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Section
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Section Title
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Description
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Hyperlink?
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2.3.2 [foot]
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Risk measures
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Coherent risk measures
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yes
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2.4.1 [foot]
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Monte Carlo simulations
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Ability to reproduce results of some such exercises analytically, i.e.
without resorting to Monte Carlo simulation techniques
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no
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2.4.2
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Statistics
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Formulae for skew (skewness) and kurtosis where different weights are
given to different observations
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yes
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2.4.3
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Fat tails
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Derivation of Cornish-Fisher asymptotic expansion
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yes
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2.4.5 [foot]
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Curve fitting
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Techniques for fitting polynomials through data series
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yes
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2.4.6
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Statistical tests for non-Normality
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skew, kurtosis and Jarque-Bera tests when n is not large (using
Monte Carlo simulations)
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no
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2.4.6
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Statistics
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Statistical tests for Normality
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yes
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2.5.2
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Statistics
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Characteristic functions for a range of distributional forms
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yes
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2.6 [foot]
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Diversification
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(excess) kurtosis of a binomial distribution
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yes
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2.7.2
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Probability distributions
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How mixtures of normal distributions can lead to fat-tails
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yes
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2.8
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Stable distributions
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Detailed analysis of stable distribution and tools for manipulating
stable distributions
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no
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2.8.2
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Stable distributions
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Special cases where Stable distribution has analytical form
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yes
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2.8.4
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Stable distributions
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Further discussion of QQ-plots for Stable distributions
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no
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2.9.2
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Extreme Value Distributions
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Features of Extreme Value Distributions
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yes
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2.10
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Parsimony
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Some dangers of over-fitting
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yes
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2.13.3
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Statistics
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Giving greater weight to observations that correspond to longer
'proper' time periods
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yes
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3.3.2
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Fat tails (in multiple return series simultaneously)
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Box counting algorithms
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no
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3.8.2 [foot]
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Curve fitting
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Arranging for curve fits to exhibit 'adequate' smoothness
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no
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3.8.5
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Relative entropy
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The concept of entropy in statistics
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no
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3.8.5
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Non-linear cluster analysis
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Defining 'similarity' by reference merely to the copula
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no
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4.3.3 [foot]
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Principal components analysis
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Weighted covariance matrices
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yes
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4.7.2
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Explaining market dynamics
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How traditional time series analysis typically uses regression
techniques
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yes
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4.8.2
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Distributional mixtures
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The EM algorithm
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yes
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4.10
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Minimisation/maximisation
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Run time constraints with large numbers of instruments
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no
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4.10.2 [foot]
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Numerical techniques
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Using golden section search techniques to find local extrema
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no
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5.4.6
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Dual benchmarks
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Position when we have two different covariance matrices
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no
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5.9.2
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Backtesting risk-reward trade-offs
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Arithmetic, geometric and logarithmic relative returns
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yes
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6.3.3
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Probability distributions
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The exponential family of distributions
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no
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6.11.6
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Monte Carlo simulations
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Simulations when the copula is 'fat-tailed'
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no
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7.4.8
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Portfolio construction
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Applying statistical tests to optimal portfolios
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no
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7.6
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Portfolio construction
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Optimal strategies in the presence of transaction costs on multiple
assets
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no
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7.9.2
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Portfolio construction
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Adjusting for time-varying volatility using weighted covariance
matrices
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yes
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7.11.2
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Portfolio construction
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Numerical integration
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no
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7.11.5
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Portfolio construction
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Need for risk measures used with non-Normal distributions to be
coherent and sub-additive
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no
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8.3.2 [foot]
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Value-at-risk
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What VaR level corresponds to the worst outcome in n events?
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yes
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