Friday, 28 June 2013

Bank Capital and Derivatives



I've spent a bit of time recently thinking about how to model banks empirically and have come to the conclusion that it's quite difficult.  There are a number of theoretical models around, which do a good job of illustrating the connections between capital, lending, reserves and rates.  It's a useful exercise to play around with these and they are helpful in understanding the way these things are related.  I've particularly looked at the role of bank capital, as it has been crucial in shaping bank behaviour before and after the global financial crisis.

However, it get's much harder once you start to look at actual data.  There are various problems that emerge, but one of them struck me as quite interesting because it played an important part in the crisis itself.  This is the transformation of banks' balance sheets that has accompanied the growth of credit derivatives and the associated impact on the relationship between bank capital and risk.

A consultative document released by BIS this week on the revised leverage ratio framework makes some attempt to address this issue, but there are some good insights into the problems with the old capital framework in this report, particularly Annex 1.  This latter report deals with capital adequacy treatment of trading book transactions.  It is useful to elaborate on the distinction between banking book and trading book for regulatory capital purposes, as it helps explain one of the key ways in which derivatives contributed to the crisis.

The banking book covers loans.  Banks are required to hold capital based on the outstanding amount of loans on the banking book.  For most of the period prior to the crash, the amount of capital required for a given loan principal was based on some fairly simple rules, under which loans fell into one of a small number of different categories.

The trading book covers the bank's trading activities (obviously), where the bank may be taking positions in various markets, such as currency, equities and interest rates.   Capital is required against (amongst other things) market risk - the risk that market movements will lead to a loss.  Because trading positions are generally short term, capital is typically calculated on some estimate of possible market movements within a short time frame (a few days).  The idea is that because the positions can be traded and the bank has staff actively managing the position, the risk can be substantially mitigated by unwinding positions if the market moves adversely.

From around the beginning of the last decade, there was a massive growth in the market for traded credit, facilitated by the increased use of asset securitisation and of credit derivatives.  The use of these instruments increasingly enabled banks to hop in and out of counterparty credit positions that would historically have sat on the banking book.  This meant that it became possible to treat these positions as trading positions, subject to market risk based capital measures.

A traded credit position can take many forms.  However, in general the amount of capital required against the risk of a default by the underlying credit is significantly lower than that required on the banking book.  This makes sense as, in a very meaningful way,  there is less risk on the trading book.  Assets on the banking book sit there till maturity which may be many years.  The risk of things going wrong is much greater over several years than it is over a few days.

This difference in capital treatment created significant incentives to develop the traded credit market.  There were other reasons as well, notably the ability to sell assets to investors who were restricted to holding rating paper.  But for banks, traded credit was able to generate much higher returns on capital than could be earned on the banking book.  This tended to lead to more capital being allocated to traded credit and more and more credit risk being repackaged into tradable form.  At the same time, the reduced capital requirement meant that the same amount of capital was able to support greater and greater risk positions.  This fuelled a demand for more and more assets, pushing banks to take on credit risks that might otherwise have been unacceptable.

Notwithstanding the lower level of risk on traded assets, there is obviously a big flaw if you look at it from a system-wide point of view.  From a single bank's perspective, risk is reduced if they can exit a position quickly.  But the risk is still in the system and if everyone wants to exit at once, there's nowhere to go.  The risk assessment measures used to evaluate capital requirements were based on normal market conditions and did not adequately cover the more remote risks, including the possibility of the market seizing up.

The problem is that risk is not a linear quality.  One position can be unequivocally less risky than another in one sense, but be just as risky in others.  For example, if I were to place my life savings on the favourite to win the Derby, that would be less risky than if I placed it on a 100-1 outsider.  But there's also clearly a sense in which it just as risky - I still stand to lose my life savings.

An overwhelming proportion of bank losses in the financial crisis were realised in traded credit positions (or positions originally on the trading book and transferred when the markets seized up).  Of course, this is only one of a number of factors behind the financial crisis and it would be a mistake to look for a single cause.  However, the explosive growth of the traded credit market, facilitated by the development of credit derivatives and asset securitisation, was an important element in what happened.

Friday, 21 June 2013

The Short Rate, the Long Rate and the Exchange Rate



Reading about the market reaction to Bernanke's comments on a possible end to monetary stimulus, I was interested to note the appreciation of the dollar being generally attributed to associated expectations of a rise in dollar short rates.

Whilst this may indeed be the case in this instance, it's a good opportunity to highlight that there are two quite distinct reasons why we might expect an announcement on asset purchases to have this effect on the exchange rate.  It would be quite reasonable to expect an exchange rate impact, even if expectations of short term interest rates remained anchored.   The mechanics behind this are closely related to the way I have looked at Modelling QE.

For this type of analysis, it can be useful to think in terms of expected single period rates of return.  To simplify, we can think in terms of two asset classes: deposits, carrying a short rate of interest and bonds with a long rate.  For our single period, the return on deposits is known, but the return on bonds is not, because the latter depends on how the bond price changes in the period.  We therefore need to use an expected return, based on what the bond price is expected to be at the end of the period.

In the simplest models, the actual return on deposits and the expected return on bonds will be equal.  The assumption is that if they were not equal, investors would keep trying to switch their portfolios until the change in demand drove the expected returns into line.

This assumes that the two assets are perfect substitutes, but in reality there are plenty of reasons for believing they are not.  More sophisticated models will recognise that the two rates will typically be different.  The difference might be attributed to a liquidity premium or a term preference.  For convenience, I am going to call the excess of the expected single period return on bonds over the short rate the term preference (noting that this value could be positive or negative).

The important point here is that  the size of the term preference is a function of demand and supply.  For whatever reasons (often institutionally), there will be some investors that want exposure to long term rates and some that want exposure to short term rates. At the same time the relative supply of short term and long term assets may vary (through QE for example).  This is going to change the value of the term preference.

We can extend this analysis to the long term.  The expected long term return on bonds will be the compound of all the expected single period returns (that is, all the future returns expected now).  The expected long term return must equal the actual return (if a Treasury yields 2% to maturity and I expect it to yield 3% to maturity, I'm clearly mistaken).  In which case, the actual yield on bonds is equal to a compound of:

1. all the expected short term rates from now until the bond maturity; and
2. all the expected values of the term preference from now until the bond maturity.

where, in each case, expected means expected now.

So, when the bond yield changes, it may represent a change in expectations of future short rates, or it may represent a change in expectations of the term preference, or maybe a combination of both.  However, whilst it's possible that a change in asset purchases might not result in any changes to the actual short rate, it is highly unlikely that it will not lead to any changes in the term preference, as that would imply that investors were indifferent between long and short rate exposure.

Therefore, where the bond yield changes in response to an announcement on asset purchases, we know for sure that the expected value of the term preference has changed, but we don't necessarily know what it implies about the expected course of future short rates.

This has all been about changes in the domestic term structure.  How does this relate to the exchange rate?  The important point here is that what matters to the exchange rate is not just the short rate on deposits, but also the expected single period rate of return on bonds.  If investors with long-term rate preference invested exclusively in the domestic market, then this might not matter.  However, this does not appear to be the case; cross-border holdings of long-dated securities are substantial.  The demand and supply for these assets (which has immediate impact on the exchange rate) depends on the single period expected return on long assets, not on the short rate.

In conclusion, an announcement on asset purchases may do two things: it will definitely have an effect on the term preference; but it may also have an effect on expectations of short term interest rates.  These two effects are quite distinct, but both will have an impact on the exchange rate.

Wednesday, 19 June 2013

Sterling Commodity Prices

This graph shows the real cost of commodities in sterling terms, monthly and as a moving average, based on the IMF price index for all commodities.

The fact that this measure remains so high, around 2.5 times its level for the period up to around 2005, goes some way to explaining continued inflationary pressure in the UK in the face of weak wage growth.






Based on:
US$ commodity price index: PALLFNF, source IMF
US$ / £ exchange rate: XUMAGBD, source Bank of England
RPI, source ONS

Tuesday, 18 June 2013

Productive Debt vs Speculative Debt



There is an interesting issue that crops up again and again in discussions about the relationship between debt and GDP.  This is the distinction between debt incurred for real expenditure and debt incurred for purchase of existing assets (whether physical or financial).

On the face of it, the immediate use of new borrowing should make a big difference since it's obvious that the former implies actual GDP spending and the latter does not.  However, if we consider the full stock-flow dynamics, the distinction is less clear.

To look at this we can consider a consumption function, where household spending (C) is a function of disposable income (YD), new borrowing (ΔL) and lagged net wealth (V-1).


                         C = α1 . YD + α2 . ΔL + α3 . V-1                                  0 ≤ α2 ≤ 1

The proportion (α2) of new borrowing used for current spending clearly has an immediate impact. However, a proper accounting framework will require that if any new debt is not spent currently, then net wealth will be correspondingly higher.  In the next period, spending will be greater as a result and will continue to be greater until any difference in net wealth has been eroded.  In its simplest form, the cumulative effect on income will be the same.

The chart below illustrates the impact for a simple model. (A specification of this model is given at the end of this post.).  The chart shows the cumulative effect on income for a one-off permanent increase in the absolute level of loans.

Cumulative GDP (deviation from base-line)
 
The results in the graph above are based on the assumption that the asset allocation of borrowed funds matches that for net wealth.  More precisely, it assumes that if households invest 30% of their net wealth in deposits, then they will also invest 30% of any money borrowed for investment purposes into deposits.  (This is the assumption used in Godley and Lavoie*).  However, in general, people do not borrow money to invest in bank deposits.  The people who hold bank deposits are not borrowers, but people with net wealth.  Where money is borrowed for financial investment, this is much more likely to be for the acquisition of housing or marketable securities.  If we reflect this in our asset allocation assumptions, the results of our simple model show that, in the long-run, debt for asset purchase actually has a greater impact than debt for spending. This is shown below:

Cumulative GDP (deviation from base-line)

This result arises because the debt creates a permanent change in the structure of investors' portfolios. The greater concentration of demand into variable price assets inflates values giving a more sustained wealth effect.

One way to think about this counter-intuitive result is as follows.  In the simple model, with government spending and tax rates fixed, any change in the level of government debt held by the private sector can only come about via differences in national income, since that is the only free variable to affect the new issuance of bonds.  The long-run impact therefore ultimately depends, not on anything that happens currently, but rather on the willingness of the private sector to hold government debt.  In the latter scenario, the decision of households to invest more into marketable securities (including government bonds) has the perverse effect of reducing overall private sector bondholdings, because of the impact of the accounting constraints on banks' balance sheets.

In the real world, there are plenty of factors which could lead to a reverse effect.  For a start, once growth is factored in, the front-loaded impact of borrowing for spending means that it may permanently push income ahead of the curve of the static steady state.  It is also worth noting that the incorporation of yields into the portfolio preference functions will affect the results.

The point I wish to make is simply that the impact of the purpose of debt is a much more complex issue than is at first apparent, and that careful consideration of the full stock-flow dynamics is necessary to really bring this out.




Model Specification

The model is based on three sectors: households, banks and government.  There are four asset classes: Bank deposits, government bonds, household loans and real assets (say, housing).  The last is represented by a quantity multiplied by a price index.  This is shown in the balance sheet matrix below:





Households
Banks
Government
Net
Deposits
D
-D

0
Bonds
Bh
Bb
-B
0
Loans
-L
L

0
Real Assets
k.p


k.p
Net
B + k.p
0
-B
k.p



Banks are assumed to have nil net worth.  This implies that household net worth must equate to total private sector bondholdings plus the value of real capital.

Variable
Definition
B
Government bonds
Bb
Bonds held by banks
Bh
Bonds held by households
C
Consumer spending
G
Government spending
L
Household loans
D
Deposits
V
Household net wealth
Y
GDP
YD
Household disposable income
k
Physical assets
p
Price index of physical assets

Greek letters are parameters.

GDP is consumer spending plus government spending

Y = C + G

Household income is the after-tax share of GDP

YD = ( 1 - τ ) . Y

The household budget constraint determines the change in money.

ΔD = YD - C + ΔL - ΔBh

Household net wealth is assets less liabilities

V = D + Bh + p . k - L

Consumer spending is based on disposable income, new borrowing and lagged net wealth.

C = α1 . YD + α2 . ΔL + α3 . V-1         

Households allocate their gross asset holdings between bonds, real capital and deposits in constant ratios.

Bh = θb . ( V + L )

p . k = θk . ( V + L )

As k is constant, this latter equation is used to determine p.
 
The assumption about portfolio allocation is modified in the alternative scenario.  New spending loans are added back into net assets and allocated as before, but the non-spending loans are assumed to be fully invested in either bonds or real assets, but not deposits.  The portfolio equations are replaced with the following:

Bh = θb . [ V + L0 + α2 . ( L - L0 ) ] + θb / ( θk + θb ) . ( 1 - α2 ) . ( L - L0 )

p . k = θk . [ V + L0 + α2 . ( L - L0 ) ] + θk / ( θk + θb ) . ( 1 - α2 ) . ( L - L0 )

where L0 is the outstanding loan balance at the start of the simulation.  This is treated as before (and assumed to be invested across all assets) to keep the simulations comparable and avoid having to change any parameters or opening stocks values.

Parameter values and opening stock values are given below:

Parameter
Value
α1
0.8
α2
1.0, 0.5 or 0
α3
0.1
θb
0.2
θk
0.5
τ
0.25


Variable
Opening Value
Bh
40
D
60
L
50
V
150
p
1.00

G is set at 25 throughout.  k is constant at 100. ΔL is zero, except for period 2 when it is 10.



*Monetary Economics - An Integrated Approach to Credit, Money, Income, Production  and Wealth, Godley W and Lavoie M, (Palgrave Macmillan) 2012