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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(xiàn)概述：
長期以來，如何實(shí)現(xiàn)各種投資成分的最優(yōu)組合一直是理財(cái)專家和有理財(cái)需求的各界人士十分關(guān)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?cè)絹碓矫鞔_地認(rèn)識(shí)到，長期投資者最好選擇對(duì)沖性質(zhì)的投資組合，以防范市場(chǎng)波動(dòng)對(duì)其投資機(jī)會(huì)的不利影響。默頓（1969年，1975年）和薩繆爾遜（1969年）的論文產(chǎn)生了巨大的影響，自此以后，人們（如理查德，1975年）對(duì)動(dòng)態(tài)投資組合各個(gè)方面的問題進(jìn)行了廣泛研究。就動(dòng)態(tài)投資組合而言，資產(chǎn)的價(jià)格是隨著資產(chǎn)的擴(kuò)散過程而變化的。
在實(shí)際理財(cái)中，人們面臨著怎樣對(duì)各種投資成分進(jìn)行分配，才能形成最優(yōu)投資組合的問題。研究人員對(duì)此提出了他們的觀點(diǎn)。馬科維茨（1959年）的研究表明，以半方差而不是方差作為風(fēng)險(xiǎn)的衡量指數(shù)，比以方差作為風(fēng)險(xiǎn)的衡量指數(shù)，有利于配置風(fēng)險(xiǎn)-收益特點(diǎn)更好的投資組合，減輕投資價(jià)值的下跌風(fēng)險(xiǎn)。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(duì)普通股收益的方差協(xié)方差結(jié)構(gòu)形式進(jìn)行迥異于通常思路的另外假定，就會(huì)發(fā)現(xiàn)只須進(jìn)行簡單的對(duì)比，就可以確定最優(yōu)的投資組合。費(fèi)什波恩（1977年）提出了一種通用的風(fēng)險(xiǎn)衡量模式，以低于目標(biāo)值的偏差程度作為衡量風(fēng)險(xiǎn)的指標(biāo)�？{曼和特沃斯基（1979年）提出，投資者對(duì)某一投資風(fēng)險(xiǎn)分析模式的信賴取決于這種風(fēng)險(xiǎn)分析模式所帶來的收益與實(shí)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(rèn)為，投資決策應(yīng)以相對(duì)于目標(biāo)收益率的下跌風(fēng)險(xiǎn)指數(shù)為依據(jù)。穆卡基（2002年）發(fā)現(xiàn)，在長期持有的前提下，與債券和票據(jù)相比，股票代表著一種更為實(shí)際的財(cái)富，相對(duì)于最低目標(biāo)值的下跌風(fēng)險(xiǎn)較低。穆卡基（2003年）還表明，目標(biāo)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(shí)現(xiàn)較高目標(biāo)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(píng)估是許多理財(cái)文獻(xiàn)（如格林布勒特和梯特曼，1995年；伊布利特，1993年）重點(diǎn)探討的問題。然而，這并不是一個(gè)新的課題，夏普（1966年）、特雷曼（1966年）和詹森（1969年）早已進(jìn)行了許多重要的研究工作。他們對(duì)投資績效的衡量是從收益與風(fēng)險(xiǎn)這兩個(gè)方面進(jìn)行的，即在同等風(fēng)險(xiǎn)下，哪種投資組合收益較高的問題�？上У氖�，投資績效并沒有精確的衡量指標(biāo)；但是，我們即使使用這種并不精確的指標(biāo)，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(duì)大多數(shù)投資者而言，任何一個(gè)單獨(dú)的數(shù)據(jù)都不足以體現(xiàn)投資組合在整個(gè)持有期限的績效表現(xiàn)，因?yàn)檫@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(yùn)用方式，并在此基礎(chǔ)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(diǎn)是著眼于完整市場(chǎng)，不放過任何一個(gè)提高收益的機(jī)會(huì)。所謂完整市場(chǎng)是指各種投資操作都能賴以實(shí)現(xiàn)的市場(chǎng)體系。他們進(jìn)而發(fā)現(xiàn)，在非完整市場(chǎng)情形下，即投資市場(chǎng)只允許一種買入期權(quán)和賣出期權(quán)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(guān)信息就能對(duì)夏普比率進(jìn)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(píng)估方法。在上述方法中，投資組合管理者的把握市場(chǎng)時(shí)機(jī)和選擇投資機(jī)會(huì)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(duì)各投資組合高于投資市場(chǎng)平均收益的部分給予量化的表達(dá)，上述高于投資市場(chǎng)平均收益的部分又稱額外收益。
關(guān)聯(lián)是指某一資產(chǎn)相對(duì)于另一資產(chǎn)的績效表現(xiàn)指標(biāo)。杰金斯（1989年）認(rèn)為，將正相關(guān)的不同資產(chǎn)納入一個(gè)投資組合，就投資收益而言并無優(yōu)勢(shì)；在同一個(gè)投資組合中，不相關(guān)資產(chǎn)的種類越多，該投資組合的風(fēng)險(xiǎn)就越低；如果一個(gè)投資組合完全由負(fù)相關(guān)資產(chǎn)組成，可以消除任何風(fēng)險(xiǎn)。博迪、凱恩和馬庫斯（2005年）指出，在同一個(gè)投資組合中，可以加入對(duì)沖資產(chǎn)，使其與該投資組合的其他資產(chǎn)正好形成負(fù)相關(guān)關(guān)系。在同一個(gè)投資組合中，不同資產(chǎn)間的關(guān)聯(lián)度越低，投資組合的收益率就越高；而且，上述資產(chǎn)配比對(duì)降低投資組合的總體風(fēng)險(xiǎn)特別有效，但投資組合的收益與上述不同資產(chǎn)收益的關(guān)聯(lián)度無關(guān)。 |
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