Module 22: Assessment of market risks Flashcards
4 Features of observed returns on individual equities
- rarely iid (inconsistent with random walk and Brownian motion models)
- volatility appears to vary over time
- volatility clustering (supporting use of ARCH & GARCH models)
- leptokurtic / excess kurtosis
5 Features of observed returns on portfolios of equities
- correlations exist between returns of different series at the same point in time
- correlations between different series vary over time
- little evidence of cross-correlation (ie between time periods t and t + 1)
- multivariate series of absolute or squared returns do show strong evidence of cross-correlation
- during periods of high volatility, the level of dependence between various returns appears to be higher.
5 Approaches to modelling market returns
- historical simulations, eg bootstrapping
- forward-looking data-based approaches, eg using a multivariate normal distribution (6-step process)
- forward-looking factor-based approaches, eg PCA (10-step process)
If there is sufficient data, alternatives to using the multivariate normal distribution or PCA include:
- use of a multivariate distribution other than normal
- combining non-normal marginal distributions using an appropriate copula distribution.
Assessing market risk under the Basel accords
Under Basel II, market risk is typically quantified by using an internal model to model the assets (as described above) and then calculating a 10-day 99% (or 1% tail) Value at Risk (VaR). The regulatory capital requirement under Pillar 1 is a multiple of this VaR loss.
A reasonable estimate of the expected return for risk-free government bonds (domestic and overseas)
Gross Redemption Yield (GRY)
Yield-to-Maturity (YTM) on a domestic government bond of a similar term as the projection period.
A reasonable estimate for the expected return for risky bonds
Can be derived from an adjustment to the expected risk-free return. Adjustments should reflect:
- credit spread
- historical default rates
- taxation
Credit spread reflects 3 factors
- expected profitability of, and loss given default - measurable, in principle, using the default history of similarly rated bonds
- the uncertainty surrounding the above (ie a risk premium)
- a liquidity premium
3 Most common ways of measuring credit spread
- nominal spread - the difference between the GRYs of risky and risk-free bonds
- static spread - the addition to the risk-free rate at which discounted cashflows from a risky bond will equate to its price
- option-adjusted spread - further adjusts this discount rate (through the use of stochastic modelling) to allow for any options embedded in the bond.
3 Main approaches to modelling interest rates
- single-factor models - eg for modelling short-term single interest rates
- two-factor models - eg Brennan-Schwartz
- PCA - eg modelling deviations from average GRYs for all durations
Assessing exchange rate risk
Exchange rate risks can be modelled in terms of the returns on short-term interest-bearing deposits denominated in different currencies. There is no additional currency return to be gained (or modelled) if working in a single denomination (currency).
Assessing contagion risks
Contagion (or systemic) risks are usually seen as an extension of market risks, but can, however, also apply to other risks, eg credit risk.
Contagion risks can be modelled as the interaction between different financial series. In particular, certain series may be linked for extreme negative values. This increased level of dependence suggests that using a copula may be a sensible approach (assuming it can be suitable parameterised).
Contagion can be considered as a feedback risk. However such (serial correlation) effects are usually ignored when modelling as it is assumed that the resulting arbitrage opportunities would be eliminated by arbitrageurs. Alternatively, some studies suggest fitting a t-copula using a situation-dependent correlation parameter.
Volatility clustering
Occurs when extreme values tend to be followed by other extreme values, although not necessarily of the same sign.
Kurtosis
Kurtosis measures the ‘peakedness’ of a distribution.
Higher kurtosis means more of the variance is due to infrequent extreme deviations, as opposed to frequent modestly-sized deviations.
Leptokurtic
A leptokurtic distribution has more acute peaks around the mean (ie a higher probability than a normally distributed variable of values near the mean)
and fatter tails (ie a higher probability than a normally distributed variable of the extreme values).
A forward-looking factor-based approach to modelling corporate bond yields might describe the complex links between variables such as: (3)
- the risk-free yield
- coupon rates
- credit spread