Level 1 - Quantitative Method - Sampling and Estimation

Sampling and Estimation

 

Standard Error

-     不同 sample 計出來的 sample mean 及 population mean 都會有偏差的，利用這些 sample mean去產生一個 Distribution，所計出來的S.D.àStandard Error (S.E.)

 

               S.E. = S.D./n^1/2 

-          Use population S.D., if N/A à use sample S.D.

-          Sample size愈大 à SE 愈小

Confidence Interval Estimation

-  在某個 % 的信心之下，一個observation/population mean的range

※Degree of Confidence = 1 – Level of Significance

-  Confidence interval = Point Estimate ± Reliability Factor * SD or SE

   ※Use S.E. when estimating population mean

       Use S.D. when estimating observations

-   Reliability Factor:

1. Z value: Z table, assume standard normal distribution, e.g. 95% two tail à1.96
2. T value: T table, 用degree of freedom (n-1)及confidence level 去查表

T Distribution

For sample，可能會有及生偏差，所以需要一個較保守的的distribution

Characteristics of T distribution:

-          Less peak à 較少central tendency

-          Fatter tail à 較多extreme value

-          Sample size increase à more peaked and thin tail à approach normal distribution

Decision rule of Z or T

Safe First Criterion

找出最低機會低於 lowest acceptable return (threshold return)的機會:

(expected return – threshold return)/S.D.

à愈大，代表 mean/expected return 與 threshold return距離愈大，較少機會低於 threshold return

 

Lognormal and Normal

假設 asset return 是 normally distributed，return 可以+ve及-ve，但 asset price 只可以是+ve，lognormal distribution就是將 return 變成一個price multiple (e^R)，distribution 由 0 開始及 positively skewed