Question

You observe the returns Rt (t = 1; 2; :::28) (in %) on your investment for the last 28 days (see the attached
Öle). Follow the steps explained in class to answer these questions:
What is the mean return (in %) on your investment, ? Explain.
Is lower than -1%? Explain.
Assume that = 0 and = 4. What is the probability that the next 30 days average return on your
investment will be greater than 1%? Explain. What is the probability that the next 15 days average return
on your investment will be greater than 1%? Explain.
Explain all the steps when answering the above questions.

Day Return % 1 0.17 2 0.64 3 -0.11 4 0.16 5 -0.26 6 0.48 7 -0.41 8 -1.03 9 -3.32 10 -3.03 11 -0.37 12 -4.49 13 -0.42 14 4.33 15 -2.86 16 4.2 17 -3.32 18 -1.65 19 -7.81 20 5.17 21 -4.87 22 -9.57 23 13.55 24 -17.94 25 5.4 26 -5.06 27 0.21 28 -4.31

Answer 1

Answer:

Given data

Assume that = 0 and = 4. What is the probability that the next 30 days average return on your
investment will be greater than 1%.

The estimate mean return on investment =

The sample standard variance ,

The sample standard deviation ,

= 5.56

The

confidence interval around the mean is given by:

Using t - distribution as the sample size n = 28 < 30

Where ,

   = 0.05 ,

  

t - distribution with degrees of freedom = 28 - 1

= 27

The true mean lies in the range ( - 3.36 , 0.75 )

(95 % confident ).

So the true mean can be greater than -1% . It is not neccessarily less than -1%.

Assuming = 0 , = 4.

Average return on investment in the next n days

Now the probability that the average return on investment is greater than 1% =

where   = 0 and   = 4.

According to the Central Limit Theorem , asymptotically

as sample size n > 30

Now , in case of finding the probability that average rate of return for next 15 days will be greater than 1%, as the sample size is small

i.e . n = 15 < 30 , then

i.e. Z is the distributed with = 15 -1

= 14

14 degrees of freedom