金融Essay代寫范文：Evaluation of Capital Asset Pricing Model Assumptions and Limitations

本文是金融專業的Essay代寫范例，題目是“Evaluation of Capital Asset Pricing Model Assumptions and Limitations（評估資本資產定價模型的假設和局限性）”，資本資產定價模型(CAPM)是一個非常有用的模型，它被廣泛應用于行業，盡管它是基于非常強的假設。根據該地區最近的發展進行討論。

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介紹

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:

在金融領域，“被問到的一個基本問題是，投資的風險將如何影響其預期回報”(Perold, 2004)。資本資產定價模型(CAPM)是在20世紀60年代早期引入并發展起來的(Fama和French, 2004)，它證明了在一個合理的均衡市場中，資產的風險和收益之間的聯系。CAPM公式的目的是評估當考慮到風險和金錢的時間價值時，與預期回報相比，股票的估值是否公平。為了計算一個資產的預期投資回報，考慮到它的風險，如圖1所示。簡單地說:

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的歷史

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世紀60年代，人們對風險的認識還很少——無論是理論還是經驗證據(Perold, 2004)。關于投資者在不確定性下的風險偏好和決策的理論直到20世紀40 / 50年代才出現，特別是通過馮·諾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?什么是資本資產定價模型?

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).

資本資產定價模型最初是由威廉·夏普(1964)、杰克·特雷納(1962)、約翰·林特納(1965)和簡·莫辛(1966)提出的，它建立在現代投資組合理論的基礎上，但基于資產價格不應總是依賴于其風險的概念。CAPM是金融市場行為的理論表征，可以用來估計公司的權益資本成本(Mullins, 1982)。MPT展示了理性的投資者應該如何根據他們的風險回報偏好建立一個有利可圖的投資組合。然而，CAPM包含了一個關系，擴展了資產應該如何在資本市場定價(Diksha, n.d.)。CAPM認為證券或投資組合的預期收益等于無風險證券的利率加上風險溢價。如果這個預期的回報沒有達到或超過理論要求的回報，就不應該進行投資”(資本資產定價模型，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資本資產定價模型的假設

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.

資本資產定價模型是近年來資本市場理論、資產定價和金融研究的基礎。該模型“假設在一定的假設條件下，資產的收益與其不可分散的風險之間存在線性關系”(Francisco, 1987)。這個模型主要基于4個假設。首先，投資者都是風險厭惡型的，他們的投資組合完全基于預期回報和回報標準差，兩者都是在同一持有期內衡量的。另一個假設是“完美資本市場”，即“所有資產都是無限可分的;沒有交易成本、賣空限制或稅收;信息是免費的，每個人都可以獲得;所有的投資者都可以以無風險利率借貸”(Perold, 2004)。該模型所基于的一個進一步的假設是，所有投資者都有平等的機會獲得相同的投資機會。最后的假設是，投資者對單個資產的預期收益、收益的標準差以及資產收益之間的相關性做出了相同的估計。

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資本資產定價模型的最新發展

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世紀60年代標準資本資產定價模型被引入以來，許多研究者決定對其進行擴展和發展。資產定價模型已經有了很大的發展，目的是改善其現實性。

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)套利定價理論(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一樣，這個理論為投資者提供了風險投資組合所需的估計回報率。套利定價理論旨在減少單因素CAPM的局限性，理解不同的股票對不同的市場因素具有替代敏感性。10 + 3的假設基于這樣一個事實，即資產取決于許多宏觀經濟因素，如通貨膨脹、匯率、市場指數、利率變化和市場情緒(Bulaki, 2019)。簡單地說，并不是所有資產或股票都能一直對一個特定的、相同的參數作出反應，因此需要考慮多因素和敏感性。

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)衍生而來，其重點是在標準CAPM的基礎上放寬單時段假設。據說使用ICAPM的投資者只關心期末收益，以及消費或投資的機會。，而標準CAPM的投資者會對其資產在本期末的財富感興趣(Elbannan, 2015)。在跨期資本資產定價模型中，存在一個完全市場的假設;沒有成本或稅收，所有資產都有有限責任，投資者相信他們的決定對市場價格沒有影響，市場總是處于均衡狀態等等。很明顯，ICAPM將CAPM擴展到一個更動態的環境，其結果幾乎與APT相對應。然而，ICAPM和APT的區別在于，ICAPM具有從資產特征判斷風險的能力(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.

該模型是標準資本資產定價模型的進一步發展，包括金融、運營和經濟杠桿。為了實現更準確的收益預測，它關注系統性和非系統性風險，包括完整的歷史數據和估計數據(Roodposhti & Amirhosseini, 2009)。在對該模型進行檢驗時，他們將R-CAPM與傳統CAPM、下行CAPM和adjusted CAPM進行了比較，發現R-CAPM與備選CAPM的預期收益指標存在顯著差異。

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結論

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.

本文的目的是討論資本資產定價模型在多大程度上是有用的，在該領域的最新發展。CAPM是所有近期發展的基礎，雖然非常簡單，但對理解資產價格的決定因素做出了根本性的貢獻(Perold, 2004)。這個模型最近的發展已經被證明是更加復雜和復雜的，解決了關于CAPM的簡單性提出的問題，使比較投資選擇更加容易。盡管對標準CAPM有各種各樣的批評，但沒有它，它的其他擴展也就不存在了。

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