Value at Risk analysis

The daily return of the asset price X follows a normal distribution with mean -0.002 and

standard deviation 0.05. What is the probability that the daily return falls below -0.10?

𝑝(𝑟𝑒𝑡𝑢𝑟𝑛<−0.10)=𝑝(𝑧<(−0.10+0.002)

0.05 )=𝑝(𝑧<−1.96)=2.5%

What is the probability that the daily return overshoot above 0.08?

𝑝(𝑟𝑒𝑡𝑢𝑟𝑛>0.08)=𝑝(𝑧>(0.08+0.002)

0.05 )=𝑝(𝑧>1.64)=5%

The daily return of the asset price Y follows a normal distribution with mean 0.001.

Considering that, the probability that a daily return falls below -0.127 is 10% what is the

standard deviation of the distribution?

𝑝(𝑟𝑒𝑡𝑢𝑟𝑛<−0.127)=10%=𝑝(𝑧<(−0.127−0.001)

𝜎)=10% → −1.28=(−0.127−0.001)

𝜎→𝜎 =

(−0.128)

−1.28 =0.10

Which asset is more risky X or Y. Please explain!

The asset Y is twice more risky than asset X given that the standard deviation is double!

Value at Risk example NEOMA Corrected

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Value at Risk analysis

The daily return of the asset price X follows a normal distribution with mean -0 02 and

standard deviation 0. What is the probability that the daily return falls below -0?

푝(푟푒푡푢푟푛&lt;−0)= 푝(푧&lt;

(

−0+ 0.

)

0.

)= 푝(푧&lt;−1)= 2%

What is the probability that the daily return overshoot above 0?

푝(푟푒푡푢푟푛&gt; 0)= 푝

(

푧&gt;

( 0 .08+ 0)

0.

)

= 푝(푧&gt; 1)= 5%

The daily return of the asset price Y follows a normal distribution with mean 0.

Considering that, the probability that a daily return falls below -0 is 10% what is the

standard deviation of the distribution?

푝

(

푟푒푡푢푟푛&lt;−0.

)

= 10%= 푝 (푧&lt;

)= 10% → −1=

→ 휎=

= 0.

Which asset is more risky X or Y. Please explain!

The asset Y is twice more risky than asset X given that the standard deviation is double!