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...
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...
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...
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
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...
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
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...
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
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
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
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...
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...
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...
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