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1. ### YouTube T2-1 Probability functions: pdf, CDF and inverse CDF

A function is a viable probability function if it has a valid CDF (i.e., is bounded by zero and one) which is the integral of the probability density function (pdf). The inverse CDF (aka, quantile function) returns the quantile associated with a probability, q = F^(-1)(p), whereas the CDF...
2. ### YouTube T1-12 Downside risk measures: semi-deviation, downside deviation, and Sortino ratio

The two typical measures of downside risk focus on only the "bad" dispersion: Semi-deviation squares returns below the MEAN return, while downside deviation squares returns below a TARGET return (aka, minimum acceptable return, MAR). The Sortino Ratio divides by the downside deviation. David's...
3. ### YouTube T1-11 Information Ratio

The information ratio is active (or residual) return divided by active (or residual) risk. Active risk is also called tracking error, so the "active information ratio" is given by (active return)/(tracking error). Alternatively, a more technical approach is to use alpha (aka, residual risk) so...
4. ### YouTube T1-10 RAPMs: Treynor, Jensen's, Sharpe

Risk-adjusted performance measures (RAPMs) include Treynor and Jensen's, both of which are functions of the CAPM/SML, and the Sharpe ratio, which can be understood in the context of the CML. David's XLS: https://trtl.bz/2EIIb6j
5. ### YouTube T1-9 Capital asset pricing model (CAPM)

The CAPM is a ex-ante single-factor model where the single-factor is the market's excess return: it says that we should expect an excess return that is proportional to the stock's beta, which is the stock's exposure to market's excess return, as measured by the stock's beta. Beta can be...
6. ### YouTube T1-8 Capital market line (CML) versus security market line (SML)

The CML contains ONLY efficient portfolios (and plots return against volatility; aka, total risk) while the SML plots any portfolio (and plots return against beta; aka, systematic risks) including inefficient portfolios. The XLS David used in the video is located here https://trtl.bz/2Fru70r
7. ### YouTube T1-7 How the portfolio possibilities curve (PPC) illustrates the benefit of diversification

When correlations are imperfect, diversification benefits are possible. The portfolio possibilities curve illustrates this and it contains two notable points: the minimum variance portfolio (MVP) and the optimal portfolio (with the highest Sharpe ratio), At the end, I summarize four features of...
8. ### YouTube T1-6 What is bootstrap historical simulation?

The key idea of Boostrap HS is "sampling with replacement:" we randomly retrieve ACTUAL daily returns and use them to simulate forward. Here is David's XLS: http://trtl.bz/2yzTYPM
9. ### YouTube T1-5 What is the (Basic) Historical Simulation approach to value at risk (VaR)?

Basic historical simulation sorts the actual loss history and, for example, the 95th HS VaR is the 6th worst out of 100 observations. Here is David's XLS: http://trtl.bz/frm-t1-5-hs-var
10. ### YouTube T1-4 What is Autocorrelation (and how does it impact scaled volatility)?

Autocorrelation is a correlation of variable (eg, returns) with itself over time; it is a violation of returns. Positive autocorrelation increases scaled volatility, while negative autocorrelation (aka, mean reversion) decreases scaled volatility. Here is David's XLS: http://trtl.bz/2wSpHrG
11. ### YouTube T1-3 How to translate volatility over time

We typically scale volatility with the square root rule, but keep in mind the key assumption (i.i.d. returns). We APOLOGIZE that the bottom-right corner is obstructed by the web camera. It contains Expected return = +10.0% such that the Absolute VaR = -10%*10/250 + 2.326*20%*sqrt(10/250); i.e...
12. ### YouTube T1-2 What is value at risk (VaR)?

Value is risk is just a statistical feature of probability distribution (the hard part is specifying the probability distribution): VaR is the quantile associated with a selected probability; i.e., what's the worst that can happen with some level of confidence? See David's XLS here...
13. ### YouTube T1-1 What is financial risk?

There is no official risk typology. The current FRM syllabus (2018-19) assigns Crouhy's Essentials of Risk Management which contains a Typology of Risk Exposures in Appendix 1.1 but it is incomplete and somewhat informed by early Basel regulations; e.g., financial risks consists of market risk...