Question

Suppose the average return on Asset A is 7.1 percent and the standard deviation is 8.3 percent, and the average return and standard deviation on Asset B are 4.2 percent and 3.6 percent, respectively. Further assume that the returns are normally distributed. Use the NORMDIST function in Excel® to answer the following questions. a. What is the probability that in any given year, the return on Asset A will be greater than 12 percent? Less than 0 percent? (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) b. What is the probability that in any given year, the return on Asset B will be greater than 12 percent? Less than 0 percent? (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) c-1. In a particular year, the return on Asset A was −4.38 percent. How likely is it that such a low return will recur at some point in the future? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) c-2. Asset B had a return of 10.9 percent in this same year. How likely is it that such a high return will recur at some point in the future?

Answer 1

	ASSET A:
	Mean	7.1	percent
	Standard Deviation	8.3	percent
	Return on asset greater than	12	percent
	Cumulative value at 12%	0.722526		(Using NORMDIST function of excel with   X=12, mean=7.1, Standard Deviation=8.3, Cumulative=TRUE)
	Probability that return is greater than 12	0.277474	(1-0.722526)
	Probability in percentage	27.75%
	Note: This can also be calculated using Standard Normal Distribution Table as shown below)
	D=(X-Mean)/Standard Dev.=(12-7.1)/8.3	0.590361
	Using Standard Normal Distribution Table:
	Cumulative area under D=0.590361	0.7224
	Less Than	0%
	Cumulative value at 0%	0.196159		(Using NORMDIST function of excel with X=0, mean=7.1, Standard Deviation=8.3, Cumulative=TRUE)
	Probability that return is Less Than 0%	0.196159
	Probability in percentage	19.62%
	ASSET B:
	Mean	4.2	percent					2.166667
	Standard Deviation	3.6	percent
	Return on asset greater than	12	percent
	Cumulative value at 12%	0.98487		(Using NORMDIST function of excel with   X=12, mean=4.2, Standard Deviation=3.6, Cumulative=TRUE)
	Probability that return is greater than 12	0.01513	(1-0.98487)
	Probability in percentage	1.51%
	Less Than	0%
	Cumulative value at 0%	0.121673		(Using NORMDIST function of excel with X=0, mean=4.2, Standard Deviation=3.6, Cumulative=TRUE)
	Probability that return is Less Than 0%	0.121673
	Probability in percentage	12.17%
	ASSET A:
	Mean	7.1	percent
	Standard Deviation	8.3	percent
	Return on asset Equal to	(4.38)	percent
	Cumulative value at (-4.38%)	0.083312		(Using NORMDIST function of excel with   X=-4.38, mean=7.1, Standard Deviation=8.3, Cumulative=TRUE)
	Probability that return is LESS than -4.38%	0.083312
	Probability in percentage	8.33%
	Probability that such low return will occur again	8.33%
	ASSET B:
	Mean	4.2	percent					2.166667
	Standard Deviation	3.6	percent
	Return on asset equal to	10.9	percent
	Cumulative value at 10.9%	0.968636		(Using NORMDIST function of excel with   X=10.9, mean=4.2, Standard Deviation=3.6, Cumulative=TRUE)
	Probability that return is greater than 10.9%	0.031364	(1-0.98487)
	Probability in percentage	3.14%
	Probability that such HIGH return will occur again	3.14%