Explain Interest rate, market, credit and operational risk:
Interest Rate:
Exposures to chagnes in interest rates (relevant for Banks)
Market risk:
Risk of changes in the market value of an instrument connected to changes in market conditions
Credit risk:
Possibility of change in counterparty’s creditworthiness
Operational risk:
Risk of loss due to failed internal process, people and system or external events (E.g. Internal fraud, damage to physical assets..)
What are the requirements for a coherent risk measure?
Monotonicity:
If a portfolio produces worse result than another portfolio for every state of the world, its risk mesaures should be greater
Tranlasation Invariance:
If an amount a of cash is added to a portfolio is added, its risk measure should go down by a
Positive Homogeneity:
Changing the size of a portfolio by a factor c while keeping the relative amounts of different itmens in the portfolio the same should result in the risk measure being multiplied by c
Subadditivity:
The risk measure for two portfolios after they have been merged should be no hreater than the sum of their risk mesasures before they were merged
Define the VaR:
What is the maximum loss tolerated over a certain time horizon, so that there is a very low probability (confidence level) that the actual loss will exceed this amount?
—> VaR is NOT coherent – violates subadditivity
Define the CVaR (aka Expected Shortfall)
What is the average loss incurred in case the loss is superior to VaR?
How can the VaR or CVaR be estimated? Compare the two approaches:
Historical Simulation:
Model Builiding Approach
Assume that the distribution of future returns will be the same as the empirical distribution of returns of past data
Assume parametric distribution for returns of market variables, estimate parameters, compute distribution of P&L analytically.
—> commonly used: joint Gaussian distribution of covariates
—> easy to implement
—> requires long-time series to provide accuracy
—> not suitable for short term financial returns due to assumption of normal distribution of market variables
What is the N-day VaR (CVaR) rule?
What is a single period VaR / CVaR?
Compute VaR and CVaR based on 1-day estimations of volatility & expected return and using a Gaussian distribution.
How do we compute the VaR and CVaR for portfolio of n assets?
Compute the VaR and CVaR of the portfolio by:
o first computing the standard deviation and mean return of the portfolio
o Second using the formulas for the univariate (Single period) case
Explain the difference between the Linear and Quadratic model for VaR and CVaR:
Linear
Quadratic
Assume that daily changes in portfolio value is linearly related to daily returns of market variables.
Only model to capture skewness in probability distribution
—> Not suitable for portfolios w/ options, as not accounting for gamma.
—> much more difficult than linear model
How can we use a Monte Carlo simulation to calculate the VaR?
- Use many iterations to build prob. distribution of Portfolio change
- VaR is the appropriate percentile of the distribution times
o E.g., with 1.000 trials, the 1 percentile is the 10th worst case
What does the Principal Component Analysis imply?
dimensionality reduction
identify the orthogonal factors, that explain the largest part of the variability in the dataset
—> Easier to estimate covariance w/ high no. of assets and market variable correlation.
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