Time and the payoff to value investing

Received: 14th April, 2003

Roland Rousseau

is responsible for quantitative investment strategies and risk management research with Deutsche Bank in South Africa. He was rated as the top quantitative analyst in 1999, 2001 and 2003 by institutional investors. He has a degree in international banking and finance (BSc Econ) and an MBA.

Paul van Rensburg*

is the Professor of Finance at the University of Cape Town. He is also Senior Portfolio Manager and Head of Equities at Kagiso Asset Management. His research interest is the pricing of equity securities.

*School of Management Studies, University of Cape Town, Private Bag, Rondebosch 7700, South Africa.

Tel: 27 21 6502 481; Fax: 27 21 6897 570; e-mail: pvanrens@commerce.uct.ac.za

Abstract Using a simulation study methodology it is found that the rewards to value investing become both larger and more reliable as the investorrsquo;s holding period lengthens. Value investors appear to be rewarded for time. Evidence is also found of a right skewness in the distributions of returns to value portfolios that becomes more pronounced over longer horizons. This implies that the rewards to value investing are not distributed evenly across stocks and time. Rather it is a minority of shares over particular periods that constitute the majority of the value effect.

Keywords: asset pricing, value investing

Introduction and prior research

lsquo;In the short run the market is a voting machine. In the long run it is a

weighing machine.rsquo;

Benjamin Graham

Since the seminal paper of Basu

(1977), who documented that New York Stock Exchange low

price-earnings ratio (P/E) shares significantly outperformed high P/E shares on a risk adjusted basis, there has been substantial confirmation of the existence of a lsquo;valuersquo; effect. Providing a perspective from a fresh data source, similar results have been observed in the South African financial

environment. Plaistowe and Knight (1987) found evidence of a market-to-book effect on the Johannesburg Stock Exchange (JSE) over the period 1973 to 1980 while Page and Palmer (1993) documented that a P/E effect existed over the period 1973 to 1984. Van Rensburg

(2001) applied a cluster analysis methodology to the monthly time-series returns of 28 characteristic-sorted hedge portfolios over the period February 1983 to March 1999. Three primary clusters of style-based risk were identified: lsquo;valuersquo;, lsquo;momentumrsquo; and lsquo;quality/sizersquo;. It was suggested that earnings yield (or P/E) be used to represent the value cluster of style-based risk on the JSE.

Purchasing lsquo;cheaprsquo; shares is not the only facet to the value investorrsquo;s approach, however. The academic literature has, to date, left unexamined the well-known fundamental analystsrsquo; adage that value investing is best viewed as a lsquo;long-runrsquo; approach to obtaining stock market outperformance. The aim of this study is to empirically examine the payoffs to purchasing low P/E securities over varying time horizons. Are value investors rewarded for time?

Data and methodology

Monthly dividend adjusted returns are collected on a sample of JSE stocks over the period January 1982 through August 1998. To avoid any problems associated with thin trading, the study focused on large capitalisation shares. On average during the sample period, approximately the top 100 shares on the JSE are represented. Not all of the shares existed in an unaltered form over the entire sample period and unbundlings, delistings and other capital events were corrected for by the Deutsche Securities Quantitative team with an explicit awareness of the issue of survivorship bias. It was also ensured that none of the stocks in the sample exhibited zero or negative earnings over the last twelve month period, allowing a ranking by P/E ratio to be used as a consistent proxy for lsquo;valuersquo;.

A simulation study methodology is used in the analysis. First, a random starting date is selected between January 1982 and August 1998. Secondly, all of the shares in the sample at that date are ranked by their P/E ratio. Thirdly, the returns earned on a equally weighted portfolio of shares comprising a particular P/E cut-off criterion over a particular time horizon is calculated. This is compared to the mean performance of the stocks in the sample over the same time horizon in order to provide a measure of the fundrsquo;s outperformance or lsquo;activersquo; return. Next, the procedure returns to step one, selecting a new starting date and the process is repeated. The iteration is repeated five hundred times, providing a distribution of the active returns of the portfolio formation rule over the time horizon selected

Six cut-off criteria for portfolio formation are specified: either the top or bottom 10 per cent, 20 per cent or 30 per cent of P/E ranked securities in the sample. For each of the six cut-off points, five time horizons are examined: holding the portfolio forward for 6, 12, 18, 24 or 30 months from the initially selected date. This provides the distributions of the active returns of 30 permutations of portfolio formation rules and time horizons. Given these distributions, it is possible to see how the active return of the top P/E stocks differs from the active returns of the bottom P/E stocks as well as to examine how they differ across various holding periods.

Empirical results

As a prelude to reporting the results on all 30 portfolios, Figure 1 focuses on the distributions of active returns on the top and bottom 30 per cent of P/E ranked stocks over a 6-month (panel 1a), 12-month (panel 1b) and 18-month (panel 1c) time horizon. Primarily for the purpose

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时间和价值投资的回报

作者：

罗兰·卢梭

负责量化投资策略和风险管理的研究。在南非和德意志银行他被评为全国定量分析师，他也是1999年，2001年和2003年机构投资者。他拥有国际银行业和金融的学士学位和MBA学位。

保罗·范·伦斯堡

是财政部在开普敦的大学教授。他也是高级投资组合经理和股票部门主管。他的研究兴趣是权益性证券的定价。

*管理研究学院，开普敦大学

ebosch7700，南非。

联系电话：27216502481;传真号码：27216897570;电子邮件：pvanrens@commerce.uct.ac.za

摘要：利用仿真研究方法可以发现，价值投资的收益增加与稳定来自于投资者的持有期延长。价值投资者得到的回报与持有期时长紧密相连。也有证券表明，持有期长的投资组合呈右偏分布。这意味着，奖励价值投资和持有时间不是分布均匀的。相反，它在某一个特定的时间段的价值效应较高。

关键词：资产定价，价值投资

1文献综述

“从短期来看，市场是一台投票机。从长远来看，它是一个称重机。”

——本杰明·格雷厄姆

巴苏（1977年）认为：纽约证券交易所低市盈率（P / E）股票股价跑赢了那些在显著风险调整的基础上的高P / E的股票，这就在实质上确认了“价值”效应确实存在。从目前观测到的新的数据源的角度来看，类似的结果已在南非金融市场有类似现象。 Plaistowe和Knight（1987）发现在约翰内斯堡证券交易所（JSE）1973-1980年年的市场与账面效应有关的证据，即PE效应确实存在。范·伦斯堡（2001）采用聚类分析方法，以28个特征排序对冲投资组合在1983年2月~1999年3月这段时间内进行测定，发现：“价值”、“趋势”、“P/E”之间确实存在联系。

购买“便宜”的股票是不是唯一的方面的价值投资者的做法？这是价值投资研究者一直探讨的话题。但是，根据知名分析师林林总总的分析结果来看，长时间的持有股票对价值升值确实是很有意义的。而本文的研究的目的是通过分析：长时间持有低P/E的证券的收益情况。

2数据和方法

每月分红调整后的收益来自于1998年8月—1982年1月期间收集的JSE股票样本，我们避免了市场交易缩量可能引起的问题，研究集中在关注度比较高的股票。及在样本期间，大约在约翰内斯堡证券交易所前100股。一个价值投资组合在整个样本期间并非是以完全不变的结构在存在的。退市等资本事件是必须要在模型中进行纠正的。还有的学者认为，还必须确保所有的样本股票在过去的一年中不能表现零或负的收益。

我们的分析方法是模拟研究法。首先，1982年1月和1998年8月之间随机选取一个起始日期，并将所有的样本用P/E比率排名。接着，计算在特定时间范围内特定的P / E值范围内的股票同等权重的投资组合的回报率。这是为了测量样本而不是在相同的时间跨度中的个股的表现，或称：利用“积极”回报衡量的平均业绩。接下来，该程序返回到步骤之一，选择一个新的开始日期和重复该过程。迭代重复五百次，在选择的时间跨度内测量所有投资组合的有效回报的分布。

投资组合的六角形特点很明显：样本中无论顶部或底部的10，20%或30%的P / E值都在较低的范围内。对于每一个六切点，我们在5倍的时间范围内进行检查：从最初选定的日期往前推6，12，18，24或30个月。这提供了组合形成的规则和时间跨度最长为30个月的排列积极回报的分布。鉴于这些分布，就可以看到顶部的P / E的股票的积极回报从底部的P / E的股票的积极回报率的不同，我们还研究它们在不同持有期的区别。

3实证结果

作为前文推断的所有30个组合的结果，图1侧重于分布每个P / E位列股票底部或顶部的30%在超过6个月、12个月、和18个月的时间跨度下的积极回报。我们在结果可视化的要求下，运用分布拟合过程的优化。人们发现，对于6个月的时间范围，逻辑分布比常态的标准假设拟合的结果更好。对于更长的时间范围，极分布被发现比正态分布更为合适。

在6个月范围内返回的股票P/E明显在顶部和底部是有明显差距的。然而，随着时间变长，价值投资组合的表现变得更加明显。这个结果提供了一个指示， 事实上价值投资是在一定时间范围类投资价值的增加。图1也说明了重要发现，随着时间变长分布变得更加偏向右边。观察所有的组合可以发现，虽然这是两个顶部和底部的P/E组合但是仍然是主流的。引用一个特定的例子：1987年10月股市崩盘后的数据库中Usko和Hiveld钢最低的P / E。Usko，未来18个月，从75美分至600美分（积极回报约650%）和Hiveld从530美分至2000美分（积极回报约为230%）。这两个股票仅贡献最突出表现。如果他们被剥离，底部10% P / E组合基准不是160%。这是一个例子：少量的股票如何扭曲了整个组合的性能值。如果投资者错过这两个或三个“明星员工”，他们不会得益于在低市盈率投资策略。

表1显示结果是所有30组模拟投资组合。一方面可以看出，P / E组合往往底部比顶部高。同时还往往低于均值，尤其是在持有期的持续时间变长，上述的表现是正确的偏态分布。列六个时间的结果进行非参数斯米尔诺夫检验时，测试是否顶部和底部P / E组合是明显不同的。

在95%的置信水平上，仅在18个月及更长的时间范围上，低市盈率投资组合的收益比高P / E组合高。同样，从报告的结果上看，高P / E组合发现随着时间的增加和相对温和的投资组合的规模变得更大，收益增加相对强烈

图2块的结果显示的是风险（标准差）回报空间。在表1的情况不同，这里的结果在技术上显示了明显不同。为了帮助解释，顶部P / E组合和底部P / E组合也在模型包括范围内。例如，“B（12，1）”指的是10%的P / E底部排在12个月期间的股票。

我们可以看到所有的低市盈率投资组合被分组在不赚不亏的范围内，虽然大多数高P / E的基准策略往往表现不佳。正如前面所讨论的，本研究的主要贡献之一是观察到这一现象表现的更明显的投资组合。

表一

图二

集群最有效的战略价值在于活跃的每单位风险的回报。他们都需要持有相对较大（因此，更多样化的）的低市盈率投资组合的时间超过18个月。图2的另一个有趣的特性在于，标准偏差较小的价值投资组合在长时间内

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