Friday, November 11, 2011

Quantitative Methods Finance for CFA & FRM Exams

This part is for CFA Level 2:

Regression


Below are the content for CFA Level 1

The areas that you will find the most interesting and require deep research are different types of distribution.
You need to understand some types of distributions, where T or F distribution and some other ones needs a greater understand so that they become useful when we do our own research or build pricing models for stocks or derivatives.

Important areas that generally students find tough:
  • Conversion of cumulative to density
  • Variance comparison of 2 values
  • Prior probability
  • Short fall risk
  • Null 2 tailed tests
  • Kurtosis
  • Mathematical form of Bayes theorem
  • Skewed
  • Seventh decile
  • Linking it properly Type 1 and Type 2
  • Chebyshev’s inequality, proportion of lying within  k deviation, 1-1/(k^2)
  • Nominal (weakest) vs. ordinal (categorized) vs. interval (stronger) vs. ratio.
  • Standard error of the mean:  s/{(n)^0.5}, here we are trying to relate sd of sample to population.
  • Bayes theorem putting this here and there and moving here and there.

Questions of these areas are of good difficulty.

Research areas:
  • Skewness derivation and maths behind it
  • Monte Carlo vs. Historical
  • More on Normal distribution
  • T Distribution, distribution analysis with both side probability
  • F distribution.

In this we have checking of means of 2 normal pop, with equal/unequal variance:
t stat = (x1-x2 )/(sp^2/n1 + sp^2/n2)^.5
sp= ((n1-1)s1^2+ (n2-1)s2^2/(n1+n2-2)
dof=  n1+n2-2.

Another are in paired comparison in intuitive t = (dbar-u )/sdbar, where dbar is sample mean diff, sd is sample std deviation.

Chi Square = (n-1)s^2/hypo pop var
s is sample variance.

Variance of normally distributed pop, vs for 2 normally distributed pop.

Interesting points:
Kurtosis greater than 3 makes fatter tails and not thin.

Tend to forget items:
  • Hypothesis
  • Videoed by root number of observation
  • Different yields etc.

Yields

Some formulas of Money market yields and Bank discount yields, there are 5-6 formula in this area which needs memorization and you can understand it later. Bank discount yield uses it face value whereas money market yield is HPY(360/t).This yield chapter has given me trouble from long time due to the enormous terminology.
The only formula with a tricky derivation is Rmm= {360*Rbd}/{360-(t*Rbd)}. 
This can be alternative viewed as conversion from Mmy to Bdy and vice versa, I will look into this formula and add its derivations and root. Rmm is money market whereas Rbd is bank discount yield respectively.

Dollar discount is the difference and is used to calculate bank discount yield, where we use 360 in Bdy.

Mmy = (HPY)*(360/t). 

Technical Analysis is the most interesting part in the entire CFA after FRA. For ex., Momentum Indicators shows are about Breadth of Market and Stocks above their 200-day moving average.
Kondratieff cycle is 54 years. Fibonacci series converge at 0.618 or 1.628. Short index ratio is the ratio of shorted/avg daily volume trading. Relative strength index shows (total-price-increase/total-price-decrease). Increasing margin debt shows bullish sentiment.

Paired comparison test

Conclusion: I have separated the quantitative techniques into areas which you can view as daunting, and also which can be seen more mathematically.

Feedback:
Feedback from a CFA Level 1 aspirant:

Hi! This is Vikas!
   Today when i was doing quant question, i found difficulty in probability n hypothesis, problem is that they are not asking practical question they are asking most question on theory basis. For ex., what is Monte-Carlo simulation, safe ratio etc. So, what i found here is that in CFA Level 1 you have to focus on theory also. Generally,  they ask near about 75% question on theory. So, when you preparing for Level 1 focus not only on practical question but also on very short point of theory.

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