuer of cash?

Plus, of course, individually we can resolve uncertainty by waiting, but if that causes a recession, it may increase uncertainty in aggregate.

My brain's not working on this yet.

Thanks, very interesting post. For the discussions on cash, DeLong has written quite a bit on what's meant by a preference for cash (high-quality liquid assets) and the effect of changing definitions/perceptions.

On a related topic, I've spent a bit of time with some corporate treasurers, treasuries of banks, and even central bank types recently. They're all basically going through their own process of redefinition of near-cash by cutting counterparty lists, rejecting certain issuers/types of paper (including sovereigns), going more short-term, etc. If you consider the increased uncertainty at the same time as redefinition of cash and money substitutes (as well as yields on T-bills dropping to within nothing of actual cash), the swings in monetary conditions/investment would certainly be expected to be much more wild than in a world where cash is just assumed to be cash and bank deposits (and near-cash is ignored).

While many will instinctually reach for the bottle of Keynes Magneto Repair Ointment after reading your note, it would be interesting to throw some real options into the mix for the Kling-ons (Arnold, that is) talking about the great recalculation debate. What happens to the recalculation process when uncertainty is high and the value of real options increase? Could there be a 'recalculation trap' (to coin a phrase) at the macro level? Would this be the same thing as a liquidity trap? Kling seems to believe everyone just waits a bit and it will all work out (it's an industrial process, not a monetary one), but what if the monetary situation creates more uncertainty - creating more demand for cash and, due to circular effects, reducing the cash-like qualities of e.g. corporate debt?

GA: Thanks!

And that's an interesting idea to apply it to Arnold Kling's recalculation story. Even if you don't have a monetary model, what happens if every investor waits for every other investor to go first? "I'm going to wait and see what you invest in, so I can learn where the economy's going and so best decide what to invest in myself"?


You say that a falling rate of change of uncertainty results in hoarding, but a rising one does as well. That leaves only a constant rate of change of uncertainty as the state of the world in which cash is not hoarded. Is this what you envision?

I think the "falling rate of change" hypothesis is incorrect because it leaves out the effect of rising asset prices (or at least the prices of claims on those assets). Falling uncertainty, all else equal, raises asset valuations. Thus, waiting has a cost: one must pay more as uncertainty is resolved, which in turn depresses returns. Only in situations where a step-function decline in uncertainty is expected, and where investors can exactly time it, are they better off waiting for uncertainty to fall.

You make the assumption that economic actors believe uncertainty will be resolved soon. If one looks at the VIX--the implied/expected volatility of the S&P500, it is down from peaks but still elevated. If investors expected uncertainty to be resolved, they could buy futures or call options on the VIX, which in turn would reduce its price, which would raise asset prices. Thus, investors would deploy cash, not hoard it, if they expected uncertainty to decline.

A better model is that cash/liquidity is a hedge on tail risk. I would note that tail risk does not necessarily behave in a linear fashion, especially if the distribution is skewed to the downside. That is, the expected value of future growth can rise without greatly impacting the area under the downside "tail" of the probability distribution. The evidence of steady bank cash holdings (around 10% of assets) in the face of a recovery implies that the magnitude of the tail risk has not declined. Given that the total debt outstanding in the economy has not materially declined, perhaps this is the market's way of saying that the total debt-to-gdp ratio might fall as the numerator falls, and not as the denominator rises. This, in essence, is the deflationary tail risk.

Nick, as of course you know, resting in dollars v. sterling v. euros has different consequences - is this interesting or just the familiar 'in uncertain times people turn to the US dollar' story?

This NY Times piece on free will is highly tangential but you might enjoy it.

David: "You say that a falling rate of change of uncertainty results in hoarding, but a rising one does as well."

That's not what I meant to say. You delay investing and hoard cash when you expect to learn a lot of information quickly just by waiting. That means your uncertainty is high today, but you expect it to be a lot lower in the near future. So the level of investment today is negatively related to the expected rate of decline in uncertainty between today and the future.

I wish I were better at information theory, measuring information, entropy, etc.

There's prices of existing (old) assets, and there's the prices and values of newly-produced investment goods. I'm talking about newly-produced investment goods. Bulldozers, machines, insulation, university degrees. If firms are holding cash, because the option value of doing nothing is currently high, because they expect uncertainty to decline, then the demand for newly-produced investment goods will be low. Given a regular upward-sloping supply curve of new investment goods, the prices of investment goods will be low. That will partly offset the leftward shift in the demand curve, by causing a rightward movement along the curve.

Frances: I think the extra liquidity of the US dollar, because it is the world's reserve currency, and so money to all the other monies, is a very big part of the story of the financial crisis. It's why the US$ exchange rate appreciated during the height of the crisis. Compared to financial assets, the extra liquidity of the US$ compared to other monies might be a big deal. But compared to real assets like new investments, that are much much less liquid than nearly all financial assets, I'm not sure the slight differences in liquidity between US$ vs Loonies makes a lot of difference. Not sure though.

@Nick: precisely, if everyone's waiting to see how everyone else recalculates, it changes the recalculation.

Somewhere in my mind there's a small model that would be interesting to work through on this, based on the fact that lots of investments require a minimum number of committed participants/purchasers (like a building or a new housing development, but can be applied to lots of different areas of activity, like even an investment fund). The basic idea is that there is a cost to committing now, say to buy the first unit in an unbuilt complex, that does not get completed (the 'commitment' is not entirely lost, but other options/courses of action cannot be acted on) unless, say, 60% of the units are not pre-sold. (Note this is leaving out price considerations, which would probably make the calculation issue worse).

If there are too many potential projects and they can't all get built, you have a coordination problem because everyone waits to see what everyone else will do.

And if no-one can break ground, all those businesses that make shovels face worse and worse business conditions, and demand falls further, making it even less likely that sufficient demand can materialize. A classic multiple equilibria problem, perhaps.

Money could make it worse but may not be required to have the problem.

But this is just a first thought/brain sketch. It may require more painful math in asssuming that projects are 'lumpy' in size and not continuously differentiated/differentiable. You're much better at working through the implications of these little mind-models than I am.


I'm with you most of the way on this, but I don't get the distinction here:

"Lots of people, Keynesian fundamentalists especially, will say "Of course! Didn't Maynard say that uncertainty creates liquidity preference?" And they are partly right, but mostly wrong. It's not uncertainty, but uncertainty that you expect to be resolved quickly, that creates liquidity preference. You can't learn anything about the dice by waiting, so you might as well place your bets and roll them now, and learn whether you win or lose. It's not the level of uncertainty that matters for liquidity preference, but the expected rate of change of uncertainty."

I'm assuming that you basically agree with them about liquidity preference, as in your loose definition of cash is basically equivalent to liquid assets? The more liquid the asset, the more cash-like it is? There doesn't seem to be much disagreement there, it just seems like using different terms to describe the same thing.

"It's not uncertainty, but uncertainty that you expect to be resolved quickly, that creates liquidity preference."

I'm not so sure about that. Maybe I'm missing something here, but if that is the case, then why is the time value of an option higher the further it is from expiration (the elimination of uncertainty)?

To bring it back to cash: If you are looking at a 5 year period of uncertainty, you would want cash in order to take advantage of underpriced opportunities in that time period. Assuming that volatility remains constant, wouldn't cash be worth more if you are expecting a 10 year period of uncertainty, as you would have twice as many opportunities to buy underpriced risky assets, and have a higher probability of observing extreme underpricing?

Isn't that the reason why short-dated options are less sensitive to volatility than long-dated options?


That may be a false dichotomy (between new and existing investment goods). An investor has a choice of starting a new project or buying an existing one. If he expects uncertainty to fall, he is better off buying an existing one at a low price and benefiting from the rise in asset prices. Take the example of an iron ore mine. An existing mine will reflect deflationary risk of lower ore prices. If an investor believes that risk will diminish, then he should buy the existing mine. Alternatively, he could buy the debt of the existing mine, causing borrowing costs to fall for future mines, and inducing someone that is waiting for uncertainty to fall to borrow. He could also buy iron ore and stock it -- same result as the higher price would induce new mine activity. In all cases, the expected decline in uncertainty results in higher asset prices and should be a spur for investment today, not in the future.

GA: I started writing down a simple model to show this, but it didn't work out as planned. Sometimes there's a first mover advantage, that could offset the benefits of waiting to learn what everyone else has done. Will have to think some more.

bob: "I'm assuming that you basically agree with them about liquidity preference,.."

Yes, at least for this post, as far as I can see.

It may be that we can only push the analogy between real and financial options so far. One big difference is that financial options usually have a terminal date at which they expire, while the option value of doing nothing may or may not have an expiry date. I was imagining it didn't expire.

Thinking out loud: suppose we know that the price of heating oil will make a big jump next year, either up or down, but won't change at all after that. (They are drilling a big oil well, and next year we will learn if it gushes or is dry). But we know the price of insulation will stay the same next year. That's when we want to wait until next year before deciding whether to invest in insulation, even if the expected return is positive this year.

It's because Expectation of Max{returns over t-1 years conditional on Information} exceeds Max{unconditional Expectation of returns over t years}.

But if the price of heating oil followed a random walk each period, with constant variance, there's no point in waiting, if the expected return is positive this year.

That's the sort of case I had in mind. Where you are going to learn a lot more this coming year than you would normally learn in average years. The variance isn't constant over time.

Not sure if this, tangentially, gets at your point.

David: for the individual investor, there may be no difference between buying new or used (unless the used machine is firm-specific, or bolted down, in which case it is irreversible at the level of the firm). But I'm taking a macro perspective, so if one firm sells used machines to another, that's zero aggregate investment. Only new investment counts for AD.


To use your above example, assume a house already exists with thick insulation. If asset markets are efficient and the house price reflects the expected capitalized energy savings from extra insulation, then an investor should be indifferent between waiting for the information about the well and investing now. That is because the value of the capitalized savings will rise if the well is dry, but then then the investor will have to pay a higher price for the house exactly equal to that amount.

The existence of real options implies that, for any given expected (mean) value, an investor should pay more for an asset that benefits from multiple states of the world than one which is single-state dependent. Cash only benefits from one state of the world: the one in which asset prices fall relative to the true value of an asset. Alternatively, cash creates real options by extending the life of the call option written by debt holders to equity holders, as that option will "expire" upon bankruptcy caused by illiquidity. Additionally, cash may create real options in the event of the failure of credit markets (as it allows actors to make investments without having to borrow). Both of these are part of the deflationary tail risk.


I see. But if the option value of waiting in cash does not exist for an individual, then how can it exist in aggregate? That is, you argue that the existence of cash on corporate balance sheet is evidence of individual firms benefiting from the option value of holding cash in expectation of a fall-off in uncertainty. If they are not doing do so (because efficient asset markets eliminate that value), then how do real options explain aggregate cash levels?

David: Houses with swimming pools nearly always sell for less than the price of an identical house without the pool, plus the cost of the pool.

If you buy a house without the pool, you always have the option of installing one. So the house with the pool can never exceed the price of house plus cost of pool.

But if you buy the house with the pool, you do not have the option of uninstalling the pool and recovering the cost of the pool.

The difference between price of house without pool, plus pool, and the price of a house with a pool, represents the option value of not having a pool -- of doing nothing, and having cash instead.

Only if the marginal buyer will always want to have a pool, and install one if needed, does that option have zero value.

(That's why you should never spend any money on your house just before selling it, unless it's something any buyer would want to do exactly the same anyway, or it's cosmetic window-dressing, or you are a handyman with a comparative advantage in doing it, especially tax free).

This applies less to insulation, because only some people want a pool, but almost everyone wants to save money on heating bills, and so will value the insulation the same.

But still, whenever you insulate your house today, you face a trade-off. You benefit by one year's profits from the insulation, but you lose from foregoing the opportunity to learn more information and choosing the optimal amount of insulation for next year based on that extra information.

Put it this way: would it ever be optimal to sign a binding contract for a contractor to install R20 insulation in your attic one year from now? (Assuming efficient forward markets, so you can't outguess the contractor on the future price of insulation). Would you give away for free the option to wait until next year before deciding?

It's true that if the irreversible investment has already been made, the loss of the option value will already be priced into the asset. So a buyer will be indifferent (if he's like all the other buyers). But it's precisely because making an irreversible investment throws away that option value, and so raises the price by less than the cost of the investment, that the potential *seller* of the house doesn't make the investment.

GA: a simple model. There are n firms, and each must choose where to invest on a circle, and when to invest. At the beginning each firm draws a private random variable ri. A firm i's optimal position on the circle (what flavour to produce), depends on ri, and on the locations chosen by all the other firms. Time is discrete. Each firm is small (n is large) so that each firm takes the other firms' choices as exogenous to its choice (that was the assumption I was looking for, since it removes first mover advantage).

There's a cost to delaying investment, since you forego one period's profits. But there's a benefit, if other firms move first, since you learn their locations, which helps you choose a more profitable location for your firm. The more firms that invest before you invest, the greater the benefits from learning.

Assume some firms earn higher profits from investing than others (so some firms will be less patient than others). Otherwise we only get mixed strategy equilibria, I think.

I think that gives a single equilibrium, but investment will be delayed longer than is socially optimal. That's because when one firm invests early, it creates an external benefit for all other firms, who learn its position on the circle.

continued: there's also strong positive feedback in when they invest (strategic complementarity). If other firms invest earlier, that makes it profitable for me to follow immediately after them, and invest earlier too. But I don't think you can get multiple equilibria. It's not like Diamond/Dybvig, for example, where every individual wants to rush to the bank just before every other individual, so they either all rush immediately, or never rush. Every firm wants to rush to invest immediately *after* every other firm. So if they all expect everyone to invest in period 1, they all wait for period 2. And if they all expect everyone to wait forever, they all invest in period 1.

@Nick: thanks, that's interesting and gets much of what I was referring to. I think multiple equilibria are possible (and removing first mover advantage helps).

But I'll return to my 'minimal investment to make a project work' idea. Probably won't work without fiddling with parameters.

N firms, X projects, each firm's investment is Y portion of a project. Any project must have Z portion of the entire project to succeed. In period 1, all firms must commit to invest or not. If Project Xi collects enough investors, they collect a decent reward (option good). If Project Xi collects less than Z, they pay a (small) penalty. If no investment (option not invest), they collect a very modest return (call it risk-free rate). If a firm invests in two projects that are option good, however, they pay a significant penalty (based on having a limited budget); if more than two projects, penalty increases exponentially. For simplicity, assume no or prohibitively expensive coordination.

I'm not good at the math; but intuitively, depending on the expected losses/rewards, the number of firms, the number of projects, and - crucially - uncertainty, investors' expectations and knowledge about these numbers and the strategies of others, the dominant strategy could easily be bad for all.

Relax assumptions at will, complicate matters by introducing costs if no projects built at all (to represent the shovel-makers), multiple period learning, whatever.

More of a prisoners' dilemma (trap) than multiple equilibria, though. Unless - aha! - you get an investor large enough and able to signal credibly in advance it will invest some large amount. Call this investor Magneto. (Magneto could also lie pretty effectively and change the outcome, as long as enough participants believed in Magneto)

This needs simplification, and someone with a better brain.

GA: That sounds like a version, not of the Hobbesian Prisoners' dilemma, but JJ Rousseau's Stag Hunt. Each individually can catch a hare, but both together can catch a stag. Half a stag beats one whole hare. But will the other choose stag or hare? Unlike PD, which has one equilibrium, SH has 2 pure strategy Nash equilibria.

If you think all the other firms will invest (hunt stag) it's individually optimal for you to invest too. If you think the others will stay in cash (hunt hare), so do you.

re: Diamond-Dybvig and the original post

The whole value of banks in DD is that they are selling depositors an option to withdraw. Because banks combine this option with socially optimal investment (in the environment without aggregate uncertainty), the existence of the option adds value relative to a cash only economy -- and has the cost of making bank runs possible.

So I think what your post does is explain the intuition behind why a fractional reserve banking system is valuable for an economy.

"I like to think of what you and I are talking about as that narrow intersection between the two sets of: Keynesian economics, with it's emphasis on disequilibrium: and Monetarism, with it's emphasis on the excess demand for money an monetary exchange".
Yes, I think so. But sincerely, Until now I just don´t know that the correct label for disequilibrium was "Keynesian"... I tend to consider me as "non orthodox monetarist", which perhaps fall into this intersection... I recognize that my favorite texts are those of Friedman, starting with "A Monetary History of U.S. ..." which I suppose makes me a bit pedestrian. I like to link facts and hypotheses, and I prefer the Marshallian- partial equilibrium than the general-Walrasian.
But I´m happy lernning a lot here.

"How much did it show?"

Not too much. I would quibble with your emphasis on short-term uncertainty, as many of the classical real option scenarios - plant suspensions, closures, etc. - are very long-dated. That also applies to some of the areas to which real option theory has been extended by "lateral" thinkers like yourself: divorce and suicide.

The short-term emphasis suits your present purposes, of course. I am not yet fully persuaded by your view (still thinking about it), but there does seem to be an asymmetry between being invested with an option to disinvest (long-dated) versus standing on the sidelines with an option to invest. This would apply not only to cash, but also to marriage, another popular real option subject. Arguably, if divorce is available, then one might as well go ahead and get married early, since there is no particular reason to think that a superior choice will be available in the near future.

Syntheticassets: "So I think what your post does is explain the intuition behind why a fractional reserve banking system is valuable for an economy."

It would be nice if it did that, but I don't think I can claim that. As far as I can see, DD explain fractional reserve banking (subject to the caveat that it seems to me a mutual fund could play the same role, and maybe better, since those savers who find they need liquidity can just sell their shares after 1 period, and if there's a run on the fund, the share price would drop, which may create a disincentive to sell, and stop the run).

My post is more about explaining why you might want to postpone an irreversible investment, even if it's expected to be profitable, to wait for better information.

Luis: "Until now I just don´t know that the correct label for disequilibrium was "Keynesian".."

Fair point. Why should "keynesians" have a monopoly on "disequilibrium"? I think though that some economists working within the Keynesian tradition did explore the consequences of disequilibrium (the spillovers of excess demands/supplies and quantity constraints in one market into excess demands/supplies in other markets) more than anyone else. So I'm happy to give "Keynesianism" credit for that.

Phil: "Not too much."

I am relieved to hear that! Thanks for letting me know. Yes, the particular macro application of real option theory I am interested in here would have a more short-term focus.

I hadn't thought about marriage and suicide in terms of real option theory. Neat!

I had made the decision to be in cash the vast majority of the time since the end of 2009. I missed a little of the run up but none of the fall since.

I like the way you have articulated the idea however. Several friends and I have had this same discussion over the first parts of this year. Holding cash is a choice (option) like any other. It's not a bad idea when you are not certain what to do or want maximum flexibility to react when you do decide to act.

Well put (pun intended).

This reminds me of Benjamin Anderson's idea that one of money's functions is that of a "bearer of options", described in his 1911 Value of Money. Not just cash, but other highly liquid securities might bear an option too.

"I think we have been living in such a time, and are slowly coming out of it."

One of the problems with an earlier post of yours advocating policies that worsen confidence in money is that this forcibly removes the period of learning allowed by cash holdings. People forced to act without the benefit of acquired knowledge will either make poor investments or move into liquid alternatives like gold and competing currencies that still afford the option to learn.

When I think in keynesian desequilibrim, I remember LEIJONHUFVUD & CLOWER.. I liked tem, but I don´t know where they fall in the keynesian distribution; I suppose near the tail.

In general, I think you either have to be assuming there is a real option on market inefficiency for most of this to work. For example, I don't think your homeowner has a real option. I think a real option requires some kind of exclusivity (for a company, literal like a patent or less tangible like competitive advantage) -- i.e. for the option to have value the NPV of the asset can't be determined by a market price (heating oil). The presumption would be that markets eliminate variance in the NPV of your project based on market prices. I think you get a real option where the homeowner isn't choosing between buying or renting heat, where you presume the NPV won't vary, but when he is choosing between insulation and freezing. The value comes because there is a presumed variance between your future housemate (or purchaser's) desire to feel their fingers and the price of insulation; i.e. the NPV. So it might be better to put off a positive NPV insulation project if you variance is high enough.

It's not uncertainty, but uncertainty that you expect to be resolved quickly, that creates liquidity preference. You can't learn anything about the dice by waiting, so you might as well place your bets and roll them now, and learn whether you win or lose. It's not the level of uncertainty that matters for liquidity preference, but the expected rate of change of uncertainty.

I think it is absolute variance that still matters. Why don't stocks decline as they approach earnings, when uncertainty is expected to decline and the real option of holding cash supposedly peaks? Because there is no benefit to the resolved uncertainty when you will have to pay for it with a market price. What makes building a new store different? Just when your NPV of the store goes up because of reduced uncertainty, so does the cost to build a store, unless you are holding an option on inefficiency.

But the option on inefficiency still seems to be about absolute uncertainty and not declining uncertainty. That is, unless you believe that declining uncertainty is correlated to inefficiency. But this isn't really option theory anymore as it is really juts a discussion of the information theory your were going through with GA. I don't see the option analogy working here insofar as it applies to your declining uncertainty theory. I do like the idea of thinking about cash as an option, and this is only paper I've found on it explicitly (applying do goods as opposed to assets).


A couple of comments.

1) Nick, it is an interesting idea, on the embedded optionality in cash. However, such optionality would be more perfect if the supply of said cash were relatively constant, at least constrained to growth of a few percent per year. But of course money has grown at far faster rates, depending on the year in question and the currency of its denomination. The purest optionality is in true "money", not necessarily the coupons that get cranked out by the Bank of Canada amongst others.

2) A tip of the hat to David Pearson for regular intelligent comments to this site, often being at least as persuasive and well thought through as the original post. I particularly enjoyed your contribution to the exchange on the inflation/deflation post "Fire in Noah's Flood" for which I attach the link here.


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