The most nagging question for investors in equities is what return they can expect from their investment. For most people it’s as simple as that, unless of course you want to bring risk and some other Greek (quant) variables into the equation.

It is stating the obvious that an investor’s total return is made up of the price rise/decline plus the dividend payment. But how does one get a handle on the expected quantum of the price movement?

I am writing this from Veysonnaz, an Alpine village in Switzerland, where I am enjoying a few days of fresh mountain air. Although I planned on taking it easy with my family, I thought it might be worthwhile to consult with the mysterious gnomes while in this haven of global finance.

The simple answer to the returns question, the gnomes tell me, is to focus on the two components of the returns calculation, namely the expected change in the price-earnings ratio of a company or stock market index and the expected growth in earnings of that company or index. (For the sake of simplicity, dividends, the third component of the returns computation, are not taken into account in this article.)

For those not well versed with the world of finance, let’s briefly review some basics. A price-earnings multiple of 10 times simply means that investors are willing to pay a price of \$10 for every \$1 of annual company earnings per share. However, if the price-earnings ratio increases to 15 without there being a change in company earnings, it means that investors are now willing to pay \$15 for company earnings of \$1. This represents a stock price rise of 50%.

If the company earnings of \$1 increases to \$1,25 without there being a change in the price-earnings ratio, it means that investors will now pay \$12.50 for company earnings of \$1.25. This represents a 25% rise in the price.

But company earnings and price-earnings ratios seldom change independently from each other. If the two examples above occur simultaneously, in other words the price-earnings ratio changes from 10 to 15 (i.e. a stock price rises from \$10 to \$15) and company earnings change from \$1 to \$1.25 (which would result in an additional price increase of 25%), the stock price will change from \$10 to \$18.75, which represents an increase of 87.5%.

So much for investment theory.

The earnings of the S&P 500 Index’s underlying companies have increased by 14% during the past 12 months compared with a historical average of 8.2% per annum since 1955. The current price-earnings ratio is 18.0 compared with the historical average of 17.2.

In order to get a feel for what these numbers mean, let’s consider the Plexus Valuation Calculator. The diagram is an easy way of determining the expected returns on the S&P 500 Index for different combinations of growth in company earnings and price-earnings ratios.

The diagram shows that if the price-earnings multiple remains unchanged and companies manage to maintain the same level of earnings growth achieved over the past 12 months, investors in the basket of S&P 500 shares can expect a return of 14% on their investment over the next year.

However, should the S&P 500 companies’ earnings be lower over the next year, say 10%, and the price-earnings ratio remains unchanged at 18.0, investors could expect a return of 10% on their investment over the next year.

But what happens when the price-earnings ratio falls to the historical average of 17.2 (still assuming 10% earnings growth)? This will result in a meagre return of only 5% over the next year. Furthermore, any combination of a price-earnings ratio of less than 17.2 and company earnings growth of less than 5% could result in a negative return over the next year.

Investors must bear in mind that companies are not all of the same quality and that any decrease in company earnings will not be the same for all the companies. There will no doubt be companies that will experience a larger decrease in earnings and there might even be some whose earnings could still increase. The same applies to the changes in price-earnings ratios.

Playing around with various combinations of earnings growth and price-earnings ratios makes for interesting reading. But, more so, it also makes it hard for me to find compelling value when considering the US stock market as a whole. The current market environment reminds me of the saying that “in these days the focus should be on the return OF capital rather than the return ON capital”. The gnomes concur.