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Questions › IIT JAM › IIT JAM 2023 › Q57
2 marksStatistics › Joint distributions, covariance and correlation › Variance of sums and portfolio applicationsModerateabout 2 min

IIT JAM 2023 Question 57: Joint distributions, covariance and correlation

A portfolio has R=wRs+(1−w)RTR=wR_s+(1-w)R_TR=wRs​+(1−w)RT​ with Var(Rs)=0.07\mathrm{Var}(R_s)=0.07Var(Rs​)=0.07, Var(RT)=0.05\mathrm{Var}(R_T)=0.05Var(RT​)=0.05, Cov(Rs,RT)=0.04\mathrm{Cov}(R_s,R_T)=0.04Cov(Rs​,RT​)=0.04. The www minimising Var(R)\mathrm{Var}(R)Var(R) is ________ (round off to 2 decimal places).

Answer and worked solution

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Plain-text version

A portfolio has R=wRₛ+(1-w)R_T with Var(Rₛ)=0.07, Var(R_T)=0.05, Cov(Rₛ,R_T)=0.04. The w minimising Var(R) is (round off to 2 decimal places).

Also written as: A portfolio has R=wR_s+(1-w)R_T with Var(R_s)=0.07, Var(R_T)=0.05, Cov(R_s,R_T)=0.04. The w minimising Var(R) is (round off to 2 decimal places).

Joint distributions, covariance and correlation has come up 61 times in 7 exams since 2005.

What this question tests

This question is on Variance of sums and portfolio applications, part of Joint distributions, covariance and correlation in Statistics.

The variance of combinations of variables and where it is used.

TestStop has 3 past-paper questions on this subtopic; the nearest in year are below.

  • IIT JAM 2021 · Q47Let X₁ ~ N(μ₁, σ₁²) and X₂ ~ N(μ₂, σ₂²) with μ₁ = 2, μ₂ = 3, σ₁² = 4, σ₂² = 9 and correlation coefficient…
Take this paper as a timed mockMore on Variance of sums and portfolio applications

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