I start a bank. I have zero capital. I borrow $100 and lend $100. What is the net worth of my bank?
Looking at the balance sheet, the answer is simple and obvious: assets $100, liabilities $100, net worth = assets minus liabilities = $0.
But looking at the income statement we may get a very different answer. If I borrow at 3%, lend at 5%, and have no administrative costs, my bank earns $2 profit per year, which discounted at 5% gives a Net Present Value of $40, so my bank is worth $40.
From the balance sheet perspective, my bank, starting with zero capital, is born on the brink of insolvency. One bad loan would make it insolvent. But from the income statement perspective, 40% of the loans would have to be bad before my bank is pushed to the brink of insolvency.
If I put up $10 of my own capital, borrow $90 at 3%, and lend $100 at 5%, the balance sheet perspective says my bank has a net worth of $10, while the income statement perspective says it has an NPV of $46. If 10% of the loans went bad it would be on the brink of balance sheet insolvency; if 46% of the loans went bad it would be on the brink of income statement insolvency.
If we include the opportunity cost of my own capital, which could be earning 5% outside the bank, the NPV of my bank's net earnings drops from $40 with zero capital to $36 with $10 capital, which shows that the higher the capital ratio the lower the productivity of the bank.
A bank can sometimes be solvent from an income statement perspective, as a going concern, and yet insolvent from a balance sheet perspective. Net worth can be destroyed when a bank is wound up and we switch from an income statement perspective to a balance sheet perspective. An extra dollar of bank capital increases balance sheet solvency by $1, but increases income statement solvency by less than $1, and reduces net worth net of opportunity costs. And for central banks, which pay no interest on their main liability (irredeemable paper money), the balance sheet perspective gives a ludicrously misleading perspective on solvency. That's the main message. It's not new, but sometimes we need to remind ourselves of old stuff.
Banks are different. Any other business can be run without borrowing money, provided the owner has enough of his own capital. The very business of a bank is borrowing and lending money. A bank with 100% capital reserves isn't a bank. A bank with 50% capital reserves is only half a bank. The productivity of a bank is inversely proportional to its capital ratio. That's why banks want to increase leverage. For any other firm, the debt ratio has no obvious effect on its productivity.
My bank is worth more as a going concern than if it were wound up. The same is true of any profitable business. But banks are nevertheless different. The reason why people are willing to lend to banks at 3%, while other people are willing to borrow from banks at 5%, is that bank deposits are liquid, while bank loans are illiquid. That's why banks exist. Their main business is to transform illiquid loans into liquid deposits (OK, they do other stuff too). Liquidity means it can be withdrawn on a whim. On a whim of its depositors, the net worth of a bank can be switched from the income statement perspective into the balance sheet perspective. The service a bank is selling its customers is the right to end that service.
Competition tends to push profits to zero. If I can borrow at 3%, lend at 5%, and have no administrative costs, other people will set up banks like mine. Competition will push up borrowing rates, push down lending rates, or push up administrative costs, until the spread between borrowing and lending rates equals the administrative costs. None of this affects the balance sheet, but it does affect the income statement.
If administrative costs were variable costs, a fixed percent per year of the bank's assets or liabilities, then in zero-profit competitive equilibrium a bank with no capital would have zero net income per year, so the income statement perspective would agree with the balance sheet perspective. The net worth of the bank would be $0, so the individual bank is worth no more as a going concern than it would be if wound up. But many administrative costs will be sunk costs (like building a reputation and customer base or assessing the riskiness of potential loans), and cannot be recovered if the bank is wound up. If sunk costs were equal to the bank's capital, any bank in competitive equilibrium would be on the brink of insolvency if wound up, but would have net worth equal to its capital as a going concern.
Central banks consistently earn large profits. They do not face competition to eliminate the spreads between their borrowing and lending rates. By choosing the rate of inflation, they choose the nominal rate of interest on bonds, and so they choose their own spread. Their main liability, paper money, pays no interest. It is recorded on their balance sheets as a liability, but from the perspective of their income statement, this liability is fictitious, because the present value of the interest payments is zero. A central bank issuing irredeemable paper money, unlike a commercial bank which promises to redeem its deposits, is not subject to the whims of its depositors. Provided all its liabilities can ultimately be redeemed in its own irredeemable paper money (i.e. providing it has no foreign currency or real liabilities), it can never be insolvent from the income statement perspective, even though it could appear to be insolvent from a balance sheet perspective.
If a prudent central bank has paper money as its only liability, invests only in treasury bills, and each year hands over all its interest earnings, minus administrative costs, back to the treasury, that central bank will always appear to be on the brink of insolvency from a balance sheet perspective. But there is no way it could ever go bust. Even if all its assets were toxic waste, and all went bad, it could not go bust. It would just have to print money to pay its economists' salaries.
Take the Bank of Canada for example. From its 2007 Annual Report, we see assets of around $50 billion, liabilities (nearly all banknotes) also around $50 billion, and net worth (capital) of a mere $154.7 million. Clearly the Bank of Canada is very close to the brink of insolvency! But its income statement shows revenues of $2.3 billion, expenses of $268 million, and a profit of just over $2 billion which it handed over to the government. A back-of-the-envelope calculation would give the same answer: 4% interest on $50 billion assets equals $2 billion interest income, minus peanuts for interest and administrative expense, equals $2 billion profit. The net worth of the Bank of Canada is the NPV of $2 billion discounted at 4% which is $50 billion. And that assumes those profits will stay constant. If paper money grows at 4% per year (2% real + 2% inflation), then profits will grow at 4% per year, so the net worth of the Bank of Canada is the NPV of $2 billion, growing at 4%, discounted at 4%, which is er…, infinite.
Even a perfectly accurate, all risks properly accounted for, balance sheet can give a very misleading perspective on a bank's solvency. (And this is quite apart from the question of mark-to-market balance sheet accounting when asset markets are frozen.) We need to look at income statements as well.
All this is mostly just an application of what I vaguely remember from reading Pesek and Saving's (1967) book some thirty years ago, and partly (on central banks) from skimming Willem Buiter's "Helicopter Money" more recently. Brad DeLong makes the same main point, but I think my way of putting it is simpler and clearer (judge for yourself), though that's perhaps because he's making some other points at the same time. It isn't really new. But when we look only at balance sheets to decide whether banks are solvent, it makes me wonder how well and widely it's understood.
Worthwhile Canadian Initiative 
Sorry. I have tried and tried, but can’t get the links to work. Don’t know if it’s me, or TypePad.
Fixed!
Nick,
Very interesting and thought-provoking post – I don’t recall seeing this sort of thing elsewhere.
The purpose of capital of course is to absorb realized risk when necessary. A zero capital bank at the outset is sort of consistent with a zero risk bank. The NPV of net income approach works then as economic value (“fair” or “market” or whatever) for the bank. Of course, there is the small problem of to whom to allocate the profits if there is no capital at the outset. But that can be solved with an uber-leveraged delta risk bank with an epsilon capital cushion (or is it the other way around).
In any event, the economic value of capital will usually trim down those 0 risk cash flows for risk.
I haven’t had time to read the Buiter or DeLong pieces yet. But I did see Buiter’s paper ‘Can Central Banks go bankrupt’. On returning to it, I see how now how he uses NPV of seigniorage as the means of recapitalization by monetization. That differs of course from the balance sheet recap perspective I had referred to earlier, which is why I was confused.
To put a different spin on this subject, perhaps along the lines of your final point, it has occurred to me that suspension of fair value accounting in some way and in some sense would be a way of recapitalizing the US banks over time via their franchise values – i.e. put bad asset accounting on the same footing as franchise accounting – i.e. accrual accounting.
Alternatively, for the same purpose, one could accelerate accounting for franchise value by bringing it into a fair value framework – along the lines of your post – although I must say this is really playing with fire in terms of accounting and risk.
I’d prefer the first approach of the two. It’s a shame that this fair value madness in the midst of market illiquidity is bringing down all these banks in such an accelerated fashion.
Thanks JKH. I was really unsure about whether to post it. I was torn between thinking “maybe everybody already understands it” and “maybe it’s all just dead wrong”. Anyway, it’s up now.
My first example was of a bank with zero capital, but only because this example was simplest and gave the starkest contrast between the two perspectives (zero vs positive net worth). Here’s another way of looking at it: suppose I have some sort of legal monopoly on retail banking in the City of Ottawa (and suppose the Bank of Canada will always lend me money at 3% to cover any run on my bank). Safe from competition, I really can borrow at 3% and lend at 5% indefinitely. And if the Ottawa market is big enough to support $100 of deposits, my bank can go on earning $2 per year forever. The value of my monopoly right is $40, so we can think of that as my capital. Or maybe I was the first bank in town, have already built up a customer base, and it would cost any new bank $0.40 per dollar deposit to do the advertising to steal customers away from me, or maybe I have already paid that $0.40 myself to build up my customer base. It doesn’t matter how I got into this position, and whether it cost me money in the past to bribe politicians to get the monopoly, because bygones are bygones. All that matters is where I am now, and where I am going in the future, and whether I could actually get my past costs back (are they sunk costs?) if my bank were wound up (can I sell the monopoly right to someone else?).
Now, all of the above is also true if I have a monopoly on retail ice cream in Ottawa, and can buy ice cream at $3 and sell at $5. But what is different between ice cream and banking is that people buying ice cream never worry about the solvency of the merchant (I should have said this in the post). The ice cream merchant’s net worth is strictly a matter between him and his accountant. And if banks borrowed for 30 years and lent for 30 years (and just did risk-pooling, not provision of liquidity services) so there was no duration-mismatch, the bank would never have to worry about a run, and being flipped from the income statement perspective to the balance sheet perspective. (Meghan McArdle’s Law: “Money is weird; finance is weird” http://meganmcardle.theatlantic.com/archives/2008/11/invidious_comparisons_1.php )
I don’t understand the last three paragraphs of your comment, which is totally my fault. Like most economists, I have a very limited knowledge of accounting. I don’t understand the difference between fair value and accrual accounting (because I don’t understand either of them). Sorry. Care to elaborate?
Nick,
Very simplified – accrual accounting is basically recognizing cash flow as accounting income while excluding changes in valuation. A bank that holds a performing mortgage to maturity would simply record the interest payments and accretion of discount (or amortization of premium) as income. A bank using fair value accounting would record periodic changes in the value of the mortgage as income as well.
Capital is at risk due to market volatility under fair value accounting. But the cumulative changes in fair value from inception to maturity would be zero, provided there were no actual credit losses. This is what some refer to as a “pull to par” effect whereby cumulative recorded volatility is overwhelmed by the maturing of the asset. (If you ever listen to a CIBC quarterly conference call where they talk about their $ 25 billion CDO portfolio, they will refer to this pull to par phenomenon as the portfolio gradually matures, in trying to explain what’s going on to analysts who are worried about the value of the portfolio.)
Accrual is an old fashioned way of accounting that banks still use for some of their portfolios. But fair value has been imposed for large sections of the balance sheet.
Fair value accounting complicates things considerably. Some have commented that if banks had used fair value accounting through the LDC crisis of the 80’s, the entire system would have gone down. A similar thing is happening now with mortgage securities due to imposition of fair value accounting on complex securities where there is no market. A number of people have come out against fair value accounting in both Canada and the US, pointing to it as an unnecessary catalyst in the severity of the bank capital problem.
Nick,
Please have a look at this posted today:
http://www.bob-mcteer-blog.com/mark-to-market-frustration/#more-346
(Fair value is pretty much the same thing as mark-to-market for purposes of this discussion)
Thanks JKH. That was clear. Sorry for the delay, I was away for 2 days.
I am going to “think out loud”, to try to get my head around this:
Let’s take a couple of simple examples to see how this works.
Example 1: I start a bank with zero capital, borrow $100 at 3%, and lend $100, in perpetuity, at 5%. Then just after I start my bank, the market interest rate on perpetual loans doubles from 5% to 10%.
On an accrual basis, nothing changes on my annual income statement, because I still receive net income of $2 per year. But the NPV of $2 per year in perpetuity falls from $40 to $20. (Note that I am ducking the question of why we should discount the NPV of my bank at the loan rate rather than the deposit rate).
On an accrual basis, nothing happens to my balance sheet also. My capital is still zero. (Is this correct?)
On a fair value (mark to market?) basis, my first annual income statement would show a loss of $48 ($2 net interest minus $50 capital loss on the loans). All subsequent income statements would show a profit of $2 (there is no “pull to par” effect in this example, because my loans are perpetuities, so never mature). The NPV of my income statements would be $2 per year discounted at 10%, which is $20, minus $50 not discounted, because I assume the interest rate went from 5% to 10% immediately), which gives minus $30.
On a fair value basis, my balance sheet shows negative $50 net worth.
On a “what is the truth” basis, my bank is still solvent as a going concern (it can make its annual obligations to depositors), its profitability is unchanged, and the same percentage of loans would need to go bad before it became insolvent (40%). But wound up, my bank is clearly insolvent, and would have a net worth of minus $50.
Conclusion: in this example, fair value accounting gives an accurate reflection of the net worth of my bank if wound up, and a very inaccurate reflection of the net worth as a going concern. Accrual accounting gives a very inaccurate reflection of the net worth if wound up, but an accurate reflection of the value of the bank as a going concern (what someone would pay me for it has dropped from $40 to $20).
Example 2. Same as example 1, but now the interest rate stays the same, but immediately after starting the bank, I learn that 20% of the loans are bad (will pay nothing).
Accrual: Annual income drops to $1 per year, and NPV drops to $20. Balance sheet says net worth drops to minus $20 as the bad loans are written off (correct?).
Fair value: First year’s income is minus $19, all subsequent years $1, NPV of income is $1 forever discounted at 5% equals $20, minus $20 immediate loss, equals zero. Balance sheet shows net worth minus $20.
Truth: As a going concern, my bank is worth $20. If wound up, minus $20.
Conclusion: As a going concern, accrual gives the right answer and fair value the wrong answer. If wound up, both accrual and fair value give the same right answer.
Meta conclusion (from both examples): NPV of present and future income statements based on accrual accounting is correct for a going concern, while fair value is incorrect. Balance sheet under fair value (mark to market?) accounting is correct for a wound up bank, while accrual is sometimes incorrect.
This is interesting. Did I make any mistakes?
JKH: Sorry, but a (semi-) personal question: I know you are not an economist (because you said so, somewhere); are you an accountant/banker (because you seem to be very well-informed on at least some accounting/banking questions, from your comments here and on Maverecon)?
Nick,
I agree with much in your examples, with some exceptions. And I’m not sure I have this right either, because the subject is debatable, particularly in the area of NPV of net income calculations:
Example 1:
On an accrual accounting basis, $ 2 in net interest income would become earnings and also increase capital by the same amount (unless paid out as a dividend).
On a fair value accounting basis, $ 2 in net interest income would be reduced by a $ 50 fair value loss for total earnings of $ (48). Capital would become negative by the same amount.
(Accrual accounting excludes fair value changes from earnings; fair value accounting includes both accrual results and fair value changes. In that sense, fair value accounting includes accrual accounting as a component. The terminology is asymmetric in this sense. The actual accounting treatment for banks is a mix of fair value and accrual accounting, depending on what part of the balance sheet you’re operating in. Bank CFOs have a hellish job trying to reconcile it all.)
Next:
On an NPV income basis, $ 2 in net interest income declines from $ 40 to $ 20 – but I would not subtract the $ 50 fair value loss from that.
NPV net income is typical of an external stock value perspective, as distinct from the internal calculation of income or balance sheet accounting results. The shareholder may arrive at a market value of the bank’s stock (i.e. equity) that is quite different than a formal fair value calculation of equity from an internal accounting perspective, for a variety of reasons. At the same time, the scope of NPV income or stock value is essentially the same as that of FV assets and liabilities – all of these should be comprehensive, albeit perhaps with different (implicit or explicit) risk and valuation parameters. In the case of a publicly traded stock, much is said about the difference between market value and book value, but not so much about the difference between market value and fair value. The NPV of $ 2 income should in theory reflect, translate or transform the net FV balance sheet position. Thus, I wouldn’t recommend combining NPV results with FV results.
I agree generally with your “what is truth” approach, although I think an actual evaluation of going concern value would take into account fair values, projected accrual results, NPV earnings, and actual stock market value to the degree its available (not combining but comparing them).
Example 2 – more or less similar qualifications.
Both examples are perhaps unusual to the extent that they include perpetual cash flow assumptions.
I doubt this does justice to your fairly clear analysis. I’m off for several weeks now, but look forward to returning to your site.
(Re personal: I’m neither an economist nor an accountant, but worked for a considerable time in finance/treasury for one of the Canadian banks.)
Nick,
I wrote:
“NPV of $ 2 income should in theory reflect, translate or transform the net FV balance sheet position.”
I’m not so sure this is right. It may depend.
The examples assume 0 book equity at the start. A normally capitalized firm at the outset would start with positive book equity, which would have some sort of relationship with either market value or the PV of net interest income, although not necessarily 1:1 in the real world. Income generated directly against equity funding is an important component of net interest margin.
The assumption of zero book equity is sort of consistent with a zero risk assumption. In this case, the discount rates for assets, liabilities, and NPV income should all really be the same – the risk free rate – and you have a pure arbitrage situation in terms of the resulting net interest margin. But in that case, the fair value of the assets and liabilities would be different than their book values at the outset. And I think the fair value of net interest income might well be the sum of the other two. Not sure. In any case, any assumption of zero risk would conflict with the portrayal of actual realized risk in the examples.
If you were starting up a bank from scratch with assets booked at 5 per cent and liabilities at 3 per cent, then presumably those would be both the starting book rates and discount rates for market value and/or fair value. Different rates reflect different levels of risk. The discount rate for the net interest margin would be different again, presumably reflecting an even higher risk level, as would normally be the case.