Over the past 80 years, the U.S. stock market had average annual return of 10%,

Question

Over the past 80 years, the U.S. stock market had average annual return of 10%, and a standard deviation of 20%. based on the history, if you buy an equity- index fund and plan to hold for 10 years ( ignoring the loads and fees of a fund, assuming the return follow the normal distribution).

1. what is the likelihood you will lose 10% or more in a year?

2. what is the likelihood you will lose 10% on average per year over the next 10 years?

3.what is the likelihood you will lose 10% or more cumulatively over 10 years?

can I have some calculation details or reasons? thanks!

Explanation / Answer

here mean return =10%

and std deviation =20%

from normal distribution z=(X-mean)/std deviation

1) P(X<-10)=P(Z<(-10-10)/20)=P(Z<-1) =0.1587

2)std error of mean for next 10 year =std deviation/(n)1/2 =20/(10)1/2=6.3245

P(X<-10)=P(Z<(-10-10)/6.3245)=P(Z<-3.1623)=0.0008

3) mean for 10 years =10*10=100

and std deviation for 10 years =20*(10)1/2 =63.245

P(X<-10)=P(Z<(-10-100)/63.245)=0.041

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