measure of financial risk

Question 1

limitation of the mean-variance framework

Answer 1

it only valid if the distribution is normal because the standard deviation measure is not an appropriate risk measurement

Question 2

limitation of var(general)

Answer 2

1. model risk: the model is based on false assumption(the normality distribution(zero mean, constant variance)

when the mean is no longer zero, ie have long run mean, then recall from the first chapter that the long run volatility calculate from var will be underestimate or overestimate.

2. implementation risk

another limitation is the parameter define the var, confidence level and the holding period, is arbitrary and depends on the context.

Question 3

limitation for var(the unique one)

Answer 3

The main drawback is var does not give the magnitude of the loss, only the probability of the loss occur

var tells the amount of loss occur when an extreme event does not occur but does not provide the exact amount of loss when the extreme occur. So two portfolios can have the same var, but very different risk exposure

the bottom line is, no value is added to the mean-variance framework for var when the distribution is normal. When the distribution is non-normal, var is not reliable.

Question 4

coherent risk measure (property)

Answer 4

The problem of var is it violates the sub-additivity principle, which means it is not a proper risk measurement. And no other coherent risk axiom is find and apply in var setting.

Question 5

expected short fall

Answer 5

the adv of expected shortfall:

1. it satisfied the sub-additivity axiom, indicating it is a better risk measurement than var
2. it gives the magnitude of the loss, even though it relies on the same parameter of the distribution as var did
3. sub-additivity indicates the portfolio risk surface is convex, which mean there always exist an optimization.