There's been a lot of recent buzz about how cheap or expensive stocks are vs. bonds. Most comparisons look at stocks relative to the 10-year Treasury. But different parts of the bond market have been going in

different directions in recent years, so relying on just one area of the bond market to make a comparison can be misleading.

At my old firm, we used to track the relative valuation of equities against a variety of bonds; I'll try to recreate some of that work here. The results of this exercise depend on some highly subjective judgments, so I'll outline my assumptions and how the conclusions would change under different outlooks. Also, the results only illustrate the valuations of different asset classes. They don't necessarily predict outperformance, as assets that look cheap sometimes get cheaper, and overvalued sectors sometimes become pricier.

Apples to Apples

To compare stock valuations with bonds, we must first try to put them on the same footing. This is usually done on a yield basis. When you buy a bond, you are entitled to its coupons. The price you pay for those coupons determines the yield of that bond. When you buy a company's stock, you are entitled to a share of that company's earnings, some of which may be returned in the form of dividends, with the remainder kept internally in the form of retained earnings, which will hopefully be used to generate future earnings. The price paid for those earnings is a stock's price-to-earnings ratio. The inverse of that ratio, earnings divided by price, is known as the earnings yield.

This earnings yield is commonly compared with bond yields. It became somewhat famous when

Federal Reserve

Chairman Alan Greenspan referred to the earnings-price ratio in a 1997

report to Congress. (It's about 85% of the way into the report in a section called "Equity Prices.") There, Greenspan compared the earnings yields with the 10-year Treasury, and pundits labeled this the "Fed model" for equity valuations.

But this method of valuation has existed for many years and in many variants. It starts with a look at earnings. P/Es are often computed by looking at either the past year's earnings or the future year's expected earnings. Both methods present problems. At my old firm, we didn't like to rely on trailing earnings, as stocks look overvalued after a period of earnings declines and undervalued near an earnings peak. Forward-looking calculations also can be problematic, especially in recent years as analysts have chosen to forecast pro forma earnings rather than reported earnings.

The choice of trailing vs. forward-looking earnings can have a big impact on the results. At my old firm, we settled on looking at what we called "current earnings," which examined the two most recent quarters and an estimate of the next two quarters. This also isn't perfect, but we felt it provided some consistency when looking back and minimized the difficulty in forecasting the future. We would then play some what-if exercises, using different inputs.

The first thing to look at is earnings. Below is a chart of the reported earnings of the

S&P 500

, using rolling four-quarter totals. After peaking at $53.70 in last year's third quarter, they declined to below $37 by this summer. I've assumed that the economy bottoms at the end of this year and then begins a

modest recovery; this would gradually push earnings up to around $45 by the end of next year. An economic bear would probably look at a rough earnings number of around $30 next year; an economic bull might be looking for a quick snapback to around $55.

S&P 500 Earnings
After peaking at $53.70 in Q3 2000, they slid to under $37 this past summer

Source: S&P

Based on my definition of current earnings, the S&P has a P/E of about 32; this translates into an earnings yield of about 3.1%. The next chart shows how the earnings yield on the S&P has acted since 1985 and contrasts it with several different types of bonds.

Stock and Bond Yields
The S&P yield since 1985 compared with Treasury and corporate issues

Source: Federal Reserve Board St. Louis

This chart shows how earnings yields have declined (P/Es have risen) since 1997, and how the yield on short Treasuries like the two-year has come down to meet them this year. Ten-year yields have fallen a bit this year, but not nearly as much as shorter Treasuries have. Investment-grade corporate-bond yields have barely budged this year.

By looking at earnings yields as a percentage of these bond yields, we can get an idea of how stocks are valued against bonds. The higher the percentage, the cheaper stocks appear.

Stock Yields as a % of Bond Yields
The higher the percentage, the cheaper stocks appear

Source: Federal Reserve Board St. Louis

Based on these numbers, stocks are yielding about 63% of 10-year Treasuries, just a touch below the 75% average over this time period. Stocks may be fairly valued by this measure. But stocks now yield about the same as a two-year Treasury, compared with an average of 86%, so stocks appear cheap on this measure. When measured against Baa corporate bonds, stocks offer just 39% of the yield, far off the historical number of 59%.

Interestingly, the stock-to-bond relationship is about the same as it was at this point in the last recession when using the 10-year Treasury as a measuring stick. Against the two-year, stocks look much cheaper than they did in early 1991, while equities appear more expensive vs. Baa corporates.

Changing your view of earnings also can affect the analysis. Using bearish earnings numbers of $30, you'd see the P/E jump above 38 and the earnings yield fall to 2.6%, making stocks look overvalued against all but the two-year and shorter maturities. Plugging in a bullish earnings number of $55, you'd see the P/E fall to 21 and the earnings yield jump to 4.7%, bringing stocks up to fair value vs. corporates and making them look cheap against other fixed-income classes.

What to Make of This?

First, the next time you see someone on TV proclaiming that stocks are cheap or expensive relative to bonds, take it with a grain of salt. These conclusions are highly subject to earnings estimates and to what type of bond is being used in the comparison.

Second, understand that institutions don't make one generic stock/bond decision. Pension plans and other institutions, which control more assets than mutual funds, will be getting their year-end statements in a month and a half in preparation for making next year's allocation decisions. Those whose bond portfolios are benchmarked against the broad bond market (which contains only about 20% Treasuries) might opt for a greater corporate-bond weighting. Those that have a high cash position and a good asset/liability position might opt for a higher equity weighting.

Third, use this analysis carefully. I've preached all year about finding the mix of stocks, bonds and cash that fits your investment needs. This method can be a tool to help determine that mix, but it's a highly subjective process. Based solely on my numbers, I'd be underweighted in short-term Treasuries, neutral on long-term governments, overweighted in corporates and neutral on stocks. But I've also shown how different assumptions could lead to entirely different weights. What's most important? Make sure that you're taking the right amount of risk for your financial situation.

Brian Reynolds is a Chartered Financial Analyst who spent more than 16 years as a fixed-income portfolio manager and economist at David L. Babson & Co. in Cambridge, Mass. He currently writes and lectures about investment issues and trades for his own account. At the time of publication, he had no positions in any of the securities mentioned in this column, although holdings can change at any time. Under no circumstances does the information in this column represent a recommendation to buy or sell. He welcomes feedback at

Brian Reynolds.