22. Analysing market risk Flashcards
Outline the characteristics of individual equities
o Returns rarely iid
o Little evidence of serial correlation, but some evidence of short term momentum effects and long term mean-reversion
o Volatility varies over time, but …
o … evidence of serial correlation in absolute or squared returns, ie volatility clustering (extreme returns appear in clusters)
o Return series leptokurtic, more peaked and fatter tails than norm
Outline the characteristics of portfolio of equities
o Correlations exit between diff return series at same point in time (also true for return series of other asset classes and economic variables)
o Correlations between diff series vary over time
o Multi-variate returns data show little evidence of cross-correlation (ie between time t and t+1)
o Multivariate series of absolute or squared returns show strong evidence of cross correlation
o Extreme returns in a series coincide with those in other series, ie when volatility is high, level of dependence between returns appears to be higher
Outline 4 approaches to modelling market returns
- Factor based using data
- Factor based using PCA
- Using another multivariate distribution that isn’t normal
Combine non-normal marginal distributions using appropriate copula
Describe how you’d use a data - factor based approach
- Decide on frequency of calc (eg daily etc)
- Pick timeframe for past data (consider volume and relevance)
- Calculate total return index, say S(t), for all asset classes
- Calculate log returns for the asset classes, ie X(t)=ln[S(t)/S(t-1)]
- Calc E[R], variance of each asset class and covariances in each class
- Simulate series of returns with same characteristics based on multivariate normal
* Use Cholesky decomposition of unbiased estimator Sigma based on past data for last two steps
Describe how you’d use a PCA in a factor based approach
- Decide on frequency of calc (eg daily etc)
- Pick timeframe for past data (consider volume and relevance)
- Calculate total return index, say S(t), for all asset classes
- Calculate log returns for the asset classes, ie X(t)=ln[S(t)/S(t-1)]
- Calc E[R], variance of each asset class and covariances in each class
- Derive matrix of deviations from ave returns by deducing average return in every period for each asset class
- Derive p.c (i.e. eigenvalues and eigenvectors of covariance matrix), and select # of these components that explain sufficiently high proportion of deviations from past returns.
- Simulate this number of independent std normal distributed RV and multiply by square root of corresponding eigenvalue
- Weight projected series of deviations by appropriate elements of relevant eigenvectors.
- Add weighted projected deviations to expected returns from each asset class to obtain vector of correlated normally distributed RV.
How would you model the expected return on government bonds
- Reasonable estimate- gry on govt bond pf similar term as projection period
- Impied forward spot yield curves can be constructed based on gry of bonds using bootstrapping. However, spurious accuracy?
- Can make allowance for the term premium
How would you model the expected return on corporate bonds
- YTM aka GRY is calculated assuming all bond payments made.
What is credit spread
Difference between yield on risky and risk free security, usually corp and govt bond resp.
Outline the factors that are reflected in a credit spread
o Expected P(Default) and E(Loss|Default) – can measure using default history of bonds w/similar credit rating
o Any risk premium attached to default risk
o Liquidity premium
What are the 3 measures of credit spread?
o Nominal spread: GRY(Risky) – GRY(Risk free)
o Static spread: addition to risk free rate s.t discounted cashflows from risky bond will equate to price of that bond
o Option-adjusted spread: further adjusts discount rate through stochastic models, allowing for embedded options in bond
Outline the risk premia that may lead to high credit spreads
o Higher volatility of returns relative to RFA (credit beta)
o Higher uncertainty of returns, esp possibility of unprecedented extreme events
o Greater skewness of potential future returns on corp debt due to default probability
o Lower liquidity of corp vs govt bonds
o Lower marketability
o Differences in tax treatments
How would you model other assets
- Can calc approp risk premium to account for uncertain income
- Historic: diff between risky asset and RFA
- Ave historical premium must allow for expected future changes
What is a benchmark
- What market risk is measured against
- Usually market indices or investor’s L
- If based on L, reference point is set of cashflows representing actual liabilities
What are the characteristics of a good benchmark
- Unambiguous
- Investable and trackable
- Measurable on reasonably frequent basis
- Appropropriate, e.g. to investor’s objectives
- Reflective of current investment opinion e.g. +, - or neutral
- Specified in advance
What are other appropriate characteristics of benchmark
May also be appropriate that it:
Contains high proportion of assets held in portfolio
Has similar investment style to portfolio, e.g. value or growth
Has low turnover of constituents
Has investable position sizes
Behaves in similar way to portfolio, i.e. shows strong + correlation between portfolio return R(i) and benchmark return R(b) in excess of market return R(m), ieρ(R_i-R_M,R_B-R_M )≫0
Has low correlation between the difference of the portfolio return and BM return, and BM return and the market return, i.e. ieρ(R_i-R_B,R_B-R_M )≈0
The variability of portfolio returns relative to benchmark returns must be lower than variability to market return
