Question

home / study / math / statistics and probability / statistics and probability questions and answers / annual returns on stocks are known to vary. suppose that during the recent year, the mean return ... Question: Annual returns on stocks are known to vary. Suppose that during the recent year, the mean return ... Annual returns on stocks are known to vary. Suppose that during the recent year, the mean return was 10.6% and the standard deviation of returns was 32.3%. Please explain why b is correct.

a) You can get an average return higher than 10.6% if you invest in an extremely large number of stocks.

b) If you invest in more and more stocks selected at random, then your average return on these stogcks will get closer and closer to 10.6%.

c) When you invest in a large numbeer of stocks chosen at random, your average return will approach a normal distribution.

Answer 1

we know that the sample standard deviation is given as

Standard deviation =

where sigma is population standard deviation and n is the sample size

As we invest in more and more stocks, this means that we are increasing the sample size n

Given stanndard deviation is sigma = 32.3

Suppose initial sample size was n = 100

So, initial sample standard deviation was Sd = 32.3/sqrt(100)

= 32.3/10

= 3.23

And if we are investing in more and more, so let us suppose that sample size is now n = 289

then the sample standard deviation sd would be given as

Sd = 32.3/sqrt(289)

= 32.3/17

= 1.9

So, we can see that as we are investing more and more, i.e. as we increasing the sample size n, the sample standard deviation becomes more and more smaller and eventually it will come close to mean value

therefore, option B is correct