Investment Risks - Review Questions

Question 1

Which of the following are examples of business risk? (Check all that are true.)

1) Interest rates
2) Reinvestment
3) Inflation
4) Change in manufacturing process
5) Leveraged buyout
6) CEO charged with unethical business practices

Answer 1

4) Change in manufacturing process
5) Leveraged buyout
6) CEO charged with unethical business practices

Business specific risks are uniquely associated with the company or entity issuing the security. Change in processes may increase short-term expenses but improve a company’s efficiency in production in the long-term. A company being bought out can be beneficial (e.g., IBM purchases lotus) or detrimental (company is broken up and sold in pieces). Charges for any illegal activities or business practices can be detrimental for the company’s stock.

Question 2

The Euro/$ is currently Euro 1.25. If the dollar depreciates by 10%, what is the new Euro/$ exchange rate?

1) 1.428
2) 1.375
3) 1.125
4) 1.250

Answer 2

3) 1.125

Answer: 1.125. If the U.S. dollar has depreciated, it will buy less Euro’s. Therefore the exchange rate will go down to reflect the lowered buying power of the dollar versus the Euro.

Question 3

Given that the S&P 500 Index has an expected pre-tax return of 11% and a standard deviation of 8%, if a client invests $10K in the S&P Index fund, what is the probability that he or she will have a return greater than 3%?

1) 95%
2) 84%
3) 16%
4) 34%

Answer 3

2) 84%

Because 3% is 1 standard deviation from the mean of 11%, the probability of getting a return between 3% and 11% is 34% (1/2 of 68%). The probability of getting a return above 11% is 50%. Therefore, the probability of a return above 3% is 84% (50% + 34%)

Question 4

Normal distribution has excess kurtosis of ?

Answer 4

Zero

Financial risk management uses tools such as Value at Risk (VAR) and downside risk to access the probability of returns being less than some predetermined amount. The issue with leptokurtic distributions is that they have a larger area in their tails (known as fat tails). These distributions are measured by kurtosis. By definition, normal distributions have kurtosis equal to three. However, most statistical package report excess kurtosis, which is kurtosis minus three. Therefore, a normal distribution has excess kurtosis equal to zero, a leptokurtic distribution has excess kurtosis greater than 0, and a platykurtic distribution has excess kurtosis less than 0.

Question 5

A leptokurtic distribution has excess kurtosis of ?

Answer 5

Greater than 0

Financial risk management uses tools such as Value at Risk (VAR) and downside risk to access the probability of returns being less than some predetermined amount. The issue with leptokurtic distributions is that they have a larger area in their tails (known as fat tails). These distributions are measured by kurtosis. By definition, normal distributions have kurtosis equal to three. However, most statistical package report excess kurtosis, which is kurtosis minus three. Therefore, a normal distribution has excess kurtosis equal to zero, a leptokurtic distribution has excess kurtosis greater than 0, and a platykurtic distribution has excess kurtosis less than 0.

Question 6

A platykurtic distribution has excess kurtosis

Answer 6

Less than 0

Financial risk management uses tools such as Value at Risk (VAR) and downside risk to access the probability of returns being less than some predetermined amount. The issue with leptokurtic distributions is that they have a larger area in their tails (known as fat tails). These distributions are measured by kurtosis. By definition, normal distributions have kurtosis equal to three. However, most statistical package report excess kurtosis, which is kurtosis minus three. Therefore, a normal distribution has excess kurtosis equal to zero, a leptokurtic distribution has excess kurtosis greater than 0, and a platykurtic distribution has excess kurtosis less than 0.

Question 7

Which distribution has greater probability of extreme events.

Answer 7

Leptokurtic distribution

Leptokurtic distributions have greater probability of extreme events. Because there is a higher probability of returns around the mean, there also becomes higher probably of an extreme event in the “tails” or far ends of the distribution.

Question 8

Which Leptokurtic tail event would include an extreme negative event such as market conditions in 2008

1) Left Tail
2) Right Tail

Answer 8

1) Left Tail

Be aware that Leptokurtic distributions have greater probability of extreme events. Because there is a higher probability of returns around the mean, there also becomes higher probably of an extreme event in the “tails” or far ends of the distribution. In addition, terminology often refers to “left tail” or “right tail” events. Consider the left tail is below average and the right tail is above average. This means reference to a left tail event would include an extreme negative event such as market conditions in 2008.

Question 9

Normal Distribution - There is approximately a 68% probability that the actual return will lie within ?

Answer 9

+ / - one standard deviation from the mean.

Question 10

Normal Distribution - There is approximately a 95% probability that the actual return will lie within ?

Answer 10

+ / - two standard deviations from the mean.

Question 11

Normal Distribution - There is approximately a 99% probability that the actual return will lie within ?

Answer 11

+ / - three standard deviations from the mean.

Question 12

What is the effective standard deviation over the holding period of 10 years of S&P 500 with Standard Deviation of 15%

1) 3.75%
2) 4.75%
3) 5.75%
4) 6.75%

Answer 12

2) 4.75%

15%/Sqaureroot(10)=4.74%≈4.75%

Returning to the probability distribution principles, holding onto the S&P for 10 years, I am 95 % certain that I will realize a return of 10% +/- (2 * 4.75%) = range of .5% to 19.5%.

Because - There is approximately a 95% probability that the actual return will lie within + / - two standard deviations from the mean.

Question 13

A mutual fund is advertised with a beta of 1.6 and a R-squared of 0.24. A sales person tries to sell the fund to you based on the fact that it will outperform the market during an expansion. What is the flaw in his or her sales pitch?

Answer 13

With an R-squared of .24, the fund’s beta is not a reliable statistic to use. Therefore, for the salesperson to imply that a beta of 1.6 will outperform the market during an expansion is inappropriate, since 76% of the fund’s variability of return is due to unsystematic (company specific) forces.

Question 14

If Coca-Cola’s correlation coefficient is 0.785, then what portion of its risk during that period is nondiversifiable?

Answer 14

The nondiversifiable portion of the return would be R-squared or the correlation of coefficient squared. (0.785)² = 0.616 or 61.6%. Therefore, 61.6% of Coca-Cola’s return for that period is based on the systematic risk.

Question 15

If Coca-Cola’s correlation coefficient is 0.785, then what portion of its risk during that period is diversifiable?

Answer 15

If Coca-Cola’s systematic risk is (0.785)² = 0.616 or 61.6%, then 1 - 0.616 = 0.384 or 38.4%. Therefore, 38.4% of Coca-Cola’s return for that period is based on its unsystematic risk and is diversifiable.

Question 16

Which of the following statements concerning portfolio diversification is correct?

1) Diversification reduces the portfolio’s expected return because diversification reduces the portfolio’s total risk.
2) If a portfolio manager increases the number of securities in a portfolio the total risk is expected to fall at a decreasing rate.
3) Systematic risk is the only risk that is reduced as diversification is increased.
4) The benefits of diversification are not realized until at least 30 individual securities are included in the portfolio.

Answer 16

2) If a portfolio manager increases the number of securities in a portfolio the total risk is expected to fall at a decreasing rate.

As the number of securities in a portfolio is increased, the total risk of the portfolio is expected to fall at a decreasing rate. Diversification benefits diminish as more securities are added to the portfolio. Diversification is possible to attain without a loss of return in a portfolio.

Question 17

A portfolio has two securities, common stock of Company A and common stock of Company B. The expected return as well as the risk of the individual stocks remain the same. If there was a change in correlation between these two securities, the result will be a change in:

1) both the expected return and the risk of the portfolio.
2) the expected return of the portfolio only.
3) the risk of the portfolio only.
4) neither the expected return nor the risk of the portfolio.

Answer 17

3) the risk of the portfolio only.

A change in the correlation of this two-asset portfolio will only cause the risk of the portfolio to change. A change in the correlation will not impact the portfolio return. A decrease in correlation will lower the portfolio risk.

Question 18

A client’s portfolio, with the below weighting has the following stocks and expected 1-year returns:

Stock Expected Return Weighting of Security
A 25% 32%
B 23% 32%
C 15% 15%
D 20% 21%

If the standard deviation has been and is expected to be 10.9%, what is the probability that this stock portfolio will have a return above 10.88%?

1) 84%
2) 50%
3) 34%
4) 68%

Answer 18

1) 84%

Sixty-eight percent of outcomes will fall within one standard deviation of the mean. The mean return of 21.81% is calculated as a weighted average of each stock’s return: (0.25)(0.32)+(0.23)(0.32)+(0.15)(0.15)+(0.20)(0.21)= 21.81%. Because 10.88% is one standard deviation from the mean of 21.81%, the probability of having a return between 10.88% and 21.81% is 34% (1/2 of 68%), and the probability of a return above 10.88% is 84% [34% plus 50% (probability to the right of the mean)].

Question 19

Which of the following are nondiversifiable risks? (Check all that are true.)

1) Purchasing Power Risk
2) Management Risk
3) Market Risk
4) Interest Rate Risk
5) Company or Industry Risk
6) Business Risk

Answer 19

1) Purchasing Power Risk
3) Market Risk
4) Interest Rate Risk

Diversifiable risk is the type of risk that is associated with an individual company, its operations, and its methods of financing. Therefore, Management Risk, Company or Industry Risk, and Business Risk are all diversifiable. The remaining choices, Purchasing Power Risk, Market Risk, and Interest Rate Risk are examples of nondiversifiable risk.

Question 20

The beta of a security is:

1) Not the same as its systematic risk level
2) Is the slope of the capital market line
3) Can be measured by the standard deviation
4) None of the above

Answer 20

4) None of the above

All of these statements are false. Beta is indeed the measure of systematic risk level of the market. Beta is not the slope of the capital market line, it measures the slope of one asset’s Security Market Line (SML), and it cannot be measured by the standard deviation. Note that “Capital Market Line” uses standard deviation as its risk measure versus the “Security Market Line” which uses Beta as its risk measure. SML = CAPM.