Consider the following table for the total annual returns for a given period of
ID: 2750250 • Letter: C
Question
Consider the following table for the total annual returns for a given period of time.
What range of returns would you expect to see 68 percent of the time for large-company stocks?
a) Expected range of returns ____________ % to ____________ %
What about 95 percent of the time?
b) Expected range of returns ____________ % to ____________ %
**Please help and show your work if you could. I really don't understand how to do this
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Series Average Return Standard Deviation Large-Company Stocks 12.3% 20.6% Small-Company Stocks 16.4 33.0 Long-term corporte bonds 6.2 8.4 Long-term government bonds 6.1 9.4 Intermediate-term government bonds 5.6 5.7 U.S. Treasury bills 3.8 3.1 Inflation 3.1 4.2Explanation / Answer
a)
What range of returns would you expect to see 68 percent of the time for large-company stocks
Using Excel Formula
Lower Limit & Upper limit Probability should be = 50% + 68%/2 = 84%
Z = normsinv(probability)
Z = normsinv(84%)
Z = 1.0
Lower range = Average Return - Standard Deviation*Z
Lower range = 12.3% - 20.6%*1.0
Lower range = -8.3%
Upper range = Average Return + Standard Deviation*Z
Upper range = 12.3% + 20.6%*1
Upper range = 32.90%
Answer
Expected range of returns -8.30 % to 32.90 %
b)
What range of returns would you expect to see 95 percent of the time for large-company stocks
Using Excel Formula
Lower Limit & Upper limit Probability should be = 50% + 95%/2 = 97.5%
Z = normsinv(probability)
Z = normsinv(97.5%)
Z = 2.0
Lower range = Average Return - Standard Deviation*Z
Lower range = 12.3% - 20.6%*2.0
Lower range = -28.90%
Upper range = Average Return + Standard Deviation*Z
Upper range = 12.3% + 20.6%*2
Upper range = 53.50%
Answer
Expected range of returns -28.90 % to 53.50 %
Note : Assuming Z value is calculated of single decimal place