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Means

Arithmetic
Mean
Arithmetic mean = 
 
Geometric Mean

Calculating investment returns over multiple period or to measure compound growth rates

RG = [(1+R1)*..*(I+RN)]1/N-1
 
Harmonic Mean
Harmonic Mean = 

 

Q: ABC was inc. on Jan 1, 2004. Its expected annual default rate of 10%. Assume a constant quarterly default rate. What is the probability that ABC will not have defaulted by April 1, 2004?

Answer:

P(No Default Year) = P(No def all Quarters)
= (1-PDQ1)*(1-PDQ2)*(1-PDQ3) * (1-PDQ4)
PDQ1 = PDQ2= PDQ3 = PDQ4 = PDQ
P(No Def Year) = (1-PDQ)4
P(No Def Quarter) = (0.9)4 = 97.4%

 





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