Estimating Market Risk Measures Flashcards
(15 cards)
Geometric Return
Ln((price at period n + interim cash flows)/price now)
Assumes that interim cash flows are continuously reinvested
Profit or Loss
Present value of future cash flows (including price sold for and interim cash flows) - price paid now
Weights in expected shortfall
1/(1-confidence level)
Lognormal Var
Var(x)=Price(1-exp(mean - Zsigma))
Confidence Interval for VaR
q + se(q) X Z > VaR > q - se(q) X Z
Se(q) = sqrt(p(1-p)/n)/f(q)
f(q) = Probability between the upper and lower limit
Arithmatic vs Geometric Return
Arithmatic return assumes interim cash flows do not earn a return
Expected Shortfall
Estimate for tail loss by averaging the VaRs
Tail divided into n slices, and n-1 vars computed
Es is a coherent spectral measure which gives equal weight to the tail quantiles
Coherent Risk Measures properties
Monotonicity
Subadditivity
Positive Homeogeneity
Translational Invariance
Value at risk measure is not coherent
Monotonicity
Portfolio with greater returns have less risk
Sabadditivity
P(X+Y)<=P(X)+P(Y)
Positive homogeneity
P(jX)=jP(X)
Translational invariance
P(X+C)=P(X)-C
Coherent Risk Measure
More general than VaR or ES. It is the weighted average of quantiles of loss distribution.Where the weights are user specific based on individual risk aversion
QQ plot
A way to visually examine if empirical data fits the reference or hypothesized theoretical distribution.
If two distributions are similar the resulting qq plot will be linear.
Q q plots are good for identifying outlers , giving a good idea about skewness and kurtosis , and a rough idea about location and scale parameters
Route map to estimating market risk
- Asking which risk measure
- Which level (portfolio or individual)
- Which method as in nonparametric, parametric, or monte carlo simulation
