Question

A day trading firm closely monitors and evaluates the performance of its traders. For each $10,000 invested, the daily returns of traders at this company can be modeled by a Normal distribution with mean = $901 and standard deviation = $2,722.

(a) What is the probability of obtaining a negative daily return, on any given day? (Use 3 decimals.)

(b) Assuming the returns on successive days are independent of each other, what is the probability of having a negative daily return for two days in a row? (Use 3 decimals.)

(c) Give the boundaries of the interval containing the middle 80% of daily returns: (use 3 decimals) ( , )

(d) As part of its incentive program, any trader who obtains a daily return in the top 2% of historical returns receives a special bonus. What daily return is needed to get this bonus? (Use 3 decimals.)

Answer 1

for normal distribution z score =(X-μ)/σx
mean μ=	901
standard deviation σ=	2722

a) probability of obtaining a negative daily return :

probability =P(X<0)=(Z<(0-901)/2722)=P(Z<-0.33)=0.370

b)

probability of having a negative daily return for two days in a row =0.370*0.370 =0.137

c)

middle 90% values are between 5% and 95% values for which z =1.2816 lower interval =mean-z*standard deviation=--2587.383 upper interval =mean+z*standard deviation=4389.383

d)

for top 2% or 98th percentile critical value of z=2.0537

therefore corresponding value=mean+z*std deviation=6491.305