When I was a banks analyst, I was always intrigued by one thing. In fact, because I actually had to justify the Target Prices (TP) in our reports, I wasn’t just intrigued, it was a problem I had to solve. It was the Price to Book Multiple (PB) of Chinese banks.

**Chinese banks had traded at a range of between 0.6–1.2x PB over the last several years**. In our research reports, we had to use fundamental tools to justify our Target Prices. For banks this was based on the Target PB multiplied by the Book Value.

**The Target PB is derived by**

**Return on Equity (ROE) minus Long Term Growth (g)**

**All divided by**

**Cost of Equity (COE) minus Long Term Growth (g)**

Now, the growth is trivial in this discussion so we can actually just remove it from the formula altogether. So the formula is basically, ROE by COE.

Over the last several years, Chinese banks’ ROE have actually ranged between 15–20%, which you can get from their annual reports.

The COE is basically the risk free rate, which say if we use the Chinese 10y bond yield is 3–4%.

You can work backwards using the slope formula in Excel or Bloomberg/Reuters provide them as well (back in the days, I like to calculate it myself as I am always weary of accuracy of third party providers) but the Beta for Chinese banks is roughly 1.0–1.2x. The common risk premium to use is about 6%. As a result, the COE works out to around 9–11%.

**Based on the ROE by COE formula above, this implies the PB of Chinese banks should be around 1.3–2.2x, which as discussed before, in reality, they are somewhere between 0.6–1.2x.**

Therefore, if purely based on this the TPs could be double that of the current price, which appears outrageous (some sectors may have 100% upside in certain stocks but for banks, this should be rare especially as a whole sector, it effectively implies intuitively you are expecting GDP growth to double or interest rates to double but without bad debts happening) and I needed to find a solution.

One can try to deduce the discrepancy from looking back at the variables. I would say that there isn’t a lot of debate in terms of the risk free rate and Beta. One could do an analysis of risk premium in China and while I haven’t done it myself, could this be a key driver for a high COE in China, which leads to the lower PB for banks?

For this, let’s look at another sector that I used to cover — Chinese brokers. Chinese brokers traded at a range of 0.8–1.5x over the last several years but their ROEs were only around 10% on average barring any significant bull market, which is not expected to sustain for long periods.

So Chinese brokers should trade at around 1.0x PB, which is consistent with reality (the 1.5x was bull market valuation). This implies the COE generally makes sense as well.

**Hence, we are left with ROE and basically, what the market is saying is that they expect the current ROE of banks to be not sustainable into the future. And there are many reasons for that such as banking reforms, interest rate liberalisation, competition and comparisons with developed market banks.**

Another variable we have ignored thus far is the book value of the bank, which is the other variable in calculating the TP. The market is likely to have assumed a significant discount in this variable as there are concerns about the loan quality.

The justification for this is that Chinese banks have an Asset to Equity multiple of around 12x. This means they hold $12 of assets for every $1 of equity hence, if $1 (or 8%) of their total asset is bad then they are in theory bankrupt.

Disclaimer: This post is not meant to provide any investment advice but merely a discussion on valuation framework.

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