Financial Risk Manager Part 1

Financial Risk Manager Part 1

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A trader purchases one single stock every day during five working days. His risk manager believes that the probability of selecting an underpriced stock at any given time is 52%. Assuming a binomial distribution, what is the probability of selecting exactly two underpriced stocks during the week out of the universe of underpriced and overpriced stocks?

TTanishq

Explanation:

Explanation

This is a binomial probability problem where:

  • n = 5 (number of trials/days)
  • x = 2 (number of successes/underpriced stocks)
  • p = 0.52 (probability of success)
  • q = 1 - p = 0.48 (probability of failure)

The binomial probability formula is:

P(X=x)=(nx)px(1−p)n−xP(X = x) = \binom{n}{x} p^x (1-p)^{n-x}

Substituting the values:

P(X=2)=(52)⋅0.522⋅0.483P(X = 2) = \binom{5}{2} \cdot 0.52^2 \cdot 0.48^3

Step-by-step calculation:

  1. Combination term: (52)=5!2!⋅3!=12012=10\binom{5}{2} = \frac{5!}{2! \cdot 3!} = \frac{120}{12} = 10

  2. Probability terms: 0.522=0.27040.52^2 = 0.2704 0.483=0.1105920.48^3 = 0.110592

  3. Final calculation: P(X=2)=10×0.2704×0.110592=0.2990P(X = 2) = 10 \times 0.2704 \times 0.110592 = 0.2990

Therefore, the probability of selecting exactly two underpriced stocks during the week is 0.299, which corresponds to option D.

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