"In 1965, arithmetic indicated expectation of a much lower rate of advance in the stock market than had been realized between 1949 and 1964. That rate had averaged a good deal better than 10% for listed stocks as a whole, and it was quite generally regarded as a sort of guarantee that similarly satisfactory results could be counted on in the future. Few people were willing to consider seriously the possibility that the high rate of advance in the past means that stock prices are ‘now too high,’ and hence that ‘the wonderful results since 1949 would imply not very good but bad results for the future."

– Benjamin Graham, The Intelligent Investor, Fourth Revised Edition, 1973

From 1949 through 1964, the S&P 500 enjoyed an average annual total return of 16.4%. In the 8 years that followed, through 1972, the total return of the index averaged a substantially lower 7.6% annually; strikingly close to the 7.5% projection that Graham had suggested based on prevailing valuations, yet still providing what Graham had suggested would likely “carry a fair degree of protection” against inflation, which averaged 3.9% over that period.

Graham was much less favorably inclined toward stocks by 1972, suggesting that “bond investment appears clearly preferable to stock investment.” During the full period from the 1972 market high to the 1982 market low, the S&P 500 actually declined in price, but enjoyed a 4.1% annual total return, entirely from dividend income. By comparison, both Treasury bill returns and U.S. CPI inflation averaged 9.0% annually. Meanwhile, Treasury bonds enjoyed a total return of 6.5% annually, which could of course be read directly from their yield-to-maturity at the beginning of the period.

The arithmetic of total returns

Value investing is at its core the marriage of a contrarian streak and a calculator.
– Seth Klarman

I’ve regularly noted that a good valuation measure is nothing but shorthand for a proper discounted cash flow analysis. In general, the denominator of a useful valuation measure should act as a “sufficient statistic” for decades and decades of future cash flows – that’s one of the reasons that earnings-based measures tend to be less reliable, while the valuation measures having the strongest correlation with actual subsequent market returns across history are those that have fairly smooth denominators that closely track corporate revenues.

The only way to hold a valuation ratio constant is for the numerator and the denominator to grow (or shrink) at the same rate. This is a useful fact for investors, because it allows us to break investment returns into underlying components that drive returns. This is the “arithmetic” that Graham describes in the opening quote above.

An example will make this arithmetic clear. During the 21 years since the bubble peak in 2000, S&P 500 revenues have grown at an average annual rate of about 3.5% annually. If the price/revenue ratio of the S&P 500 had remained fixed at its 2000 high of 2.36, that’s also the rate at which the S&P 500 Index would have gained. Instead, the price/revenue ratio closed last week at 3.09, the highest level in history. That change in valuations was worth another (3.09/2.36)^(1/21)-1 = 1.3% in annual return. Add an average dividend yield of about 2% during this period, and one would estimate that the total return of the S&P 500 should have averaged about (1.035)*(1.013)-1 + .02 = 6.8% annually. That estimate matches the actual return of the S&P 500.