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Holiday shopping season reminded us yet again that shopping for gifts and shopping for stocks are a lot alike. Both involve the search for a great deal.

What makes both activities so difficult is that there's no clear definition of a great deal. Some shoppers feel they get a deal by paying the lowest price for a no-name product. Others think the best deal involves owning a well-known, name-brand product.

In the investment world, most value investors would fall into the former category while most growth investors would fall into the latter category. There is risk to either approach, when taken to the extreme.

Bargain hunters risk a "buy cheap, get cheap" scenario in which paying a low price results in an inferior, short-lived product. At the other extreme, shoppers can risk overpaying for a product that overpromises but underdelivers.

Good shoppers, like successful investment managers, try to find a balance between paying a good price and getting something of high quality in return.

To understand what we're paying for a stock, we use the price-to-book (P/B) ratio. The P/B ratio compares the price of a stock to its book value per share – the value of a company's assets net of the company's liabilities. The higher a stock's P/B ratio, the more expensive the stock since investors are willing to pay more for each dollar of a company's net assets.

It's important to keep in mind that buying an expensive stock with a high P/B ratio isn't necessarily a bad thing. After all, our roads are full of expensive, luxury cars, so people must feel they are getting value in return for the high cost.

How does one evaluate what you get in return for buying a stock? One of the more common ways is to measure its level of profitability, often referred to as its return on equity (ROE), or the rate at which a company generates earnings for each dollar of net assets.

The higher a company's ROE, the more profitable it is. Just as cars with higher horsepower garner higher prices, companies with higher ROEs typically garner higher P/B multiples since investors tend to pay a higher price for shares of companies that are more profitable.

We can apply this same relationship to measure the entire stock market. Aggregating the P/B multiples and ROE ratios for individual stocks gives us insight into whether the stock market is priced reasonably.

The top chart shows the historic relationship between what Canadian investors have been willing to pay for stocks (the red line) and what they are getting in return (the blue line). The red line represents the P/B ratio for the median stock in Canada. This ratio currently stands at 1.4, meaning investors are willing to pay 1.4 times book value for the typical company.

There have only been two other times in the past 30 years when this ratio has been lower (during the recessions of 1990-92 and 2008-09). Canadian investors are currently paying a 15-per-cent discount below the long-term average P/B ratio so there is no doubt that Canadian stocks offer good value.

But is this a case of buy cheap, get cheap? To answer this question, we must evaluate what investors are getting for their money. The blue line is the return on equity (ROE) for the typical Canadian stock, and is a measure of corporate profitability. We subtract the 90-day T-bill rate – a common measure of the risk-free rate of return – from ROE to reflect investors' requirement for higher profitability at higher rates of interest. (If the risk-free interest rate rises high enough relative to corporate profitability, investors would be better off investing in T-bills.)

The blue line shows that Canadian stocks currently offer a profitability premium of 4.5 per cent above T-bills, well above the long-term average premium of 2.6 per cent. The conclusion is that Canadian investors are currently paying less than average for stocks and getting higher than average net profitability in return. This is a good environment for Canadian investors since it means there are plenty of opportunities for profitable stock returns.

Turning our attention to the U.S. market in the bottom chart, we see a somewhat different picture. U.S. investors are currently paying 2.5 times the book value for the typical U.S. stock. This represents a 15-per-cent premium above the long-term average, an indication that U.S. stocks are not cheap.

But the blue line suggests the high P/B multiple is justified. The typical U.S. stock currently offers a net return-on-equity well above the long term average value, an indication that U.S. stocks are highly profitable. As long as companies remain highly profitable, stock valuations can remain at elevated levels for extended periods, as they did in the mid-2000s.

Analyzing the relationship between what investors are paying and what they are getting in return is crucial to understanding the environment in which investors must operate. An informed shopper is a happy (and successful) shopper.

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