Asset Portfolio Analyst
&&&&&&&&公司行业：&&金融/投资/证券公司性质：&&外资（非欧美）公司规模：&&50-150人 &&&
发布日期：工作地点：上海招聘人数：若干语言要求：英语&熟练薪水范围：面议&&&
职位职能:&&投资银行财务分析&&其他
Job Description:- Run real estate asset portfolio cash flow models, ensure cash flow models are accurate, in standard format and reflect realistic assumptions.- Responsible for asset portfolio returns calculation including all sensitivities and analytics.- Coordination across different departments and parties to collect materials and information- Communicate with both internal and external parties for requirements of analysis and reports.- Prepare various reports based on the cash flow models and returns analysis with quality and on time.- Ad hoc projects as needed.Requirements:- Bachelor’s degree or above, 1 - 3 years of cash flow modeling experience- Real estate experience highly desirable- A can-do, positive attitude and willingness to work hard- Analytically inclined, detail oriented and organized with focus on deliverables- Fluency in Mandarin and English- Strong interpersonal skills, team player, ability to interact with colleagues
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KaiLong is a leading player in Greater China's vibrant investment and asset management market. Our professional team identifies, evaluates and executes transactions innovatively. We also provide comprehensive investment and asset management for a wide range of institutional and individual investors and our own funds.We combine international capital markets expertise with a meticulous knowledge of Greater China markets and innovative thinking. We have a profound understanding of China's rules and regulations. We maintain a broad and vital local network, and we provide expert skills to negotiate deals, financing, asset management and disposition in the whole investment process. We are recognized as a competent and successful investment and asset manager within the Greater China real estate environment, creating a global advantage in this competitive sector.KaiLong was founded in 2004 with Greater China headquarters in Shanghai and offices in Beijing and Hong Kong.As one of the few pioneers who have successfully raised RMB real estate private equity fund, we have raised four funds with a total fund size of about Rmb 1.5 billion since 2010 while the first fund was exited in 2013 with very outstanding result.In 2013, we successfully launched our maiden US dollar fund and the fund targets up to US$200 ~ 300 million.KaiLong has invested in 24 real estate projects with a total investment of over Rmb 8.4 billion, 12 of these projects were exited and generated very good risk-adjusted returns.凯龙瑞是一家专门从事投资管理及资产管理的专业机构，我们专业且富于创见的团队在生机勃勃的大中华市场上为国内外投资者及我们的基金寻找、评估及收购具有良好发展前景和投资价值的项目，同时提供全面的投资管理及资产管理。我们的团队具有全球资本市场的专业知识，同时拥有对大中华地产市场深刻理解和创新思维，我们熟知大中华区域的法律法规，拥有广泛而且非常重要的本土业务伙伴关系，对交易谈判、资本运筹、资产管理和资产处置各环节都拥有丰富的经验，被公认为是大中华房地产投资领域中卓有成就和极具竞争性的投资管理和资产管理者。集团成立于2004年，中国区总部位于上海，并在北京与香港设有办公机构。凯龙瑞是为数不多成功募集人民币地产私募基金的先驱，从2010年至今已成功募集了四支人民币基金，总募集规模约为人民币15亿元。首支人民币基金已成功退出，并为投资者带来丰厚回报。2013年底，首支美元基金成功成立，基金目标规模2 ~ 3亿美元。我们至今已投资管理了24个项目，总投资超过人民币84亿元，其中12个项目已成功退出并实现了良好的业绩。
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新版企业粉丝团终于上线了，全新的界面展示，更多的互动体验，千年等一回，Let's go go go！Mean Variance在经济学中指什么意思_百度知道
Mean Variance在经济学中指什么意思
果说一个投资者在投资中遵循Mean Variance原则？还有什么其它意义，Mean Variance中文怎么说？还有，是不是就是指效用最大化的意思
提问者采纳
波动率 衡量的是风险。Mean 即期望。Variance 即方差。 Variance相同时，衡量的是预期收益，Mean越大越好，Variance越小越好Mean Variance就是 均值方差方法就是所当Mean 相同是
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而M点以上的曲线部分称作efficient&return（代表风险）;第二步还需要加入无风险资产;Asset&nbsp，尝试解答一下吧;当然://a，表示承担同样的风险，即你构造的资产组合所能控制的最小风险，这幅图里没有显示;risky&deviation&是&nbsp，所以又叫Markowitz&nbsp，通过调整无风险资产与原有资产组合作为一个整体的权重;free&nbsp.jpg" esrc="http.hiphotos://a。&of&第三步，比曲线内的点（如S）有更高的期望收益，为了找到客户所需要的最优资产组合;Minimum-variance&nbsp。&nbsp，表示你构造的资产组合所不能达到的收益，风险承受能力等等得到客户的风险收益的无差异曲线.baidu最近刚好在学这方面的知识，可以绘制出一个曲线X轴为Standard&free&nbsp。如下图所示;asset，希望有所帮助。绿色直线与y轴的截距是无风险资产的收益，通过找到无差异曲线与Portfolio&nbsp.of&nbsp，如Q;这大概就是这个理论的大概思路。&nbsp，如绿色的直线所示;of&nbsp。&nbsp，最后最优的资产投资组合;optimization&nbsp。&nbsp。T点以后的绿线部分需要进行卖空（借出）无风险资产进行操作实现，找到对于此客户来说;因为曲线上的点在风险相同的情况下;asset的切点.hiphotos。M点称作Global&nbsp，y轴为Expected&Variance&有效边境;投资学中的一个重要分析方法.jpg" target="_blank" title="点击查看大图" class="ikqb_img_alink"><img class="ikqb_img" src="/zhidao/wh%3D450%2C600/sign=b2d4aac6e42d0c/267f9e2f4c08f1Portfolio，这只是第一步。&and&nbsp://a：&Model（MM）,曲线上的点并不是最优资产组合的最后结论，它的斜率由它与原资产的曲线相切所决定;portfolio&nbsp，所得到的不同风险处的期望收益;frontier&绿色曲线上的点表示加入无风险资产后，该资产组合所能达到的最大收益。是由Markowitz&nbsp，通过构造一个风险投资组合(Risky&nbsp。&nbsp。切点使我们找到原有资产组合最优点的风险权重;portfolio&nbsp,表示通过调整这个资产组合里不同资产的权重;Mean-variance&nbsp.baidu.risky&Portfolio)在不同的风险处的不同期望收益;risk&整个曲线称作Minimum-Variance&Mean&nbsp。&nbsp
可以这么说.通过计算均值方差权衡最高收益边际和最低风险.当然了在可承受的有效收益边界内风险越大收益越高.
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已经有帐号？From Wikipedia, the free encyclopedia
(Redirected from )
"Portfolio analysis" redirects here. For theorems about the mean-variance efficient frontier, see . For non-mean-variance portfolio analysis, see .
Modern portfolio theory (MPT) is a theory of
that attempts to maximize portfolio expected
for a given amount of portfolio risk, or equivalently minimize
for a given level of expected return, by carefully choosing the proportions of various . Although MPT is widely used in practice in the financial industry and several of its creators won a
for the theory, in recent years the basic assumptions of MPT have been widely challenged by fields such as .
MPT is a mathematical formulation of the concept of
in investing, with the aim of selecting a collection of investment assets that has collectively lower risk than any individual asset. This is possible, intuitively speaking, because different types of assets often change in value in opposite ways. For example, to the extent prices in the
move differently from prices in the , a collection of both types of assets can in theory face lower overall risk than either individually. But diversification lowers risk even if assets' returns are not negatively correlated—indeed, even if they are positively correlated.
More technically, MPT models an asset's return as a
distributed , defines
of return, and models a portfolio as a weighted combination of assets, so that the return of a portfolio is the weighted combination of the assets' returns. By combining different assets whose returns are not perfectly positively , MPT seeks to reduce the total
of the portfolio return. MPT also assumes that investors are
and markets are .
MPT was developed in the 1950s through the early 1970s and was considered an important advance in the mathematical modeling of finance. Since then, some theoretical and practical
have been leveled against it. These include evidence that financial returns do not follow a
or indeed any symmetric distribution, and that correlations between asset classes are not fixed but can vary depending on external events (especially in crises). Further, there remains evidence that investors are not
and markets may not be . Finally, the low volatility anomaly conflicts with 's trade-off assumption of higher risk for higher return. It states that a portfolio consisting of low volatility equities (like blue chip stocks) reaps higher risk-adjusted returns than a portfolio with high volatility equities (like illiquid penny stocks). A study conducted by Myron Scholes, Michael Jensen, and Fischer Black in 1972 suggests that the relationship between return and
might be flat or even negatively correlated.
The fundamental concept behind MPT is that the
in an investment
should not be selected individually, each on its own merits. Rather, it is important to consider how each asset changes in price relative to how every other asset in the portfolio changes in price.
Investing is a tradeoff between
and expected . In general, assets with higher expected returns are riskier. The stocks in an efficient portfolio are chosen depending on the investor's risk tolerance, an efficient portfolio is said to be having a combination of at least two stocks above the minimum variance portfolio. For a given amount of risk, MPT describes how to select a portfolio with the highest possible expected return. Or, for a given expected return, MPT explains how to select a portfolio with the lowest possible risk (the targeted expected return cannot be more than the highest-returning available security, of course, unless negative holdings of assets are possible.)
Therefore, MPT is a form of . Under certain
and for specific
definitions of risk and return, MPT explains how to find the best possible diversification strategy.
introduced MPT in a 1952 article and a 1959 book. Markowitz classifies it simply as "Portfolio Theory," because "There's nothing modern about it." See also this survey of the history.
In some sense the mathematical derivation below is MPT, although the basic concepts behind the model have also been very influential.
This section develops the "classic" MPT model. There have been many
MPT assumes that investors are risk averse, meaning that given two portfolios that offer the same expected return, investors will prefer the less risky one. Thus, an investor will take on increased risk only if compensated by higher expected returns. Conversely, an investor who wants higher expected returns must accept more risk. The exact trade-off will be the same for all investors, but different investors will evaluate the trade-off differently based on individual risk aversion characteristics. The implication is that a
investor will not invest in a portfolio if a second portfolio exists with a more favorable
– i.e., if for that level of risk an alternative portfolio exists that has better expected returns.
Note that the theory uses standard deviation of return as a proxy for risk, which is valid if asset returns are
or otherwise . There are problems with this, see .
Under the model:
Portfolio return is the
of the constituent assets' returns.
Portfolio volatility is a function of the
ρij of the component assets, for all asset pairs (i, j).
In general:
Expected return:
is the return on the portfolio,
is the return on asset i and
is the weighting of component asset
(that is, the proportion of asset "i" in the portfolio).
Portfolio return variance:
between the returns on assets i and j. Alternatively the expression can be written as:
Portfolio return volatility (standard deviation):
For a two asset portfolio:
Portfolio return:
Portfolio variance:
For a three asset portfolio:
Portfolio return:
Portfolio variance:
An investor can reduce portfolio risk simply by holding combinations of instruments that are not perfectly positively
( ). In other words, investors can reduce their exposure to individual asset risk by holding a
portfolio of assets. Diversification may allow for the same portfolio expected return with reduced risk. These ideas have been started with Markowitz and then reinforced by other economists and mathematicians such as Andrew Brennan who have expressed ideas in the limitation of variance through portfolio theory.
If all the asset pairs have correlations of 0—they are perfectly uncorrelated—the portfolio's return variance is the sum over all assets of the square of the fraction held in the asset times the asset's return variance (and the portfolio standard deviation is the square root of this sum).
Main article:
Efficient Frontier. The hyperbola is sometimes referred to as the 'Markowitz Bullet', and is the efficient frontier if no risk-free asset is available. With a risk-free asset, the straight line is the efficient frontier.
As shown in this graph, every possible combination of the risky assets, without including any holdings of the risk-free asset, can be plotted in risk-expected return space, and the collection of all such possible portfolios defines a region in this space. The left boundary of this region is a hyperbola, and the upper edge of this region is the efficient frontier in the absence of a risk-free asset (sometimes called "the Markowitz bullet"). Combinations along this upper edge represent portfolios (including no holdings of the risk-free asset) for which there is lowest risk for a given level of expected return. Equivalently, a portfolio lying on the efficient frontier represents the combination offering the best possible expected return for given risk level.
are preferred for calculations of the efficient frontier.
In matrix form, for a given "risk tolerance" , the efficient frontier is found by minimizing the following expression:
is a vector of portfolio weights and
(The weights can be negative, which means investors can
a security.);
for the returns on the ass
is a "risk tolerance" factor, where 0 results in the portfolio with minimal risk and
results in the portfolio infinitely far out on the frontier with both expected retur and
is a vector of expected returns.
is the variance of portfolio return.
is the expected return on the portfolio.
The above optimization finds the point on the frontier at which the inverse of the slope of the frontier would be q if portfolio return variance instead of standard deviation were plotted horizontally. The frontier in its entirety is parametric on q.
Many software packages, including , ,
and , provide
routines suitable for the above problem.
An alternative approach to specifying the efficient frontier is to do so parametrically on the expected portfolio return
This version of the problem requires that we minimize
subject to
for parameter . This problem is easily solved using a .
One key result of the above analysis is the . This theorem states that any portfolio on the efficient frontier can be generated by holding a combination of any two given portfo the latter two given portfolios are the "mutual funds" in the theorem's name. So in the absence of a risk-free asset, an investor can achieve any desired efficient portfolio even if all that is accessible is a pair of efficient mutual funds. If the location of the desired portfolio on the frontier is between the locations of the two mutual funds, both mutual funds will be held in positive quantities. If the desired portfolio is outside the range spanned by the two mutual funds, then one of the mutual funds must be sold short (held in negative quantity) while the size of the investment in the other mutual fund must be greater than the amount available for investment (the excess being funded by the borrowing from the other fund).
Main article:
The risk-free asset is the (hypothetical) asset that pays a . In practice, short-term government securities (such as US ) are used as a risk-free asset, because they pay a fixed rate of interest and have exceptionally low
risk. The risk-free asset has zero variance in returns (hence is risk-free); it is also uncorrelated with any other asset (by definition, since its variance is zero). As a result, when it is combined with any other asset or portfolio of assets, the change in return is linearly related to the change in risk as the proportions in the combination vary.
When a risk-free asset is introduced, the half-line shown in the figure is the new efficient frontier. It is tangent to the hyperbola at the pure risky portfolio with the highest . Its vertical intercept represents a portfolio with 100% of holdings in the risk- the tangency with the hyperbola represents a portfolio with no risk-free holdings and 100% of assets held in the portfolio occurring a points between those points are portfolios containing positive amounts of both the risky tangency portfolio and the risk- and points on the half-line beyond the tangency point are
portfolios involving negative holdings of the risk-free asset (the latter has been sold short—in other words, the investor has borrowed at the risk-free rate) and an amount invested in the tangency portfolio equal to more than 100% of the investor's initial capital. This efficient half-line is called the
(CAL), and its formula can be shown to be
In this formula P is the sub-portfolio of risky assets at the tangency with the Markowitz bullet, F is the risk-free asset, and C is a combination of portfolios P and F.
By the diagram, the introduction of the risk-free asset as a possible component of the portfolio has improved the range of risk-expected return combinations available, because everywhere except at the tangency portfolio the half-line gives a higher expected return than the hyperbola does at every possible risk level. The fact that all points on the linear efficient locus can be achieved by a combination of holdings of the risk-free asset and the tangency portfolio is known as the , where the mutual fund referred to is the tangency portfolio.
The above analysis describes optimal behavior of an individual investor. Asset pricing theory builds on this analysis in the following way. Since everyone holds the risky assets in identical proportions to each other—namely in the proportions given by the tangency portfolio—in market equilibrium the risky assets' prices, and therefore their expected returns, will adjust so that the ratios in the tangency portfolio are the same as the ratios in which the risky assets are supplied to the market. Thus relative supplies will equal relative demands. MPT derives the required expected return for a correctly priced asset in this context.
Specific risk is the risk associated with individual assets - within a portfolio these risks can be reduced through diversification (specific risks "cancel out"). Specific risk is also called diversifiable, unique, unsystematic, or idiosyncratic risk.
(a.k.a. portfolio risk or market risk) refers to the risk common to all securities—except for
as noted below, systematic risk cannot be diversified away (within one market). Within the market portfolio, asset specific risk will be diversified away to the extent possible. Systematic risk is therefore equated with the risk (standard deviation) of the market portfolio.
Since a security will be purchased only if it improves the risk-expected return characteristics of the market portfolio, the relevant measure of the risk of a security is the risk it adds to the market portfolio, and not its risk in isolation. In this context, the volatility of the asset, and its correlation with the market portfolio, are historically observed and are therefore given. (There are several approaches to asset pricing that attempt to price assets by modelling the stochastic properties of the moments of assets' returns - these are broadly referred to as conditional asset pricing models.)
Systematic risks within one market can be managed through a strategy of using both long and short positions within one portfolio, creating a "market neutral" portfolio. Market neutral portfolios, therefore will have a correlations of zero.
Main article:
The asset return depends on the amount paid for the asset today. The price paid must ensure that the market portfolio's risk / return characteristics improve when the asset is added to it. The
is a model that derives the theoretical required expected return (i.e., discount rate) for an asset in a market, given the risk-free rate available to investors and the risk of the market as a whole. The CAPM is usually expressed:
, Beta, is the measure of asset sensitivity to a movement i Beta is usually found via
on historical data. Betas exceeding one signify more than average "riskiness" in the sense of the asset's contribution to ov betas below one indicate a lower than average risk contribution.
is the market premium, the expected excess return of the market portfolio's expected return over the risk-free rate.
The derivation is as follows:
(1) The incremental impact on risk and expected return when an additional risky asset, a, is added to the market portfolio, m, follows from the formulae for a two-asset portfolio. These results are used to derive the asset-appropriate discount rate.
Market portfolio's risk =
Hence, risk added to portfolio =
but since the weight of the asset will be relatively low,
i.e. additional risk =
Market portfolio's expected return =
Hence additional expected return =
(2) If an asset, a, is correctly priced, the improvement in its risk-to-expected return ratio achieved by adding it to the market portfolio, m, will at least match the gains of spending that money on an increased stake in the market portfolio. The assumption is that the investor will purchase the asset with funds borrowed at the risk-free rate, ; this is rational if .
i.e.&#160;:
i.e.&#160;:
is the "beta",
return— the
between the asset's return and the market's return divided by the variance of the market return— i.e. the sensitivity of the asset price to movement in the market portfolio's value.
This equation can be
statistically using the following
where αi is called the asset's , βi is the asset's
and SCL is the .
Once an asset's expected return, , is calculated using CAPM, the future
of the asset can be
using this rate to establish the correct price for the asset. A riskier stock will have a higher beta and will be discoun less sensitive stocks will have lower betas and be discounted at a lower rate. In theory, an asset is correctly priced when its observed price is the same as its value calculated using the CAPM derived discount rate. If the observed price is higher than the valuation, then the it is undervalued for a too low price.
Despite its theoretical importance, critics of MPT question whether it is an ideal investing strategy, because its model of financial markets does not match the real world in many ways.
Efforts to translate the theoretical foundation into a viable portfolio construction algorithm have been plagued by technical difficulties stemming from the instability of the original optimization problem with respect to the available data. Recent research has shown that instabilities of this type disappear when a regularizing constraint or penalty term is incorporated in the optimization procedure.
The framework of MPT makes many assumptions about investors and markets. Some are explicit in the equations, such as the use of
to model returns. Others are implicit, such as the neglect of taxes and transaction fees. None of these assumptions are entirely true, and each of them compromises MPT to some degree.
Investors are interested in the optimization problem described above (maximizing the mean for a given variance). In reality, investors have utility functions that may be sensitive to higher moments of the distribution of the returns. For the investors to use the mean-variance optimization, one must suppose that the combination of utility and returns make the optimization of utility problem similar to the mean-variance optimization problem. A quadratic utility without any assumption about returns is sufficient. Another assumption is to use exponential utility and normal distribution, as discussed below.
Asset returns are ()
variables. In fact, it is frequently observed that returns in equity and other markets are not normally distributed. Large swings (3 to 6 standard deviations from the mean) occur in the market far more frequently than the normal distribution assumption would predict. While the model can also be justified by assuming any return distribution that is , all the joint elliptical distributions are symmetrical whereas asset returns empirically are not. Bouchaud and Chicheportiche (2012)
empirically reject the elliptical hypothesis, writing "intuitively, the failure of elliptical models can be traced to the inadequacy of the assumption of a single volatility model for all stocks."
Correlations between assets are fixed and constant forever. Correlations depend on systemic relationships between the underlying assets, and change when these relationships change. Examples include one country declaring war on another, or a general market crash. During times of financial crisis all assets tend to become positively correlated, because they all move (down) together. In other words, MPT breaks down precisely when investors are most in need of protection from risk.
All investors aim to maximize economic utility (in other words, to make as much money as possible, regardless of any other considerations). This is a key assumption of the , upon which MPT relies.
All investors are rational and . This is another assumption of the . In reality, as proven by , market participants are not always
or consistently rational. The assumption does not account for emotional decisions, stale market information, "herd behavior", or investors who may seek risk for the sake of risk.
clearly pay for risk, and it is possible that some stock traders will pay for risk as well.
All investors have access to the same information at the same time. In fact, real markets contain , , and those who are simply better informed than others. Moreover, estimating the mean (for instance, there is no consistent estimator of the drift of a brownian when subsampling between 0 and T) and the covariance matrix of the returns (when the number of assets is of the same order of the number of periods) are difficult statistical tasks.
Investors have an accurate conception of possible returns, i.e., the probability beliefs of investors match the true distribution of returns. A different possibility is that investors' expectations are biased, causing market prices to be informationally inefficient. This possibility is studied in the field of , which uses psychological assumptions to provide alternatives to the CAPM such as the overconfidence-based asset pricing model of Kent Daniel, , and Avanidhar Subrahmanyam (2001).
There are no taxes or transaction costs. Real financial products are subject both to taxes and transaction costs (such as broker fees), and taking these into account will alter the composition of the optimum portfolio. These assumptions can be relaxed with more complicated versions of the model.[]
All investors are price takers, i.e., their actions do not influence prices. In reality, sufficiently large sales or purchases of individual assets can shift market prices for that asset and others (via .) An investor may not even be able to assemble the theoretically optimal portfolio if the market moves too much while they are buying the required securities.
Any investor can lend and borrow an unlimited amount at the risk free rate of interest. In reality, every investor has a credit limit.
All securities can be divided into parcels of any size. In reality, fractional shares usually cannot be bought or sold, and some assets have minimum orders sizes.
Risk/Volatility of an asset is known in advance/is constant. In fact, markets often misprice risk (e.g. the US mortgage bubble or the European debt crisis) and volatility changes rapidly.
More complex versions of MPT can take into account a more sophisticated model of the world (such as one with non-normal distributions and taxes) but all mathematical models of finance still rely on many unrealistic premises.
The risk, return, and correlation measures used by MPT are based on , which means that they are mathematical statements about the future (the expected value of returns is explicit in the above equations, and implicit in the definitions of
and ). In practice, investors must substitute predictions based on historical measurements of asset return and
for these values in the equations. Very often such expected values fail to take account of new circumstances that did not exist when the historical data were generated.
More fundamentally, investors are stuck with estimating key parameters from past market data because MPT attempts to model risk in terms of the likelihood of losses, but says nothing about why those losses might occur. The risk measurements used are
in nature, not structural. This is a major difference as compared to many engineering approaches to .
theory and MPT have at least one important conceptual difference from the
done by nuclear power [plants]. A PRA is what economists would call a structural model. The components of a system and their relationships are modeled in . If valve X fails, it causes a loss of back pressure on pump Y, causing a drop in flow to vessel Z, and so on.
But in the
equation and MPT, there is no attempt to explain an underlying structure to price changes. Various outcomes are simply given probabilities. And, unlike the PRA, if there is no history of a particular system-level event like a , there is no way to compute the odds of it. If nuclear engineers ran risk management this way, they would never be able to compute the odds of a meltdown at a particular plant until several similar events occurred in the same reactor design.
—Douglas W. Hubbard, 'The Failure of Risk Management', p. 67, John Wiley & Sons, 2009.
Essentially, the mathematics of MPT view the markets as a collection of dice. By examining past market data we can develop hypotheses about how the dice are weighted, but this isn't helpful if the markets are actually dependent upon a much bigger and more complicated
system—the world. For this reason, accurate structural models of real financial markets are unlikely to be forthcoming because they would essentially be structural models of the entire world. Nonetheless there is growing awareness of the concept of
in financial markets, which should lead to more sophisticated market models.
Mathematical risk measurements are also useful only to the degree that they reflect investors' true concerns—there is no point minimizing a variable that nobody cares about in practice. MPT uses the mathematical concept of
to quantify risk, and this might be justified under the assumption of
returns such as
returns, but for general return
other risk measures (like ) might better reflect investors' true preferences.
In particular,
is a symmetric measure that counts abnormally high returns as just as risky as abnormally low returns. Some would argue that, in reality, investors are only concerned about losses, and do not care about the dispersion or tightness of above-average returns. According to this view, our intuitive concept of risk is fundamentally asymmetric in nature.
MPT does not account for the personal, environmental, strategic, or . It only attempts to maximize risk-adjusted returns, without regard to other consequences. In a narrow sense, its complete reliance on asset
makes it vulnerable to all the standard
such as those arising from , , and . It also rewards corporate fraud and dishonest accounting. More broadly, a firm may have strategic or social goals that shape its investment decisions, and an individual investor might have personal goals. In either case, information other than historical returns is relevant.
Modern portfolio theory has also been criticized because it assumes that returns follow a . Already in the 1960's,
showed the inadequacy of this assumption and proposed the use of
presented strategies for deriving optimal portfolios in such settings.
More recently, financial economist
has also criticized modern portfolio theory on this ground, writing:
After the stock market crash (in 1987), they rewarded two theoreticians, Harry Markowitz and William Sharpe, who built beautifully Platonic models on a Gaussian base, contributing to what is called Modern Portfolio Theory. Simply, if you remove their Gaussian assumptions and treat prices as scalable, you are left with hot air. The Nobel Committee could have tested the Sharpe and Markowitz models—they work like quack remedies sold on the Internet—but nobody in Stockholm seems to have thought about it.
Diversification eliminates non-systematic risk. As unsystematic risk is not associated with increased expected return, this is considered one of the few "free lunches" available. Following MPT means portfolio managers can invest in assets without analyzing their fundamentals, specially weighting each asset by the markets weight in the asset. Because the investor purchases assets in proportion to their market weights, there is no relative increase in demand for one asset versus another, and thus no impact on the expected returns of the portfolio.
Since MPT's introduction in 1952, many attempts have been made to improve the model, especially by using more realistic assumptions.
extends MPT by adopting non-normally distributed, asymmetric measures of risk. This helps with some of these problems, but not others.
optimization is an extension of unconstrained Markowitz optimization that incorporates relative and absolute `views' on inputs of risk and returns.
In the 1970s, concepts from Modern Portfolio Theory found their way into the field of . In a series of seminal works, Michael Conroy[] modeled the labor force in the economy using portfolio-theoretic methods to examine growth and variability in the labor force. This was followed by a long literature on the relationship between economic growth and volatility.
More recently, modern portfolio theory has been used to model the self-concept in social psychology. When the self attributes comprising the self-concept constitute a well-diversified portfolio, then psychological outcomes at the level of the individual such as mood and self-esteem should be more stable than when the self-concept is undiversified. This prediction has been confirmed in studies involving human subjects.
Recently, modern portfolio theory has been applied to modelling the uncertainty and correlation between documents in information retrieval. Given a query, the aim is to maximize the overall relevance of a ranked list of documents and at the same time minimize the overall uncertainty of the ranked list.
Some experts apply MPT to portfolios of projects and other assets besides financial instruments. When MPT is applied outside of traditional financial portfolios, some differences between the different types of portfolios must be considered.
The assets in financial portfolios are, for practical purposes, continuously divisible while portfolios of projects are "lumpy". For example, while we can compute that the optimal portfolio position for 3 stocks is, say, 44%, 35%, 21%, the optimal position for a project portfolio may not allow us to simply change the amount spent on a project. Projects might be all or nothing or, at least, have logical units that cannot be separated. A portfolio optimization method would have to take the discrete nature of projects into account.
The assets of financial p they can be assessed or re-assessed at any point in time. But opportunities for launching new projects may be limited and may occur in limited windows of time. Projects that have already been initiated cannot be abandoned without the loss of the
(i.e., there is little or no recovery/salvage value of a half-complete project).
Neither of these necessarily eliminate the possibility of using MPT and such portfolios. They simply indicate the need to run the optimization with an additional set of mathematically expressed constraints that would not normally apply to financial portfolios.
Furthermore, some of the simplest elements of Modern Portfolio Theory are applicable to virtually any kind of portfolio. The concept of capturing the risk tolerance of an investor by documenting how much risk is acceptable for a given return may be applied to a variety of decision analysis problems. MPT uses historical variance as a measure of risk, but portfolios of assets like major projects don't have a well-defined "historical variance". In this case, the MPT investment boundary can be expressed in more general terms like "chance of an ROI less than cost of capital" or "chance of losing more than half of the investment". When risk is put in terms of uncertainty about forecasts and possible losses then the concept is transferable to various types of investment.
The Security Market Line and
are often contrasted with the
(APT), which holds that the
of a financial asset can be modeled as a
of various
factors, where sensitivity to changes in each factor is represented by a factor specific .
The APT is less restrictive in its assumptions: it allows for a statistical model of asset returns, and assumes that each investor will hold a unique portfolio with its own particular array of betas, as opposed to the identical "market portfolio". Unlike the CAPM, the APT, however, does not itself reveal the identity of its priced factors—the number and nature of these factors is likely to change over time and between economies.
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"New Approaches for Portfolio Optimization: Parting with the Bell Curve — Interview with Prof. Svetlozar Rachev and Prof.Stefan Mittnik"
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