Tobin's q

Overview

Tobin's q (or the q ratio, and Marris's v), is the ratio between a physical asset's market value and its replacement cost. It was first introduced by Robin Marris as a firm-level microeconomic variable in his 1964 book The Economic Theory of Managerial Capitalism, and was shortly afterwards further analysed by Richard Kahn in early drafts of his paper Notes on the Rate of Interest and the Growth of Firms (not published until 1972). Nicholas Kaldor in 1966, without acknowledgement to his Cambridge colleagues Marris and Kahn, repurposed the valuation ratio as a macroeconomic variable in his paper: Marginal Productivity and the Macro-Economic Theories of Distribution: Comment on Samuelson and Modigliani. It was popularised a decade later by James Tobin, who in 1970, described its two quantities as:

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 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.

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 =

(Equity Market Value + Liabilities Market Value) (Equity Book Value + Liabilities Book Value)

{\displaystyle {\frac {\text{(Equity Market Value + Liabilities Market Value)}}{\text{(Equity Book Value + Liabilities Book Value)}}}}

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

Tobin's q =

(Equity Market Value + Liabilities Book Value) (Equity Book Value + Liabilities Book Value)

{\displaystyle {\frac {\text{(Equity Market Value + Liabilities Book Value)}}{\text{(Equity Book Value + Liabilities Book Value)}}}}

. Even if market and book value of liabilities are assumed to be equal, this is not equal to the "Market to Book Ratio" or "Price to Book Ratio", used in financial analysis. The latter ratio is only calculated for equity values: Market to Book Ratio=

Equity Market Value Equity Book Value

{\displaystyle {\frac {\text{Equity Market Value}}{\text{Equity Book Value}}}}

. Financial analysis also often uses the inverse of this ratio, the "Book to Market Ratio", i.e. Book to Market Ratio=

Equity Book Value Equity Market Value

{\displaystyle {\frac {\text{Equity Book Value}}{\text{Equity Market Value}}}}

For stock-listed companies, the market value of equity or market capitalization is often quoted in financial databases. It can be calculated for a specific point in time by

number of shares

×

share price

{\displaystyle {\text{number of shares}}\times {\text{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 =

value of stock market corporate net worth

{\displaystyle 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.

Effect on capital investment

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. 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, so that q > 1, the company can issue shares and with the proceeds invest in capital, thus obtaining economic profit. 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, or that the company could increase profit by getting rid of some capital stock, either by selling it or by declining to replace it as it wears out. 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 insights show that movements in stock prices will be reflected in changes in consumption and investment, although empirical evidence shows that the relationship is 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.

Marris's v, Kaldor's repurposing of v, and Tobin's q

Robin Marris invented the valuation ratio as a microeconomic variable in his 1964 book The Economic Theory of Managerial Capitalism and used it extensively also in all his later work on the growth of firms. In an appendix of his 1966 paper Marginal Productivity and the Macro-Economic Theory of Distribution: Comment on Samuelson and Modigliani, and without acknowledgement of its source, Nicholas Kaldor used a macroeconomic version of Marris's valuation ratio as part of his broader theory of distribution that was non-marginalist. This theory is today known as the 'Cambridge Growth Model' after the location (University of Cambridge, UK) where the theories was devised. In the paper Kaldor writes:

The "valuation ratio" (v) [is] the relation of the market value of shares to the capital employed by corporations." Kaldor then goes on to explore the properties of v at a properly macroeconomic level. He ends up deriving the following equation:

v =

1 c

⋅

[

s w

g

⋅

Y K

−

s w

s c

( 1 − i ) − i ( 1 − c )

]

{\displaystyle v={\frac {1}{c}}\cdot \left[{\frac {sw}{g}}\cdot {\frac {Y}{K}}-{\frac {sw}{sc}}(1-i)-i(1-c)\right]}

where c is net consumption out of capital, sw is the savings of workers, g is the growth rate, Y is income, K is capital, sc is savings out of capital and i is the fraction of new securities issued by firms. Kaldor then supplements this with a price, p, equation for securities which is as follows:

p =

g ( 1 − i )

s c

Cassel's q

In September 1996, at a lunch at the European Bank for Reconstruction and Development (EBRD), attended by Tobin, Mark Cutis of the EBRD and Brian Reading and Gabriel Stein of Lombard Street Research Ltd, Tobin mentioned that "in common with most American economists, [he] did not read anything in a foreign language] and that "in common with most post-War economists [he] did not read anything published before World War II". He was therefore greatly embarrassed when he discovered that in the 1920s, the Swedish economist Gustav Cassel, had introduced a ratio between a physical asset's market value and its replacement value, which he called 'q'. Cassel's q thus antedates both Marris's and Tobin's by a number of decades.

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. During periods of very high inflation, 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. 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)

See also

P/E ratio Dividend yield Intrinsic value (finance) § Equity Replacement value

External links

Tobin's Q Moderately Bullish on U.S. Equities (as of March 2009) The Manual of Ideas Launches Tobin's Q Research Service Based on James Tobin's Q Indicator Robert Huebscher on "The Market Valuation Q-uestion" Archived 2013-10-21 at the Wayback Machine Andrew Smithers' Q-Ratio FAQ Q-Ratio Graphs and Data