Question

In: Finance

The Chief Risk Officer at JP Manzan Bank has calculated that the bank's portfolio return's profit/loss...

The Chief Risk Officer at JP Manzan Bank has calculated that the bank's portfolio return's profit/loss (denoted by R) is normally distributed with mean -0.27 and standard deviation1.65.

Calculate:

(1) P(R < 1.89) = _________

(2) P(|R| > 1.6 ) = _____________

(3) P(-2.47 < R < 1.49) = ___________

(4) P(R > _________ ) = 0.966

Solutions

Expert Solution

USING FORMULA AND Z TABLES
1.
=Pr(Z<(1.89-(-0.27))/1.65)
=Pr(Z<1.3091)
=0.904748220844048

2.
=Pr(R<-1.6)+Pr(R>1.6)
=Pr(Z<(-1.6-(-0.27))/1.65)+Pr(Z>(1.6-(-0.27))/1.65)
=Pr(Z<-0.8061)+Pr(Z>1.1333)
=Pr(Z<-0.8061)+1-Pr(Z<1.1333)
=0.3386

3.
=Pr(R<1.49)-Pr(R>-2.47)
=Pr(Z<(1.49-(-0.27))/1.65)-Pr(Z>(-2.47-(-0.27))/1.65)
=Pr(Z<1.0667)-Pr(Z>-1.3333)
=Pr(Z<1.0667)-1+Pr(Z<-1.3333)
=0.765727588078623

4.
Pr(R>X)=0.966
=>Pr(R<X)=1-0.966
=>Pr(Z<(X-(-0.27))/1.65)=0.0340

=>Pr(Z<(X-(-0.27))/1.65)=Pr(Z<-1.825)

=>(X+0.27)/1.65=-1.825

=>X=-1.825*1.65-0.27

=>X=-3.28125

USING EXCEL
1.
=NORMDIST(1.89,-0.27,1.65,TRUE)=0.904748220844048

2.
=NORMDIST(-1.6,-0.27,1.65,TRUE)+1-NORMDIST(1.6,-0.27,1.65,TRUE)=0.3386

3.
=NORMDIST(1.49,-0.27,1.65,TRUE)-NORMDIST(-2.47,-0.27,1.65,TRUE)=0.765727588078623

4.
=-NORMINV(1-0.966,-0.27,1.65)=3.281261255

jeff jeffy answered 2 years ago
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