# Tobin's q

Tobin's q[1] is the ratio between a physical asset's market value and its replacement value. It was introduced in 1968 by James Tobin and William Brainard,[1] although the use of the letter "q" did not appear until Tobin's 1969 article "A general equilibrium approach to monetary theory".[2][3] Tobin (1969) writes

One, the numerator, is the market valuation: the going price in the market for exchanging existing assets. The other, the denominator, is the replacement or reproduction cost: the price in the market for the newly produced commodities. We believe that this ratio has considerable macroeconomic significance and usefulness, as the nexus between financial markets and markets for goods and services.[4]

## Measurement

### Single company

Although it is not the direct equivalent of Tobin's q, it has become common practice in the finance literature to calculate the ratio by comparing the market value of a company's equity and liabilities with its corresponding book values as the replacement values of a company's assets is hard to estimate:

Tobin's q = $\frac{\text{(Equity Market Value + Liabilities Market Value)}}{\text{(Equity Book Value + Liabilities Book Value)}}$

It is also common practise to assume equivalence of the liabilities market and book value, yielding:

Tobin's q = $\frac{\text{(Equity Market Value + Liabilities Book Value)}}{\text{(Equity Book Value + Liabilities Book Value)}}$

For stock listed companies, the market value of equity is often quoted in financial databases. It can be calculated for a specific point in time by $(number of shares) \times (share price)$.

### Aggregate corporations

Another use for q is to determine the valuation of the whole market in ratio to the aggregate corporate assets. The formula for this is: $q=\frac{\text{value of stock market}}{\text{corporate net worth}}$

The following graph is an example of Tobin's q for all U.S. corporations. The line shows the ratio of the US stock market value to US net assets at replacement cost since 1900.

## Application

If the market value reflected solely the recorded assets of a company, Tobin's q would be 1.0.

If Tobin's q is greater than 1.0, then the market value is greater than the value of the company's recorded assets. This suggests that the market value reflects some unmeasured or unrecorded assets of the company. High Tobin's q values encourage companies to invest more in capital because they are "worth" more than the price they paid for them.

$q = \frac{\text{Market value of installed capital}}{\text{Replacement cost of capital}}$

If a company's stock price (which is a measure of the company's capital market value) is $2 and the price of the capital in the current market is$1, the company can issue shares and with the proceeds invest in capital. In this case q>1.

On the other hand, if Tobin's q is less than 1, the market value is less than the recorded value of the assets of the company. This suggests that the market may be undervaluing the company.

John Mihaljevic points out that "no straightforward balancing mechanism exists in the case of low Q ratios, i.e., when the market is valuing an asset below its replacement cost (Q<1). When Q is less than parity, the market seems to be saying that the deployed real assets will not earn a sufficient rate of return and that, therefore, the owners of such assets must accept a discount to the replacement value if they desire to sell their assets in the market. If the real assets can be sold off at replacement cost, for example via an asset liquidation, such an action would be beneficial to shareholders because it would drive the Q ratio back up toward parity (Q->1). In the case of the stock market as a whole, rather than a single firm, the conclusion that assets should be liquidated does not typically apply. A low Q ratio for the entire market does not mean that blanket redeployment of resources across the economy will create value. Instead, when market-wide Q is less than parity, investors are probably being overly pessimistic about future asset returns."

Lang and Stulz found out that diversified companies have a lower Q-ratio than focused firms because the market penalizes the value of the firm assets.

Tobin's discoveries show us that movements in stock prices will be reflected in changes in consumption and investment, although empirical evidence reveals that his discoveries are not as tight as one would have thought. This is largely because firms do not blindly base fixed investment decisions on movements in the stock price; rather they examine future interest rates and the present value of expected profits.

## Other influences on q

Tobin's q measures two variables - the current price of capital assets as measured by accountants or statisticians and the market value of equity and bonds - but there are other elements that may affect the value of q, namely:

• Market hype and speculation, reflecting, for example, analysts' views of the prospects for companies, or speculation such as bid rumors.
• The "intellectual capital" of corporations, that is, the unmeasured contribution of knowledge, goodwill, technology and other intangible assets that a company may have but aren't recorded by accountants. Some companies seek to develop ways to measure intangible assets such as intellectual capital. See balanced scorecard.

Tobin's q is said to be influenced by market hype and intangible assets so that we see swings in q around the value of 1.

## Tobin's marginal q

Tobin's marginal q, is the ratio of the market value of an additional unit of capital to its replacement cost.

## Price-to-book ratio (P/B)

In inflationary times, Q will be lower than the price-to-book ratio.[6] During periods of very high inflation, by contrast, the book value would understate the cost of replacing a firm's assets, since the inflated prices of its assets would not be reflected on its balance sheet.

## Criticism

Olivier Blanchard, Changyong Rhee and Lawrence Summers found with data of the US economy from the 1920s to the 1990s that "fundamentals" predict investment much better than Tobin's q.[7] What these authors call fundamentals is however the rate of profit, which connects these empirical findings with older ideas of authors such as Wesley Mitchell, or even Karl Marx, that profits are the basic engine of the market economy.

Doug Henwood, in his book Wall Street, argues that the q ratio fails to accurately predict investment, as Tobin claims. "The data for Tobin and Brainard’s 1977 paper covers 1960 to 1974, a period for which q seemed to explain investment pretty well," he writes. "But as the chart [see right] shows, things started going away even before the paper was published. While q and investment seemed to move together for the first half of the chart, they part ways almost at the middle; q collapsed during the bearish stock markets of the 1970s, yet investment rose." (p. 145)[8]

## Notes

• ^ Tobin's q is sometimes written as "Tobin's-q", "Tobin's Q" or simply Q. It is also called Tobin's Quotient, since the Q stands for Quotient. Sometimes, people call it the "Brainard-Tobin Q."[9]

## References

1. ^ Brainard, William C.; James, Tobin (1968). "Pitfalls in Financial Model Building". American Economic Review 58 (2): 99–122. JSTOR 1831802. edit
2. ^ Tobin, James (1969). "A General Equilibrium Approach To Monetary Theory". Journal of Money, Credit and Banking 1 (1): 15–29. JSTOR 1991374. edit
3. ^ American Economic Association Biography of William C. Brainard: http://www.aeaweb.org/PDF_files/Bios/Brainard_bio.pdf.
4. ^ "Asset Markets and the Cost of Capital." James Tobin and W.C. Brainard, 1977, Economic Progress, Private Values and Public Policy
5. ^ Source of data: Valuing Wall Street. The data from 1952 on comes from the "Flow of Funds Accounts of the United States Z1”, which is published quarterly by the Federal Reserve. Earlier data are available from a variety of sources from 1900 as compiled by Stephen Wright, University of London
6. ^
7. ^ Blanchard, Olivier; Rhee, C. & Summers, L. (1993). "The Stock Market, Profit, and Investment". Quarterly Journal of Economics 108 (1): 115–136. doi:10.2307/2118497.
8. ^ Henwood, Doug (1997). Wall Street. London and New York: Verso. p. 372. ISBN 0-86091-670-7.
9. ^ Bond, Stephen R.; Cummins, Jason G. (2004). "Uncertainty and Investment: An Empirical Investigation Using Data on Analysts' Profits Forecasts". FEDS Working Paper No. 2004-20. SSRN 559528.