Question

It is known that the expected monthly return of stock ABS is 2%. Also the monthly standard deviation is estimated to be 6%. You can assume that the monthly returns are normally distributed.

a) compute the probability that any given months return will exceed 4%

b) compute the probability that the average monthly return is any given year exceed 4%

c) Design a 99% confidence interval for the monthly return of the stock. Also use the relevant graph to support your answer.

Answer 1

Let X be the monthly return of the stock.

Let X~N(mu=2, Sigma=6).

a) We want to find P(X>4)?.

= P(X-2/6>4-2/6). Standardized variable

= P(z>0.333).

= 0.6305587. By using normal table

P(X>4)=0.6305587.

b) now we want to find the probability that the average monthly return is any given year is 4%.

, that is find P(X>4).

P(X>4)

=P(X-2/6>4-2/6). Standardized variable.

=P(Z>0.333).

=0.63055. By using normal table

c) alpha=1%.

The confidence interval for the monthly returns of the stock is

LCI= mu- Sigma/√n*Zalpha/2. And UCI = mu + Sigma/√n*Zalpha/2.

Here n=1 and Zalpha/2= 2.58

LCI= 2-6*2.58

=2-15.48

LCI=-13.48

UCI=2+6*2.58

UCI=17.48