Extreme Events – Specimen Question A.7.3
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Question and Answer Summary
Suppose that the regimes in A.7.2
have the following distributional characteristics and transition probabilities:
Distributional characteristics
|
|
Regime 1
|
Regime 2
|
|
|
Means
|
Covariances
|
Means
|
Covariances
|
|
Asset
|
|
A
|
B
|
|
A
|
B
|
|
A
|
0.03
|
0.01
|
0.005
|
0.01
|
0.02
|
0.02
|
|
B
|
0.06
|
0.005
|
0.02
|
-0.01
|
0.02
|
0.03
|
Transition probabilities
|
|
State at start of next period
|
|
State at start of this period
|
Regime 1
|
Regime 2
|
|
Regime 1
|
|
|
|
Regime 2
|
|
|
where 
and 
.
(a) What are the
conditional means and covariance matrices of the distributions for the next
period if the world is in (i) Regime 1, (ii) Regime 2?
Answer/Hints
(b) What in broad terms is
the impact on optimal portfolios of increasing and
by equal
amounts, i.e. the likelihood that we switch states over the coming period
whatever the state of the world we are currently in?
Answer/Hints
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