06-02, 2022

本文是金融专业的Essay代写范例，题目是“Evaluation of Capital Asset Pricing Model Assumptions and Limitations（评估资本资产定价模型的假设和局限性）”，资本资产定价模型(CAPM)是一个非常有用的模型，它被广泛应用于行业，尽管它是基于非常强的假设。根据该地区最近的发展进行讨论。

The Capital Asset Pricing Model (CAPM) is a very useful model and it is used widely in the industry even though it is based on very strong assumptions. Discuss in the light of recent developments in the area.

**Introduction介绍**

In finance, “a fundamental question asked, is how the risk of investment is going to impact its expected return” (Perold, 2004). Introduced and developed in the early 1960’s (Fama and French, 2004), the Capital Asset Pricing Model (CAPM) demonstrates the link between the risk and return of an asset, in a reasonable equilibrium market. The aim of the CAPM formula is to assess whether a stock is valued fairly when considering risk and time value of money, compared to its expected return. In order to calculate the expected return of investment for an asset, given its risk, is illustrated through Image 1. Put simply:

在金融领域，“被问到的一个基本问题是，投资的风险将如何影响其预期回报”(Perold, 2004)。资本资产定价模型(CAPM)是在20世纪60年代早期引入并发展起来的(Fama和French, 2004)，它证明了在一个合理的均衡市场中，资产的风险和收益之间的联系。CAPM公式的目的是评估当考虑到风险和金钱的时间价值时，与预期回报相比，股票的估值是否公平。为了计算一个资产的预期投资回报，考虑到它的风险，如图1所示。简单地说:

Return = Risk free rate + Beta (Market Return – Risk free rate).

This essay plans to evaluate assumptions based on the CAPM, whilst discussing limitations faced by the model. It will consider how useful CAPM is, when the returns of an asset should earn, dependent on its risk. Whilst recognising the recent developments of this model, the essay will critically compare and discuss the models’ usefulness.

**History of CAPMCAPM的历史**

There was very little understanding of risk until as late as the 1960’s – whether in terms of theory or empirical evidence (Perold, 2004). Theories regarding investor’s risk preferences and decision-making under uncertainty only emerged in the 1940s/1950s, particularly through the work of von Neumann and Morgenstern.

直到20世纪60年代，人们对风险的认识还很少——无论是理论还是经验证据(Perold, 2004)。关于投资者在不确定性下的风险偏好和决策的理论直到20世纪40 / 50年代才出现，特别是通过冯·诺伊曼和摩根斯坦的研究。

In the 1950s, Harry Markowitz introduced the Modern Portfolio Theory (MPT), being among one of the first to discuss the relationship between risk and the rate of return (Raei, 2011). “Harry Markowitz provided the first truly rigorous justification for selecting and diversifying a portfolio with the publication of his paper “Portfolio Selection”” (Sullivan, 2006). This theory argues that the characteristics of an investment’s risk and return shouldn’t be considered solely but should recognise the broad impact the investment has on the portfolio’s risk and return. The MPT assumes that investors are all risk averse, which means they will opt for the least risky asset when investing, given its level of return. This suggests that an investor will engage in more risky investments, with the expectation of a higher return.

**What is the Capital Asset Pricing Model?什么是资本资产定价模型?**

Originally introduced by William Sharpe (1964), Jack Treynor (1962), John Lintner (1965) and Jan Mossin (1966), the Capital Asset Pricing Model builds upon concepts from the Modern Portfolio Theory, yet based on the concept that the price of an asset should not always be dependent on its risk. CAPM is a theoretical representation of the behaviour of financial markets, can be employed in estimating a company’s cost of equity capital (Mullins, 1982). The MPT demonstrates how rational investors should build a profitable portfolio regarding their risk-return preferences. Whereas, the CAPM includes a relationship, expanding on how assets should be priced in the capital market (Diksha, n.d.). “CAPM holds that the expected return of a security or a portfolio equals the rate on a risk-free security plus a risk premium. If this expected return does not meet or beat a theoretical required return, the investment should not be undertaken” (Capital Asset pricing model, 2014).

资本资产定价模型最初是由威廉·夏普(1964)、杰克·特雷纳(1962)、约翰·林特纳(1965)和简·莫辛(1966)提出的，它建立在现代投资组合理论的基础上，但基于资产价格不应总是依赖于其风险的概念。CAPM是金融市场行为的理论表征，可以用来估计公司的权益资本成本(Mullins, 1982)。MPT展示了理性的投资者应该如何根据他们的风险回报偏好建立一个有利可图的投资组合。然而，CAPM包含了一个关系，扩展了资产应该如何在资本市场定价(Diksha, n.d.)。CAPM认为证券或投资组合的预期收益等于无风险证券的利率加上风险溢价。如果这个预期的回报没有达到或超过理论要求的回报，就不应该进行投资”(资本资产定价模型，2014)。

The graph below illustrates portfolio opportunities and explains the story of CAPM. The axis which runs horizontally across indicates portfolio risk which is measured by the standard deviation of portfolio return. The axis that’s vertical, illustrates the expected return. The abc curve (known as the minimum variance frontier) demonstrates the combination of expected return and the risk of assets which minimize return.

**Assumptions of the Capital Asset Pricing Model资本资产定价模型的假设**

The CAPM is the basis for most of the recent works in capital market theory, asset pricing and finance. This model “postulates that under certain assumptions, there is a linear relationship between the return of an asset and its non-diversifiable risk” (Francisco, 1987).There are 4 main assumptions on which this model is based. The first being that investors are all risk averse, basing their investment portfolios entirely through expected returns and standard deviation of return, both measured during the same holding period. Another being the assumption of the “Perfect Capital Market”, where “all assets are infinitely divisible; there are no transactions costs, short selling restrictions or taxes; information is costless and available to everyone; and all investors can borrow and lend at the risk-free rate” (Perold, 2004). A further assumption on which the model is based, is that all investors have equal access to the same investment opportunities. And the final assumption is that investors make the same estimates of individual asset expected returns, standard deviations of return as well as the correlations among asset returns.

资本资产定价模型是近年来资本市场理论、资产定价和金融研究的基础。该模型“假设在一定的假设条件下，资产的收益与其不可分散的风险之间存在线性关系”(Francisco, 1987)。这个模型主要基于4个假设。首先，投资者都是风险厌恶型的，他们的投资组合完全基于预期回报和回报标准差，两者都是在同一持有期内衡量的。另一个假设是“完美资本市场”，即“所有资产都是无限可分的;没有交易成本、卖空限制或税收;信息是免费的，每个人都可以获得;所有的投资者都可以以无风险利率借贷”(Perold, 2004)。该模型所基于的一个进一步的假设是，所有投资者都有平等的机会获得相同的投资机会。最后的假设是，投资者对单个资产的预期收益、收益的标准差以及资产收益之间的相关性做出了相同的估计。

Limitations/Flaws of the Capital Asset Pricing Model

The capital asset pricing model is often faulted as a result of the basis of its assumptions. Although the CAPM is widely used as it measures the expected rate of return of a security and relates it to expected risk, however, the empirical evidence shows that it is “poor enough to invalidate the way it is used in applications” (Fama & French, 2004). It can be said, the reason for this, is that the Capital Asset Pricing Model was developed at a time when “the theoretical foundations of decision making under uncertainty were relatively new and when basic empirical facts about risk and return in the capital markets were not yet known” (Perold, 2004). The fact that the model assumes the capital market is going to be perfect is unreasonable and is evident the capital markets aren’t perfect.

**Recent Developments of the Capital Asset Pricing Model资本资产定价模型的最新发展**

Since being introduced, many researchers have decided to extend and develop the standard Capital Asset Pricing Model since the 1960s. Asset pricing models have evolved considerably with the aim of improving its realism.

自20世纪60年代标准资本资产定价模型被引入以来，许多研究者决定对其进行扩展和发展。资产定价模型已经有了很大的发展，目的是改善其现实性。

Three Factor Model

“One critical assumption in CAPM is the risk premium estimation, the residual between the market return and the risk-free interest rate” (Gustafsson and Gustavsson, 2019). The Three-Factor Model was developed and proposed by Fama and French in response to accumulating empirical evidence that the CAPM performed poorly in explaining realised returns (Gaunt, 2004). When developing the standard CAPM, Fama and French added two factors in the aim of better explaining the returns of the portfolio, including market capitalisation and book-to-market value. In 1995, they identified a covariance between the company’s book-to-market ratio and size, in the aim of measuring the return of the stock. After testing the Three Factor Model empirically, it was confirmed that this model had higher explanatory power than the one factor CAPM (Gaunt, 2004). This means that the main advantage of this model is that it includes the size and value of the firm, and the market risk factor used in the CAPM.

Five Factor Model

After developing the three-factor model, Fama and French went on to further expand on this theory, introducing the Five-Factor model. This model was directed at not only taking into consideration the size and value of the firm, and the market risk factor – but it also considers the profitability of the stocks, and the investment patterns in average stock returns (Fama and French, 2014). The empirical tests of the five-factor model aim to explain average returns on portfolios formed to produce large spreads in size, profitability and investment (Musarurwa, 2019). “With the addition of profitability and investment factors, the value of the previous three-factor model becomes redundant” (Fama and French, 2015).

**Arbitrage Pricing Theory (APT)套利定价理论(APT)**

Like CAPM, this theory gives investors an estimated required rate of return on portfolios which are of risk. The Arbitrage Pricing Theory aims to reduce the limitations of the one-factor CAPM, with the understanding that different stocks will have alternative sensitivities to different market factors. The APT bases its assumption on the fact that an asset is dependent on numerous macroeconomic factors, i.e. inflation, exchange rates, market indices, changes in interest rates and market sentiments (Bulaki, 2019), to name a few. Simply, not all assets or stocks can be expected to react to a specific and same parameter all the time, thus the requirement to consider the multifactor and sensitivities.

和CAPM一样，这个理论为投资者提供了风险投资组合所需的估计回报率。套利定价理论旨在减少单因素CAPM的局限性，理解不同的股票对不同的市场因素具有替代敏感性。10 + 3的假设基于这样一个事实，即资产取决于许多宏观经济因素，如通货膨胀、汇率、市场指数、利率变化和市场情绪(Bulaki, 2019)。简单地说，并不是所有资产或股票都能一直对一个特定的、相同的参数作出反应，因此需要考虑多因素和敏感性。

Zero-Beta CAPM

Developed by Black in 1972, the Zero-Beta CAPM showed that the results from CAPM do not require a risk-free asset which has returns constantly in every state of nature. A zero-beta portfolio is one which is built without systematic risk. The zero-beta CAPM implies that beta is still the correct measure of systematic risk, and that the model still has a linear specification. This means that the value of the portfolio doesn’t fluctuate with market movements. Without systematic risk in a zero-beta portfolio, the return is the same as the risk-free rate. Thus, the return on a portfolio with zero-beta is going to be low, and without the volatility of the market exposed, it does not allow the portfolio to benefit from potential upswings in value of the overall market (InvestingAnswers, 2009).

**Inter-Temporal CAPM跨期CAPM**

Derived from Merton (1973), ICAPM focuses on relaxing the single time period assumption from the standard CAPM. It is said that investors who use ICAPM are only concerned with the end-of-period payoff, as well as the chance to consume or invest this payoff., whereas investors of the standard CAPM would be interested about the wealth of their assets at the end of the current period (Elbannan, 2015). With the Inter-temporal CAPM, there is the assumption of a perfect market; no costs or taxes, all assets have limited liability, investors believe their decision has no impact on the market price and the market is always in an equilibrium etc. It’s evident that the ICAPM extends the CAPM to a more dynamic environment, where the results almost mirror that of the APT. The difference between ICAPM and APT, however, is that the ICAPM has the ability to determine risks from characteristics of the assets (Krause, 2001).

ICAPM由Merton(1973)衍生而来，其重点是在标准CAPM的基础上放宽单时段假设。据说使用ICAPM的投资者只关心期末收益，以及消费或投资的机会。，而标准CAPM的投资者会对其资产在本期末的财富感兴趣(Elbannan, 2015)。在跨期资本资产定价模型中，存在一个完全市场的假设;没有成本或税收，所有资产都有有限责任，投资者相信他们的决定对市场价格没有影响，市场总是处于均衡状态等等。很明显，ICAPM将CAPM扩展到一个更动态的环境，其结果几乎与APT相对应。然而，ICAPM和APT的区别在于，ICAPM具有从资产特征判断风险的能力(Krause, 2001)。

Downside CAPM (Downside BETA)

Downside BETA, or Downside-CAPM is another extension from the CAPM. This concept dates back to as Beta is used within the standard CAPM as a way of calculating the expected return of an asset. Downside beta is a way to measure the downside risk of an asset, the risk associated with loss (Pedersen & Hwang, 2007). Investors may try and consider constructing their portfolios by minimising the downside beta. The reason for this is to ensure they can maintain the value in times of market decline.

**Revised CAPM修改后的CAPM**

This model is a further development of the standard Capital Asset Pricing Model, which includes financial, operational and economic leverages. In order to achieve a more accurate prediction of return, it focuses on systematic and unsystematic risk, including historical and estimating data completely (Roodposhti & Amirhosseini, 2009). When testing this model, they compared R-CAPM with the traditional CAPM, Downside CAPM and the Adjusted-CAPM, and found that there was a meaningful difference between the measures of expected return for R-CAPM and the alternative CAPMs.

该模型是标准资本资产定价模型的进一步发展，包括金融、运营和经济杠杆。为了实现更准确的收益预测，它关注系统性和非系统性风险，包括完整的历史数据和估计数据(Roodposhti & Amirhosseini, 2009)。在对该模型进行检验时，他们将R-CAPM与传统CAPM、下行CAPM和adjusted CAPM进行了比较，发现R-CAPM与备选CAPM的预期收益指标存在显著差异。

Consumption CAPM (Co-CAPM)

Founded by Robert Lucas (1978) and Douglas Breeden (1979), the Consumption CAPM is an additional extension of the standard CAPM. “Co-CAPM quantity market risk is measured by movement of the premium with consumption growth. Thus, the Co-CAPM explains how much the entire stock market changes related to the consumption growth” (Raei, 2011). This model is argued to be the best theoretical model, however the basic link between consumption and stock returns assumed by the Co-CAPM cannot hold. The Co-CAPM is used more from an academic perspective as it covers many forms of wealth, beyond stock market wealth, providing an understanding of variation in returns over a number of periods.

Reward CAPM (Reward-BETA)

It was stated by Graham Bornholt in 2006, that investors require a better methodology in order to estimate the expected returns within the stock market. With this in mind, he developed the Reward-BETA CAPM. This model is based on assumptions which are consistent with the Arbitrage Theory; dividing returns of stocks into two parts: expected and unexpected stock returns.

**Conclusion结论**

The purpose of this essay was to discuss the extent to which the Capital Asset Pricing Model is useful in light of recent developments in the area. The CAPM is the basis of all recent developments, and although very simple, is a fundamental contribution to the understanding of the determinants of asset prices (Perold, 2004). Recent developments from this model have proved to be more intricate and complex, solving issues which were raised regarding the simplicity of the CAPM, allowing ease when comparing investment alternatives. Although there have been various criticisms of the standard CAPM, without it, the other extensions from it would not exist.

本文的目的是讨论资本资产定价模型在多大程度上是有用的，在该领域的最新发展。CAPM是所有近期发展的基础，虽然非常简单，但对理解资产价格的决定因素做出了根本性的贡献(Perold, 2004)。这个模型最近的发展已经被证明是更加复杂和复杂的，解决了关于CAPM的简单性提出的问题，使比较投资选择更加容易。尽管对标准CAPM有各种各样的批评，但没有它，它的其他扩展也就不存在了。

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