Question

1. Below are the historical arithmetic average returns and standard deviations for different asset classes.

Asset class	Mean return	Standard deviation
T-bills	0.035	0.031
Corporate bonds	0.063	0.084
Small company stocks	0.169	0.323
Large company stocks	0.121	0.202

Assume that the returns are normally distributed. Use Excel's NORM.DIST() function to answer the following questions.

a. What is the probability that the return on corporate bonds will be less than 4%?

b. What is the probability that the return on small company stocks will be less than 4%?

c. What is the probability that the return on large company stocks will be greater than 20%?

2. Meraki Inc. has an expected annual return of 8% with a standard deviation of 13%. Assume returns are normally distributed.

a. What is the probability of earning a return between -5% and 21%?

3. Investing Shark Burgers has an expected annual return of 28% and a standard deviation of 14%.

a. What is the probability of losing money on this investment? Assume that returns are normally distributed.

4. Meraki Inc. has an expected annual return of 8% with a standard deviation of 33%. Assume returns are normally distributed.

a. What is the probability of earning a return less than -25%?

b. What is the probability of earning a return less than 74%?

c. What is the probability of earning a return between -25% and 74%?

Answer 1

1). The probabilities are as follows:

Asset class	Mean return	Standard deviation	return	Probability
Corporate bonds	0.063	0.084	<4%	0.39212
Small company stocks	0.169	0.323	<4%	0.34481
Large company stocks	0.121	0.202	>20%	0.3479

Note that the NORM.DIST() function calculates probabilities for less than a given value so for large company stocks (since probability is for MORE than 20% return), the probability is calculated by subtracting the probability for less than 20% return (using NORM.DIST()) by 1.

2). Probability that Meraki earns less than -5% = 0.15866

Probability that Meraki earns less than 21% = 0.84134

Therefore, the probability that return is -5% < return < 21% is 0.84134 - 0.15866 = 0.68269