This blog is an extension of our blog on Foundations of Risk Management.

In this session, we had share Tips of Quantitative Methods:

Probability:

1. If you understand the question and the basic formula of probability which is , you can answer every question on probability

2. To solve Conditional Probability you must understand Bayes’ Theorem as it is quite important. There are two ways you can solve Bayes’ based questions, one is to remember the formula which can be a nightmare (for me at least!). Second way is to use the Tree Diagrams. If you understand Tree diagrams properly; you will be able to solve most the questions.

3. Never forget two basic properties of probability which are: a) Sum of probabilities of all exhaustive events is always 1, b) Probability of any event lies between 0 and 1

Basic Statistics:

1. It is important to note that we need to use ‘n’ whenever we are calculating population standard deviation or variance and use ‘n-1’ while calculating sample standard deviation or variance

2. Whenever volatility is mentioned in the question, it refers to standard deviation and not variance

3. A quick way to solve some questions on progressions is to always remember: AM > GM > HM

4. Understand the conceptual difference between GM and AM. Try to understand where you can use which one and why.

5. Many candidates get confused between Covariance and Correlation. Always remember the relationship between the two and how can you convert from first to the second. This problem is faced often in portfolio variance . When covariance is not given and correlation factor is given then we can convert the covariance to correlation in the above formula and solve it.

6. Do not undermine the importance of skewness and kurtosis. Understand what kind of data can have negative skew and positive excess kurtosis.

7. There are comparatively new topics named ‘Coskewness’ and ‘Cokurtosis. Master these topics as there are higher chances of getting questions on relatively new topics.

Distributions & Hypothesis Testing:

1. Understand in detail about Random Variable.

2. Binomial Distribution is the second most important distribution topic for FRM exam. Do not memorize the formula, but try to understand the concept behind the formula.

3. Whenever you get any question on Normal Distribution, draw a rough diagram and solve. It will be much easier than mental calculations. As they say a picture is worth 1000 words.

4. To decide whether it is a one-tail test or two-tail test, try to visualize if the result what we want is on one side of the distribution (e.g. less than or greater than) or on both sides (e.g. different or not)

Linear Regression:

1. Properties of the ‘Random Error Component’ constitute a very important part of this topic.

2. You can expect some kind of question on the Relationship between ‘Total Variation’, ‘Explained Variation’, ‘Unexplained Variation’ and R2

3. Many times you will get simple question based on t-statistics. You shall know that large value of t-stat (or low values of standard error) means significant and low values of t-stat (or large values of standard error) means insignificant variables

4. It is important to know the difference between ‘Conditional’ and ‘Unconditional’ Heteroskedasticity

5. In multiple regression, multicollinearity is an important violation of the assumption of the model, which refers to the condition when two or more independent variables in a multiple regression are highly correlated with each other

Estimating Volatilities and Correlations:

1. This topic is also covered in VaR section. Concept of ‘Mean Reversion’ and the Speed of ‘Mean Reversion’ is important to learn in GARCH

2. In EWMA, we give higher weights to recent observations, because what happened yesterday is more important than what happened 5 years ago. Memorize the formula as there are simple questions based on the formula quite often.

3. Monte Carlo simulation is a method to generate random paths by choosing a random process to model changes in financial assets.