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45-416: The model takes into account the asset's sensitivity to non-diversifiable risk (also known as systematic risk or market risk ), often represented by the quantity beta (β) in the financial industry, as well as the expected return of the market and the expected return of a theoretical risk-free asset . CAPM assumes a particular form of utility functions (in which only first and second moments matter, that

90-519: A stochastic economic process is characterized by the same aggregate result (but potentially different distributional outcomes), the process then has no aggregate risk. Systematic or aggregate risk arises from market structure or dynamics which produce shocks or uncertainty faced by all agents in the market; such shocks could arise from government policy, international economic forces, or acts of nature. In contrast, specific risk (sometimes called residual risk, unsystematic risk , or idiosyncratic risk )

135-510: A higher rate; less sensitive stocks will have lower betas and be discounted at a lower rate. Given the accepted concave utility function , the CAPM is consistent with intuition—investors (should) require a higher return for holding a more risky asset. Since beta reflects asset-specific sensitivity to non-diversifiable, i.e. market risk , the market as a whole, by definition, has a beta of one. Stock market indices are frequently used as local proxies for

180-442: A portfolio context—i.e. its contribution to overall portfolio riskiness—as opposed to its "stand alone risk". In the CAPM context, portfolio risk is represented by higher variance i.e. less predictability. In other words, the beta of the portfolio is the defining factor in rewarding the systematic exposure taken by an investor. The CAPM assumes that the risk-return profile of a portfolio can be optimized—an optimal portfolio displays

225-566: A portfolio's exposure to systematic risk by sacrificing expected returns. An important concept for evaluating an asset's exposure to systematic risk is beta . Since beta indicates the degree to which an asset's return is correlated with broader market outcomes, it is simply an indicator of an asset's vulnerability to systematic risk. Hence, the capital asset pricing model (CAPM) directly ties an asset's equilibrium price to its exposure to systematic risk. Consider an investor who purchases stock in many firms from most global industries. This investor

270-550: A reasonable expected return for its risk. Individual securities are plotted on the SML graph. If the security's expected return versus risk is plotted above the SML, it is undervalued since the investor can expect a greater return for the inherent risk. And a security plotted below the SML is overvalued since the investor would be accepting less return for the amount of risk assumed. Once the expected/required rate of return E ( R i ) {\displaystyle E(R_{i})}

315-457: A result, capital accumulation and the overall productivity level of the economy can decline. In economic modeling, model outcomes depend heavily on the nature of risk. Modelers often incorporate aggregate risk through shocks to endowments ( budget constraints ), productivity , monetary policy, or external factors like terms of trade. Idiosyncratic risks can be introduced through mechanisms like individual labor productivity shocks; if agents possess

360-405: Is calculated using CAPM, we can compare this required rate of return to the asset's estimated rate of return over a specific investment horizon to determine whether it would be an appropriate investment. To make this comparison, you need an independent estimate of the return outlook for the security based on either fundamental or technical analysis techniques , including P/E, M/B etc. Assuming that

405-595: Is equal in either state of the world. Now consider an example with aggregate risk. The economy is the same as that described above except for endowments: in state 1, agent 1 is endowed two units of the good while agent 2 still receives zero units; and in state 2, agent 2 still receives one unit of the good while agent 1 receives nothing. That is, ω 1 = ( 2 , 0 ) {\displaystyle \omega _{1}=(2,0)} , ω 2 = ( 0 , 1 ) {\displaystyle \omega _{2}=(0,1)} . Now, if state 1

450-498: Is highly vulnerable to idiosyncratic risk. Aggregate risk can be generated by a variety of sources. Fiscal , monetary , and regulatory policy can all be sources of aggregate risk. In some cases, shocks from phenomena like weather and natural disaster can pose aggregate risks. Small economies can also be subject to aggregate risks generated by international conditions such as terms of trade shocks. Aggregate risk has potentially large implications for economic growth. For example, in

495-753: Is realized, the aggregate endowment is 2 units; but if state 2 is realized, the aggregate endowment is only 1 unit; this economy is subject to aggregate risk. Agents cannot fully insure and guarantee the same consumption in either state. It can be shown that, in this case, the price ratio will be less than the ratio of probabilities of the two states: p 1 / p 2 < π 1 / π 2 {\displaystyle p_{1}/p_{2}<\pi _{1}/\pi _{2}} , so p 1 / π 1 < p 2 / π 2 {\displaystyle p_{1}/\pi _{1}<p_{2}/\pi _{2}} . Thus, for example, if

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540-461: Is risk is measured by variance, for example a quadratic utility) or alternatively asset returns whose probability distributions are completely described by the first two moments (for example, the normal distribution ) and zero transaction costs (necessary for diversification to get rid of all idiosyncratic risk). Under these conditions, CAPM shows that the cost of equity capital is determined only by beta. Despite its failing numerous empirical tests, and

585-823: Is risk to which only specific agents or industries are vulnerable (and is uncorrelated with broad market returns). Due to the idiosyncratic nature of unsystematic risk, it can be reduced or eliminated through diversification ; but since all market actors are vulnerable to systematic risk, it cannot be limited through diversification (but it may be insurable). As a result, assets whose returns are negatively correlated with broader market returns command higher prices than assets not possessing this property. In some cases, aggregate risk exists due to institutional or other constraints on market completeness . For countries or regions lacking access to broad hedging markets , events like earthquakes and adverse weather shocks can also act as costly aggregate risks. Robert Shiller has found that, despite

630-426: Is the future price of the asset or portfolio. The CAPM returns the asset-appropriate required return or discount rate—i.e. the rate at which future cash flows produced by the asset should be discounted given that asset's relative riskiness. Betas exceeding one signify more than average "riskiness"; betas below one indicate lower than average. Thus, a more risky stock will have a higher beta and will be discounted at

675-460: Is the nominal risk-free rate available for the market, while the slope is the market premium, E( R m )−  R f . The security market line can be regarded as representing a single-factor model of the asset price, where β is the exposure to changes in the value of the Market. The equation of the SML is thus: It is a useful tool for determining if an asset being considered for a portfolio offers

720-424: Is too low (the asset is currently undervalued), assuming that at time t + 1 {\displaystyle t+1} the asset returns to the CAPM suggested price. The asset price P 0 {\displaystyle P_{0}} using CAPM, sometimes called the certainty equivalent pricing formula, is a linear relationship given by where P T {\displaystyle P_{T}}

765-441: Is vulnerability to events which affect aggregate outcomes such as broad market returns, total economy-wide resource holdings, or aggregate income. In many contexts, events like earthquakes, epidemics and major weather catastrophes pose aggregate risks that affect not only the distribution but also the total amount of resources. That is why it is also known as contingent risk, unplanned risk or risk events. If every possible outcome of

810-493: Is vulnerable to systematic risk but has diversified away the effects of idiosyncratic risks on his portfolio value; further reduction in risk would require him to acquire risk-free assets with lower returns (such as U.S. Treasury securities ). On the other hand, an investor who invests all of his money in one industry whose returns are typically uncorrelated with broad market outcomes ( beta close to zero) has limited his exposure to systematic risk but, due to lack of diversification,

855-622: The globalization progress of recent decades, country-level aggregate income risks are still significant and could potentially be reduced through the creation of better global hedging markets (thereby potentially becoming idiosyncratic, rather than aggregate, risks). Specifically, Shiller advocated for the creation of macro futures markets . The benefits of such a mechanism would depend on the degree to which macro conditions are correlated across countries. Systematic risk plays an important role in portfolio allocation . Risk which cannot be eliminated through diversification commands returns in excess of

900-523: The reward-to-risk ratio for any security in relation to that of the overall market. Therefore, when the expected rate of return for any security is deflated by its beta coefficient, the reward-to-risk ratio for any individual security in the market is equal to the market reward-to-risk ratio, thus: The market reward-to-risk ratio is effectively the market risk premium and by rearranging the above equation and solving for E ( R i ) {\displaystyle E(R_{i})} , we obtain

945-459: The risk-free rate (while idiosyncratic risk does not command such returns since it can be diversified). Over the long run, a well-diversified portfolio provides returns which correspond with its exposure to systematic risk; investors face a trade-off between expected returns and systematic risk. Therefore, an investor's desired returns correspond with their desired exposure to systematic risk and corresponding asset selection. Investors can only reduce

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990-426: The CAPM is correct, an asset is correctly priced when its estimated price is the same as the present value of future cash flows of the asset, discounted at the rate suggested by CAPM. If the estimated price is higher than the CAPM valuation, then the asset is overvalued (and undervalued when the estimated price is below the CAPM valuation). When the asset does not lie on the SML, this could also suggest mis-pricing. Since

1035-631: The CAPM is either circular or irrational. The circularity refers to the price of total risk being a function of the price of covariance risk only (and vice versa). The irrationality refers to the CAPM proclaimed ‘revision of prices’ resulting in identical discount rates for the (lower) amount of covariance risk only as for the (higher) amount of Total risk (i.e. identical discount rates for different amounts of risk. Roger’s findings have later been supported by Lai & Stohs. Systematic risk In finance and economics , systematic risk (in economics often called aggregate risk or undiversifiable risk )

1080-493: The Krusell and Smith (1998) model, showing that solution accuracy can depend heavily on solution method. Researchers should carefully consider the results of accuracy tests while choosing solution methods and pay particular attention to grid selection. Systematic risk exists in projects and is called the overall project risk bred by the combined effect of uncertainty in external environmental factors such as PESTLE , VUCA , etc. It

1125-446: The UK or US will render the portfolio sufficiently diversified such that risk exposure is limited to systematic risk only. This number may vary depending on the way securities are weighted in a portfolio which alters the overall risk contribution of each security. For example, market cap weighting means that securities of companies with larger market capitalization will take up a larger portion of

1170-463: The ability to trade assets and lack borrowing constraints, the welfare effects of idiosyncratic risks are minor. The welfare costs of aggregate risk, though, can be significant. Under some conditions, aggregate risk can arise from the aggregation of micro shocks to individual agents. This can be the case in models with many agents and strategic complementarities ; situations with such characteristics include: innovation, search and trading, production in

1215-720: The aggregate endowment of this economy is one good regardless of which state is realized; that is, the economy has no aggregate risk. It can be shown that, if agents are allowed to make trades, the ratio of the price of a claim on the good in state 1 to the price of a claim on the good in state 2 is equal to the ratios of their respective probabilities of occurrence (and, hence, the marginal rates of substitution of each agent are also equal to this ratio). That is, p 1 / p 2 = π 1 / π 2 {\displaystyle p_{1}/p_{2}=\pi _{1}/\pi _{2}} . If allowed to do so, agents make trades such that their consumption

1260-419: The capital asset pricing model (CAPM). where: Restated, in terms of risk premium, we find that: which states that the individual risk premium equals the market premium times β . Note 1: the expected market rate of return is usually estimated by measuring the arithmetic average of the historical returns on a market portfolio (e.g. S&P 500). Note 2: the risk free rate of return used for determining

1305-466: The earlier work of Harry Markowitz on diversification and modern portfolio theory . Sharpe, Markowitz and Merton Miller jointly received the 1990 Nobel Memorial Prize in Economics for this contribution to the field of financial economics . Fischer Black (1972) developed another version of CAPM, called Black CAPM or zero-beta CAPM, that does not assume the existence of a riskless asset. This version

1350-465: The efficient frontier. Because the unsystematic risk is diversifiable , the total risk of a portfolio can be viewed as beta . All investors: In their 2004 review, economists Eugene Fama and Kenneth French argue that "the failure of the CAPM in empirical tests implies that most applications of the model are invalid". Roger Dayala goes a step further and claims the CAPM is fundamentally flawed even within its own narrow assumption set, illustrating

1395-409: The entire distribution of allocational outcomes is a state variable which must be carried across periods. This gives rise to the well-known curse of dimensionality . One approach to the dilemma is to let agents ignore attributes of the aggregate distribution, justifying this assumption by referring to bounded rationality . Den Haan (2010) evaluates several algorithms which have been applied to solving

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1440-406: The existence of more modern approaches to asset pricing and portfolio selection (such as arbitrage pricing theory and Merton's portfolio problem ), the CAPM still remains popular due to its simplicity and utility in a variety of situations. The CAPM was introduced by Jack Treynor (1961, 1962), William F. Sharpe (1964), John Lintner (1965a,b) and Jan Mossin (1966) independently, building on

1485-433: The expected return of the asset at time t {\displaystyle t} is E ( R t ) = E ( P t + 1 ) − P t P t {\displaystyle E(R_{t})={\frac {E(P_{t+1})-P_{t}}{P_{t}}}} , a higher expected return than what CAPM suggests indicates that P t {\displaystyle P_{t}}

1530-440: The form π 1 ∗ u i ( x 1 i ) + π 2 ∗ u i ( x 2 i ) {\displaystyle \pi _{1}*u_{i}(x_{1i})+\pi _{2}*u_{i}(x_{2i})} where π 1 {\displaystyle \pi _{1}} and π 2 {\displaystyle \pi _{2}} are

1575-419: The lowest possible level of risk for its level of return. Additionally, since each additional asset introduced into a portfolio further diversifies the portfolio, the optimal portfolio must comprise every asset, (assuming no trading costs) with each asset value-weighted to achieve the above (assuming that any asset is infinitely divisible ). All such optimal portfolios, i.e., one for each level of return, comprise

1620-400: The market—and in that case (by definition) have a beta of one. An investor in a large, diversified portfolio (such as a mutual fund ), therefore, expects performance in line with the market. The risk of a portfolio comprises systematic risk , also known as undiversifiable risk, and unsystematic risk which is also known as idiosyncratic risk or diversifiable risk. Systematic risk refers to

1665-423: The modified beta models. The SML graphs the results from the capital asset pricing model (CAPM) formula. The x -axis represents the risk (beta), and the y -axis represents the expected return. The market risk premium is determined from the slope of the SML. The relationship between β and required return is plotted on the security market line (SML), which shows expected return as a function of β. The intercept

1710-453: The portfolio, making it effectively less diversified. In developing markets a larger number of securities is required for diversification, due to the higher asset volatilities. A rational investor should not take on any diversifiable risk, as only non-diversifiable risks are rewarded within the scope of this model. Therefore, the required return on an asset, that is, the return that compensates for risk taken, must be linked to its riskiness in

1755-485: The presence of credit rationing, aggregate risk can cause bank failures and hinder capital accumulation . Banks may respond to increases in profitability-threatening aggregate risk by raising standards for quality and quantity credit rationing to reduce monitoring costs; but the practice of lending to small numbers of borrowers reduces the diversification of bank portfolios ( concentration risk ) while also denying credit to some potentially productive firms or industries. As

1800-472: The presence of input complementarities, and information sharing. Such situations can generate aggregate data which are empirically indistinguishable from a data-generating process with aggregate shocks. The following example is from Mas-Colell, Whinston, and Green (1995) . Consider a simple exchange economy with two identical agents, one (divisible) good, and two potential states of the world (which occur with some probability). Each agent has expected utility in

1845-635: The probabilities of states 1 and 2 occurring, respectively. In state 1, agent 1 is endowed with one unit of the good while agent 2 is endowed with nothing. In state 2, agent 2 is endowed with one unit of the good while agent 1 is endowed with nothing. That is, denoting the vector of endowments in state i as ω i , {\displaystyle \omega _{i},} we have ω 1 = ( 1 , 0 ) {\displaystyle \omega _{1}=(1,0)} , ω 2 = ( 0 , 1 ) {\displaystyle \omega _{2}=(0,1)} . Then

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1890-433: The risk common to all securities—i.e. market risk . Unsystematic risk is the risk associated with individual assets. Unsystematic risk can be diversified away to smaller levels by including a greater number of assets in the portfolio (specific risks "average out"). The same is not possible for systematic risk within one market. Depending on the market, a portfolio of approximately 30–40 securities in developed markets such as

1935-419: The risk premium is usually the arithmetic average of historical risk free rates of return and not the current risk free rate of return. For the full derivation see Modern portfolio theory . There has also been research into a mean-reverting beta often referred to as the adjusted beta, as well as the consumption beta. However, in empirical tests the traditional CAPM has been found to do as well as or outperform

1980-522: The two states occur with equal probabilities, then p 1 < p 2 {\displaystyle p_{1}<p_{2}} . This is the well-known finance result that the contingent claim that delivers more resources in the state of low market returns has a higher price. While the inclusion of aggregate risk is common in macroeconomic models , considerable challenges arise when researchers attempt to incorporate aggregate uncertainty into models with heterogeneous agents . In this case,

2025-442: Was more robust against empirical testing and was influential in the widespread adoption of the CAPM. The CAPM is a model for pricing an individual security or portfolio. For individual securities, we make use of the security market line (SML) and its relation to expected return and systematic risk (beta) to show how the market must price individual securities in relation to their security risk class. The SML enables us to calculate

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