VALUING STOCK MARKETS AND THE EQUITY RISK PREMIUM ARTICLES The purpose of this article is to present a framework for valuing stock markets. Since any yardstick Valuing stock markets aimed at valuing stock markets is surrounded by a large degree of uncertainty, it is advisable to use and the equity a broad range of measures. The article starts out by discussing how stock prices are determined and risk premium why they may deviate from a rational valuation. Subsequently, several standard valuation metrics are derived, presented and discussed on the basis of euro area data. 1 INTRODUCTION for monetary analysis, because of the interplay between the return on money and the return on Stock prices may contain relevant, timely other fi nancial assets, including equity. and original information for the assessment of market expectations, market sentiment, However, the information content of stock prices fi nancing conditions and, ultimately, the with regard to future economic activity is likely outlook for economic activity and infl ation. to vary over time. Stock prices can occasionally More specifi cally, stock prices play an active drift to levels that are not considered to be and passive role in the monetary transmission consistent with what a fundamental valuation process. The active role is most evident via would suggest. For example, this can occur in wealth and cost of capital effects. For example, times of great unrest in fi nancial markets, during as equity prices rise, share-owning households which participants may overreact to bad news become wealthier and may choose to increase and thus push stock prices below fundamental their consumption. Alternatively, higher stock valuation levels. Moreover, there are indications prices tend to lower the cost to fi rms of raising that, from time to time, investors become overly additional equity capital. This, in turn, can optimistic regarding the prospects of future stock have an impact on the prospects for economic returns, giving rise to what is usually termed an activity and infl ation in the economy as a “asset price bubble”.1 In either case, such whole through its potential impact on aggregate situations tend to blur the information content of investment and potential output. stock prices and may lead to a misallocation of resources. Stock price misalignments could thus The passive role played by stock prices is related become a concern, because they can distort to the information they provide about future economic and fi nancial decisions. Indeed, history economic developments according to equity has shown that the boom-bust cycles of stock investors. This channel is characterised by the markets associated with such periods can harm fact that stock prices, like other fi nancial asset the entire economy. prices, are inherently forward-looking. To this end, stock prices should refl ect the discounted In order to draw inferences about stock price present value of expected future dividends, movements that are as accurate as possible, a where dividends are usually paid out as a fraction number of valuation models can be used. The of earnings. Earnings among a pool of fi rms purpose of this article is to present, from a are in turn crucially dependent on aggregated methodological perspective, the most standard demand. As a result, stock prices may refl ect measures used within central banks and the the expectations of market participants about fi nancial community. Needless to say, all stock the future course of the economy. Indicators of market valuation models presented here are future economic activity can also be obtained surrounded by a large degree of uncertainty from other sources, such as business and and should be seen more as suggestive tools consumer surveys, but most stock price-based for medium-term analysis than as measures to indicators have the advantage of being available predict short-term directions of stock prices. more quickly. Furthermore, an assessment of the 1 For a detailed description of stock price bubbles and monetary value of stock markets and thus an insight into policy see the article entitled “Asset price bubbles and monetary the expected return on equity is also important policy” in the April 2005 issue of the Monthly Bulletin. ECB Monthly Bulletin November 2008 87 The article is structured as follows. Section 2 The model, in this simple theoretical elaborates on the theoretical determination representation, is based on very few assumptions. of stock prices and also discusses why stock However, when turning to its practical application, prices may occasionally depart from a rational it is necessary to rely on further assumptions. As valuation approach. Section 3 presents a number evident from the pricing equation, there are two of standard stock market valuation indicators on unknown components: fi rst, the stream of future the basis of euro area data. Section 4 concludes. dividend payments and, second, the expected future rates of return. To implement the model in practice, some simplifying assumptions regarding 2 THEORETICAL DETERMINATION OF STOCK the expected behaviour of these two components PRICES are needed. One way to go about this is by viewing the expected real rate of return on the THE RATIONAL VALUATION APPROACH stock (r) and the real growth rate of dividends (g) as constant. In this case, the present value relation In general, the price of a fi nancial asset at any is reduced to the “Gordon growth model”: point in time consists of the net present value D (1+ g) of the future cash fl ows investors expect to P t t = r erp g receive by holding the asset. The discount rates f + − (2) applied are the expected rates of return that investors demand for holding the asset in their Again, prices are high when dividend growth portfolios. For stock prices, the cash-fl ow is expected to be high or the expected rate of component consists of current and expected return on the stock is low. future dividends, whereas the discount rate is made up of the risk free interest rate and a risk For stock market valuation purposes, it premium. This results in the present value is common to scale stock prices by some relation, which is known as the dividend component related to the cash fl ow. The two discount model: 2 most common indicators are the dividend yield and the price-earnings ratio. Taking these in ⎡ ∞ D ⎤ turn, equation (2) can be rewritten to give a P E ∑ t+k t = t ⎜ k ⎜ ⎣ k=1 (1+ r) ⎦ (1) simple expression for the dividend yield: where D is the payout in the form of dividends D r +erp−g t = f and r is the discount rate. Again, the expected Pt 1+g (3) rate of return must compensate for both the passage of time and the uncertainty related According to this relation, the dividend yield to future cash fl ows derived from the stock. will be low when investors expect high future Hence, the expected rate of return can be written dividend growth g, a low real risk-free rate of as the sum of the expected real return from a return rf , a low equity premium erp, or some risk-free asset (rf ) and an equity risk premium combination thereof. In these cases, the current (erp) related to the cash fl ow uncertainty. For stock price is high relative to the current level of the time being, it is assumed that investors dividend payments. expect both entities to remain constant over time. The way in which the equity risk The pricing relation (2) may also be rewritten in premium may be determined under more terms of earnings instead of dividends. Given the general conditions is dealt with later on. The assumption that a constant fraction (θ) of earnings present value model thus states that high prices today must relate to either high expected future 2 For a thorough description of the model see the article entitled “The stock market and monetary policy” in the February 2002 dividend payments, low expected future rates issue of the Monthly Bulletin. For ease of exposition, here we of return or some combination of the two. assume a constant expected stock return. ECB Monthly Bulletin 88 November 2008 ARTICLES is paid out as dividends, the following holds: the difference between the earnings or dividend Valuing stock markets Dt = θEt. Hence equation (2) may be used to yield and the yield on a long-term nominal bond and the equity obtain an expression of the price-earnings ratio: should be proxied by the equity risk premium risk premium minus the expected rate of infl ation. Empirical Pt θ(1+ g) measures of these valuation yardsticks will be = r Et f + erp−g (4) shown in Section 3. The price-earnings ratio will thus be high when As mentioned above, the equity risk premium is earnings are expected to grow at a high rate, when an important determinant of stock prices and the the expected rate of return on the stock is low or derived valuation ratios. It is the risk compensation when some combination of the two holds. required by investors in order to hold a given stock. Thus the equity premium of a stock must Another popular valuation metric is the “Fed contain both a measure of risk and the price of a model”. By assuming a 100% payout ratio, this unit of risk. Stock pricing models often defi ne the model relates the expected return on stocks to risk component as the co-movement of the stock’s N the return on nominal government bonds rf : return with specifi c fi nancial or macroeconomic variables, while the price of risk is linked to the Et Dt N degree of risk aversion exhibited by investors.