# 夏普比率：风险分析的害群之马_RCM Alternatives_HIT45

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Sharpe Ratio: the Black Sheep of Risk Analysis - RCM Alternatives​www.rcmalternatives.com

We can’t believe it’s been almost 4 years since we last spent time talking about the most popular, and most controversial risk adjusted ratio out there, the Sharpe Ratio. For those of you who have never heard of it before, the “e” is silent. We had a newcomer in the office that pronounced it with an “e” like the Sharpie highlighter until someone finally had mercy and corrected them.

Now just what is a Risk Adjusted Ratio. They are used quite often in the Alternative Investment Space, because they seek to evaluate investments not only on returns, but on how much risk it takes to get those returns. The Sharpe ratio is one of the most frequently used risk adjusted ratios, and calculates return per unit of risk as measured by volatility. Here’s the formula:

“(Compound Annual Rate of Return – Risk Free Rate) / (Annualized Standard Deviation of Returns)”

(复合年收益率-无风险利率)/(年收益率标准差)

A Little History

The idea of the Sharpe Ratio was developed by Stanford professor Dr. William Forsyth Sharpe in 1966, based on an idea presented over a decade earlier by A. D. Roy, though it was eventually edited in 1994 by Sharpe himself to reflect the fact that a risk-free rate changes with time. It started to become heavily used in the financial space in the 80s and 90s, and to this day is still found as a prime metric for any alternative investment.

Risk Free? I’ll take some of that please.

The inclusion of the term ‘risk free’ has caused more than a few people pause, and Mr. Sharpe surely came up with the ratio before debt ceiling debates and the US losing a notch on its credit rating. But the idea is that any portion of an investment (or portfolio’s return) based on things like US Treasury Bills shouldn’t be included in the ratio, as it will push up the return without having any effect on the volatility (in the world of volatility = risk, there’s no volatility if you don’t have risk of losing money – check with the boys at Long Term Capital Management and their off the run T-Bill portfolio if that’s always true). Most practioners these days remove the risk free rate, in part because rates have been zero for so long, and in part because the idea of a risk free rate has been tarnished some.

“无风险”一词的兴起已经引起了很多人的犹豫不决，夏普先生在债务上限辩论之前肯定提出了这个比率，而美国在信用评级上也被降了一个等级。但这种想法是，任何基于美国国债之类的东西的投资（或投资组合的回报）都不应该包括在这个比率中，因为它会推高回报率，而不会对波动性产生任何影响（在波动与风险相等同的世界里，如果你没有损失资金的风险，就不存在波动——与长期资本管理公司(Long Term Capital Management)的伙计们核对一下，以及他们持有的之前发行的短期债券（T-Bill）投资组合(如果这总是正确的话)。最近大多数从业者都不再关注无风险利率，部分原因是长期以来利率一直为零，部分原因是无风险利率的观念受到了一些玷污。

But what does a 0.58 Sharpe Ratio Mean?

When you put all those numbers together, you are left with a number like 0.58 or 0.92. This is confusing to some because it’s not actually showing a percentage return or the like. Meaning, we can’t visualize what 0.58 looks like on a chart, or if that means more or less returns. It would be easier if investments had Sharpe ratios of 2, 3,4, or 5 – and we could intuitively know that a Sharpe of 2 means returns twice as much return as volatility, and 5 five times the volatility, and so on. But here in the real world, most investments are lucky to get returns that are half the volatility (a 0.50 Sharpe). All told, if you’re just look at the number by itself, nothing, it doesn’t mean much until you compare it with another investment’s Sharpe Ratio. For instance the Attain Trend Following Fund has a Sharpe Ratio of 0.89, while the S&P 500 has a Sharpe of 0.55 over that same time span {Past performance is not necessarily indicative of future results}. Simple right?

Because it’s math, and most marketers steer clear of that in their messaging. And because the main advertisers of things financial (mutual funds, insurance, retirement plans, and ETFs) are benchmarked to stock and bond indices – thus don’t much care to advertise how much return their delivering per unit of risk – they just want to talk about how much return they are delivering compared to their benchmark.

But you might start hearing more about it in Alternatives, like Managed Futures outperforming stocks in 2014, become more mainstream. Alternative Investments don’t care if they’re outperforming of underperforming the stock market, or other investments. Alternative Investments try and deliver (for the most part) better risk adjusted returns than traditional stock and bond investments.

Newsflash: the Sharpe Ratio has some Issues

It would be easy to end the post there. Convince you the Sharpe Ratio is just one of those things you should be more aware of. But we wouldn’t be telling you the real issue. The Sharpe Ratio gets a bad rap, and while it’s not as bad as some make it out to be, there is some truth what they have to say. The main complaint is this ratio relies on the notions that risk equals volatility and that volatility is bad. We’ve talked time and time again, that volatility isn’t “bad” per se; and simple logic will tell you that the more you reduce volatility, the less likely you are to be able to capture higher returns. But the bigger problem for the Sharpe is that it treats all volatility the same. Basically, the ratio penalizes strategies that have upside volatility (said another way… big positive returns), and some people just don’t think big positive returns should be viewed as a negative thing.

A Better Way?

We argue that using one risked adjusted ratio alone doesn’t tell you the whole story, and is really just one chapter in the story of each investment. It’s hard to argue there isn’t more to risk than just volatility, when there’s so much more to look at; such as drawdown, downside volatility, and many more. These other risk factors are incorporated into other ratios in the following ways:

Negative Returns: In order to avoid penalizing upside volatility, some investors in the industry prefer to utilize the Sortino Ratio. The formula is the same as the Sharpe, although the denominator is the Annualized Standard Deviation of Negative Returns. But no ratio is perfect, including the Sortino. The issue with this concept of only looking at the negative returns, is it assumes that positive and negative performance is equally weighted over time. For example, there are just as many months of positive performance as negative. This is where Red Rock Capital comes in; they argue the Sortino Ratio should look at the deviations of the realized return’s underperformance from the target return.

Drawdown: This is the most common “risk” the financial world talks about, although it remains an underused metric for anyone outside of the alternatives space. The simple definition of a drawdown is the pain experienced by an investor between a peak (new highs) and subsequent valley (a low point before moving higher). But there are multiple variations of a drawdown.

Max Drawdown: The Max Drawdown is the worst depth from peak to valley experienced since the investments inception. This is yet another component when considering risk when using the Mar and Calmar Ratios. These ratios aim to find how much return is offered per unit of risk, as measured by drawdown (Comp Ror) / (Max DD).

Average Drawdown: Say you care more about the average pain incurred, instead of just the worst period. For those with such a view, the Sterling Ratio (more info here) steps in to measure returns over risk, as measured by the average annual drawdown.

Overall Pain: We’ll admit this isn’t a technical term for risk, but some people want to try to figure out a way to merge the concepts of worst case pain and the average pain together. That’s the goal of the appropriately named Ulcer Index, which measures the downside volatility, frequency of losses, magnitude of drawdown, and length of drawdown together into one number, measuring the overall pain an investor would have felt. This is one of the only risk adjusted ratios where the lower the ratio, the less pain an investor experiences to get the returns.