[原稿]

 

    Literature review:

 

    The question of optimal portfolio allocation has been of long-standing interest for academics and practitioners in finance. While the mean-variance analysis of Markowitz (1952) is still commonly used among portfolio managers it has been well understood since Merton (1971) that long-term investors would prefer portfolios that include hedging components to protect against fluctuation in their investment opportunities. Prompted by the seminal papers of Merton (1969, 1975) and Samuelson (1969), studies have explored various aspects of the dynamic portfolio problem when asset prices follow diffusion processes (e.g., Richard 1975).

 

    As for how to allocate the portfolio and construct optimal portfolio in practice, there are several arguments from past researchers. Markowitz (1959) indicates that measuring risk by semi-variance, instead of variance, produces better portfolios based on downside risk have better risk-return characteristics than those based on variance. In a series of papers of  Edwin, Martin and Manfred (1976,1978), they have shown that under alternative sets of assumptions about the form of the variance covariance structure of common stock returns, simple ranking devices can be used to determine optimal portfolios. Fishburn (1977) presents a general model that measures risk as deviations below a fixed target, and Kahneman and Tversky (1979) indicate that investor utility depends on returns compared to a largest return. Lee (1990) observes that the proportion of the optimal mean-variance efficient portfolio invested in stocks increase with the investment horizon. Academics have also suggested that investment decisions should be based on downside risk measures relative to target returns.  Mukherji (2002) finds that stocks provide greater real wealth and lower downside risk relative to minimum targets, compared to bonds and bills, over long holding periods. Mukherji (2003) also shows that the stock allocations of optimal portfolios increase with the target return as well as with the holding period. For a high target return, stocks are the primary component of the optimal portfolio. For medium and high target returns over a long holding period, the optimal portfolio consists solely of small stocks.

 

    Measurement and evaluation of investment performance has received considerable interested in the finance literature. (see Grinblatt and Titman, 1995; Ippolito, 1993;among others).  However, the topic is not new. Important work has been done by Sharpe (1966) Treynor (1966), and Jensen (1969). This past work has been concerned with measuring performance in two dimensions, return and risk. That is, how do returns and the portfolios similar levels of risk? Unfortunately, there is no accurate measure of performance, but they can determine superior (inferior) performance of available securities. The problem here is no one number suffices to describe portfolio behaviour over the horizons most investors use to evaluate performance. There are too many significant systematic factors. Therefore, Spurgin (2002) reviews some techniques for gaming Sharpe ratios and introduces a new Sharpe ratio manipulation method. Goerzmann et al. (2002) construct a Sharpe ratio maximizing distribution, assuming complete markets in contingent claims. They show further that manipulation is possible without complete market, given only one call and one put. Winston (2005) provides some information-less techniques that can be used to manipulation scar rating. Hendriksson and Merton (1981), Lehmann and Modest (1987), Moses, Chaney, and Veit (1987), Grinblatt and Titman (1989), Okunev (1990) and others, developed new ways to evaluate portfolio performance. In their methods, management market timing and selection abilities received increasing attention. The general idea common to most of these works is that the method assigns to every portfolio a numerical score, often called excess return.

 

    By correlation, we refer to a measure of how the returns of one asset behave in relationship to another. Jenkins (1989) argues that there is no advantage in putting assets with positive correlation together in a portfolio, the number of uncorrelated assets in a portfolio becomes large, the risk of the portfolio will be reduced, and for the portfolio combining negatively related assets, risk would be eliminated Bodie, Kane and Marcus (2005) points out that a hedge asset has negative correlation with the other assets in the portfolio. The lower the correlation between the assets, the greater the gain we can get in efficiency.  Moreover, such assets will be particularly effective in reducing total risk but expected return is unaffected by correlation between returns.

 

    [译文]

 

    文献概述：

 

    长期以来，如何实现各种投资成分的最优组合一直是理财专家和有理财需求的各界人士十分关心的问题。马科维茨（1952年）提出的均值方差分析法至今仍被投资组合管理者广泛使用，但自默顿（1971年）以来，人们越来越明确地认识到，长期投资者最好选择对冲性质的投资组合，以防范市场波动对其投资机会的不利影响。默顿（1969年，1975年）和萨缪尔逊（1969年）的论文产生了巨大的影响，自此以后，人们（如理查德，1975年）对动态投资组合各个方面的问题进行了广泛研究。就动态投资组合而言，资产的价格是随着资产的扩散过程而变化的。

 

    在实际理财中，人们面临着怎样对各种投资成分进行分配，才能形成最优投资组合的问题。研究人员对此提出了他们的观点。马科维茨（1959年）的研究表明，以半方差而不是方差作为风险的衡量指数，比以方差作为风险的衡量指数，有利于配置风险-收益特点更好的投资组合，减轻投资价值的下跌风险。爱德文、马丁和曼弗里德（1976年，1978年）发表了一系列论文，他的研究表明，对普通股收益的方差协方差结构形式进行迥异于通常思路的另外假定，就会发现只须进行简单的对比，就可以确定最优的投资组合。费什波恩（1977年）提出了一种通用的风险衡量模式，以低于目标值的偏差程度作为衡量风险的指标。卡纳曼和特沃斯基（1979年）提出，投资者对某一投资风险分析模式的信赖取决于这种风险分析模式所带来的收益与实际最大收益的比较。李（1990年）发现，均值方差系数最优的投资组合在股份投资中所占的比例是随着投资期限的增长而增长的。研究人员还认为，投资决策应以相对于目标收益率的下跌风险指数为依据。穆卡基（2002年）发现，在长期持有的前提下，与债券和票据相比，股票代表着一种更为实际的财富，相对于最低目标值的下跌风险较低。穆卡基（2003年）还表明，目标收益越高，持有期限越长，股票投资在最优投资组合中所占的比例越大。在最优投资组合中，股票是实现较高目标收益的主要成分。在中高收益和长期持有的情形下，最优投资组合完全是由各种小盘股股票组成的。

 

    投资绩效的衡量和评估是许多理财文献（如格林布勒特和梯特曼，1995年；伊布利特，1993年）重点探讨的问题。然而，这并不是一个新的课题，夏普（1966年）、特雷曼（1966年）和詹森（1969年）早已进行了许多重要的研究工作。他们对投资绩效的衡量是从收益与风险这两个方面进行的，即在同等风险下，哪种投资组合收益较高的问题。可惜的是，投资绩效并没有精确的衡量指标；但是，我们即使使用这种并不精确的指标，也能确定哪种证券的绩效表现良好（或较差）。我们面临的问题是，对大多数投资者而言，任何一个单独的数据都不足以体现投资组合在整个持有期限的绩效表现，因为这里涉及到许多系统性因素。在这种情况下，斯帕金（2002年）研究了夏普比率的各种运用方式，并在此基础上提出了新的夏普比率处理方法。戈茨曼等人（2002年）提出了夏普比率最大化的投资组合模式，这种模式的特点是着眼于完整市场，不放过任何一个提高收益的机会。所谓完整市场是指各种投资操作都能赖以实现的市场体系。他们进而发现，在非完整市场情形下，即投资市场只允许一种买入期权和卖出期权的情形下，也能使用上述新的夏普比率处理方法。温斯顿（2005年）提出了一些不需要相关信息就能对夏普比率进行上述处理的方法。亨德里克森和默顿（1981年）、莱曼和莫德斯特（1987年）、莫西斯、查尼和维特（1987年）、格林布勒特和提特曼（1989年）、奥库涅夫（1990年）等人都就投资组合的绩效表现提出了新的评估方法。在上述方法中，投资组合管理者的把握市场时机和选择投资机会的能力显得尤为重要。总体上说，这些研究工作的基本思路是对各投资组合高于投资市场平均收益的部分给予量化的表达，上述高于投资市场平均收益的部分又称额外收益。

 

    关联是指某一资产相对于另一资产的绩效表现指标。杰金斯（1989年）认为，将正相关的不同资产纳入一个投资组合，就投资收益而言并无优势；在同一个投资组合中，不相关资产的种类越多，该投资组合的风险就越低；如果一个投资组合完全由负相关资产组成，可以消除任何风险。博迪、凯恩和马库斯（2005年）指出，在同一个投资组合中，可以加入对冲资产，使其与该投资组合的其他资产正好形成负相关关系。在同一个投资组合中，不同资产间的关联度越低，投资组合的收益率就越高；而且，上述资产配比对降低投资组合的总体风险特别有效，但投资组合的收益与上述不同资产收益的关联度无关。