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The argument about whether equity markets are too expensive rages on, while, at the same time, stock prices in Canada and the U.S. have arranged themselves into a comprehensible assessment of fair value that no one’s talking about.

Price to book value (P/BV) - a measure of stock price divided by the per share wealth on the corporate balance sheet - and return on equity (total profits divided by shareholders equity, a measure of profitability) are the two variables that matter in the new valuation regime.

A closer look will allow investors to uncover promising opportunities.

In 2018 , Goldman Sachs equity analyst David Kostin noted that U.S. sector valuations fell neatly into a trend based on price to book value and return on equity. The first accompanying chart – updated to current values - shows how this is working.

The P/BV for each market sector in the S&P 500 is plotted along the x-axis and return on equity is measured on the Y-axis. On the far left, it shows that the S&P 500 consumer discretionary index (which includes Amazon.com Inc.) has a price to book value of 8.4 times and a return on equity of 30.2 per cent.

The important point for investors is that all U.S. market sectors have neatly arranged themselves close to the trend line. This strongly implies that profit margins – the efficiency with which revenue translates into earnings per share - are driving stock prices. The higher the ROE, the higher the stock prices relative to book value.

When I first tried to apply this trend to Canadian stocks, it didn’t work. The problem was that the health care and technology sectors didn’t fit the pattern. The lack of diversification in the health care index – it’s dominated by volatile cannabis stocks – distorted the chart. In technology, Shopify Inc. performance completely overshadowed every other company in the index, making it unusable as well.

Once those two sectors are removed, the valuation pattern for Canadian stocks looks a lot like the S&P 500. On the second chart, the domestic equity sectors consistently organize around the trend line in terms of price to book value and ROE.

On the far left of the chart, the real estate sector shows a price to book value of 1.2 and return on equity of 7.8 per cent. At the far right, we have the industrial stocks with an average P/BV of 4.1 times and an ROE of 18.2. As with U.S. stocks, price to book value rises with profitability.

If we accept that the trend line represents some semblance of fair value, this implies that the sectors above the line are undervalued. Financials, for example, with an ROE of 11.6, should be trading at a much higher P/BV – the dot on the chart should move rightwards towards the trend line.

By the same token, the dots below the line suggest these sectors are trading at P/BVs above where they should. Materials stocks, with an ROE of just 5.8, should be trading at a lower P/BV according to the chart.

Importantly, I’m not willing to put too much emphasis on either of these charts as a source of trading signals, buy or sell. The results are interesting, but the valuation method is too new and untested.

The key point for investors is that while conventional valuation methods like price to earnings indicate that North American equities are extremely expensive relative to history, the market itself has developed its own internal logic in pricing stocks based on profitability. As long as the pattern holds, markets are neither cheap or expensive – they are fairly valued according to the new methodology.

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