No Economist Left Behind Test II:

### What Assumption Should We Make on Pension Returns?

Many analysts are now arguing that public pension funds should only assume a nominal rate of return of 4.5 percent on the stock they hold. This is the rate of return on 30-year government bonds and is considered the risk free rate of return.

In contrast, most pension funds are now assuming that the stocks that they hold will give around a 10 percent nominal rate of return. This is roughly the average rate of return on stocks over the last hundred years. It is also a rate of return that is consistent with the current price to earnings ratios in the market (@14 to 1), which is roughly equal to the average price-to-earnings ratio in the market over the last hundred years.

Price-to-Earnings Ratios (1962-2050)

 Start projections in Q -- baseline starts in 2011Q1 Nominal rate of return on stocks .% -- baseline 9.48% Real GDP growth relative to CBO .pp -- baseline 0.00pp Long-run earnings growth relative to GDP .pp -- baseline 0.00pp (show me) Dividend share of earnings .% -- baseline 70.0%
Earnings Share of GDP (1962-2050)

Source Data
Data ItemTime PeriodSource
Nominal GDP1947Q1-2010Q4BEANIPA Table 1.1.5, Line 1
1949-2021CBOJanuary 2011 Budget and Economic Outlook
Pre-Tax Profits1947Q1-2010Q4BEANIPA Table 1.10, Line 17
1949-2021CBOJanuary 2011 Budget and Economic Outlook
After-Tax Profits1947Q1-2010Q4BEANIPA Table 1.12, Line 15
Net Dividends1947Q1-2010Q4BEANIPA Table 1.12, Line 16
Market Value1952Q1-2010Q4 FRBFlow of Funds Table L.213, Line 23
Outstandings: Series FL893064195Q

Methods for Projection

Annual data from CBO was resampled to quarterly by finding consistent mid-year values. These consistent mid-year values are such that the interpolated mid-quarter values for a given year average the annual source data.

Gross Domestic Product (Nominal)
Projections for GDP are derived from CBO but assume a slightly higher (3.0 percent) long-run rate of inflation. Any assumed changes in long-run growth assumption are phased in over 2011Q1-2021Q4.

Earnings
Baseline projections for after-tax profits were computed from CBO pre-tax data by multiplying by the 2010Q3 ratio of after-tax corporate profits to pre-tax profits from BEA. Assumed changes to the long-run profits growth relative to GDP are phased in over the CBO projection period, and the long-run profits assumptions are phased in over the next year. Earnings are taken to be the average after-tax profit share of GDP for the 40 quarters ending in the current quarter, multiplied by current GDP.

Dividends
Long-run projected dividends are a constant share of earnings, with the share phased in over the CBO projection period.

Market Value of Domestic Corporations (Price)
Stock prices are projected to rise or fall as necessary to maintain the total rate of return to be constant, given the projected path for dividends.

The red line above shows the path for the price-to-earnings ratio that is consistent with stocks providing a nominal yield of 4.5 percent, if the growth projections for the economy and corporate profits prove accurate. These projections are from the Congressional Budget Office (CBO), which is widely viewed as the authoritative source for economic projections. CBO surveys all the major forecasters and constructs projections that are broadly consistent with the mainstream of the economics profession.

Since the dividend yield is currently close to 4.0 percent, stock prices can only rise at the rate of 0.5 percent annually, to keep the total return (dividend plus the rise in the stock price) from being above 4.5 percent. However, corporate profits are projected to grow 4.5 percent annually, the same rate as the economy. (Over long periods, corporate profits generally grow at the same rate as the economy.) If the stock price only rises by 0.5 percent and corporate profits rise 4.5 percent, then the ratio of stock prices to corporate earnings would be falling, as shown in the graph.

However, if the stock price falls relative to earnings, then the ratio of dividends to the share price will rise. (If the stock price is \$10 a share,earnings are \$1 a share and dividends are 40 cents a share, then the dividend yield would be 4.0 percent. If the stock price fell in half, so that the share price was just \$5 but the stock still paid a dividend of 40 cents a share, then the dividend yield would be 8.0 percent [40 cents divided by \$5].)

The higher dividend yield implies that the stock price would have to fall even more rapidly in future years in order to keep the total return from exceeding the 4.5 percent level. For example, if the dividend yield were 8.0 percent, as in the case above, then the stock price would have to fall by 3.5 percent the following year to keep the return at 4.5 percent. However, with profits again rising by 4.5 percent, this would push the price-to-earnings ratio even lower and make the dividend yield even higher. Eventually, the stock price would actually have to fall so far that it became negative, as shown in the chart. This would imply that people would actually get paid to hold stock.

This is of course absurd. However it makes the point that it is not easy to find plausible scenarios in which stocks will only produce the 4.5 percent risk-free rate that many policy analysts are now arguing that pension fund managers should use in assessing the returns on their stock holdings. Use the calculator to see if you can construct a plausible story that has stocks providing only a 4.5 percent rate of return.

If the dividend yield fell below the 70 percent shown here it would imply that investment is growing more rapidly than projected, which would mean that the CBO growth projections understate the true growth rate of output and profits. If profits grow more rapidly, then the stock price will have to rise more rapidly in order to keep the price-to-earnings ratio constant.

Designed by David Rosnick, Center for Economic and Policy Research