THE UNIVERSITY OF NORTH CAROLINA AT WILMINGTON
Economics 377
Lab 3
1. Enter the data that I give you in class. These data are stock returns for and S&P 500 returns.
a. Using the formulas from class, calculate the mean, variance, and standard deviation of the returns for the stock
and the stock index. To calculate a sum, type “=Sum(a1:a20)” if the data you desire to sum is in cells a1:a20. You
will also need a deviation column and a deviation squared column to calculate the variance.
b. Next calculate the covariance and the correlation coefficient. To do this, you need to multiply your deviation
columns.
c. Now, let’s use excel commands to calculate these. Average = “AVG (a1:a20)”, Variance = “VAR(a1:a20)”,
Standard Deviation = “STDEV(a1:a20)”, Covariance = “COVAR(a1:a20,b1:b20)”, and “CORREL(a1:a20,b1:b20)”.
d. Why aren’t COVAR and CORREL consistent?
2. The Normal Distribution in Excel. Start this in another spreadsheet.
A random variable is distributed normally with mean 1 and variance 4. Find the probability that X ≤ 2 (Pr X ≤ 2).
a. In cell c1, enter “number”, in cell c2, enter “mean”, in cell c3, enter “s dev”.
b. In cell d1, enter 2, in cell d2, enter 1, and in cell d3, enter 4.
c. In cell c5, enter “probability”. In cell d5, click the right side of the Sum button, enter statistical, and scroll down
to NORMDIST. In the top cell for X, enter d1. For mean, enter d2. For standard deviation enter d3. Next, enter
true. The value that appears is the probability that that X ≤ 2.
d. Let’s experiment a bit. Change the value in cell d1 to 3. What happens to the value in cell d5? What does this
value tell you?
e. Now, let’s see if you understand what you’re doing. Find the probability that X is greater than 1.5. Find the
probability that X is between 3 and 4.
3. NORMINV: This function returns the number from a normal distribution that has a probability that X is below
that value: Pr (X ≤ x) = .65.
a. In cell f1, enter “probability”, in cell f2, enter “mean”, in cell f3, enter “s dev”.
b. In cell g1, enter .65, in cell g2, enter 1, and in cell g3, enter 4.
c. In cell c5, enter “number”. In cell d5, click the right side of the Sum button, enter statistical, and scroll down to
NORMINV. In the top cell for probability, enter g1. For mean, enter g2. For standard deviation enter g3. The
value that appears is the probability number for X that satisfies Pr (X ≤ x) = .65.
d. Let’s experiment a bit. Change the value in cell g1 to .5. What happens to the value in cell d5? What does this
value tell you?
e. Now, let’s see if you understand what you’re doing. Find the value of X which satisfies Pr(X > x) = .3.
4. Conversion to Standard Normal.
a. In cell c7, enter “conversion”. In cell d7, enter (d1-d2)/d3.
b. In cell c9, enter “probability”. In cell d9, click the right side of the Sum button, enter statistical, and scroll down
to NORMSDIST. In the empty cell, enter d7. What is the probability that you get?
c. In f7, enter “std. number”. In cell d9, click the right side of the Sum button, enter statistical and scroll down to
NORMSINV. In the empty cell, enter g1. In cell f9, enter number. Convert the standard normal number to a value
for the N(1,4) distribution, by multiplying g7 by the standard deviation and adding the mean.
Homework:
1. Coke attempts to fill cans to 12 ounces. However, suppose that the filling machine is set so that the distribution
of the number of ounces in a coke can is normal with mean 12.3 and standard deviation of .5. What is the
probability that a coke will have less than 12 ounces in a can? What is the probability that a coke will have 12 or
more ounces in a can? Check your work by converting to a standard normal distribution.
2. Companies that sell stock mutual funds charge their investors expense fees to offset the cost of research and
administrative activities. In 1999 the average expense fee as expressed as a percentage of total assets invested in the
fund was 0.93%. Assume that the distribution of expense fees is distributed as a normal random variable with a
mean of 0.93% and a standard deviation of 0.3%. Using the commands for BOTH a Normal distribution and a
Standard Normal distribution in Excel:
a. Find the probability that a stock mutual fund has an expense fee greater than 0.95%.
b. Find the probability that a stock mutual fund has an expense fee greater than 1.5%.
c. Find the probability that a stock mutual fund has an expense fee greater than 0.5%.
d. What proportion of stock mutual funds have an expense fee between 0.75% and 1.25%?
e. The expense fee for 75% of stock mutual funds is greater than what value?
f. The expense fee for 95% of stock mutual funds is less than what value?