# Pbr and roe relationship

### The ABCs of bank PBRs: What drives bank price-to-book ratios?

ROE = Return on Equity. CoE = Cost of (Equity) Capital g = Long Term Growth Rate. The above equation – also known as the “Net Asset Value. We find that in terms of prediction accuracy, PBR is the best, while in portfolio . with the definition of ROE=EPS0/(Book value of equity), PBR equals {[ROE*( Payout .. Basu, S., "The Investment Performance of Common Stocks in Relation to. Apply clean surplus relationship to DDM and rearrange terms. ▫ Various multi- stage versions of the DDM. – 3 stages model growth, steady state and decline gk.

I think this is correct to a first approximation. But different financial companies experience different financial results; they have different ROEs. How sustainable are those different ROEs? ROEs tend to revert to mean; competition drives that. How fast ROEs revert to mean derives from the length of the businsess written.

You have the first equation wrong, it should be: Second, if you did that the a and b would be different, because regression minimizes the squared differences of the dependent variable actual versus expected.

So, with respect to what I said above, I would not do the math your way. Dividing and differentiating by ROE neglects the meaning of the original equation. All models are just that, models. So, I can answer your second question, but not your first question. Such would be true with long duration coverages like in the life industry.

The reason the life industry is different is that the companies with high ROEs are expected to maintain those high ROEs for a longer period of time, because coverages are long, and pricing adjusts slowly.

With other insurance coverages, pricing adjusts annually or nearly so. For a life company with a low ROE, the adjustment will happen slowly, or it may never happen. Perverse dynamics kick in when a company with long-tail coverages finds itself earning very little to nothing. Short accruals get validated every year. If you were an actuary inside the long-tailed life insurer, you would get some data telling you that your assumptions were optimistic, right, or pessimistic.

But it takes a while to figure out whether the last few years are a deviation or a trend. Good actuaries dig in, and look at the causes for claims, trying to see if the reasons for policyholders making claims matches up with the original estimate of what the subject population would be likely to die or have disability or LTC claims from. Too many abnormal claims may imply that the business has been underwritten wrong, and needs to be adjusted.

That analysis takes some doing, because long-tail life coverages are low-frequency and high-severity. Following the Great Financial Crisis GFCprofitability has been hamstrung by a protracted period of tepid economic growth, muted demand for banking services, unusually low interest rates and flat yield curves.

Now that near-term economic prospects have brightened substantially, the outlook for banks' bottom line is finally improving. Client demand is rising and intermediation margins are starting to widen, supporting revenue growth. As a result, following the recent finalisation of the Basel III package of regulatory reforms BCBS a and given the progress that has already been made in complying with the new capital and liquidity requirements BCBS ba window of opportunity is opening up for banks to finalise their adjustment to the new post-crisis environment BIS Despite this improved outlook, however, price-to-book ratios PBRs remain low for many banks, especially in Europe.

The PBR is the ratio of the market value of a bank's equity to its accounting, or book, value. On this basis, PBRs are often thought of as a yardstick of franchise value - that is, investors' expectations of how much shareholder value the company's management will be able to create from a given stock of assets and liabilities. As such, PBRs are also an indicator of banks' health and their ability to support economic activity.

What explains these stubbornly low valuations, and what - if anything - can be done about them? Are the sources of post-crisis bank valuation much different from the pre-crisis ones? And, if so, could tighter bank regulation be responsible for the lower post-crisis valuations?

This special feature seeks to answer these questions by analysing the drivers of bank PBRs. We find that, while current bank PBRs are indeed rather low, they are not generally out of line with what would be predicted from our valuation model, which is estimated on a sample based on both pre-and post-GFC data.

With some of the key drivers under direct management control, this suggests that banks are well placed to improve their valuations through time-tested measures, such as the proactive management of non-performing loans NPLs and tight control of non-interest expenses. As such, with key drivers that are unrelated to regulatory reform explaining much of the observed change in PBRs, our findings cast some doubt on explanations that assign a large role to regulation as a source of low current bank PBRs eg Chousakos and Gorton In terms of methodology, we apply a bank valuation model based on earnings and intangibles, as described in Calomiris and Nissimto an international sample of banks.

On the one hand, our valuation equation VE proxies expected cash flow via banks' return-on-equity ROE and other bank income measures. On the other hand, our VE assumes that bank value derives in part from the intangible value created by banks' core loan and deposit relationships.

We capture this through various accounting metrics derived from bank balance sheets and income statements. The remainder of the paper is organised as follows. The second section introduces the PBR concept and reviews recent trends in bank valuations.

The third section undertakes the econometric analysis and estimates the valuation equation. The fourth discusses the implications of the results, followed by various robustness checks. The final section concludes, with policy-relevant implications. Recent trends Our variable of interest is bank value, as measured by PBRs. A bank's PBR is defined as the ratio of the market value of equity to its book value. This suggests that, in order to understand the drivers of PBRs, one should start from observed book values and then examine the degree to which various measures of bank activity contribute to a market premium above or discount from these book values.

In PBR terms, values above one would suggest positive market premia from intangibles eg from the funding advantage afforded by stable and relatively cheap deposit funding and related cross-selling of serviceswhile values below one would suggest discounts eg due to delayed loss recognition in the recorded book value of bank assets.

As measured by PBRs, bank values have been subject to a number of broad global trends that a satisfactory bank valuation approach would have to capture. First, there was a widespread decline in bank valuations during the GFC Graph 1left-hand panel.

## ROE - g / r-g

Average bank PBRs hovered around a level of two times book value right before the GFC, indicating large valuation premia. They then plummeted to values below one inand recovered only recently - while remaining below their pre-crisis levels. Bank valuation and price-to-book ratios PBRs What's special about valuing banks? One key factor is regulation, which is much more stringent for banks than for corporates.

Specifically, banks are typically required to maintain predefined regulatory capital adequacy ratios based on their book value of equity. More importantly, however, the accounting treatment of banks and their activities can differ substantially from that of non-financial corporates. As a result, book values are often more meaningful measures of value for financial firms than for non-financial ones. Accounting for bank assets.

Accounting practices are important for bank valuations for two reasons. First, the assets held by banks are typically in the form of financial instruments loans, bonds and other securities as well as derivatives that have well defined cash flows.

The majority of bank assets loans, investments and other assets are reported at amortised cost.

However, for larger banks many financial instruments are traded in relatively liquid markets, at least under normal conditions, or are substantially similar to traded assets. This is why marking traded and, in some cases, non-traded assets to market has long been established practice among banks. With a significant portion of assets on banks' balance sheets treated in this way, book values are much closer to market values than is the case for non-financial corporates, where most of the assets are carried at amortised cost.

Similarly, depreciation, which can be a key driver of book values for corporates, tends to be much less important for banks, which hold relatively few real assets. Second, it is natural for bank assets to be subject to credit and other risks that can imply the potential for large, possibly abrupt losses, with loss provisions being made to report estimated credit losses as an allowance reducing the value of the loan portfolio and reported earnings.

In practice, banks have discretion in setting their provisioning policies. For a given loan portfolio, conservative banks will set aside more for loan losses, implying lower profits during good times than those generated by their more aggressive peers. Indeed, the literature suggests that delayed loss recognition or "purposeful understatement of losses"; Huizinga and Laeven has been a significant factor for US banks during the recent financial crisis, especially in the context of their mortgage market exposures.

Expected credit loss accounting, due to be implemented globally duringis intended to improve the incorporation of forward-looking credit risks into book asset valuations and earnings.

Against this background, depressed PBRs would tend to reflect the effect of accounting rules on recognised book values as well as attempts by bank managers to preserve their institutions' book capital positions. Implications for bank valuation metrics. For banks and other financial firms, therefore, combining book- and market-based valuation metrics can provide useful information.

In particular, price-to-book ratios PBRs above one - which have tended to prevail under normal market conditions - will tend to be driven by the market value of intangible assets and liabilities, which in turn may be affected by market developments and the competitive environment in ways that are not reflected in their book values.

Changing economic conditions would thus be expected to affect PBRs largely via their effect on intangibles, on both the asset eg Diamond and liability sides Gorton and Pennacchi of the balance sheet.

For example, if interest rates are low for an extended period, having a stable base of core deposits may be less valuable to banks, to the extent that they are unable to reprice deposit rates in line with rates earned on the asset side of their balance sheets BIS Similarly, loan relationships may lose value if the economic environment implies a lower ability for banks to benefit from the cross-selling of services. For a more detailed discussion, see Damodaran and Calomiris and Nissim See Cohen and Edwards Second, while advanced economy banks shared the crisis-induced decline and subsequent partial recovery, cross-country differences have been substantial.

Euro area banks, in particular, stand out, with valuations underperforming those of many of their international peers Graph 1centre panel.

A closer look at the euro area data, in turn, suggests that the evolution of bank valuations there reflected more than just the effects of the euro area sovereign debt crisis Graph 1right-hand panel.

Most euro area banks' valuations have yet to recover from their collapse during the GFC, but cross-country differences remain, for instance between German and Spanish banks. This suggests that important banking system-level drivers, including - but not limited to - home market macroeconomic performance, have been at play. Modelling bank valuations Analytical setup We investigate observed bank PBRs by way of a panel regression framework.

Our approach is based on a bank valuation model emphasising the value created by banks' core loan and deposit relationships Calomiris and Nissim ; in addition to investors' earnings expectations, as proxied by the return-on-equity ROE.

### The Relationship Between Price over Book and ROE

In this setting, PBRs would be driven by the market value of intangibles and other drivers of future earnings GordonDamodaranto the extent that these are not already reflected in observed book values see box.

Our approach thus investigates the cross-sectional and time series relationship between bank PBRs and a variety of indicators measuring the intensity of different banking activities, based on accounting metrics derived from bank balance sheet and income statement information. This approach yields our baseline regression, which is estimated for a sample of 72 banks from 14 jurisdictions using annual data over the period the stock exchange-listed banks from the Brei and Gambacorta database.

Formally, it is set up as follows: There are four sets of explanatory variables, which can affect PBRs through both economic and signalling effects: We cluster the standard errors across both banks and time.

See the discussion below for more detail on the various variables. When extending the analysis, we add macroeconomic and macro-financial data to capture drivers such as the business cycle via the output gap and the financial cycle via the credit-to-GDP gap. A key extension of our approach relative to earlier work, such as Calomiris and Nissimis the multi-country setup; most previous research has focused on US banks. This requires that we restrict ourselves to explanatory variables that are consistently available for a broad international sample of banks.

In addition, given our focus on the time series variation in bank valuations, we deviate from Calomiris and Nissim by not including time fixed effects in our baseline specification, and by adding current ROE as a proxy for investors' return expectations.

Given our multi-country approach, legal and accounting differences can affect some of the standard accounting metrics used in our empirical approach.

The definition of NPLs, in particular, is known to differ substantially across jurisdictions, including among euro area economies where more standardised definitions were phased in only during the later stages of our sample period; see EBA In addition, differences in workout procedures imply that even identically defined NPLs can have a different meaning economically eg Fitch Ratings We account for these effects by allowing for country-level variation in NPL coefficients.

Main results The estimated coefficients from our baseline VE are mostly statistically significant and have the economically expected sign Table 1Model 1. Provisioning levels relative to book equity show up positively once NPLs are controlled for, highlighting that investors seem to value attempts by banks to address asset quality issues in a proactive fashion.

While income measures generally enhance value, higher non-interest rate expenses depress it, underlining the value of cost reductions, or their signals, for market valuations.