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[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.
[譯文]
文獻概述：
長期以來，如何實現(xiàn)各種投資成分的最優(yōu)組合一直是理財專家和有理財需求的各界人士十分關心的問題。馬科維茨（1952年）提出的均值方差分析法至今仍被投資組合管理者廣泛使用，但自默頓（1971年）以來，人們越來越明確地認識到，長期投資者最好選擇對沖性質的投資組合，以防范市場波動對其投資機會的不利影響。默頓（1969年，1975年）和薩繆爾遜（1969年）的論文產生了巨大的影響，自此以后，人們（如理查德，1975年）對動態(tài)投資組合各個方面的問題進行了廣泛研究。就動態(tài)投資組合而言，資產的價格是隨著資產的擴散過程而變化的。
在實際理財中，人們面臨著怎樣對各種投資成分進行分配，才能形成最優(yōu)投資組合的問題。研究人員對此提出了他們的觀點。馬科維茨（1959年）的研究表明，以半方差而不是方差作為風險的衡量指數(shù)，比以方差作為風險的衡量指數(shù)，有利于配置風險-收益特點更好的投資組合，減輕投資價值的下跌風險。愛德文、馬丁和曼弗里德（1976年，1978年）發(fā)表了一系列論文，他的研究表明，對普通股收益的方差協(xié)方差結構形式進行迥異于通常思路的另外假定，就會發(fā)現(xiàn)只須進行簡單的對比，就可以確定最優(yōu)的投資組合。費什波恩（1977年）提出了一種通用的風險衡量模式，以低于目標值的偏差程度作為衡量風險的指標�？{曼和特沃斯基（1979年）提出，投資者對某一投資風險分析模式的信賴取決于這種風險分析模式所帶來的收益與實際最大收益的比較。李（1990年）發(fā)現(xiàn)，均值方差系數(shù)最優(yōu)的投資組合在股份投資中所占的比例是隨著投資期限的增長而增長的。研究人員還認為，投資決策應以相對于目標收益率的下跌風險指數(shù)為依據。穆卡基（2002年）發(fā)現(xiàn)，在長期持有的前提下，與債券和票據相比，股票代表著一種更為實際的財富，相對于最低目標值的下跌風險較低。穆卡基（2003年）還表明，目標收益越高，持有期限越長，股票投資在最優(yōu)投資組合中所占的比例越大。在最優(yōu)投資組合中，股票是實現(xiàn)較高目標收益的主要成分。在中高收益和長期持有的情形下，最優(yōu)投資組合完全是由各種小盤股股票組成的。
投資績效的衡量和評估是許多理財文獻（如格林布勒特和梯特曼，1995年；伊布利特，1993年）重點探討的問題。然而，這并不是一個新的課題，夏普（1966年）、特雷曼（1966年）和詹森（1969年）早已進行了許多重要的研究工作。他們對投資績效的衡量是從收益與風險這兩個方面進行的，即在同等風險下，哪種投資組合收益較高的問題。可惜的是，投資績效并沒有精確的衡量指標；但是，我們即使使用這種并不精確的指標，也能確定哪種證券的績效表現(xiàn)良好（或較差）。我們面臨的問題是，對大多數(shù)投資者而言，任何一個單獨的數(shù)據都不足以體現(xiàn)投資組合在整個持有期限的績效表現(xiàn)，因為這里涉及到許多系統(tǒng)性因素。在這種情況下，斯帕金（2002年）研究了夏普比率的各種運用方式，并在此基礎上提出了新的夏普比率處理方法。戈茨曼等人（2002年）提出了夏普比率最大化的投資組合模式，這種模式的特點是著眼于完整市場，不放過任何一個提高收益的機會。所謂完整市場是指各種投資操作都能賴以實現(xiàn)的市場體系。他們進而發(fā)現(xiàn)，在非完整市場情形下，即投資市場只允許一種買入期權和賣出期權的情形下，也能使用上述新的夏普比率處理方法。溫斯頓（2005年）提出了一些不需要相關信息就能對夏普比率進行上述處理的方法。亨德里克森和默頓（1981年）、萊曼和莫德斯特（1987年）、莫西斯、查尼和維特（1987年）、格林布勒特和提特曼（1989年）、奧庫涅夫（1990年）等人都就投資組合的績效表現(xiàn)提出了新的評估方法。在上述方法中，投資組合管理者的把握市場時機和選擇投資機會的能力顯得尤為重要�？傮w上說，這些研究工作的基本思路是對各投資組合高于投資市場平均收益的部分給予量化的表達，上述高于投資市場平均收益的部分又稱額外收益。
關聯(lián)是指某一資產相對于另一資產的績效表現(xiàn)指標。杰金斯（1989年）認為，將正相關的不同資產納入一個投資組合，就投資收益而言并無優(yōu)勢；在同一個投資組合中，不相關資產的種類越多，該投資組合的風險就越低；如果一個投資組合完全由負相關資產組成，可以消除任何風險。博迪、凱恩和馬庫斯（2005年）指出，在同一個投資組合中，可以加入對沖資產，使其與該投資組合的其他資產正好形成負相關關系。在同一個投資組合中，不同資產間的關聯(lián)度越低，投資組合的收益率就越高；而且，上述資產配比對降低投資組合的總體風險特別有效，但投資組合的收益與上述不同資產收益的關聯(lián)度無關。 |
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