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Extreme Events – Specimen Question A.7.3

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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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