Chapter 22: Assessing Market risk

Question 1

Features assumed for individual equities VISCAL MM

Answer 1

• Varying volatility over time
• IID distribution NOT TRUE
• Serial correlation NOT PRESENT
• Clustering of volatility
• Absolute or squared terms show serial correlation
• Leptokurtic
• Momentum effect and mean reversion

Question 2

Features assumed for equity portfolios CAUSE

Answer 2

• Cross correlation cannot be assumed
• Absolute/squared returns show cross correlation • Unstable correlation between different series
• Systemic volatility
• Extreme returns between series coincide

Question 3

Changes in equity returns characteristics when observed data increase LIC:

Answer 3

• Leptokurtic nature decreases – higher peaked and fatter tailed distributions decreases
• IID more likely
• Clustering of volatility reduces

Question 4

Data-based modelling
Assumes changes in logarithms of returns can be linked to a MVN distribution FRICAS

Answer 4

1. Frequency of calc chosen
2. Range of historical data chosen
3. Index of return chosen
4. Calculate log returns for each asset class
5. Average return, variance and correlation for each asset class
6. Simulate a series based on MVN assumptions

Question 5

Factor-based modelling (PCA)
Compute factors that cause deviation form the average return FRICA APSWA

Answer 5

1. Frequency of calc chosen
2. Range of historical data chosen
3. Index of return chosen
4. Calculate log returns for each asset class
5. Average return, variance and correlation for each asset class
6. Average deviations matrix derived
7. Principal components derived - select components that explain a sufficient amount of variation: Eigen value: The volatility of the independent factor. Eigen vector: The weight of influence of the independent factor on the variables
8. Simulate random normal variables and multiply with eigenvalue’s square root - calculate deviations
9. Weight projected series deviations by eigenvectors
10. Add projected deviations to expected returns from each asset class – vector of correlated normally distributed variables created

Question 6

Measures of credit spread SON:

Answer 6

o Static spread – the addition to the risk-free rate to equate the cashflows of the risky bond with its price
o Option adjusted spread – adjustment of discount rate through stochastic modelling to allow for options in the bond
o Nominal spread – differences in GRYs of risky and risk-free bonds

Question 7

Why credit spreads are usually higher than implied by historical defaults on bonds SMUL TV

Answer 7

 Skewness of corporate bonds is high
 Marketability – high trading cost
 Uncertainty in of returns
 Liquidity is low – difficult to sell
 Tax differences
 Volatility

Question 8

Features of a good benchmark IS RUIM

Answer 8

• In line with objectives
• Specified in advance
• Reflective of current investment opinion
• Unambiguous
• Investable and trackable
• Measurable

Question 9

Benchmark portfolio CATS

Answer 9

• Correlation between actual and benchmark portfolio movements
• Assets held in actual portfolio also held here
• Turnover of constituents is low
• Style of investment is similar

Question 10

One factor, Two factor and PCA approach to model interest rates PMCS VET MAG

Answer 10

o Price movements of long and shorted bond assumed are positively correlated - not always so
o More than one interest rate requires modelling for complex derivatives
o Constant volatility terms assumed – interest rates are heteroskedastic
o Single source of randomness and short term interest modelling
 Volatility of interest rates is influence by the size of the interest rate – for short- and long-term rates
 Expectations theory – short term interest rates tend to long term interest rates
 Two points of maturity considered in interest rate modelling
o Multiple factors influencing level and shape of the yield can be found
o Applied to GRYs, forward rates or bond prices
o Granularity in the assessment can be increased