One of the most important and fundamental concepts in Risk Management and modeling is Mathematics (Probability) and Statistics! Probability defines the chance of events and is the most basic tool for modeling risk. Statistics gets into rigorous analysis and creates models for prediction. GARP gives a good weight to Quantitative Analysis with 20% weight for FRM Part I and 10% weight for FRM Full Exam.
This weight might not appear significant, but if we look closely, most of the questions in Value at Risk (VaR) and Credit Risk (those involving calculation of probability of default, correlations, etc.) are again based on the quantitative analysis part. It would not be wrong to say that most of the syllabus (including financial markets and products and market risk) hinges upon clear understanding of quantitative analysis, probability and statistics. For this reason we would concentrate on how to crack the quantitative analysis section of the FRM Examination.
It is always a good strategy to try first for the low hanging fruit. Basically Quantitative analysis has a lot of syllabus to cover. If we broadly divide the syllabus, it would consist of:
- Probability (Including Counting Principles and Joint Prob. Etc.)
- Probability Distributions
- Moments (Mean, Variance, Skewness, Kurtosis)
- Sampling Theorem
- Hypothesis Testing
- Correlation and Regression (And its Hypothesis testing)
- Volatility (Variance as a random variable)
- Monte Carlo Simulation
If you take a look at it, the syllabus of quantitative analysis is HUGE! Each topic in itself would be like a 4 credit course!! If you don’t have a Mathematics and Statistics background, the quantitative analysis syllabus can be intimidating!
So to prepare well for the examination requires patience and hard work. You need to work on the problems, see what is the theory part involved and formulate a strategy to crack the exam.
We found that the Damodar N. Gujarati is a good basic book to cover a large portion of the learning objectives of quantitative analysis. So to learn the syllabus till Hypothesis Testing of Regression, Damodar N. Gujarati provides a solid foundation.
If we take a closer look at the pattern of the examination (Based on the FRM Sample paper 2009), we can try to judge the easier to attempt portion. Then instead of covering the full syllabus of quantitative analysis with equal depth, we can try to be selective and make sure that the important part is well covered. Please note that this is purely from FRM Exam preparation perspective. The topics covered in quantitative analysis are definitely very important and over time, mastering them is a must for any risk professional.
If we were to see the pattern for FRM Exam 2009, we find that more than 50% of the syllabus is covered by non-quant and stats topics. These are essentially Estimating Volatility and Monte Carlo Simulations. I will take them one by one:
Estimating Volatility: Looks can be deceptive! This is the statement, which describes this topic. This is essentially the easiest portion as far as Quantitative Analysis is concerned. The only thing to remember in this â€“ Volatility (Variance) is a random variable! There are a couple of formulas â€“ Remember them and there is no way you can get the question wrong:
Return = ln(P(t)/P(t-1))
(Sigma(n))^2 = lambda * (Sigma(n-1))^2 + (1 â€“ lambda) * U(n-1)^2
(Sigma(n))^2 = alpha * V(L) + Beta* (Sigma(n-1))^2 + Gamma * U(n-1)^2
Where, alpha + beta + gamma = 1
Another variant, alpha * V(L) = omega
That’s it!! And the icing on the cake â€“ This is one of the most important topics from VaR perspective as well. So if you remember the above 3-4 terms, you are going to crack VaR as well!!
Monte Carlo is again a simple portion of quantitative analysis! There is hardly any scope of a numerical question from simulation (If it is there, it could be based on a step iteration for GBM â€“ for which everything would be given, you just have to plug values!). There is a high chance that the question would be based on assumptions. So study the model carefully!
Correlation Regression: Again here, one of the easiest questions would be to find the %age variance explained by your regression line. This is simple R^2, and the easiest thing to calculate:
SST = SSR + SSE
R^2 = SSR/SST
SEE = (SSE/(n-2) )^1/2
The other kind of question can be based upon finding the significance of regression parameters â€“ Look at the p-value in the table given, and find the parameters that are significant. This is ONE question, you should not miss in the FRM exam!!
Portfolio Variance: Again questions (Usually multiple) from this concept have been coming in the examination for the last so many years. Again something that you should not miss!!
VaR(Portfolio)= wa^2*?a^2 + wb^2*?b^2 + 2*wa*wb*?a*?b*Corelation(a,b)
Probability Distributions: Usually in this part of quantitative analysis there is either a question on Normal Distribution, where you have to identify the relevant area and find the value or you are given a binomial distribution, and you have to find the chances of none-of the bonds defaulting!! If you have practiced well, you can get these questions right!! Now the difficult part (for atleast those who don’t have a background in Quantitative Analysis) â€“ Basic Probability!! Again this is a vast topic!! Run through the definitions and work on problems. If you can get it right in the exam â€“ great!! Otherwise don’t panicâ€¦ Even if you get 80% answers correct in the exam, you have cracked it!! So strategize â€“ Find your strengths and play on them!!