If you are new to this blog, you are invited to read first “The Largest Heist in History” which was accepted as evidence and published by the British Parliament, House of Commons, Treasury Committee.

"It is typically characterised by strong, compelling, logic. I loosely use the term 'pyramid selling' to describe the activities of the City but you explain in crystal clear terms why this is so." commented Dr Vincent Cable MP to the author.

This blog demonstrates that:

- the financial system was turned into a pyramid scheme in a technical, legal sense (not just proverbial);

- the current crisis was easily predictable (without any benefit of hindsight) by any competent financier, i.e. with rudimentary knowledge of mathematics, hence avoidable.

It is up to readers to draw their own conclusions. Whether this crisis is a result of a conspiracy to defraud taxpayers, or a massive negligence, or it is just a misfortune, or maybe a Swedish count, Axel Oxenstierna, was right when he said to his son in the 17th century: "Do you not know, my son, with how little wisdom the world is governed?".

Tuesday, 21 July 2009

On capital requirement v loan to deposit ratio



(This is a technical article justifying the assertion that if banks are lending with loan to deposit ratio above 100% then no capital requirements are going to prevent the financial system collapse.)

The banks are lending with loan to deposit ratio (L/D). Their balance sheets grow at exponential pace adding X*L/D^n at each deposit multiplication cycle, where X is an initial deposit. The value of the balance sheets at some point in time equals the sum of values at each cycle over a number of cycles from initial deposit until this point in time plus the initial deposit.

The regulatory approach is that banks should hold a certain fixed percentage of the value of their balance sheets as a reserve (R).

1. "Fractional-reserve banking" - case of loan to deposit ratio < 100%, i.e. in fraction representation L/D < 1

(Please note that R is also represented in fraction rather than percentage.)

If a L/D is below 100% (in a deposit multiplication) then the value of banks’ balance sheets at cycle n is represented by a formula: X*((1-L/D^n)/(1-L/D)). Accordingly the upper limit of the value of banks’ balance sheets generated from initial deposit X is X*(1/(1-L/D)), i.e. it is finite.

Let us assume that reserve R is required by a regulator. Then the difference between banks’ balance sheets and the reserves is X*((1-L/D^n)/(1-L/D)) – R* X*((1-L/D^n)/(1-L/D)), i.e. (1 – R)* X*((1-L/D^n)/(1-L/D)). Therefore the upper limit, i.e. when n tends to infinity, is (1 – R)*X*(1/(1-L/D)), i.e. it is finite.

It should also be noted that the difference between a loan given out and reserve generated, according to a prevailing requirement, at each deposit multiplication cycle tends to zero.


Blue line shows growth of balance sheets at L/D = 90%

Red line shows growth of reserves at L/D = 90% and R = 20%

Green line shows the growth of difference between balance sheets and reserves (i.e. balance sheets not covered by reserves) at L/D = 90% and R = 20%

Please note that L/D = 90% generates automatically a reserve 10% so another 10% would have to come from something else.

2. "Depleting-reserves banking" - case of loan to deposit ratio > 100%, i.e. in fraction representation L/D > 1

(Please note that R is also represented in fraction rather than percentage.)

If a L/D is above100% (in a deposit multiplication) then the value of banks’ balance sheets at cycle n is represented by a formula: X*((1-L/D^n)/(1-L/D)). Accordingly there is no upper limit of the value of banks’ balance sheets generated from initial deposit X since X*((1-L/D^n)/(1-L/D)) tends to infinity.

Let us assume that reserve R is required by a regulator. Then the difference between banks’ balance sheets and the reserves is X*((1-L/D^n)/(1-L/D)) – R* X*((1-L/D^n)/(1-L/D)), i.e. (1 – R)* X*((1-L/D^n)/(1-L/D)). Therefore there is no upper limit since (1 – R)*X*((1-L/D^n)/(1-L/D)) tends to infinity.

It should also be noted that the difference between a loan given out and reserve generated, according to a prevailing requirement, at each deposit multiplication cycle tends to infinity. It is practically very important, albeit irrelevant matter in this analysis, where this reserve is going to come from if L/D is above 1.


Blue line shows growth of balance sheets at L/D = 160%

Red line shows growth of reserves at L/D = 160% and R = 20%

Green line shows the growth of difference between balance sheets and reserves (i.e. balance sheets not covered by reserves) at L/D = 160% and R = 20%

The green line shows the growth of a pyramid scheme in the banking system despite the compliance with 20% reserve requirement.

Please note that when L/D is above 100% there is no reserve generated from a deposit multiplication cycle, so 20% reserve would have to come from something else. But this issue is irrelevant to this proof.

ANALYSIS:

It does not matter how large R is, even if it is ridiculously high like 99.999999%, this would only slightly slow the growth process, as 0.000001% coefficient of exponential function a^x (where x > 1) makes very little practical difference compared if R was 0%. It is still a pyramid scheme.

The difference between banks’ balance sheets and reserves grows to infinity at exponential pace. when L/D is above 1. Such process constitutes a pyramid scheme that is bound to collapse. Therefore even assuming that banks’ reserves are as good and as liquid as cash, since the difference between banks’ balance sheets and reserves grows without any upper limit at exponential pace, no fixed R (even 99.999999%) will prevent a pyramid building.

Consequently even assuming that banks reserves are as good as cash (or cash only) banks balance sheets are turned into toxic waste by lending with loan to deposit ratio above 100% since if it were not the case, the difference between banks' balance sheets and reserves would grow to without any bounds to infinity at an exponential pace (which is not possible).

If banks are lending with loan to deposit ratio (L/D) above 100% the financial system will still collapse being a pyramid scheme, regardless of how arbitrary high the reserve requirement (R) is and the banks’ compliance with it.

NOTES:

1. Please note that this proof does not even rely on the fact that banks’ reserves were turned into a toxic waste.

2. It is in my view criminally negligent that financial professionals responsible for running and oversight of the system especially regulators like Lord Turner do not appear to have a slightest clue about such basic and rudimentary arguments. A reader is invited to draw his/her own conclusions on the future of the financial system and indeed the economy.

3. The case of loan to deposit ratio equal 100% is left to an interested reader.

4. I would like to thank Stuart AJ, whose inquiry prompted finalisation and improvement of this proof.

15 comments:

  1. (This is a technical article justifying the assertion that if banks are lending with loan to deposit ratio above 100% then no capital requirements are going to prevent the financial system collapse.)pengar snabbt

    ReplyDelete
  2. Each color represents a financial entity: loan, deposit, etc. Cells with the same color represent two views of the same entity, freecreditreport

    ReplyDelete
  3. This is surely a very good blog, thanks a lot for sharing such nice information here.payday loans online for virginia

    ReplyDelete
  4. Once you make a loan, you will be able to post a comment on the lending page, and that will be sent via SMS to the borrower buy perfect money e-voucher with credit card

    ReplyDelete
  5. This website is really very interesting and helpful. I save this and revisit tomorrow. loans no guarantor

    ReplyDelete
  6. Loan Express Limited is a registered and authorized loan company, they offer loans to all blacklisted citizen, no credit check, same day approval and instant pay out. they are interested in your financial well-being.
    Qualification:
    1. Blacklisted can apply
    2. No credit check
    3. Debt review or court order can apply
    4. ITC can apply
    5. Low credit score can apply.
    Home Loans up to R2M
    Personal Loans of Up to R450 000
    plus Debt Consolidation Loans of Up to R1,000,000
    Business Loans of Up to R10M
    Payday Loan up to R80 000
    Interested Applicant should reply to this advert by emailing them at: [ infoexpresslimited@gmail.com ] and you will be surprise the way they will attend to you within 5 minute.
    Good,, Bye to Debt & Poverty. This is Quick cash that help me, they can help you too!!! I was blacklisted,, so they can help you too

    ReplyDelete
  7. The need for emergency funds in certain situations is what has kept payday loans online in business helping people will small financial problems. Unfortunately, negative reviews speak louder than positive ones but a few benefits of these types of loans are: 1 000 dollar loans online

    ReplyDelete
  8. I am Sam McNally. We Are Currently Offering Private,
    Commercial and Personal Loans with very Minimal annual Interest
    rates as Low as 3% within a 1 year to 30 years repayment duration
    period to any part of South Africa. We give out loans within the minimum
    range of R5,000 to the maximum of R500,000,000,00 ZAR. Our loans are
    well insured for maximum security is our priority.

    * Are you financially Squeezed?
    * Do you seek funds to pay off credits and debts
    * Do you seek finance to set up your own business?
    * Are you in need of private or business loans for various purposes?
    * Do you seek loans to carry out large projects
    * Do you seek funding for various other processes?

    If you have any of the above problems then contact our customer
    service (info@amazinggracefinancialloan.co.za) We can be of
    assistance to you but I want you to understand that I give out my
    loans at an interest rate of 3%.

    * Borrow any amount up to R500,000,000 ZAR
    * Choose between 1 to 30 years to repay.
    * Choose between Monthly and Annual repayments Plan
    * Flexible Loan Terms.

    E-mail:info@amazinggracefinancialloan.co.za
    Company: Amazing Grace Financial Loan
    Company reg. no.: 69376238
    Legal Reg.: 2012-083148-07

    ReplyDelete
  9. Quick No Credit Check loans up to R4,000,000.00,Apply now

    You are welcomed to CASH FLOW FINANCIAL SERVICE,Our obligation is helping the needy to gain financial stability in order to meet with the demands of living.
    We give out loans from the range of 10,000Rand to 4,000,000Rand, at 3% interest rate Our loans are well insured and maximum security is our priority, Cash flow LOANS is a legitimate and well known lending company based in SOUTH AFRICA.

    We offer loans to individuals as well as organizations who have intentions of renovating houses and institutions, debt consolidation, re-financing and also establishment of business outfits. We give out our Loan in an currency of your choice.Please email us at:(info.cashflowfinance@gmail.com) for an application form.

    * Are you financially Squeezed?
    * Do you seek funds to pay off credits and debts
    * Do you seek finance to set up your own business?
    * Are you in need of private or business loans for various purposes?
    * Do you seek loans to carry out large projects
    * Do you seek funding for various other processes?

    We offer the following types of loans:

    *Commercial Loans.
    *Personal Loans.
    *Business Loans.
    *Investments Loans.
    *Development Loans.
    *Acquisition Loans .
    *Construction loans.
    *Business Loans And many More:

    Requirement Needed For Loan To Be Approved.

    1. Copy of ID
    2. Proof of Residence
    3. 3 months bank statement

    Qualification:

    1. Blacklisted can apply
    2. No credit check
    3. Debt review or court order can apply
    4. ITC can apply

    Your Satisfaction and Financial Success is Our Aim.We are hoping to hear from you soon
    Please email us at: (info.cashflowfinance@gmail.com) for an application form..
    All replies must be to that email above. Thanks and stay bless

    ReplyDelete

  10. We are muslim Organization formed to help people in needs of helps,such as financial help. So if you are going through financial difficulty or you are in any financial mess,and you need funds to start up your own business,or you need loan to settle your debt or pay off your bills,start a nice business, or you are finding it hard to obtain capital loan from local banks,contact us today via email (powerfinance7@gmail.com) So do not let these opportunity pass you by because Allah is the same yesterday, today and forever more. Please these is for serious minded and Allah fearing People.

    LOAN APPLICATION FORM
    **********************
    1) Full Name:.....
    2) Gender:........
    3) Loan Amount Needed :...
    4) Loan Duration:...............
    5) Country:.......
    6) Home Address:..
    7) Mobile Number:.....
    8) Occupation:....
    9) Monthly Income:......
    10) Salary Date:....
    11) Purpose of loan;...

    Awaiting your swift response.
    May Allah bless you.
    IBRAHIM MUSA
    Leverage Pvt Ltd.
    Associate Director
    power Financial Service Pvt.
    Contact Us At :powerfinance7@gmail.com

    ReplyDelete
  11. Hello All

    I am Fredrick by name, and am a very simple man. I give out loans with a very low interest rate of 3%. I give out all kinds of loan in which you need.

    I need only serious applicants, so don't come here and play with my business.

    Feel free to contact us today through our email address and Whatsapp Number Below:

    Email: fpadoin@yahoo.com
    WhatsApp: +2347059073801

    I kindly wait for your Application
    fpadoin.m@gmail.com
    +2347059073801
    Fredrick Padoin Manson

    ReplyDelete
  12. I will instantly grab your rss feed to stay informed of any updates.
    Samuel

    ReplyDelete
  13. We are really grateful for your blog post. You will find a lot of approaches after visiting your post. Great work
    loanmoney.com.sg

    ReplyDelete
  14. Pretty good post. I just stumbled upon your blog and wanted to say that I have really enjoyed reading your blog posts. Any way I’ll be subscribing to your feed and I hope you post again soon. Big thanks for the useful info.
    www.loanmoney.com.sg/

    ReplyDelete
  15. This is a great inspiring article.I am pretty much pleased with your good work.You put really very helpful information. online installment loans

    ReplyDelete