爱轻尘之家

本文翻译：Kevin

衡量风险和回报，第一部分

简介

到目前为止，我们始终停留在告诉你某个基金回报怎么怎么好或者怎么怎么不稳定，但我们还要学会把风险和回报综合起来看待，那就是要学会在一定风险水平下衡量该基金收益的方法。在下文中，我们将会介绍常用的两种方法：阿尔法比率和夏普比率。你在晨星的基金报告中也可以看到这些数字。

阿尔法的定义

它是指衡量一定风险水平(贝塔值)下证券的实际收益与预期收益之间的差。阿尔法值为正，表示证券的表现好于贝塔值所显示的预期水平；阿尔法值为负，则表示证券没有达到贝塔值所指示的预期水平。我们在讲解风险的第一节课时提到过，贝塔值告诉了我们如何预测回报以次来调整我们的基准。比如有个ABC的基金相对于某个股指的贝塔值为1.1，假设该股指每年带来的收益率为30%，那么这个ABC的基金的预期回报就是33%（30% * 1.1）。因为互惠基金没有必要通过贝塔值来预测回报，所以阿尔法值对于投资者来说就很有用处。要计算阿尔法值，首先要从原始回报中扣除90天的国库券所带来得回报（原因是互惠基金的回报至少要比无实际风险的投资回报要高，所以我们首先要去掉这些无实际风险投资回报），然后我们需要扣除根据贝塔值得到的预期回报，这样我们就得到了阿尔法值。阿尔法值取决于一个基金的回报和风险，所以两个相同回报的基金，阿尔法值可能不同。进一步看，高贝塔值可能带来负阿尔法值。为什么呢？高贝塔值代表高市场期望（或者说是风险水平），那么基金也就必须产生出高回报来提高阿尔法值，当实际收益小于预期收益时，阿尔法就是负值了。投资者总是想从他们的高风险投资行为中获得更多的回报。 

如何使用阿尔法值

综上所述, 你肯定想找高阿尔法值的基金。（Kevin：中间这句话没有翻译）但是阿尔法值有些特性。对于初始投资人来说，阿尔法值是相对于贝塔值基金表现的衡量方法，任何对贝塔值不利的影响同样也会作用于阿尔法值。如果因为R平方根值过低（低于75%）使得贝塔值没有过多的参考价值，同样阿尔法值也就失去了参考价值。另外阿尔法值不能够体现出该基金是由于基金公司缺乏能力导致基金弱势还是由于开支问题导致基金弱势。举个例子，指数基金的经理们不选择股票，所以这些基金不会增值或者贬值太多。那么理论上讲的话，指数基金的阿尔法值应该为0，然而很多指数基金的阿尔法值为负值，其实这里阿尔法值仅仅反映了基金开支拖累基金表现的程度。最后，要想判断阿尔法值是否反映了管理人的技巧或者仅仅是他们极好的运气是不可能的。阿尔法值是变化的，当前并不代表未来。 

夏普比率的定义

夏普比率利用标准差来定义在一定风险下基金的回报。一个基金的夏普比率越高，那么它所承担的风险也就越大。因为夏普比率采用了标准差，所以它能够把不同基金种类在一定风险下的回报作比较。夏普比率取自一个人名，诺贝尔奖获得者william sharpe，这个方法量化了基金在一定时间的投资后（比如90日的国库券）相关于标准差的基金回报。从基金回报中扣除国库券带来的回报，然后把得到的数字除以标准差就得到了夏普比率。假设一个基金回报是25%，标准差失10，国库券回报为5%，那么夏普比率=(25-5)/10= 2.0。夏普比率越高，说明基金单位风险所获得的风险回报越高。例如，基金A和B三年的回报都是8.5%，A的夏普比率是0.12，B的夏普比率是0.23，这说明B基金承担相对于A基金较低的风险，取得的回报是一样的。（Kevin：以下省略一句，大同小意）。

如何使用夏普比率

夏普比率较阿尔法值有优势。标准差衡量了某个基金回报的绝对值，而不是相对值（阿尔法值）。阿尔法值只有在一个基金的平方根比较高时才有意义，而夏普比率在任何时候都具有意义。用标准差来比较各种基金要方便的多，并且可以跨基金类型比较，比如债券或者股票基金。但是夏普比率只是一个数字， 给你一个夏普比率为1.5的数字，你不能判断这是个数字是好还是坏，只有当你把两个基金的夏普比率相比较，你才会知道哪个基金的回报风险比好。

附原文如下：

Course 205: 

 Gauging Risk and Return Together, Part 1

Introduction

  Up until now, we've focused on yardsticks that tell you either how good or how volatile a fund's returns have been. But we shouldn't neglect the measures that treat performance and risk together: risk-adjusted performance measures. We'll cover two of the more-common yardsticks, alpha and the Sharpe ratio, in this session. You can find both of these figures on the Morningstar Fund Report. 

 Alpha Defined

  In a nutshell, alpha is the difference between a fund's expected returns based on its beta and its actual returns. Alpha is sometimes called the value that a portfolio manager adds to the performance. If a fund returns more than what you'd expect given its beta, it has a positive alpha. If a fund returns less than its beta predicts, it has a negative alpha. As you'll recall from our first session on risk, beta tells you how much you can expect a fund's returns to move up or down given a movement of its benchmark. For example, if the ABC Fund has a beta of 1.1 in comparison with the S&P 500 and the S&P 500 returns 30% for the year, you would expect ABC Fund to return 33%. (30% x 1.1 = 33%.) Since mutual funds don't necessarily produce the returns predicted by their betas, alpha can be helpful to investors. To calculate a fund's alpha, first subtract the return of the 90-day Treasury bill from the fund's raw return (the idea being that the return of a mutual fund should, at the very least, exceed that of a risk-free investment). That gives you a fund's excess return. From that, subtract the fund's expected return based on its beta. What's left over is the alpha. Because a fund's return and its risk both contribute to its alpha, two funds with the same returns could have different alphas. Further, if a fund has a high beta, it's quite possible for it to have a negative alpha. That's because the higher a fund's risk level (beta), the greater the returns it must generate in order to produce a high alpha. Just as a teacher would expect his or her students in an advanced class to work at a higher level than those in a less-advanced class, investors expect more from their higher-risk investments. 

 How to Use Alpha

  It seems to follow, then, that you would want to find high-alpha funds. After all, these are funds that are delivering returns higher than they should be, given the amount of risk they assume. But alpha has its quirks. For starters, because alpha measures performance relative to beta, any drawbacks that apply to beta also apply to alpha. If a fund's beta isn't meaningful because its R-squared is too low (below 75), its alpha isn't valid, either. Secondly, alpha fails to distinguish between underperformance caused by incompetence and underperformance caused by fees. For example, because managers of index funds don't select stocks, they don't add or subtract much value. Thus, in theory, index funds should carry alphas of zero. Yet many index funds have negative alphas. Here, alpha merely reflects the drag of the fund's expenses. Finally, it's impossible to judge whether alpha reflects managerial skill or just plain old luck. Is that high-alpha manager a genius, or did he just stumble upon a few hot stocks? If it's the latter, a positive alpha today may turn into a negative alpha tomorrow. 

 Sharpe Ratio Defined

  The Sharpe ratio uses standard deviation to measure a fund's risk-adjusted returns. The higher a fund's Sharpe ratio, the better a fund's returns have been relative to the risk it has taken on. Because it uses standard deviation, the Sharpe ratio can be used to compare risk-adjusted returns across all fund categories. Developed by its namesake, Nobel Laureate William Sharpe, this measure quantifies a fund's return in excess of a guaranteed investment (the 90-day Treasury bill) relative to its standard deviation. To calculate a fund's Sharpe ratio, first subtract the return of the 90-day Treasury bill from the fund's returns, then divide that figure by the fund's standard deviation. If a fund produced a return of 25% with a standard deviation of 10 and the T-bill returned 5%, the fund's Sharpe ratio would be 2.0: (25 - 5)/10. The higher a fund's Sharpe ratio, the better its returns have been relative to the amount of investment risk it has taken. For example, both Monterey PIA Equity MNTEX and AXA Rosenberg U.S. Small Capitalization Fund BRSCX had 3-year returns of 8.5% through August 2002. But Monterey PIA Equity had a Sharpe ratio of 0.12 compared with AXA Rosenberg U.S. Small Cap's 0.23, indicating that AXA Rosenberg took on less risk to achieve the same return. The higher a fund's standard deviation, the larger the denominator of the Sharpe ratio equation; therefore, the fund needs to generate high returns to earn a high Sharpe ratio. Conversely, funds with modest standard deviations can carry high Sharpe ratios if they generate good returns. 

 How to Use the Sharpe Ratio

  The Sharpe ratio has a real advantage over alpha. Remember that standard deviation measures the volatility of a fund's return in absolute terms, not relative to an index (as alpha does). So whereas a fund's R-squared must be high for alpha to be meaningful, Sharpe ratios are meaningful all the time. Moreover, it's easier to compare funds of all types using standard-deviation-based Sharpe ratio than with beta-based alpha. Unlike beta--which is usually calculated using different benchmarks for stock and bond funds--standard deviation is calculated the exact same way for any type of fund, be it stock or bond. We can therefore use the Sharpe ratio to compare the risk-adjusted returns of stock funds with those of bond funds. As with alpha, the main drawback of the Sharpe ratio is that it is expressed as a raw number. Of course, the higher the Sharpe ratio the better. But given no other information, you can't tell whether a Sharpe ratio of 1.5 is good or bad. Only when you compare one fund's Sharpe ratio with that of another fund (or group of funds) do you get a feel for its risk-adjusted return relative to other funds.