永存於交易市場

傳統的投資風險被認為是資產的市場價值與真實價值之間的波動或標準偏差。標準偏差表示的是投資價值與平均收益之間的波動幅度。投資的產品越不穩定，它的價格就越有可能圍繞歷史平均值波動（利弊共存），也就說明該資產或投資類別的風險性越大。

比如，下圖1顯示了全球股市與全球證券的正常回報對比。用摩根士丹利世界指數表示（MSCI）代表全球股市，全球證券由花旗集團(Citigroup)投資級債券指數表示。

如果在過去十年中你同時投資全球股市與證券，那麼現在你的投資組合價值應該幾乎相等，分別為168美元以及165美元（股市的年風險收入比是非常令人沮喪的，這一點要另當別論）。然而，全球股市波動性比證券大得多，因此從定義上來講，它的風險也更大。按照日回報率的時間序列來計算它們的標準偏差的話，那麼全球股市為2.53% 而全球證券則為0.50%。

圖 1: 全球股市& 全球證券10年的正常回報率

 
有許多衡量風險的傳統方法比如風險價值分析法或條件風險價值（CVaR）。這些方法現在已經被大量的投資者沿用至今。
然而，與我密切相關同時也對我來說最重要的是爆倉的風險。這些年來，我的靈感以及經驗來源於許多市場專家和基金經理。他們成功地塑造了我的交易思維並且看到風險的觀念，其中“交易成本虧損的風險”是最重要的一點。
那麼，我們要如何量化虧損風險？我所知道的兩種方法，它們來自D.R. Cox與H.D Miller所著的《隨機過程理論》。

1、固定交易規模、倉位不變（比如，無論交易本金如何變化，持倉手數不變）。

R= 失去交易資本z的風險百分比（概率）。
e = 自然對數的指數， 2.71828。
z = 如果我們想計算失去帳戶一半本金的風險，那麼z值輸入0.5.
a = 交易的平均回報，需要與d同一個週期。比如，如果a使用日平均回報，那麼d就使用日回報的標準偏差。如果a使用週平均回報，那麼d就使用週回報平均偏差。
d=回報的標準偏差，需要與前面提到的平均回報處於一個時間框架。

2、固定交易百分比（比如，本金的2%）。

R=失去交易資本z的風險百分比（概率）。
e =自然對數的指數， 2.71828。
ln(1-z) = (1-z)的自然對數
z =如果我們想計算失去帳戶一半本金的風險，那麼z值輸入0.5.
a = 交易的平均回報，需要與d同一個週期。比如，如果a使用日平均回報，那麼d就使用日回報的標準偏差。如果a使用週平均回報，那麼d就使用週回報平均偏差。
d=回報的標準偏差，需要與前面提到的平均回報處於一個時間框架。
你或許希望將這些算法應用於計算資金管理工具中，並計算出交易中最重要的交易風險。保持交易的長久性，是一場在外匯交易中生存下來的遊戲。

Live To Trade Another Day
In traditional investing, risk is viewed as volatility or standard deviation of the asset’s marked to market value. Standard deviation tells you how much an investment’s value will fluctuate from the average return. The more volatile the investment is likely to swing (both positively and negatively) around it’s own historical average, the more risky an investment or asset class is.

For example, Chart 1 below shows the normalised returns of Global Equities, as represented by MSCI World Index, versus Global Bonds, as represented by Citigroup Broad Investment Grade Bonds Index.

If you had invested $100 in both Global Equities and Global Bonds for the past 10 years, your portfolio value of either would be fairly similar, which is $168 for Global Equities and $165 for Global Bonds. (pretty dismal annualised returns per unit risk for Global Equities but that’s another story altogether) However, Global Equities is more volatile than Global Bonds and hence more risky by definition. The standard deviation of a time series of daily returns for Global Equities is 2.53% versus 0.50% for Global Bonds. 

Chart 1: Normalised Returns For Past 10 Years For Global Equities & Global Bonds

There are many more traditional measures of risk such as Value-at-Risk or Conditional-Value-at-Risk, which is an extension of VAR. These measures are widely used by the vast majority of investors for many years now.

However the most important and relevant risk to me when I trade is the Risk of Ruin. There were many sources of inspiration and influences (the “Market Wizards” type of traders and successful fund managers) through the years in shaping my thoughts on trading and this concept of looking at risk as the “risk of losses of trading capital” has been one of the most important.

So how do we quantify the risk of ruin? I came across these 2 methods as described below. They were referenced from D.R. Cox and H.D Miller in “The Theory of Stochastic Processes”.

For fixed trade size without dynamic position sizing (i.e. fixed trade size regardless of trading capital changes)
 
R= Risk of losing z fraction of the trading capital in percentage terms (probability)
e = Base of natural logarithm, 2.71828
z = If we want to calculate the risk of losing half the account, input 0.5
a = mean return of the trades, must be same time frame as d. For example if daily mean returns are used, then use standard deviation of daily returns. If weekly mean returns are used, then use standard deviation of weekly returns.
d = standard deviation of returns, must be same time frame as mean returns mentioned earlier.

For fixed trade percentage (e.g. 2% of capital per trade)
 
R= Risk of losing z fraction of the trading capital in percentage terms (probability)
e = Base of natural logarithm, 2.71828
ln(1-z) = natural logarithm of (1-z)
z = If we want to calculate the risk of losing half the account, input 0.5
a = mean return of the trades, must be same time frame as d. For example if daily mean returns are used, then use standard deviation of daily returns. If weekly mean returns are used, then use standard deviation of weekly returns.
d = standard deviation of returns, must be same time frame as mean returns mentioned earlier.

You may wish to incorporate these calculations in your money management tools to give you an idea of the risk of ruin which is so important in trading. Live to trade another day. It is all about survival in this game!

本文翻譯由兄弟財經提供

文章來源：http://www.fxstreet.com/education/technical/live-to-trade-another-day/2014/07/23/