Liquidity and risk: liquidity as the value of an option to sell at the market price

Is this a risk crisis or a liquidity crisis? What's the difference?

We can define "risk" and "liquidity" any way we like, but some definitions are more useful than others. A useful definition would explain why "risky" assets need high yields to make people willing to hold them, and why "illiquid" assets need high yields to make people willing to hold them. And useful definitions of "risk" and "liquidity" would allowed us to distinguish the two.

Here's my distinction between risk and liquidity:

The value of an asset can be decomposed into two parts: the value of the stream of dividends (where redemption counts as a final dividend) to the owner of the asset; and the value of the right (or option) to sell the asset at any time at the market price. We should use "risk" to talk about the effect of uncertainly on the value of the stream of dividends; and use "liquidity" to talk about the value of the right to sell the asset. The value of liquidity is the value of an option to sell at the market price whenever I choose to exercise that option.

This distinction between risk and liquidity seems to work. Paper money pays no dividends and is worthless to hold if we cannot sell it. Its value is 100% due to its liquidity. My toothbrush is very useful to me (it pays dividends in services not cash), but nobody would buy it, so my right to sell it is worthless. It is totally illiquid.

You can see how our understanding of "risk" has changed over time. We used to think of "risk" as the variance of return on an asset. Then we saw that variance didn't matter if it could be diversified away. Only the variance of the total portfolio mattered. The Capital Asset Pricing Model changed the definition of "risk" to the covariance of return with the market portfolio. Then we saw that the variance of return of the total portfolio only mattered if it caused variance in consumption, and the CAPM was modified to become the Consumption CAPM. The "risk" that mattered was the (negative) covariance of return with the marginal utility of consumption.

According to the CCAPM, an asset which gave its highest return in good times was the highest risk, and needed the highest expected yield to make people willing to hold it. An asset with its highest return in bad times, like when your house burned down and were most poor (and so had a high marginal utility of consumption) had negative risk. We called it house insurance. People would be willing to hold insurance even at a negative (expected) yield.

We changed our understanding of "risk" as a result of asking "why should people be willing to accept a lower yield to avoid risk?" Let's try the same route to understanding "liquidity". How should we define "liquidity" if we want to understand why people should be prepared to accept a lower yield to gain liquidity?

I started out by thinking of liquidity in terms of transactions costs. Transactions costs include things like agents' and brokers' fees, commissions, bid-ask spreads, the cost of advertising, checking the quality of the good, etc. If I buy an asset, and think I might want to sell it again in the future, those transactions costs will reduce my net capital gains (or increase my capital losses). If I expect to hold the asset for one year, then a 1% higher transactions cost will mean I will require a 1% higher yield to be willing to buy the asset. We can think of those transactions costs as the costs of a "round trip": buying the asset and selling it again immediately.

High transactions costs reduce the value of the option to sell an asset at the market price, and so reduce its liquidity.

But then I started thinking about the market for lemons. If I buy a new car, I find out by owning and driving it whether it is a lemon. But a prospective buyer cannot tell whether or not it's a lemon. That means that most used cars offered for sale will be lemons, and buyers know this, so the market price of a used car will be lower than the value of the average used car. If I buy a new car, and sell it after one year, I will face a capital loss due to the lemons problem over and above any depreciation of the fundamental value, and over and above any "round trip" transactions cost I would face in buying a used car and selling it again immediately. I should not buy a new car if I might want to sell it again soon. It is an illiquid asset.

Both transactions costs and lemons costs reduce the value of the option to sell an asset at the market price, and so reduce its liquidity.

But then I thought about the "rush to the exits" problem. Physical capital goods are like putty-clay. We can convert resources into any sort of capital goods we want (putty), but once we have built the capital goods, we cannot easily convert them back into anything else (clay). By issuing shares in a capital good, we make the capital good liquid (putty) for the individual investor, who can sell his shares to another. But it is still illiquid (clay) in aggregate; we can't all sell our shares and convert them into cash. If we try to do so, the price falls to zero.

Whether this is a problem for the individual holding the shares depends on whether his need for cash will be correlated with others' needs for cash. If the correlation is zero (and each individual is small relative to the market), the shares are perfectly liquid. If the correlation is one, the shares are perfectly illiquid. For an illiquid asset, where everyone rushes to the exit at the same time, the market price falls just when you most need the cash. We can understand illiquidity as the (negative) correlation between the marginal utility of cash and price of the asset.

That way of thinking about liquidity (or illiquidity) is sounding very similar to the CCAPM definition of risk.

So, transactions costs, lemons costs, and a negative correlation between market price and my need for cash, all reduce the value of an option to sell the asset at its market price, and so reduce its liquidity.

We are willing to pay a higher price for a more liquid asset because the option to sell that asset is worth more, even if the dividends are the same. Once you include the value of the option to sell the asset, a value that rises over time as the exercise date approaches, liquid and illiquid assets should all have the same yield.

I just wish I understood option theory better. Then I might understand liquidity better.

 

Comments

[bob]

I haven't had a chance to read it fully, but I think this might be just the ticket:

Longstaff, F., 2004 “The Flight-To-Liquidity Premium in U.S. Treasury Bond Prices”
http://fmg.lse.ac.uk/upload_file/150_Francis_Longstaff.pdf

some of the other issues are also dealt with in this paper by John Hull at Rotman, who is a top options expert:

Bond Prices, Default Probabilities and Risk Premiums1
John Hull, Mirela Predescu, and Alan White
http://www.rotman.utoronto.ca/%7Ehull/DownloadablePublications/CreditSpreads.pdf

[bob]

sorry, one more link that might be of interest:

Y2K Options and the Liquidity Premium
in Treasury Bond Markets
http://www.newyorkfed.org/research/staff_reports/sr266.pdf

sorry to drop a bunch of links without comments, it's a really interesting topic and I hope to have some thoughts together on the original article later tonight or tomorrow morning, but right now I'm off to the Raptors game to unwind:)

[Nick Rowe]

Thanks bob. I read through those papers, briefly. They give good empirical confirmation of my view that liquidity premia exist, and are big enough to matter. If anything, I would say those papers understate the size of liquidity premia. Since they can only look at assets that are very similar in terms of risk, they would tend to be similar in terms of liquidity as well. So the liquidity spreads between very different assets could be much bigger, but you can't easily estimate them, because you can't separate out the risk spread from the liquidity spread.

But they don't say anything about option value. They don't really have theories of liquidity at all (except for some empirical judgments that liquidity should depend on various things - reasonable judgments, but they don't really amount to a theory).

I do wish I understood option theory better. For example, I buy a new car. I am buying two things: the right to use the services of the car (the dividends); and the option to sell the car. The value of the stream of services is declining over time, as the car gets older. What is happening to the value of the option to sell it? Is it rising, or falling over time? And what is the optimal time to exercise that option? Is it when the value of the option is at a maximum? Or growing at less than the rate of interest? Or when? That's where I get muddled.

[anon]

How do you distinguish between the liquidity of your toothbrush and the market value destruction attributable to personalized use?

[anon]

A put option typically includes a certain strike price. Liquidity upon exercise is perfect.

An option without a known strike price is close to being useless. Name me an asset you can't at least ATTEMPT to sell at an unknown strike price. How does that advance your liquidity theory?

[Nick Rowe]

anon 8.25: my using my toothbrush once destroys its liquidity (and value to anyone else). But the value of the toothbrush to me is not destroyed by my using it once; it slowly loses its value to me as I use it more and more (and it wears out).

anon 8.33: a put option *typically* includes a pre-specified strike price. But let's think of a put option at the market price instead. I know it's weird to think about put options that way, because when you buy something you almost always buy the right to sell it whenever you wish. But there probably are a few examples where you buy the right to use an object, but are not allowed to sell that right to someone else. (Probably someone can think up a real-life example). But let's think about liquidity that way, and see what we get.

Put it this way. If I sold you the use of a car for as long as you wanted to use it, but I did not allow you to sell it to someone else, would you pay as much for the car as you would if you could also sell it to someone else? No. Not unless you were absolutely certain you would never want to sell it to someone else (the option would be valueless to you, because you knew for certain you would never want to sell it).

How much would not having the option reduce the value of:
a toothbrush? 0%. Toothbrushes are extremely illiquid.
a car? maybe 30%? cars are not very liquid.
a 30-year treasury? maybe 50% or more? it is very liquid.
a $20 bill? 100%. Extremely liquid.

[Nick Rowe]

Here's a real-life example (I think). You buy a 12-month tenancy on an apartment, and the lease says you are not allowed to sublet.

You do not buy the option to sell the asset (12 month's use) at the market price. It is totally illiquid.

[bob]

yep, I suspect though that if they were to redo that research today, they would find the liquidity premium to be off the charts (for example, the agency spread, although there is still some question of differing risks there).

I think I may be able to help with the options theory.

"Once you include the value of the option to sell the asset, a value that rises over time as the exercise date approaches, liquid and illiquid assets should all have the same yield."

I think this is backwards. With an (American) option there are two basic components, the time-value (extrinsic value) and the exercise value (intrinsic value). The exercise value corresponds to the value of an option if it were exercised at the moment. Options that are out of the money have an exercise value of 0, while options that are in the money have an exercise value corresponding to the difference between the mark price and its strike price. The time-value is mainly derived from volatility (likelihood that the option could swing towards the money) and time to expiry (length of time left for you to take advantage of swings). As the expiry date approaches, you have less and less time to catch a swing, so the time-value of an option decays exponentially (the greek "theta" tracks this rate of decay in the time-value). On the date itself, time-value goes to zero, and only the intrinsic exercise value remains, so the value of an option is at a maximum the further away from expiry that it is. As it approaches expiration, the options seller profits from the decay, while the option buyer pays for the decay of the time-value.

In terms of the liquidity related option value difference between on-the-run & off-the-run bonds, it always goes to zero at expiry. Convergence trades (long off-the-run/short on-the-run) attempt to exploit this. LTCM were doing this, but were caught in a liquidity shock, so the usually-decaying liquidity premium that they were shorting exploded.

[Adam]

Nick,

I don't think your concept of liquidity as the value of the option to re-sell makes much sense. Let's take the housing market as an example and compare the price of a house to the present value of the costs of renting the house. In the recent house price bubble purchase prices where way above the pv of rents, people were willing to pay much more for ownership then it would have cost them to simply consume the housing services. Was this because houses had suddently become much more liquid?

Well, the housing market had become more liquid in the sense there was an unusually high volume of transactions. But the relevant comparison is between the liquidity of house ownership and the liquidity of a rental contract. Perhaps the rental contract isn't perfectly liquid because you can't just walk away, you need to wait until it expires or sublet if allowed. So, during that time perhaps owning the house was the more liquid route to consumption of the housing services. But the question is, could just this extra liquidity account for the huge increase in price/rent ratios? I just don't see it, this was a time when people were feeling pretty secure in their jobs for the most part. I can't imagine the possibility of moving at just a few months notice was really that valuable. Furthermore, a certain number of the house buyers were investors buying to let. Did the buy-to-let investors accept negative carry because they wanted an investment that could be sold quickly, even if they didn't expect price appreciation? Clearly no, the house price increases were due to people expecting to sell for a higher price, not because people attached an extremely high value just to the possibility to re-sell quickly.

It seems to me that if you are willing to pay more for an asset if you can re-sell it then this is just a reflection of speculative behaviour. In fact, I'm getting this from a David Kreps paper (1982, JET I think) where he defines speculation this way.

Moreover, your car example also doesn't really work. The fact that as soon as I drive my new car off the lot it loses 25% of it's value in the secondary market (due to the lemons problem) has nothing to do with liquidity, it's just the risk-adjusted value in the market (people price based on expected dividends and a lemon won't provide as many dividends). Suppose I buy a car for $10,000, I drive it home and it's now only worth $7,500. Once I've accounted for the markdown is the car as good as $7,500 cash? Clearly not, the difference between the car and cash is that the cash can, immediately, be turned into $7500 worth of food. The car can't, the time and search involved in transforming the car into $7500 worth of food (or other goods) is what makes it illiquid. This, once the price is marked down, has nothing to do at all with the lemons problem.

[Adam]

Also, your response to anon doesn't make any sense. You said:

anon 8.33: a put option *typically* includes a pre-specified strike price. But let's think of a put option at the market price instead.

An option (call or put) whose strike was always exactly at the market price has value exactly equal zero. I think anon's point was that the strike price of a typical option is fixed, it doesn't change.

[Adam]

While you've got me thinking about it, I do agree with Bob that liquidity premiums are high. And I do think you can use a comparison with the pv of the expected future dividend stream (risk-neutral expectation to adjust for risk) to define liquidity premia.

The way it has to work though, is that the market price of the asset is less than the risk-neutral expected pv of dividends, the difference in yield is the liquidity premium.

But the logic does not go: liquidity increases value because of the option to resell.

Instead the logic is: lack of liquidity decreases value because of the possiblity I might be forced to sell at a time when the market price is below my private valuation. This will be tricky to cast as the value of an option.

[Adam]

Actually, let me change the last sentance of my last comment. I think the logic goes like this:

lack of liquidity decreases value because if I'm forced to sell quickly I might have to take a lower price than the market price in order to sell in time (or I simply may not be able to sell in time at any price).

If, in a forced sale, the market price is below my private valuation but I am able to sell, immediately, at the market price that's not a lack of liquidity, that's just risk. To continue the car example from above, if the car is worth $7500 but selling it at that price necessitates a 3 month wait (to find a buyer) but in order to sell in 3 days I need to post a much lower price (or maybe I simply can't get the sale done in 3 days), that's illiquidity.

[Nick Rowe]

Adam: if someone gave me the option to sell my asset at the market price, that option would be worthless, agreed. But that's because I already own that option (except in very rare cases like the apartment lease where I am not allowed to sublet). But suppose someone took away my option to sell may asset at the market price (for example, the government, like in Cuba, said I could continue to live in my house rent-free as long as I wanted to, but was not allowed to sell it). Would I be worse off? Yes, if the asset were liquid, and I valued that liquidity.

Yes, Cuban houses are a good example (or were, till the Cubans figured out a way to get around the law). You own the right to live in the house, but not the right to sell.

Am going to think some more about your and bob's other points before replying.

[Nick Rowe]

Still thinking through your comments.

When you own an asset (unless we are talking about a house in Cuba, or an apartment lease where you cannot sublet, etc.) you are buying two things: first, the right to use that asset (receive dividends); and second, an American put option, with no expiry date, with a strike price equal to the spot market price net of transactions costs.

In principle you can assign a separate value to the put option, by asking what you would be prepared to pay for the asset with and without that put option. For an asset that is highly liquid, that put option is worth a lot. For an asset that is very illiquid, that put option is worth very little (the right to sell it isn't worth much if it is very hard to sell, with high transactions costs, etc.).

[Adam]

Well yes but most of your examples aren't really about this. The toothbrush and car examples are really examples of your private value differing from the market value. In the toothbrush case you can't resell because nobody else values your used toothbrush, it's not a liquidity problem.

[bob]

I think the main problem with using options to model liquidity is that our traditional models do a very bad job (actually no job at all) of modeling liquidity. This is very important and a key cause of the recent crisis. There is a whole discipline called Real Options that is dedicated to applying options principles to pragmatic problems like Nick's, however they don't really deal with liquidity because the traditional models assume constant liquidity.

The lack of accounting for liquidity risk is the gaping hole in Black-Scholes that brought down Schole's own LTCM. There have been some attempts to model this, traditionally based on the convenience yield found in commodities, some newer research is based on a stochastic supply curve:

Option Pricing with Liquidity Risk
http://www.cam.cornell.edu/~umut/bspaper3.pdf

Pricing Options in an Extended Black Scholes Economy
with Illiquidity: Theory and Empirical Evidence
http://people.orie.cornell.edu/~protter/WebPapers/Options31.pdf

I think that convenience yield for commodities, liquidity cost of options (or whatever we call it) and liquidity premium in bonds, all refer to a similar phenomenon related to increasing desire for liquidity and/or shortened time-preference and/or reduced carrying cost (lower interest rates on other assets = lower opportunity cost). I'm still not totally clear on it. John Cochrane alleges that the same convenience yield effect can be found in stocks, and was at the root of the NASDAQ bubble:

Stocks as Money: Convenience Yield and the Tech-Stock Bubble.
John H. Cochrane
http://faculty.chicagobooth.edu/john.cochrane/research/Papers/cochrane_stock_as_money.pdf

I think that the convenience yield probably is at the heart of explaining why excess liquidity tends to cause bubbles. Low interest rates and huge influxes of liquidity increase the convenience yield of a particular asset, driving up the price and attracting more liquidity (volume) in a self-reinforcing process.

[bob]

To get back to Nick's original point, I think that liquidity premium is best characterized as a component of an option's extrinsic time-value, similar to vega (sensitivity to volatility) or rho (sensitivity to interest rates), but one that has yet to be fully incorporated in options theory.

Most options theorists these days are probably saying:

"I just wish I understood liquidity theory better. Then I might understand options better."

[Scott Sumner]

Nick, This is slightly off topic, but I got into this late. I believe you said earlier that the problem today is not enough liquidity, so liquid assets such as cash have become more valuable and then inflation falls below target. So the solution is for the government to increase the amount of liquidity. But here is the dilemma: Having the Treasury issue more T-bills and less T-bonds would seem to increase liquidity, but it would also reduce the incentive of the central bank to pursue a policy of increasing inflation in futures years. In other words, it increases liquidity today at the expense (possibly) of lower future expected liquidity. I am not sure at all if this is a problem in practice, just wondering if has come up in the liquidity discussion.

[calmo]

So the $20bill is very "liquid" --unless you are at the laundry and the absent owner has installed the coin dispenser that handles only $5 and $10.
And if you are an investment bank that would like to sell some under-performing assets, the first move is to let the regulatory agencies know that your position is "illiquid": your MBS is not being accepted, even with generous discounts to those folks who used to do the laundry there. You cannot afford to acknowledge your assets as liabilities: your reputation is finance...and no one expects you to be able to do anything else.
The laundry market knows these securities are "toxic" --those mortgages are not bein paid, those income streams from those "assets" dried up a long time ago. These are experienced laundry people who can tell a slug from a quarter.
So it looks like Geithner's gonna supply tax-payer quarters for these slugs...and unlike the $20 bill which would become liquid the moment the laundry operator returned, the slugs are slugs...and enough of them might debase the value of a real quarter, yes?

[Nick Rowe]

Adam 11.03:

I like your example of comparing the liquidity of owning a house vs renting (where you can walk away from a rental with a month's notice say). A renting an apartment (and putting the cash you would have spent on a house into a savings account say) is (almost always) more liquid than owning a house. If it cost more to buy than rent, we cannot explain this as a liquidity premium on houses, since houses are less liquid than renting. So it would have to be a bubble (given those assumptions).

But let's think about the Kreps definition of speculation. It can't be quite right, because people sometimes don't want to live in the same house forever (the house will live longer than they will anyway).

Let's work through a simple example. I buy a new car. Assume no uncertainty. The car gives me a flow of services which I value F(t). F(t) declines steadily over time, as the car ages. At some date s, when F(s)=0, I would scrap the car (assume zero scrap value). Take the present value of the remaining flow of services and call it V(t). It too declines towards zero at date s.

If I were not allowed to sell the car, I would be willing to pay a price V(0) for a new car.

Now add in the option value of selling it when I want. There is a spot price for the car (net of transactions and lemons costs) P(t). When I walk out the dealership, P(t) immediately drops 25%. Thereafter, P(t) declines slowly over time, as the car ages.

If P(t) is always below V(t), I will never exercise my option to sell the car. I drive it till I scrap it. Under certainty, the option is worthless to me, and I place zero value on the liquidity of the car. But if I value the services of an older car less than the market (I really need reliability, or whatever) P(t) and V(t) will cross at some date x. I will sell the car at a date z, after x, when F(z) = rP(z) + dP(z)/dt (the flow of services just equals the foregone interest plus price depreciation, so I am just indifferent between selling the car now and selling it one day later). In that case I place a value on the liquidity.

If I sell the car at date z the value of a new car to be is V(0) + PV{P(z)-V(z). That second term is the liquidity premium. If the (Cuban) government were to take away my right to sell the car, that's what I would lose. Buying a car with the option to sell it at the market is worth more than buying an indefinite lease which I cannot break or re-sell.

I see where Kreps is going with that definition of speculation, but it doesn't work. Everyone who bought a new car planning to sell it rather than drive it into the ground (or at least, under uncertainty, of their need for cash etc.) would be a speculator. Instead, they are valuing liquidity.

I need to reflect more on other comments.

[Nick Rowe]

Correction: the formula should read F(z) = rP(z) - dP(z)/dt

[Nick Rowe]

Scott: "... Having the Treasury issue more T-bills and less T-bonds would seem to increase liquidity, but it would also reduce the incentive of the central bank to pursue a policy of increasing inflation in futures years."

I had to think about that. The longer the term to maturity of the debt, the longer it takes for nominal interest rates to reset when the debt is rolled over, and so the bigger the government's gains from a surprise inflation. So there is a trade off between increasing AD by increasing liquidity, and increasing AD by increasing expected inflation. Maybe. I'm still trying to get my head around the liquidity question.

[Nick Rowe]

Adam: "The toothbrush and car examples are really examples of your private value differing from the market value. In the toothbrush case you can't resell because nobody else values your used toothbrush, it's not a liquidity problem."

This is definitely where I disagree. ALL liquidity problems are examples of where the private value differs from the market value. The only reason we ever sell stuff is because our private value falls below the market value. (I sell my car because I value $x more than the car and the buyer values the car more than $x). If we didn't have these differences, we would never sell, and so liquidity would be irrelevant.

Now, the reason I sell my car could be because my view of the car has changed, or because my view of cash has changed ("I hate this car" vs "I really need cash"). But in either case, my private value of the car relative to cash has fallen relative to the market price.

[JKH]

Nick,

Both economists and non-economists take liberties in defining risk and risk paradigms – the point being that economists have no monopoly on the truth of what risk is. (De long is a good example.) Do you sense I’m going to present something different?

Those who transact in financial markets generally acknowledge liquidity to be a type of risk. In any paradigm of risk, it is going to be different from other types of risk. But risk paradigms are often best presented as a sort of Rubik’s Cube for risk analysis. E.g. Liquidity is a risk that intersects with credit risk, interest rate risk, and foreign exchange risk. All of these risks intersect with solvency risk, where solvency is defined in balance sheet equity terms. My own sense of the right paradigm is that liquidity and solvency are overarching dimensions, and the others I mentioned here are one level down.

You’ve presented something quite deep here with respect to the definition of an option, and its relationship to the definition of liquidity.

Option analysis normally presumes an ability to “exercise” the option, which is a sort of elementary liquidity event.

You’re suggesting there is a deeper optionality that underlies the presumption of exercisability according to the usual parameters in an option contract, such as price and time.

If there is no option to transact, then there cannot be an option structure in the usual sense.

E.g. restricted stock or stock options heretofore common in executive compensation typically include vesting requirements. During the vesting period, effectively no liquidity exists, because the executive cannot exercise and cannot assign his options.

But a toothbrush is always optionable in this sense. There is no restriction on being able to offer it on Ebay. If you are an economist who develops a ground breaking theory on liquidity and options, your toothbrush may be worth a lot to some failed but envious graduate student somewhere.

[JKH]

Scott, Nick,

“Having the Treasury issue more T-bills and less T-bonds would seem to increase liquidity, but it would also reduce the incentive of the central bank to pursue a policy of increasing inflation in futures years.”

I suggested somewhere that Treasury should be issuing 30 year treasuries now, as a partial hedge against its own policy induced inflation, even while the Fed is buying 10 year treasuries in an attempt to get mortgage rates down. (10 years is a closer duration match for 30 year mortgages with prepayments). Also, as noted at Scott’s blog, the Fed does have some additional short funding risk already due to paying interest on reserves, so some term extension on the Treasury funding program otherwise would seem prudent.

[westslope]

I'm enjoying this thread. A clarification if I may.

In the formula V(0) + PV{P(z)-V(z), is not the present value of resale value of the car already included in V(0)?

[Adam]

I think Nick intends V(0) to be private value, to you, of consuming the stream of dividends/services. My guess is that he has in mind that if it ever happens that P(z) > V(Z) you can sell the car and capture a sort of surplus analogous to the consumer surplus of elementary demand theory.

[Adam]

Nick: "ALL liquidity problems are examples of where the private value differs from the market value. The only reason we ever sell stuff is because our private value falls below the market value."

Really? Here's a quote from a recent Krugman blog (http://krugman.blogs.nytimes.com/2009/03/21/more-on-the-bank-plan/):

"But banks can also fail even if they haven’t been bad investors: if, for some reason, many of those they’ve borrowed from (e.g., but not only, depositors) demand their money back at once, the bank can be forced to sell assets at fire sale prices, so that assets that would have been worth more than liabilities in normal conditions end up not being enough to cover the bank’s debts."

Now, it could be that Krugman has in mind an informational/lemons problem. The bank can't sell its loan book because it has private information on the credits in its book that can't be transferred to a potential buyer. However, it seems to me that givn enough time that private information could be transferred. It just takes a while for the buyer of the loans to review the due diligence of the selling bank. The liquidity problem is that while selling the loan book at full value takes a long time, demand depositors will want their cash on the spot, without delay. Clearly these banks are selling assets even though they don't think they're recovering their true value.

[bob]

JKH, great comment

"You’ve presented something quite deep here with respect to the definition of an option, and its relationship to the definition of liquidity.

Option analysis normally presumes an ability to “exercise” the option, which is a sort of elementary liquidity event.

You’re suggesting there is a deeper optionality that underlies the presumption of exercisability according to the usual parameters in an option contract, such as price and time."

Yes, I think Nick has stumbled on a very deep issue in risk models right here. B-S assumes perfect liquidity and zero transaction costs. Some other assumptions have been compensated for, but liquidity risk has yet to be incorporated. I think that the reason for this was the "great moderation". For a long time, it was plausible to simply assume liquidity.

"The Black–Scholes model disagrees with reality in a number of ways, some significant. It is widely used as a useful approximation, but proper use requires understanding its limitations – blindly following the model exposes the user to unexpected risk.
Among the most significant limitations are:
the underestimation of extreme moves, yielding tail risk, which can be hedged with out-of-the-money options;
the assumption of instant, cost-less trading, yielding liquidity risk, which is difficult to hedge;
the assumption of a stationary process, yielding volatility risk, which can be hedged with volatility hedging;
the assumption of continuous time and continuous trading, yielding gap risk, which can be hedged with Gamma hedging." (wikipedia)

Scholes blindly followed his own model with regard to liquidity risk (because it ignores liquidity risk, it led him to believe that being short liquidity risk was actually pure alpha generating arbitrage), and predictably got clobbered.

I think that the liquidity of the asset underlying an option forms part of any option's time-value. This solves a lot of shortcomings in B-S, like explaining the volatility smile & other observable deviations from B-S that LTCM misidentified as risk-free arbitrage opportunities. The options liquidity risk theory in the Cornell papers I posted above could lead to a Nobel prize some day, as it provides a really innovative and much-needed basis for understanding systemic liquidity risk. you heard it here first.

[Nick Rowe]

westslope: Yes, what Adam said at 2.07. V(0) is my value of a new car, if there were a clause in the purchase agreement that I could never sell it. The value to me of me using it.

Adam @2.35: If the bank's depositors all demand their money back at once, the value of cash to the bank suddenly increases. Even if the value of continuing to hold the assets (in the bank's eyes) stays the same, that value *relative to cash* suddenly falls. (It's like when I suddenly decide to sell my car because I learn I need cash to pay for food. In other words, V(t) is measured in $, not in utils. It is the MRS between car services and cash. V(t) can fall because I run out of food, not just because the car breaks down.

JKH @12.23: I think you are right. Risk vs liquidity is a false dichotomy. I did not think through the logic correctly.

Even under certainty (perfect foresight) we can define liquidity. Like in my car example, I can define the "hold-to-maturity value" V(t) and the liquidity value PV{P(z)-V(z)} even under certainty. Uncertainty affects the "hold-to-maturity value" as well as the liquidity value. And in each case, how uncertainty affects the value depends on the correlation between the value and my marginal utility of the value. For V(t) for example, if my car breaks down, does it do so on sunny warm days or on rainy cold days, when I need it most? And for liquidity value, does the price fall when I am rich, or when I am poor, and most need to sell it (exercise my option) and raise cash?

bob: That John Cochrane paper you linked is quite a find. A great paper. He is thinking along very similar lines, and shows the empirical relevance quite convincingly. He calls it "convenience yield"; I think of it as a "liquidity premium". From money at one extreme, to totally illiquid assets at the other, the equilibrium yield will vary, and the velocity of circulation ("turnover") will vary. There's a whole spectrum of assets and yields, along that dimension. In my view, a major part of this/a financial crisis is a shift of and along that spectrum.

I like the analogy to "real options", where we think about other problems (like building a factory) in terms of options, even when we don't actually observe an option explicitly. When I buy a car I never think about the option to sell explicitly, because that option is almost always bundled in with the purchase of the car. (It's only in weird cases, like Cuba, where we can own the car without owning the option to sell it). But it can help theoretically if we decompose the car into two assets: the "Cuban" car (I can use but not sell); plus the option to sell.

In my car example above, what is happening over time to the option value? And what is happening to that option value at time z, when I exercise it? Is it at a maximum?? (I can't get my head around it, and that's in a case of certainty.)

[JKH]

Experiment:

There may be a logical conundrum underlying your “elementary” car liquidity option.

Suppose you buy a car and you’re interested the value of the (embedded) option to sell it.

Proposition:

It must be the case that if you can determine the value of the liquidity option, you can then derive the value of the car without the option; i.e. the value of the car on a hold to scrap yard basis. You just subtract the value of the option from the value of the car with the option.

But how can you determine the value of a perfectly non-liquid car? If the car has no liquidity, there is no effective meaning to the idea of calculating its value. Its value is akin to the sound made by a tree falling in the middle of a forest - a sound that is never heard. No positive price or value that you put on it will ever be confirmable. The only price or value that will ever be confirmable is zero, and that won’t be due to a sales transaction. So there is no way of calculating a value for a perfectly non-liquid car.

And if you can’t determine the value of the car without the option, this contradicts the premise and proposition above that you can determine the value of the liquidity option.

[bob]

Nick, I think your car example might be bringing in a bunch of variables that aren't necessarily related to option value itself. I think the apartment option to sublet example might be better.

Say you are renting an apartment for one year at $1000 per month. There are no laws against charging more to your subletter than you pay in rent. Your landlord offers to a sell you the right (option) but you have to pay in advance $240 for the whole year.

At the beginning of the year your option is at maximum time-value (which is the option value we're concerned with here). Every month that goes by without exercise, it is generally worth less money, because you have less time to take advantage of market movements and market liquidity. 2 reasons here:

1) the main traditional one is volatility. If the price in the market (craigslist postings) for your apartment is volatile, any time the price you can get goes over $10XX per month, you can sublet to someone, and then collect the different between your rent + the cost of option vs. the income from subletting. The ability to capture these fluctuations over time is why you pay a higher price for options with volatile underlying assets. If apartment prices were swinging from $500 to $1500, your option is worth a lot more. As you move towards expiry, the option is worth less and less, because there is less time left to capture swings

2) liquidity premium. If the volume of ads on craigslist is low, this reduces the number of opportunities to exercise your option, and increases transaction costs, reducing the value of your option. If liquidity is high and there is a high volume of ads on craigslist, each discrete time period offers you more opportunities to exercise the option, increasing the options value. As with the time-value component related to volatility, the liquidity premium also decays exponentially as you approach expiry. If you didn't sublet your room by the last week of the lease, your option would be worth very little, because there is very little time left to take advantage of the asset's liquidity.

In any case, the time-value of an option (which the liquidity premium) is usually worth the most as soon as it is purchased, and loses value exponentially as it approaches expiry, because at expiry, the time-value (including liquidity premium) is zero. The time value generally decays, but it could increase rapidly if there is an increase in the volatility of the underlying asset, or if there is an increase in that asset's liquidity relative to other assets (or both as in the case Cochrane studies).

[bob]

one other thing, I also prefer the term "liquidity premium" and I think that term should be used across bonds, options, commodities & FX. It seems to capture the same fundamental phenomenon in each case, despite being called by different names.

[bob]

one more point: if there is no expiry (in the sense of a real option on a diamond, not a term lease), the option-value of the diamond is determined by the volatility of the market and the liquidity of the market. the liquidity premium makes up part of the option-value, but not all of it. The value of the real option is at a maximum when volatility and liquidity are at a maximum (as in the Cochrane paper)

[Nick Rowe]

JKH: I don't see the problem (at least in principle). I can run an experiment, and find out what people are prepared to pay for a car with and without the option to re-sell it. In other words, I can offer an indefinite non-transferable lease on a car, and see how much money people would be prepared to pay up-front for such a lease. That tells me V(0). And the I can offer them the same car for sale under normal terms (with the option to re-sell it). The difference gives me the value they place on the liquidity of the car.

bob: yes. I think your apartment example is better than the car, because we know the price, F(t), and V(t) of a car will be declining over time, which complicates things.

Two disagreements:

1. Your discussion of the example misses out what is happening to F(t) (i.e. the value per month to me of staying put in the apartment). I think it is volatility in Rent(t)-F(t) which is driving the value of the option to sell, rather than just volatility in Rent(t). (I don't think you would disagree, and it doesn't really affect the rest of what you say, but you were implicitly assuming no volatility in F(t)). Even if market rents didn't change, if my own value of staying in the apartment were highly volatile, the option would have a higher value.

2. You speak of "liquidity" as though it were something that affected the value of the option to sublet, rather than *being* the value of the option to sublet. In other words, your discussion of "liquidity" thinks only of the traditional transactions cost approach (and could maybe include a "lemons" approach as well if people say "there must be something wrong with any apartment offered for sublet, so I won't pay as much rent for it"). I would say that these transactions costs and lemons costs are part of the reason why apartment leases are illiquid (why the option to sublet is not very valuable), but they do not represent the whole measure of "liquidity". The volatility of Rent(t) and F(t), or rather a positive correlation between Rent(t) and F(t) are a more important reason for a low value of the option to sublet.

3. Putting 1 and 2 together: Capitalise remaining market rents on a 12 month lease, net of transactions costs, net of lemons costs, into P(t). And capitalise what it's worth to me to stay on for the remainder of the lease into V(t). Assume the option expires when the lease expires. Then we can (I think) define the value of the option to sublet as a function of the volatility of [P(t)-V(t)]. If P(t) and V(t) are highly correlated, the option will have little value. If P(t) and V(t) have high variance but low (or especially negative correlation), the option to sublet will have high value.

[Nick Rowe]

Yep. V(t) represents my own valuation of the asset relative to my value (need) for cash. P(t) represents the market's valuation of my asset relative to the market's value (need) for cash.

(Il)liquidity depends on the covariance of V(t) and P(t). If the market needs cash most when I need cash most, the value of the option to sell (the value of liquidity of the asset) is low. If the market stops needing apartments when I stop needing an apartment, the value of the option to sell (the value of liquidity of the asset) is low also.

It's volatility in max{0,P(t)-V(t)} that matters. Transactions costs and lemons costs reduce (net) P(t) and reduce the value of the option. High covariance between P(t) and V(t) reduce the value of the option.

[Nick Rowe]

Let me stick my neck right out, and say it as provocatively as possible: The problem with existing analyses of liquidity is that they ignore the possibility that my need for cash might be correlated with the market's need for cash.

(That can't be right, can it?)

[JKH]

Nick,

I disagree.

There is no such thing as an indefinite lease that I’m aware of.

Who would agree to enter into one and agree to make monthly payments indefinitely?

Nobody would sign a lease without some specified term and repurchase agreement.

The closest thing to “indefinite” would be a term that matches the expected life of the car.

The fundamental economic attribute of a lease is a specified repurchase price.

In this case, the repurchase price becomes zero.

In which case, the lease is economically and financially equivalent to a sale.

And the lessee has no economically useful rights at the termination of the lease if the repurchase price is zero.

There would be no purpose to such a lease, which as I said probably doesn’t exist.

So the presumed difference won’t get you anywhere in terms of deriving a liquidity premium.

Correct me if I’m wrong; I’m making this up as I go along.

[JKH]

Nick,

I really like the phrasing of your correlation observation. But I wouldn't say its a problem that's been entirely ignored by everybody else. Perhaps its not up front in academic theory, but one should certainly be thinking about it. "Rush to the exits" is another way of saying it.

[Nick Rowe]

JKH: What I had in mind was making one fixed payment for an indefinite lease on a car. I would happily pay about $10,000 for the indefinite use of a (good) new car, without the option to resell it. Or I would be willing to pay about $400 per year in perpetuity (British government consuls, or perpetuities, can still be bought at about 4% I hear, to allow me to hedge). Or any stream of payments with the same present value as $10,000 today. (If the price of the same car were $20,000, I expect I am saying that the liquidity of the car is worth 50% of its total value to me).

Of course, it is hard to think of any circumstances where I and the seller of the new car would agree to such a deal. The liquidity value is worth so much to me, and so little to the seller.

But we do get cases where people (pensioners, widows?) are given the use of a house rent-free for as long as they wish to live there, but not the option to sublet. That's a gift of a perfectly illiquid asset. It has a value, but less than the same value if it had the right to sublet (option to sell the right to live in it during the pensioner's/widow's remaining life).

Yes, people (including Keynes) have talked about the rush to the exits. But is it built into models/theories of liquidity?

[bob]

1. yep, that's one part that I left out for simplicity's sake. In the world of stocks, the utility of holding a stock is partially determined by dividends. When this dividend changes, that introduces dividend risk into the option pricing, similar to changes in your marginal utility calculation for the value of your apartment.

2. I think there is an issue here that JKH raised: at the limit, if there is are no transactions in the underlying asset the option value drops to zero. It's kind of like buying the right to swim in a pool, but then finding the pool dry. The right to sell at a certain price is rendered nugatory if you can't actually sell.

BUT this is also true if volatility drops to zero while liquidity persists, because an option on something that never changes price is also pointless - it would have no extrinsic time-value. The right to sell something at a certain price is nugatory if there is never deviation from that price. So the option-value is dependent on both liquidity and volatility. Liquidity alone can't account for it. There are also other determinants of option value (& convenience yield) that we are not dealing with here, namely the (usually negligible) influence of interest rates on carry-cost ("rho" in the options lexicon).

I think that if you try to subsume the entire option-value under liquidity alone, you may run in to theoretical problems.

"If the market needs cash most when I need cash most, the value of the option to sell (the value of liquidity of the asset) is low. If the market stops needing apartments when I stop needing an apartment, the value of the option to sell (the value of liquidity of the asset) is low also."

I think you are co-mingling the supply and demand for the underlying asset causing a movement in the price and increasing an options Intrinsic value and supply-and-demand for liquidity increasing the Extrinsic value, obscuring the relationship between liquidity and option value. I can see where you are going with it, in terms of a general inverse correlation between demand for goods and demand for cash, and that this in turn is correlated across the whole market, but I think it is besides the immediate point, and obscures the optionality that Cochrane observes in stock prices.

Here I think it is important to get back to the commodity convenience yield. research shows that the convenience yield can be closely modeled on a call option. Part of the option value is determined by liquidity as well as volatility and interest rate influence on carrying cost. Volatility is usually by far the largest factor in determining option price and therefore the "convenience yield" or optionality of spot commodities. This study doesn't take into account the liquidity or interest rate information of options, so they conclude (erroneously IMO) that the convenience yield is ENTIRELY volatility based (the flip-side of your liquidity-based convenience yield):

The Information Content of the Implied Convenience Yield: Using American Call Option Based Structural Model

Abstract:
This study examines the relationship between volatility and the spread of two commodity futures with different maturities in the NYMEX crude oil market. We find that convenience yield behaves like an American call option, which suggests that the information content of convenience yield is volatility behavior. Our model successfully quantifies the sensitivity of the spread with respect to volatility and provides satisfactory predicting power. For practical applications, we show how to calibrate our model in a trading strategy that can generate significant profit. Our structural framework lays the groundwork for studies on how volatility dynamics are related to commodity fundamentals.

Chen, Te-Feng, Lin, Ming-In and Wang, Kehluh, "The Information Content of the Implied Convenience Yield: Using American Call Option Based Structural Model" (January 2007). Available at SSRN: http://ssrn.com/abstract=957621

Mark Thoma attempted to model the convenience yield, and found the main influence to be interest rates & liquidity (although he doesn't separate them, which he should because they have related, but different effects):
http://economistsview.typepad.com/economistsview/2008/06/even-more-spe-1.html

In truth, I think that the real optionality of an asset = convenience yield. If you want to break apart the components, you need to break apart the option-value, and there is no avoiding any of the variables that need to go in to option pricing. you can't discount any one of the three: volatility, liquidity, interest rates, time. They are all important & interrelated parts of options pricing, although liquidity and interest rates tend to have a small effect at most times, and therefore have not received adequate attention until recently. Chen & Thoma's analyses are both flawed, because they only look at one aspect of the option value, and presume that it is the entire value. Cochrane's analysis is better.

[JKH]

Nick,

It’s becoming clearer.

“Of course, it is hard to think of any circumstances where I and the seller of the new car would agree to such a deal. The liquidity value is worth so much to me, and so little to the seller.”

It’s worse than this, in my view, which gets to the crux of the thing. The liquidity value is worth zero to the lessor in my view. It means there is a conundrum to this lease structure, such that it constitutes a false choice when compared to a purchase of the vehicle, and therefore a false basis to determine a liquidity premium.

This is because such a lease (“indefinite”) by definition includes a car residual value of zero. If the return value is zero, there is no economic reason for the lessor to insist that the car be returned at all. Equivalently, there is no reason for the lessor to insist that the lessee forgo the liquidity that is otherwise available to him with a purchase. Economically, such a lease is equivalent to a purchase, and the value to the lessor of imposing a zero liquidity option on such a lease is zero. It’s economically the same as a purchase, so you can’t derive a liquidity premium by comparing the two.

I haven’t thought about the sublet problem.

[Nick Rowe]

bob: "2. I think there is an issue here that JKH raised: at the limit, if there is are no transactions in the underlying asset the option value drops to zero. It's kind of like buying the right to swim in a pool, but then finding the pool dry. The right to sell at a certain price is rendered nugatory if you can't actually sell."

Agreed, but we would also agree (I think) that if nobody would buy your asset (at any price) then it is perfectly illiquid (like my toothbrush). And the option to sell the asset would be valueless. So the "value of an option to sell" measure of liquidity is giving exactly the right answer in this case. Liquidity = 0.

Must think more about the rest of your comment.

[JKH]

Bob,

I haven’t been taking the time to read your comments closely; I should; but I think the convenience yield concept is very germane to this discussion. I’m no expert in it, but I believe it’s very important in understanding the oil market for example, particularly in explaining the behaviour of the oil futures curve vis a vis contango and backwardation. And it is an option like concept.

Here’s a thought on time value:

Time value for a typical option (fixed strike price) is a function of the asymmetry, and the expansiveness of the volatility in stretching out the value of the asymmetry.

The “elementary” liquidity option is an option to transact in symmetric risk. Time value for symmetric risk per se is zero by definition. Symmetric risk includes a long embedded call and short embedded put, and the long and short time values for these embedded options cancel one another.

But time value for a liquidity option on symmetric risk may be different again.

The elementary option includes the right but not the obligation to sell a symmetric risk asset. So it includes the right to exercise the embedded call when value high but not the obligation to be exercised on the embedded put when value is low (“to be exercised” is the synthetic equivalent of “sell”).

The advantage of upside volatility in a symmetric position is due to the embedded call. So the liquidity option takes advantage of the embedded call and its time value. All of a sudden it doesn’t seem that much different than a regular option. But it is.

I think the difference here is that a symmetric asset with or without a liquidity option still includes the embedded exposure of a short put option. Even though you’re not forced to sell, with or without a liquidity option, you’re still exposed to downside volatility. That’s not the case with a regular option, which would only include the upside call exposure.

[Nick Rowe]

bob: "BUT this is also true if volatility drops to zero while liquidity persists..." OK. I see where you are going now. So if there's some asset, for which V is constant, and P is constant, and V is therefore always above P (because I wouldn't have bought it otherwise), then the option to sell it has no value. Agreed. And this would be true even if the asset were perfectly "liquid" in the sense of zero transactions costs.

OK. So what I have is not a measure of liquidity (if we agree for the sake of argument that this asset is "liquid"), but a measure of *my value* of that "liquidity". It makes no difference to me if transactions costs, bid-ask spreads, etc. were zero or infinite. But it might matter to someone else, whose V(t) did fluctuate.

So what I perhaps have is a measure of the *value* of liquidity of an asset, and that value of liquidity will vary from one person to another.

Must think some more about the rest of your comment.

JKH: The cost of the option to the seller of the car is zero (once he has sold the indefinite use of the car), but the benefit to the buyer of the car is not zero. It's the benefit to the buyer that measures the value of liquidity.

[bob]

"OK. So what I have is not a measure of liquidity (if we agree for the sake of argument that this asset is "liquid"), but a measure of *my value* of that "liquidity". It makes no difference to me if transactions costs, bid-ask spreads, etc. were zero or infinite. But it might matter to someone else, whose V(t) did fluctuate.

So what I perhaps have is a measure of the *value* of liquidity of an asset, and that value of liquidity will vary from one person to another."

yep, but I think this might be a case of economists are from mars traders are from venus. For me, because i only acquire assets based on an expected higher selling price, I don't really care about V. P can be thought of as aggregate V, that is revealed over time by the market price, and that's what I'm after. What I'm interested in doing is predicting the difference between aggregate V now vs aggregate V later, as calculated by the marketplace through a continual stochastic process. My own V doesn't really matter. When I'm buying a barrel of oil, my own marginal utility for oil (0) doesn't matter, I'm looking at the future marginal utility of oil for all actors in the aggregate.

[bob]

JKH,

"I haven’t been taking the time to read your comments closely; I should; but I think the convenience yield concept is very germane to this discussion. I’m no expert in it, but I believe it’s very important in understanding the oil market for example, particularly in explaining the behaviour of the oil futures curve vis a vis contango and backwardation. And it is an option like concept."

If I recall correctly, you were involved discussing this over at Interfluidity about a year ago. It is a very interesting topic that I have discussed with Randy Waldman via email. I'm surprised he hasn't found his way over here yet, as I would imagine that this type of discussion would be right down his alley.

In terms of the oil market, I agree. Lack of convenience yield was the key flaw in Krugman's basic futures model that caused him to miss the oil bubble. He admitted the flaw in his model, but never actually corrected the model or admitted that his "no bubble" conclusion was therefore wrong. Either way, it was proven wrong by the market within 1 week.
http://krugman.blogs.nytimes.com/2008/06/27/matters-of-convenience-very-wonkish/

I'm trying to understand your option example, but I think i need to think it over some more.

[JKH]

bob,

You’re right.

Here’s the convenience yield discussion at Interfluidity:

http://www.interfluidity.com/posts/1214354098.shtml

(For some reason, I used an anon handle in that discussion, which occurred last June).

Nick, you may find it interesting, as it’s an extensive dialogue on the option-like nature of convenience yield.

More generally, you’d probably enjoy the odd discussion at Interfluidity. Steve Randy Waldman enjoys thinking out of the box, to say the least.

[reason]

Adam,
do you have a blog? You should visit Mark Thoma's place sometime. Your comments are consistantly brilliant. An exchange between you and Bruce Wilder would be a pleasure to read.

[reason]

Surely, we can't know the extent to which speculation was driving the spot price of oil until the world economy recovers? And "speculation" by suppliers deciding that the value of their oil left in the ground is worth more than alternative investments is not speculation it is asset management.

[reason]

And if you want to say it is too speculation because they are taking a view of future price movements, I say in that case then so is every investment - so there is no such thing as speculation?

[Nick Rowe]

Thoughts this morning:

1. I'm beginning to think that bob may be right. I have cast my conceptual net, and I think I may have caught liquidity, or at least a lot of liquidity, but maybe I've caught a lot of other stuff as well. Here's one problem with my definition: suppose there are 1-month bills and 2-month bills. But suppose there is absolutely no market in those bills (they have the original buyer's name on them, and the government absolutely refuses to transfer the payment to anyone else). So both have zero liquidity-value under my definition, because you can't sell them. But the 1-month bill gives you cash in 1 month, and the 2-month bill gives you cash in 2 months. So I want to say the former is closer to cash, and more liquid. But my definition says it isn't.

2. But, bob says that as a trader he doesn't care about fluctuations in his V(t). I don't think that's right. Suppose bob buys an oil share. Then he learns that gold is a great buy, so he wants to sell the oil share so he can invest in gold instead. Nothing wrong with the oil share, no bad news, same expected P(t) of oil. But bob's personal V(t) of oil, relative to cash (which he can convert into gold shares) has just fallen below P(t), so he sells oil. Or bob faces a margin call on his oil shares, so his value (need) for cash rises. Those are cases where he cares about the liquidity of his oil shares, that I would model as a fall in bob's V(t) for oil shares.

3. Yes, my thinking about liquidity (especially) has been influenced by reading Randy Waldmann's posts. I really like his stuff. In some ways, this and the last liquidity post are sort of my response to his view that liquidity should not be as important as it seems to be (stating his views somewhat crudely).

4. Thanks to bob especially for his patience. My head is not as clear on this as I thought it might be. Still think I'm on to *something* though. Just not so sure what it is.

[Adam]

reason, thanks for the compliment, score one for the canadian educational system :). I have occasionally read Thoma's blog but never commented. This is the only blog where I've posted comments and that only started a couple weeks ago in Nick's return of monetarism post. I've enjoyed the debates over here though so I'll certainly make a point of checking out Thoma's blog more regularly.

[bob]

"2. But, bob says that as a trader he doesn't care about fluctuations in his V(t). I don't think that's right. Suppose bob buys an oil share. Then he learns that gold is a great buy, so he wants to sell the oil share so he can invest in gold instead. Nothing wrong with the oil share, no bad news, same expected P(t) of oil. But bob's personal V(t) of oil, relative to cash (which he can convert into gold shares) has just fallen below P(t), so he sells oil. Or bob faces a margin call on his oil shares, so his value (need) for cash rises. Those are cases where he cares about the liquidity of his oil shares, that I would model as a fall in bob's V(t) for oil shares."

True, in a way I do have a V that is influenced by my own situation. The price I'm willing to pay for oil depends on the carry cost (storage + foregone interest) minus the usefulness of having the commodity to trade (convenience yield).
This wikipedia article shows how the convenience yield is incorporated as an adjustment to carry cost. High & increasing convenience yield gives spot commodities positive carry (which Krugman never realized)

http://en.wikipedia.org/wiki/Convenience_yield

Because my carry costs & foregone interest tend to be the same as other market actors, that's why I say that I don't really care about my own V(t). My own V(t) calculation for oil may show a higher convenience yield than the market, but that's because I see the convenience yield of oil increasing for all other actors, that it is generally underpriced. If everyone else starts to think that "cash is trash" and oil is the market to be in, the convenience yield will adjust to reflect this, and then I can sell at a profit. So my ideas about carry cost, opportunity cost & convenience yield are still highly related to future P(t). I think this brings out the relationship between convenience yield and bubble-momentum-trading, the cashness of hot assets the Cochrane found..

[bob]

Adam,
Don't wander off to EV! Canada has enough brain drain as it is. I'm trying to only really comment here, as my own little "blog canadian" mercantilist campaign. I hope that some more members of the Canadian brain-drain diaspora find their way back here:)

[Nick Rowe]

If total inventories of oil are zero, backwardation can occur (people want to run down their inventories to negative levels, but cannot.

Is it possible that backwardation can occur even if inventories are above zero? (If so, why?) If you still have inventory, while there is bacwardation, you are foregoing profits. But maybe you think that the backwardation will be even bigger tomorrow, so you keep part of your inventory to take advantage of even bigger profits tomorrow?

If this explanation makes sense, then the "convenience yield" is really just a proxy for the possibility of even greater potential profits from having strictly positive inventory tomorrow.

In the limit, as the probability of future inventory being lower than today's goes to zero, the size of inventory goes to zero. (If it didn't, and you always had some unused inventory, you could make a profit by selling it, to save the carry costs.)

I'm not sure if the convenience yield concept is like the liquidity premium. Money is special, because it is the most liquid of all assets, so all other exchanges of one asset for another asset go through money, the medium of exchange. Only oil can serve as oil; only wheat can serve as wheat; but you can only trade oil for wheat via money. Dunno. It depends how far you want to push the analogy between convenience yields and liquidity yields.

[Reggie]

I think that I have the answer. It is that you dont know how much value you are going to get out of futures. That is sort of because you dont know what your opportunity costs are going to be. So the risk of investing in futures is the scale of this uncertainy.