The Wall Street Journal had a column this week that would terrify its readers, if they took its columns seriously. The piece, by Andy Kessler, derided the 7.5 percent return assumed by the Calpers, the public employer pension fund in California. Other pensions, both public and private, make comparable return assumptions.

The piece tells readers:

"Who wouldn't want 7.5%-8% returns these days? Ten-year U.S. Treasury bonds are paying 1.74%. There is almost zero probability that Calpers will earn 7.5% on its $255 billion anytime soon.

"The right number is probably 3%. Fixed income has negative real rates right now and will be a drag on returns. The math is not this easy, but in general, the expected return for equities is the inflation rate plus productivity improvements plus the expansion of the price/earnings multiple. For the past 30 years, an 8.5% expected return was reasonable, given +3%-4% inflation, +2% productivity, and +3% multiple expansion as interest rates plummeted. But in our new environment, inflation is +2%, productivity is +2% and given that interest rates are zero, multiple expansion should be, and I'm being generous, -1%."

Pretty scary, one wonders if Mr. Kessler tells his hedge fund clients that they should expect to lose 1 percent a year with the money they invest with him.

Anyhow, this is a case where Mr. Arithmetic can provide a big hand. Pension funds like Calpers typically invest around 70 percent of their assets in equities, including the money invested in private equity. The expected return on stock is equal to the rate of the economy's growth, plus the payouts in dividends and share buybacks. It also should include a term for the expected change in the price to earnings ratio, but with the PE ratio pretty much in line with long-term trends, there is little reason to expect much change.

Okay, the long-term growth of nominal GDP is projected at around 4.8 percent, 2.3 percent real growth and 2.5 percent inflation. (The inflation assumption may prove high, but projected pension fund costs will adjust pretty much one to one to a different assumption.) Companies typically pay out about two-thirds of their earnings as either dividends or share buybacks. With a current ratio of price to trend earnings, the yield is around 7 percent. Two thirds of this yield gives us a payout of 4.7 percent. Adding the two together we get 4.8 + 4.7 = 9.5 percent.

With 70 percent of their money in equities, Calpers could get 6.6 percentage points of its 7.5 percent return assumption from its equity holdings. If the fund holds 20 percent of it assets in long-term bonds that provide an average yield of 4.5 percent, this gets us another 0.9 percentage point to get us to 7.5 percent. Any return on the remaining 10 percent is just frosting. (Return assumptions are examined more carefully here.) 

In short, the return assumptions used by Calpers are quite realistic. It would be difficult to envision a situation where the long-term return was markedly worse than it assumes. Arithmetic can be a very valuable tool in addressing such issues. It should be used more frequently.