**Means**

Arithmetic

Arithmetic

**Mean**

Arithmetic mean =Â

Â

**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 =Â

Â

Q:Â 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-PDQ_{1})*(1-PDQ_{2})*(1-PDQ_{3}) * (1-PDQ_{4})

PDQ_{1}Â = PDQ_{2}= PDQ_{3}Â = PDQ_{4}Â = PDQ

P(No Def Year) = (1-PDQ)^{4}

P(No Def Quarter) = (0.9)^{4}Â = 97.4%

Â