**P1 Focus Review, 3rd of 8 (Quantitative Methods--continued): Videos, Practice Questions and Learning Spreadsheets**

- The 3rd (of 8) Part 1 Focus Review video (Quantitative Methods, continued) is located here.
- Associated practice question sets:
- P1.T2.Stock, Chapters 2-7 [reviewed in P1.FR2]
- P1.T2. Rachev, Chapters 2 & 3
- P1.T2. Joroin, Chapter 12
- P1.T2. Hull, Chapter 2

- The learning spreadsheets will soon be published into a single consolidates (T2) workbook

**Concepts:**

- Rachev's Distributions
- Monte Carlo Simulation
- Volatility (in VaR)

**Rachev's Distributions**

In the FRM's introduction to econometrics, we were primarily concerned with the so-called sampling distributions (i.e., normal and student's t for test of sample mean, chi-square for test of sample variance, and F distribution for joint regression coefficient and variance comparisons). Here, the two Rachev chapters are very short. The idea is to introduce some common non-normal distributions. Among this catalog of distributions, I think the following are most relevant exam-wise:

- The three discrete distributions: Bernouill, binomial and Poisson.

*You should, at this point, be able to illustrate a financial use-case for each of these.* - The normal (of course). Already reviewed in Stock & Watson.
- Exponential. Primarily because, if given a hazard rate (instantaneous probability of default) of, say, 1.0%, the cumulative n-year PD is 1 - exp(-1.0%*n).
- Beta. You may just want to superficially register the beta as the most common distribution used to model loss given default (LGD) due to its flexibility. It's function will not be quizzed.
- Lognormal. Because this is the distribution used to model equities in T3 & T4 (e.g., BSM); i.e., log returns are normal such that price levels are lognormal.
- Normal mixture. I included in the FR because it's uniquely flexible.

**do not need to quantitatively memorize (pdf, CDF)**: Weibull, Chi-Square, Gamma, Beta, Logistic, EVT distributions (GEV and GPD), and skewed normal.

**Monte Carlo Simulation**

In the FR, I shared a couple of examples of the most common exam-type question: figuring the next step or two in a discrete GBM. The other concepts you should be familiar with:

- Inverse transformation of a random uniform variable [0,1] into a distributional deviate
- The (qualitative) idea that, in general, reducing the standard error by a multiple of 1/X (i.e., improving the MCS accuracy) requires X^2 additional trials. Increases in accuracy have a quadratic, not linear, expense.

**Volatility (in VaR)**

Hull Chapter 22 (volatility) is

*one of the more important quantitative readings*. As reviewed in the FR, make sure you practice solving for an estimate of current volatility under both EWMA and GARCH. Exam questions here will be quantitative. There is a ton of GARCH(1,1) theory but you probably will just need to solve for a GARCH estimate given the lagged variance and return, and the key params. So, most of the theory you will not need.

Other thoughts:

- What's the key difference between moving average volatility versus ARCH? between EWMA and GARCH? (you should understand the differences between the three volatility models sufficiently that you can express them BRIEFLY)
- GARP loves to quiz the long-run (unconditional variance) using omega/(1 - alpha - beta)
- I probably would memorize the GARCH volatility FORECAST
- GARP has asked about EWMA for correlations (Hull 22.7) in a previous exam, which is otherwise unexpected