簡談RISK

1. 什麽是RISK?

RISK是指投資回報率的不確定性. 數學上用均方差來表述. 老外說:VOLATILITY 或STANDARD DEVATION.

2. 數學意義

Sigma^2=SUM(r-E(r))^2

Sigma-RISK

r- Period return

E(r)- Mean

用EXCEL很容易計算它.

3. 物理意義

回報率14%,RISK為10.83%是個什麽概念? 它是指68%的時間內投資的回報率在14%±10.83%,既14%-10.83%=3.17 與14%+10.83%=24.83%之間波動,95%的時間內在14%±2*SIGMA之間,即-7.66%~35.86%之間波動. 換句話說,投資回報率有32%的概率可能低於3.17%, 5%的概率可能低於-7.66%. RISK是用過去曆史數據對未來回報率的波動範圍的估計.

4. 如何得當RISK係數

(A) 從網站上查:

可以從GLOGBEFUND的網業上查到RISK係數:

http://globefunddb.theglobeandmail.com/gishome/plsql/gis.analyser.

它是用三年數據計算出的年度係數.

(B) 自己計算:

方法如下:

1. 查得某MF的每月豈止UNIT 價格,共查出三年的曆史數據;

2. 用EXCEL列表計算每月回報率(RETURN);

3. 用EXCEL的STDV函數計算出月均方差,然後乘以SQRT(12),即為年度RISK.

5. 如何計算PORTFOLIO的RISK係數

PORTFOLIO 的RISK可用如下公式計算:

Sigma(p)=SUM[w(i)^2Xsingma(i)^2+所有可能的2XSingm(i)XSingma(j)XCorrelation(i,j))]

式中

sigma(i)j, - 是第i(j)個MF的RISK係數

Correlation(i,j)- 是第i,j MF之間的協方差係數;

w(i)- 是第i個MF在PORFOLIO中的權係數;

6. 應用:

(a) 直接評估MF的風險. 越小RISK的MF,其風險(波動)越小.

(b) SHARP RATIO: =ANNUALIZED RETURN/ANNUALIZEED 比數,可用來評估MF的風險回報性能. SHARP RATIO越大,MF的風險回報性能越佳.

7. 計算實例 :

以CIBC ENRGY FUND為例,說明如何計算RISK

DATE CIBC ENERGY CIBC ENERGY Month Return

Jan-03 $16.8765

Feb-03 $16.9587 0.49%

Mar-03 $17.6664 4.17%

Apr-03 $16.6121 -5.97%

May-03 $17.0796 2.81%

Jun-03 $18.2810 7.03%

Jul-03 $18.5154 1.28%

Aug-03 $18.8037 1.56%

Sep-03 $20.1982 7.42%

Oct-03 $19.1889 -5.00%

Nov-03 $19.2932 0.54%

Dec-03 $19.4811 0.97%

Jan-04 $20.0228 2.78%

Feb-04 $21.0185 4.97%

Mar-04 $22.7372 8.18%

Apr-04 $22.3115 -1.87%

May-04 $22.9894 3.04%

Jun-04 $22.7627 -0.99%

Jul-04 $22.5520 -0.93%

Aug-04 $23.6348 4.80%

Sep-04 $22.8949 -3.13%

Oct-04 $25.7939 12.66%

Nov-04 $26.1593 1.42%

Dec-04 $28.0874 7.37%

Jan-05 $25.2241 4.01%

Feb-05 $27.0805 7.36%

Mar-05 $29.9702 10.67%

Apr-05 $30.0476 0.26%

May-05 $27.5195 -8.41%

Jun-05 $28.3839 3.14%

Jul-05 $30.3137 6.80%

Aug-05 $33.1271 9.28%

Sep-05 $37.1142 12.04%

Oct-05 $38.6859 4.23%

Nov-05 $35.9033 -7.19%

Dec-05 $38.1171 6.17%

Jan-06 $39.4000 3.37%

CIBC Performance

Total Return 170.40%

Arithmetic Monthly Mean 2.93%

Arithmetic Annualized Mean 35.11%

Monthly geometric Return 2.80%

Annualized geometric Return 39.32%

Monthly Standard Deviation 5.11%

Annualized Standard Deviation (risk) 17.69%