Bank Lending Feedback

As seen in the model developed by von Peter (2009), the existence of capital constraints on the banking system impacts lending. The very fact that banks must fulfill capital constraints causes them to ration lending, which has a feedback impact on the economy. This feedback is included in the leverage calculation.

Lending Feedback Effects on Leverage

The relation (4.37) is only valid if the capital–asset ratio is non-binding. In the (more realistic) case, where the capital–asset ratio is binding, if the capital–asset ratio is denotedC ARand the asset priceqt+1 is less than q∗, then the capital–asset ratio is binding. When the capital–asset

ratio is binding, then, following the von Peter’s (2009) model, the economy will enter a capital crunch. The asset price depreciation now follows the slope of C AR−1_{. So, since q}

t+1 > q∗,

equation (4.37) is still valid, but forq_t+1≤q_∗, the slope becomesC AR−1_.

In summary, there is a bull spread inq_t+1 fromq_∗ toq_e, and then a put with strike q_∗ lever- aged byC AR. To create a bull spread with puts, one needs to be long put with strike q_∗and short put with strikeq_e. The bull spread can therefore be written

B u l l S p r ead = (q_∗H−q_t+1H)+−(q_eH−q_t+1H)+

So, instead of a short put with strikeq_e,

4.3. MACROPRUDENTIAL IMPLEMENTATION 149 one has the bull spread plus the leverage short put inq_∗:

q_∗−qt+1 + − qe−qt+1 + −C AR−1 q_∗−qt+1 +

This mean that one can rewrite (4.37) with the feedback condition as

Kt+1= (1+rt)Kt−(qeH−qt+1H)++ (1−C AR−1)×(q∗H−qt+1H)+

So, by applying the constraint (4.35), that is,E_t(K_t+1) =K_t, one obtains the relation

Et –₁ r_t θe−θt+1 + ™ −(1−C AR−1)×Et –₁ r_t θ∗−θt+1 + ™ = 1 L_t (4.43) whereθ_e =q_e/q_t andθ_∗=q_∗/q_t. Calculation ofθ_∗

The first thing to do is to calculate the value ofθ_∗, whereθ_∗is the value when the capital–asset ratio becomes binding:

θ_∗= q∗

q_t

given the fact that, by definition,

C AR= Kt q_∗H Then θ_∗= 1 C AR K_t q_tH = 1 C AR×L_t

It is also known that

θe =R−

C o po r t at e P r o f i t_t

(1−αHL/H)×BankAs s e t_t−1

So one has everything needed to calculate (4.43).

Numerical Implementation

The calculation is very similar to that in Section (4.3.2) on generalist banks. I takeC AR=8%. The following figure shows the historical volatility of the assets of generalist banks in dark and the implied volatility, using the model described previously in (4.3.4), in clear.

150CHAPTER 4. ASSET PRICE INVOLVEMENT IN MACRO-PRUDENTIAL POLICY

Figure 4.11: Asset Volatility with Feedback: Historical vs. Implied (C AR=8%)

The picture here is more reassuring than the previous numerical implementation for good times, but worse in bad times. This is consistent with the literature, since capital asset requirements make banks more robust during good times but trigger lending rationing during bad times.

4.3. MACROPRUDENTIAL IMPLEMENTATION 151 One notes that the sensitivity to theC ARis strong, as can be seen in the case whereC AR=

7% we obtain the following figure.

152CHAPTER 4. ASSET PRICE INVOLVEMENT IN MACRO-PRUDENTIAL POLICY

As in Section (4.3.3), a volatility criterion is used to define where bank capital should be, but in this case a much lower volatility thresholdσ_L=15% is used, and in the following figure

C AR=8%.

Figure 4.13: Bank Asset Capital Ratio with Feedback: Historical, Implied and withσ_L=15%

One observes that this choice of threshold is often stricter than the conventional capital–asset ratio.

4.3.5 Intermediate Conclusion

A macroprudential model is developed that says if the banking system capital is to be kept stable, a link exists between inflation or the returns of the asset collateral of bank loans and the overall banking system’s leverage. Since one of the aims of financial macroprudential policy is to keep bank capital stable, this model can help define ideal levels of aggregate leverage. This model may be important, since it addresses one of the oldest issues with asset price bubbles, as described in the historical analysis by Kindleberger & Aliber (1996): rapid credit extension that leads to asset price bubbles that ultimately burst, depreciating asset prices. With the tool developed here, macroprudential regulators may have ways of estimating what asset bubbles are a direct risk to

4.3. MACROPRUDENTIAL IMPLEMENTATION 153 the financial system and how to quantify them.

This model shows how to develop a tool that sets a maximum volatility with which the banking system should be able to cope. As soon as the set level of volatility σ_L has been publicized, this tool acts as a rule to limit the level of leverage within the banking system. This has all the benefits of a rule-based system—for example, predictability—but it also provides good incentives for banks to avoid concentrations of collateral assets. Banks look forward, and if they diversify their collateral assets, their overall leverage will not be impacted.

This is only one tool, among many, to define what should be the ideal level of aggregate leverage, since it only helps to take into account the damages that can cause asset price bubbles. This tool does not replace overall leverage limitations, since in quite a few cases of the numerical examples previously shown the ideal leverage this tool gives is infinite. This tool can be use in conjunction with the standard maximum level of leverage, which protects, for example, against the underes- timation of risk.

This link between collateral assets and financial stability is critical, now more than ever, be- cause of the expansion of securitization. The amount of securitized products is a very well documented issue in terms of the opacity of pricing and creating liquidity, but this thesis notes that it has also increased the cost of crises. This leads to the recommendation of greater trans- parency and more information to assess the systemic importance of securitized products.

The main limitations of the tool developed here is that it is based on option pricing, with all its pertinent issues. I implement pricing with both short- and long-tailed probability densities as examples, but this pricing is always dependent on the density used. More work needs to be done on this subject to determine the probability density that best fits this phenomenon. Another op- tion pricing issue is the use of expected future asset inflation: If future asset inflation is estimated incorrectly—which is what happened with real estate prices—the option pricing is also incorrect.

Another limitation has to do with the fact that the model developed here has only two assets; in reality, loan collateral can be of many different types. The solution obtained in this section to

154CHAPTER 4. ASSET PRICE INVOLVEMENT IN MACRO-PRUDENTIAL POLICY

carrying out an empirical investigation is to use an index that summarizes actual loan collateral assets. It is not clear that this is the best possible approach to investigate this kind of bank risk, since future price expectations and volatility are not asset specific but, rather, index related. A possible approach is to find a way to assign a specific future price expectation, volatility, and probability density for each type of asset. This would in itself be a possible future contribution.