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Risk and returns

E(Rp) = wAE(RA) + wBE(RB)
 

 
Var(Rp)= w2Aσ2(RA) + w2Bσ2(RB) + 2wA * wB * σ(RA) * σ(RB) * ρ(RA,RB)
 

σP  = 

 

 

Sample Questtion


Question:

  • σ2 return of stock P = 100.0
     
  •  σ2 return of stock Q = 225.0
  • Cov(P, Q) = 53.2
     
  • Current Holding $1 million in P.
     
  • New Holding: $1 million in Q and $3 million in stock P. What percentage of portfolio risk (σP) is reduced?

 w= 0.75
 

σP2 = 100 * (0.75)2 + 225 * (0.25)2 + 2 * 0.25 * 0.75 * 53.2
 

σP= 9.5      old σ = √100 = 10
 

Reduction = 5%

 

 

 

 

 





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