**Level:** Undergraduate 1st

**Written by:** Carl R

## Executive Summary

Capital Asset Pricing Model (CAPM) and Dividend Discount Model (DDM) are among the most commonly used models in valuation. Their key appeal is simplicity, which is achieved by making rather strong assumptions about the market and its participants. Although DDM is rooted in theoretically sound Discounted Cash Flow (DCF) models, its application is mainly limited to firms with large, stable dividends. One if its key inputs, the discount rate, needs to be estimated using a cost of equity model such as CAPM. The CAPM makes numerous assumptions about the market that have been commonly criticised. However, extensions of the model have been proposed that incorporate some of the anomalies in the observed pricing dynamics.

## Introduction

One of the key aspects of financial markets relevant to investors is determining whether a stock of overpriced or underpriced. An asset’s fundamental value is generally understood as the present value of future cash flows, with numerous approaches having been proposed on how to estimate this value. The present essay focuses on two major models that have been commonly employed in stock valuation, namely the Capital Asset Pricing Model (CAPM) and the Dividend Discount Model (DDM). While these models have received a lot of critique for making unrealistic assumptions, they remain appealing due to their simplicity and intuitiveness.

## Capital Asset Pricing Model (CAPM)

### Background

The main rationale of the CAPM is that risky investments should be more rewarding than risk-free assets (Fama and French, 2004). The model assumes that the expected returns on a risky asset should exceed the returns on a risk-free asset by an amount that is proportional to equity premium (Fama and French, 1996). The latter represents the reward for investing in stocks over risk-free assets, and is measured as the expected return on the market portfolio less the return on the risk-free asset (French, 2017). The coefficient of proportionality is called the asset beta, and it represents the correlation of asset returns with market returns (Fama and French, 2004). Assuming that the market portfolio is efficient in terms of mean-variance optimisation, the CAPM implies that asset returns linearly depend on the equity premium (Cochrane, 2017).

The CAPM makes several assumptions regarding investors and markets. Most importantly, the model assumes that investors act rationally, have homogeneous expectations, and are mean-variance optimisers (Mayers, 1973; Galagedera, 2007). Another assumption is that the assets are traded publicly (French, 2017). Furthermore, it is assumed that investors are able to borrow and lend at the risk-free rate, implying that there is no difference in the optimal portfolio between lenders and borrowers (Roll, 1977). In addition, the baseline CAPM makes simplifying assumptions such as there being no taxes or transaction costs (Fama and French, 1996). More generally, the CAPM can be linked to the framework of the Efficient Market Hypothesis (EMH) which assumes that all available information is incorporated in market prices (O’Sullivan, 2018).

### Strengths and weaknesses

The CAPM is sufficiently simple to understand and easy to apply (Rossi, 2016). In practice, estimating the model only requires making decisions about the data to be used, such as the choice of the estimation window, the frequency of the data, or the benchmark index (O’Sullivan, 2018). Furthermore, the model represents volatility of an asset relative to the market as a single value, beta, which can be especially convenient when comparing different assets (Cochrane, 2017). Considering the ubiquity of discounted cash flow (DCF) models in valuation (Pinto et al., 2019), one of the key applications of CAPM is estimating cost of equity as the discount factor for present value calculations (d'Amico and De Blasis, 2020).

However, CAPM has been heavily criticised for making strong assumptions about the market (Fama and French, 2004). For example, unrestricted risk-free borrowing and lending is not realistic and may imply unlimited liability. As a result, collateral requirements would increase and limit the ability to reinvest profits (Fama and French, 1996). The assumptions of zero taxes and no transaction costs are also problematic. Investors are likely to differ in terms of after-tax returns and as such would have different optimal portfolios of risky assets (Roll, 1977). Another unrealistic assumption is that investors only care about mean and variance of returns for a single-period portfolio (Elbannan, 2015). This leads to a major weakness of CAPM, which is failing to account for important dimensions of risk that are not captured by return variability (French, 2017).

In practice, market return is proxied by return on a market index such as S&P500. However, a major critique of the model is that the market portfolio is not observable which makes CAPM not testable (Roll, 1977). Empirical tests appear to confirm that CAPM struggles to accurately describe stock return dynamics including the so-called market anomalies (Kroll et al., 1988; Reinganum, 1981; Fama and French, 2004; Rossi, 2016). This has been attributed to the static nature of the CAPM as well as deviations of real markets from the model of rational, utility-maximising investors (Fama and French, 2004; Brunnermeier et al., 2021). Notably, behavioural effects and biases such as overconfidence or herding may greatly distort asset pricing (Tversky and Kahneman, 1992; Hirshleifer, 2015).

### Extensions and alternatives

Some of the CAPM’s limitations have been addressed in its extensions. In particular, extended models have been considered that explicitly address specific model assumptions such as assumptions on borrowing restrictions (Roll, 1977), assets being publicly traded (Mayers, 1973), and investors having a single-period investment horizon (Merton and Samuelson, 1992; Barberis et al., 2015). For example, intertemporal CAPM (ICAPM) is an extension of the base CAPM where investors are allowed to consider how their future wealth will be affected by current investment decisions (Fama and French, 2004; Khan, 2008). ICAPM implies that investors maximise the expected utility of lifetime consumption, and that current prices can be influenced by the uncertainty in future investment opportunities (Elbannan, 2015).

Multi-factor models are probably among the most commonly used extensions of CAPM. Such models augment CAPM by introducing additional explanatory terms besides market risk. The most prominent example is the Fama-French three-factor model which adds two new factors, namely size and value (Fama and French, 1996). Size refers to the differences in returns on portfolios of small and large stocks, while value represents the difference in returns on stocks with high and low book-to-market ratio. It has been argued that the model successfully captures some of the dimensions of systematic risk that are ignored by the CAPM (Fama and French, 2015). The three-factor model has been further extended to include other factors such as momentum, profitability, liquidity, and investment (Liu, 2006; French, 2017; Blitz et al., 2018). Multi-factor models are often formulated within the Arbitrage Pricing Theory (Ross, 1978) where some of the unrealistic assumptions of the CAPM are relaxed.

## Dividend Discount Model (DDM)

### Background

The Dividend Discount Model (DDM) describes prices as a function of several characteristics of future dividends, namely size, certainty, and timing (Barker, 1999; Lazzati and Menichini, 2015). DDM posits that the share price is equal to the present value of the expected stream of dividend payments (Bask, 2020). The model is rooted in the more general perspective of viewing an asset’s intrinsic long-term value as the present value of future cash flows (d'Amico and De Blasis, 2020). The key inputs that are required for applying DDM are future dividends and the measure of risk (Damodaran, 2012). Risk is represented by a discount rate which is usually taken to be the cost of equity and estimated using other techniques (Foerster and Sapp, 2005). Information about future dividends is captured by two parameters, namely the dividend amount and the dividend growth rate (Irons, 2014).

In essence, DDM is rooted in discounted cash flow (DCF) methods as it views firm value as the dividend amount discounted at an appropriate rate (Drake and Fabozzi, 2008). However, it requires significantly fewer inputs than a general DCF valuation while still allowing for some flexibility. In particular, the Modigliani-Miller hypothesis on dividends implies that it does not matter to investors whether a firm pays out dividends (Brennan, 1971; Handley, 2008). Assuming the hypothesis is true, it is possible to apply DDM when the stock does not pay any dividends. Specifically, one can replace the stock’s dividend with earnings per share, although this requires making assumptions on the earnings growth rate (Damodaran, 2012).

### Strengths and weaknesses

The main appeal of DDM is its simplicity, with the model being easy to implement and intuitive to understand (Payne and Finch, 1999; Drake and Fabozzi, 2008). Fundamentally, DDM is based on the same principles as DCF valuation, and as such shares the advantages of DCF methods such as the ability to capture the time value of money (Irons, 2014). DDM may produce accurate valuations as long as the stocks pay out large and stable dividends (McLemore et al., 2015; Mugoša and Popović, 2015; Gacus and Hinlo, 2018), although it may still be less accurate than a full DCF valuation (Ivanovski et al., 2015).

At the same time, the simplicity of DDM is also its main drawback. The model depends on several inputs, namely the discount factor and the dividend growth rate, and as such it is sensitive to assumptions on these inputs (Payne and Finch, 1999; Ivanovski et al., 2015). The discount factor is often taken to be the cost of equity estimated using another model such as CAPM. It follows that DDM inherits the weaknesses of the underlying cost of equity model (Drake and Fabozzi, 2008). The model’s structure and assumptions make it less applicable to firms that do not have a stable dividend policy (d'Amico and De Blasis, 2020). Furthermore, the model may be less relevant for firms that are not paying out large dividends as a result of using share buybacks to reduce taxes. This leads to lower dividend cash flow and consequently an underestimated firm value as implied by DDM (Damodaran, 2012). Another issue with DDM is its assumption of constant growth of dividends. This assumption is not realistic and may lead to the overestimation of firm value. DDM may be less relevant for certain markets depending on their cyclicality and other industry-level factors. Notably, DDM appears to be more widely used in the financial industry compared to other markets (Imam et al., 2008). Accuracy of DDM might also depend on the structure of risk in the market, and how this risk is incorporated into the model (Bao and Feng, 2018).

### Extensions and alternatives

While discounted cash flow (DCF) models are acknowledged as a theoretically sound valuation method, DDM is generally viewed as being too simplistic to fully realise the strengths of DCF models (Imam et al., 2008). Nevertheless, numerous extensions and alternatives to DDM have been considered. Although the assumption of constant dividend growth is not realistic, it can be relaxed by considering a multi-stage model (Drake and Fabozzi, 2008). A related extension of DDM is a Markov chain model where the dividend growth rate is represented by a Markov process (d'Amico and De Blasis, 2020). The dividend growth increases or decreases with a certain probability in each period, which allows the model to provide a more flexible and realistic description of future dividend cash flow.

DDM ignores the value of certain assets and it may underestimate firm value if the dividend cash flow is reduced. Notably, this is the case for firms that practice share buybacks. Nevertheless, DDM can be adjusted to directly incorporate the values of such assets in the dividends flow (Damodaran, 2012). Stochastic DDM can be used to allow dividends to be random and evolve according to some evolution process, shifting away from the basic DDM setting of deterministic growth and discount rates (Agosto and Moretto, 2015). DDM has also been extended to a dynamic model with explicitly endogenous choice of investment (Lazzati and Menichini, 2015). DDM can be coupled with APT which would allow for more accurate estimation of long-germ risk premium (Jawadi and Prat, 2017). Overall, the practical implications of DDM seem to be limited as many companies pay no or little dividends, which makes full DCF models such as discounted free cash flow more useful (Imam et al., 2008; Pinto et al., 2019).

## Conclusion

CAPM and DDM provide simple and intuitive modelling frameworks at the cost of making strong assumptions about the market. DDM is valuation method rooted in DCF methods and it can be viewed as a one-period DCF model. Its key drawback is that application to firms with unstable or small dividends may be problematic. The main input to DDM is cost of equity which can be estimated by employing a model such as CAPM. The latter makes numerous assumptions about the market and its participants, but a variety of extensions have been proposed that more accurately describe pricing dynamics.

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