Q: If the arithmetic mean return of a portfolio is 12% and the standard deviation is 20%, what is the approximate geometric mean return?

$$12\% - \frac{1}{2} \times (0.20)^2$ = 12\% - 2\% = 10\%$$

Question 1

Suppose you purchase a stock for $$40, receive a 3 $$dividend at year-end, and sell the stock for $50. What is your total percent return on this investment?

Accepted Answer

$$\frac{3 + (50 - 40)}{40} = 32.5\%$$

Question 2

Which of the following best describes the 'risk premium' for an asset?

Accepted Answer

The excess return on a risky asset over the risk-free rate.

Question 3

If the historical average return on large-company stocks is 12.2% and the average return on U.S. Treasury bills is 3.3%, what is the historical risk premium for large-company stocks?

Accepted Answer

$$12.2\% - 3.3\% = 8.9\%$$

Question 4

Which of the following statements about the relationship between risk and return is supported by historical capital market data?

Accepted Answer

Assets with higher risk tend to have higher average returns.

Question 5

You invest $$1,000 in a stock. At the end of the year, the stock price has increased by 10% and you receive a 20 $$dividend. What is your total dollar return?

Accepted Answer

$$100 + 20 = \120$

Question 6

Which of the following is the correct formula for the geometric average return over $$T$$ periods, given returns $$R_1$$, $$R_2$$, ..., R_T$$?

Accepted Answer

$$\left[ \prod_{t=1}^{T} (1 + R_t) \right]^{1/T} - 1$$

Question 7

If the arithmetic mean return of a portfolio is 12% and the standard deviation is 20%, what is the approximate geometric mean return?

Accepted Answer

$$12\% - \frac{1}{2} 	imes (0.20)^2$ = 12\% - 2\% = 10\%$$

Question 8

Which of the following statements about market efficiency is TRUE according to the Efficient Market Hypothesis (EMH)?

Accepted Answer

In an efficient market, prices reflect all available information and it is impossible to consistently achieve abnormal returns.

Question 9

A stock paid a dividend of $$D_{t+1} = 1.50$$ and its price increased from $$P_t = 30 to$$ $$P_{t+1} = 33. $$What is the percent return?

Accepted Answer

$$\frac{1.50 + (33 - 30)}{30} = 15\%$$

Question 10

Which of the following is NOT a characteristic of a normal distribution?

Accepted Answer

It is always appropriate for modeling all asset returns.

Question 11

If a market is semi-strong form efficient, which of the following strategies is LEAST likely to consistently outperform the market?

Accepted Answer

Trading based on publicly available financial statements.

Question 12

Which of the following best explains why the geometric mean is always less than or equal to the arithmetic mean for a series of returns?

Accepted Answer

Because the geometric mean accounts for volatility drag, which reduces compounded growth.

Question 13

A small investor hears about a 'hot' IPO and plans to buy shares as soon as trading begins. According to market efficiency concepts, what is the most likely outcome?

Accepted Answer

The investor is unlikely to earn abnormal returns because the information is already reflected in the price.

Question 14

Which of the following is the correct formula for the variance of returns $$R$$ over $$T$$ periods?

Accepted Answer

$$	ext{VAR}(R) = \frac{1}{T-1} \sum_{t=1}^{T} (R_t - \bar{R})^2$

Question 15

Which of the following is a key implication of the Efficient Market Hypothesis (EMH) for investors?

Accepted Answer

On average, investors will earn a return appropriate for the risk they undertake.

Question 16

If the standard deviation of annual returns for a stock is 25%, what does this indicate about the stock's risk?

Accepted Answer

The stock's returns are highly volatile, indicating higher risk.

Question 17

Which of the following is TRUE regarding the use of a logarithmic scale to visualize long-term investment growth?

Accepted Answer

A logarithmic scale accurately represents constant percentage growth over time.

Question 18

Which of the following is a common misconception about efficient markets?

Accepted Answer

Efficient markets mean you cannot make money.

Key Lessons from Capital Market History: Returns, Risk, and Market Efficiency

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