Suppose you gathered the following return data on these types of investments ove

Question

Suppose you gathered the following return data on these types of investments over the previous three decades:

Investment                                      Average Return                      Standard Deviation
Large-Company Stocks                   14.3%                                    21.1%
Small-Company Stocks                    21.2%                                   35.3%
Long-term corporate bonds              9.7%                                     10.4%
Long-term government bonds          7.5%                                      8%
U.S Treasury bills                             5.6%                                     5.2%

During this 30-year period, what was the risk premium on large-company stocks?
6%
7.8%
9.3%
8.7%
6.5%

If you were to plot the distribution of returns for each of these investments, which investment would have the tightest distribution? In other words, which investment would have the most observations near the average and the narrowest distribution curve?

US Treasury Bills
Short-term government bonds
Long-term government bonds
Large-company stocks
small-company stocks

Which investment exposes the investor to the greatest chance of negative returns in a given year?

US Treasury Bills
Short-term government bonds
Long-term government bonds
Large-company stocks
small-company stocks

What is the probability of observing a return on large-company stocks that is greater than 35.4%? Assume a normal distribution.
About 16%
About 68%
About 32%
About 34%
About 95%

Explanation / Answer

a.

Risk premium on large-company stocks = Average return of large stock - Average return of treasury bill

= 14.30% - 5.60%

= 8.70%

Risk premium on large-company stocks is 8.70%

Option (D) is correct answer.

b.

Standard deviation of US Treasury Bills is lowest among all investment. So, US Treasury Bills have the most observations near the average and the narrowest distribution curve

Option (A) is correct answer.

c.

Standard deviation of small-company stocks is highest among all investment. So, small-company stocks exposes the investor to the greatest chance of negative returns in a given year.

Option (E) is correct answer.

d.

Average return of Large company Stock = 14.30%

Standard deviation = 21.10%

Observed return greater than 35.40%.

So, to calculate probability distribution, calculate Z value.

Z = (35.40% - 14.30%) / 21.10%

= 21.10% / 21.10%

= 1

Z value is 1.

Z value is 1 at 68% confidence interval.

So, option (B) is correct answer.

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