Laying a Solid Foundation for My Theory of Asset-Pricing


In the comments my previous post concerning my theory of asset prices – comments that have, I should add, been extremely productive so far – Nick Edmonds raised some questions as to whether I was dealing with stocks and flows. After a bit of back and forth I realised that what we were dealing with touched on some of the fundamental problems that I noticed with my theory just prior to publication. Therefore, in this post I am going to lay out in very clear terms exactly what we are dealing with and then briefly consider what implications this slightly altered approach has for one of my key conclusions – namely, what I have termed ‘the paradox of speculative profits’.

First and foremost there was some confusion about what I meant by ‘financial saving’ in the paper. I’ve decided that the best way to approach this is to work with my original intuition: financial saving will be any income accrued through the sale of financial assets. As the original paper already stated (note that government includes the central bank here),


What that means is that if I, say, take out a loan of $100 and buy $100 worth of assets from you my investment causes an equivalent rise in your savings. The same is the case for government purchases of financial assets and any taxes levied on these assets. All this is basically identical to the typical Keynesian macro-aggregate identity. Are we talking about stocks or flows? Well, we can talk about either so far as I can see.

So, how might we calculate this build-up in financial savings? Well, let’s take it from a stock point-of-view. Let’s also pretend that all assets are bought using borrowed money to avoid the problems that arise from buying assets using already existing savings. We can put down a simple formula to calculate this (note that for the rest of this post I will ignore the government side to avoid complications)**.


What that means is that financial savings/investment is equal to the sum of all realised bid prices. In order to conceptualise this it is probably best to give an example. Imagine that in a given period we have three distinct bids for an asset. These run as follows,


What this means is that there was three distinct sales of a financial asset in our imagined economy – it doesn’t matter whether this was three sales of the same asset or three sales of different assets of the same type. The sum of all these realised bids will be the amount of financial savings/investment in our economy; in this case, $330.

Now, there is also a different variable that we must consider to fully understand the dynamics here: namely, the final value of the asset in the final period. As Ramanan pointed out in the last post’s comments, this is something like the capital gains from a rise in the price of an asset. At the end of our period it is clear that the asset has risen from $100 to $120. The end value of all assets – i.e. the rise in capital gains – will be the number of assets outstanding times the final realised bid price. Or,


Let us imagine now that in our hypothetical economy there were only three of the asset in question. That means that the total end period value will be $120 times 3 or $360. This, again, is a final stock measure.

Now, how does this relate to my theory? Well, it should be clear that the final realised bid price in a given period is equal to the price level generally. So, we can now convert what we have laid out into the language of my article (note that I am dropping the small delta elasticity variable and no longer equating price with financial savings/investment – this relates to the flaws I pointed out in my original post),


We already know, of course, what the formula for this price on the demand side is. So, we can now put this in here (note that I am introducing time periods to make the exposition clearer),


While this is certainly a fairly substantial revision of the theory – one, in part, that I had been considering when I published the paper – most of the results obtained in the original still hold, albeit in a modified form. The paradox of speculative profits, for example, will now be dependent on the price expectations that each investor had at each successful bid. Thus, in contrast to how I originally formulated the theory, there will no longer be an aggregate of “average expectations” and so forth. Rather, each successful bid will have its own specified version of equation 1.5. I will discuss this in more detail in a forthcoming post.

While I think the above framework is much clearer and consistent than what I originally laid out and also avoids the problems that I noted when I published the paper it is by no means complete. The other variables – taking account of supply-side effects and ‘real’ demand-side effects for ‘impure assets’ – must be added in and I am still working out how to do this properly. The above, however, provides a firmer base from which to do it.

Comments welcome, as always. They were rather helpful in forcing me to write out the above in detail. I appreciate that as, until now, I have been working on this completely on my own and while I think I have most of the intuitive problems solved formalising these is very difficult to do without the criticism that spurs clarification and the illumination of errors.


**Apologies in advance for any poor use of algebra. Input welcome on this front.


About pilkingtonphil

Philip Pilkington is a macroeconomist and investment professional. Writing about all things macro and investment. Views my own.You can follow him on Twitter at @philippilk.
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15 Responses to Laying a Solid Foundation for My Theory of Asset-Pricing

  1. Oliver says:

    Maybe I missed out on your original definition, but this: What that means is that if I, say, take out a loan of $100 and buy $100 worth of assets from you my investment causes an equivalent rise in your savings. does not seem in line with conventions. If I sell you an asset worth $100 for $100 in bank deposits, my savings haven’t changed. Neither have yours, for that matter. You just added $100 in assets to $100 in new debt. Net change = 0.

    • Think it through. How does net saving increase in the real economy? If investment = savings (I = S) does this mean that net savings cannot change because if already existing savings are used to finance investment then there is no net changes and if investors take on debt to finance investment there is no net change because of an offsetting liability? Does that mean that there is no such thing as net savings?

      • Oliver says:

        I can only recite what little I know, but I’d be glad if one of the accountants came to my (or your) rescue:

        saving = income not spent on consumption. income = (new) output. So saving is income not spent on the consumption of new output. Or, put differently, saving leaves output unconsumed = investment. In your example above, nothing new was produced. So neither saving nor investment took place, nor was income generated which to save from.

        Another example: if you borrow $100 to commission a painting from me, you have then invested those $100. The $100 have financed a corresponding new asset. To me, those $100 are income (corresponding to my output) which, if I do not spend them on consumption, are saved. I can buy another asset with those $100 and I still have $100 worth of savings.

        In any case, assuming for a minute that my accounting is correct, it does leave your example unexplained. The ‘investment’ you describe is an act of speculative financing after which there are $2 of financial claims circulating for every 1$ worth of real asset. My claim is, that it is the difference between your example and mine, namely the duplication (or even multiplication) of claims against real assets, that marks the departure point from fundamental value to asset price inflation.

    • NeilW says:

      Phil’s savings have changed. *Prior* to the loan he didn’t have any assets or liabilities. The created bank deposit was his initial asset, which he then swapped with you.

      The start position is

      Assets $0, Liabilities $0

      Assets $100, Equity $100

      Assets $0, Liabilities $0

      The end position is

      Assets $100, Loans $100

      Bank Deposits $100, Equity $100

      Loans $100, Bank Deposits $100

      See how the balance sheets have expanded, and although the net change is zero (because it always is), the dynamic circulation has increased. Without that loan, the asset swap transaction would not have taken place.

      The bank increased the liquidity of the system and allowed economic activity to happen.

      Before the loan, the actual *market* price of your assets was zero, because there was no bid. You *expected* $100 however. The bank enabled the bid, and confirmed the expectations.

      • Oliver says:

        I disagree.

        By your account, I could just borow money from the bank to save. Apart from the fact that that is absurd, it also violates the definition of saving because saving can only come from income. And borrowing money from a bank without corresponding output does not generate income. Further, before the loan, the book value of the house is not 0. If you own a house and fill out your tax return, you have to enter the book value of that house. After selling the house, that book value is then exchanged for a deposit which you must also declare (not that the two can’t differ).

        What I’m basically saying is: money =/= income. In Phil’s example, the amount of money has increased (expansion of balance sheets, as you say) whereas the amount of income, and thus saving, hasn’t.

      • You’re both correct — well, sort of. Neil, you should also include the central bank operation to increase the money supply. Oliver, you’ve sort of missed the point. What I call financial saving and investment does not add to aggregate demand/real income/output. That is why I count it separately. In the original paper I write,

        It should be noted that the standard national income identities measure aggregate demand and national income; while this is true of the ‘real’ variables introduced later in our approach it is not true of the financial asset variables. These components generate only financial income and are not to be thought of as being included in, for example, measures of gross domestic product or aggregate demand. (p28)

      • Oliver says:

        I suspected as much, hence the disclaimer in my first reply. I admit I only skimmed your paper…

      • Sure. I assume you see the importance of taking into account financial income though, right? It has effects on real income through the wealth effect and also through the effect, for example, rising asset prices have on home construction.

      • Oliver says:

        If you’re interested, the proponents of the Theory of Monetary Emissions (Rossi, Cencini, Gnos, Schmitt etc.) make the same distinction as you do. What you call financial income they call money, as opposed to income that has a real world counterpart. I was arguing along their lines. There’s a good interoduction to the theory in the Handbook of Alternative Monetary Economics by Arestis & Sawyer which one can download for free somewhere in the internet.

      • Interesting. I may check that out and do a post on it. Thanks.

      • Oliver says:

        I assume you see the importance of taking into account financial income though, right?

        Absolutely! I’m just not sure income is the right word. But then, there always seem to be too few words for too many, often conflicting, concepts.

      • Well, when I liquidate an asset I certainly view the money I receive as income. I can spend it just as well as that which comes from my paycheck.

      • NeilW says:

        ” Neil, you should also include the central bank operation to increase the money supply.”

        There is no such operation unless the deposit moves banks.

        I was keeping it simple.

      • NeilW says:


        Yep. The plague of these discussions are humpty dumpty words. Everything is loaded with context and the first ten hours of the discussion is agreeing on terms.

  2. William Allen says:

    Reference URL for Hanbook by Arestis et al

    Click to access %5BPhilip_Arestis,_Malcolm_Sawyer_(editors)%5D_A_Handb(

    I am so happy to find this on the web for free as my book budget for this year is used up! Funny thing, this makes me more likely to purchase more recent books on topics/authors I find interesting… Hear that Mr Edward Elgar?

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