Module 6 Types of investment Risk, Quantitative Investment Concepts Flashcards
Which of the following is the most appropriate and accurate indicator for determining a client’s risk tolerance level?
A)
There is no single appropriate method for determining risk tolerance.
B)
Questionnaire
C)
Standard deviation
D)
Beta
a A client’s risk tolerance level is an intangible and subjective factor. No single method accurately determines that risk level.
LO 6.2.5
STU Corporation stock has an average rate of return of 24% and a standard deviation of 10%. The risk-free rate of return is 4%. Assuming the historical returns for STU stock are normally distributed, calculate the probability that this stock will have a return in excess of the risk-free rate of return.
A)
34.0%
B)
95.0%
C)
2.5%
D)
97.5%
d The answer is 97.5%. The probability of a return above 24% is 50%. The probability of a return between 4% and 24% is 47.5% (95% ÷ 2).
Therefore, the probability of a return above 4% is 97.5% (50% + 47.5%).
LO 6.2.2
What is the covariance between OPC and NIR stocks with a standard deviation of 9.13% and 11%, respectively, and a correlation coefficient of 0.85?
A)
23.77
B)
85.37
C)
28.69
D)
29.05
b The answer is 85.37. The covariance between the two stocks is 85.37 (9.13 × 11 × 0.85). Covariance measures the extent to which two variables move together, either positively (together) or negatively (opposite).
LO 6.2.4
ABC Mutual Fund has a correlation coefficient of 0.93 with the S&P 500 Index. How much of the price movement of the fund can be explained by the S&P 500 Index?
A)
7%
B)
93%
C)
86%
D)
14%
c The answer is 86%. The correlation coefficient (R) has been given, so it needs to be squared (R2) in order to come up with the coefficient of determination. (0.932 = 0.8649, or 86%)
LO 6.2.5
You are considering buying a stock that has a mean return of 14% and a standard deviation of 20. You can expect the return to fall within what range 95% of the time?
A)
–0.26 to 0.54
B)
–0.06 to 0.34
C)
–0.46 to 0.74
D)
Cannot be determined from the information given
a A stock with a standard deviation of 20 will deviate from the mean by one standard deviation 68% of the time, two standard deviations 95% of the time, and three standard deviations 99% of the time. So for this stock, plus or minus 40 from the mean of 14% would be –26% and +54%.
LO 6.2.2
The Mountain Fund has a standard deviation of 22, a mean return of 15%, and a correlation coefficient with the S&P 400 Mid-Cap Index of 0.85. Mountain Fund is subject to how much systematic risk?
A)
72%
B)
22%
C)
85%
D)
90%
a R-squared gives us the amount of systematic risk, and we have been given R (correlation coefficient). So, we square 0.85 to come up with an R-squared of 0.7225, or 72%.
LO 6.2.5
Bobby owns ABC stock that has mean return of 10.65%, a beta of 1.12, and a standard deviation of 9.05%. He decides to purchase MEJ stock that has a mean return of 11.5%, a beta of 0.98, and a standard deviation of 12.3%. Assume these stocks are weighted in the portfolio 70% for ABC and 30% for MEJ. Also, these stocks exhibit a covariance of 19.86. Calculate the standard deviation for this two-asset portfolio.
A)
1.16%
B)
7.88%
C)
3.23%
D)
10.02%
b The answer is 7.88%. To determine the standard deviation of a two-asset portfolio, use this formula:
[W2Aσ2A + W2Bσ2B + 2WAWB(COVAB)]1/2
[(0.72 × 9.052) + (0.32 × 12.32) + (2 × 0.7 × 0.3 × 19.86)]1/2
[(0.49 × 81.90) + (0.09 × 151.29) + (8.3412)]1/2
[40.1310 + 13.6161 + 8.3412]1/2
62.08831/2
= 7.8796, or 7.88%
Note the standard deviation for the portfolio is lower than the standard deviations for each security. This result directly supports the low correlation between the returns of ABC and MEJ.
LO 6.2.4
A beta coefficient of 1.3 indicates that a stock
A)
has less unsystematic risk than the market.
B)
is less volatile than the market.
C)
is more volatile than the market.
D)
has more unsystematic risk than the market.
c The answer is that the stock is more volatile than the market. A beta that is higher than 1.0 indicates that the stock’s volatility and risk are higher than that of the market.
LO 6.2.1
Shari would like to know the weighted beta coefficient for her portfolio. She owns 100 shares of BDL common stock with a beta of 1.3 and total current market value of $8,000; 400 shares of XTP common stock with a beta of 0.9 and total current market value of $13,000; and 200 shares of SPR common stock with a beta of 0.6 and total current market value of $10,000.
What is the overall weighted beta coefficient for Shari’s portfolio?
A)
0.93
B)
1.26
C)
0.91
D)
0.99
c The answer is 0.91. Calculations are shown below:
Market Value Weighting Beta Weighted Beta
$8,000 ÷ $31,000 = 0.258 × 1.3 = 0.3354
$13,000 ÷ $31,000 = 0.419 × 0.9 = 0.3771
$10,000 ÷ $31,000 = 0.323 × 0.6 = 0.1938
$31,000 0.9063
LO 6.2.1
Stock XYZ has an average return of 12%; its returns fall within a range of –2% to +26% approximately 68% of the time. Which one of these numbers is closest to the standard deviation of returns of Stock XYZ?
A)
19%
B)
8%
C)
28%
D)
14%
d A standard deviation of 14% means an investor can expect a return on an investment to vary ±14 from the average return approximately 68% of the time.
LO 6.2.2
A distribution with a mean that is less than its median most likely
A)
symmetrical.
B)
is negatively skewed.
C)
is positively skewed.
D)
has negative excess kurtosis.
b The answer is that the distribution is negatively skewed. A distribution with a mean that is less than its median is a negatively skewed distribution. A negatively skewed distribution is characterized by many small gains and a few extreme losses. Note that kurtosis is a measure of the peakedness of a return distribution. In a symmetrical distribution, the mean, median, and mode are all equal.
LO 6.2.2
Most fixed-income securities are subject to which of the following risks?
Purchasing power risk
Liquidity risk
Default risk
Reinvestment rate risk
A)
II, III, and IV
B)
I and II
C)
I, III, and IV
D)
I, II, III, and IV
d Fixed-income securities are subject to a number of risks including purchasing power, liquidity, default, and reinvestment rate risk.
LO 6.1.2
Which of the following is the risk that disappears in the portfolio construction process?
A)
Interest rate risk
B)
Unsystematic risk
C)
Purchasing power risk
D)
Systematic risk
b Unsystematic risk (diversifiable risk) is the risk that is eliminated when the investor builds a well-diversified portfolio.
LO 6.1.1
You have recommended a growth mutual fund to a new client. The client considered your recommendation and asked why he should not invest in another fund that he had been following, which appeared to have a better performance over the past three years. You explained the concept of risk-adjusted performance and obtained this information about the two funds:
Your Fund Client Fund
Three-year total return 13.5% 14.75%
Average P/E ratio 20% 24%
Standard deviation 19% 23%
Beta 1.03 1.24
Which fund would you recommend based on each fund’s relationship between risk and return?
Your fund, because its coefficient of variation is 1.41, compared to the client’s coefficient of variation of 1.56
Client fund, because its higher beta dictates that its return should also be higher, which in fact occurred
Client fund, because standard deviations and betas change over time and the statistics are close enough so that the fund with the better return should be chosen
A)
II and III
B)
I and III
C)
I only
D)
II only
c The answer is I only. The standard deviation is divided by the total return to obtain the coefficient of variation. A beta is higher does not mean that any higher return is acceptable. The client’s fund has higher risk as measured by both standard deviation and beta, but taking this higher risk does not provide sufficient return based on the coefficient of variation calculation.
LO 6.2.3
Element Corp had these annual returns over the past four years: +12%, +6%, –8%, and +20%. What is the standard deviation for Element Corp. over the past four years?
A)
12.4%
B)
7.5%
C)
15%
D)
11.8%
d Explanation
The answer is 11.8%.
HP 10bII+ Keystrokes:
12, ∑+
6, ∑+
8, +/-, ∑+
20, ∑+
SHIFT, Sx,Sy (8 key) for standard deviation = 11.8%
TI BA II+ Keystrokes:
Step 1: press “2nd” then “7”. This activates the data screen.
Step 2: press “2nd” then “CE/C” to clear all your existing work.
Step 3: enter the first return “12” into the first “X01” screen and press enter.
Step 4: hit the down arrow button “↓” and scroll past “Y01” and hit “↓” one more time until you get to “X02.”
Step 5: input the next return value which would be “6” and hit enter. Follow this process until you input all four values.
Step 6: press “2nd” then “8” which is the “STAT” screen.
Step 7: press “2nd” then “enter” which is the “SET” screen. Keep hitting the “2nd” and “enter” button until you see “1-V.”
Step 8: press “↓” to scroll through the calculated statistics. You will hit the “↓” button three times before you reach the standard deviation screen which will start with “Sx” and should equal “11.8.”
LO 6.2.2
Which of these statements concerning portfolio diversification is CORRECT?
A)
The benefits of diversification are not realized until at least 25 individual securities are included in the portfolio.
B)
Only systematic risk is reduced as diversification is increased.
C)
Diversification reduces the portfolio’s expected return because diversification reduces a portfolio’s total risk.
D)
By increasing the number of securities in a portfolio, the total risk would be expected to fall at a decreasing rate.
ddddddddd The answer is by increasing the number of securities in a portfolio, the total risk would be expected to fall at a decreasing rate. As more and more securities are added to a portfolio, diversification benefits begin to diminish. The main attraction of diversification is the reduction of risk without an accompanying loss of return.
LO 6.1.1
Bill and Jane are considering adding additional assets to their investment portfolio. They consider themselves moderate-to-high-risk investors. Based on safety of principal, point out the investment that would offer the couple the least amount of protection from risk.
A)
High-grade common stock
B)
Futures
C)
Real estate
D)
Balanced mutual funds
b The answer is futures. Based on the risk-return pyramid, futures will offer the couple the least amount of protection. However, due to their high risk, futures may offer the greatest amount of return.
LO 6.1.1
You are about to recommend the purchase of an additional mutual fund to add to a client’s portfolio, with the objective of reducing the portfolio’s total risk. Upon analysis of several funds, you determine that the standard deviations of the current portfolio and each of the potential new funds are equal, but that the correlation coefficients of these funds with the current portfolio are as shown in the answer choices below.
Which of the funds should you recommend?
A)
Fund D: correlation coefficient = –0.08
B)
Fund A: correlation coefficient = +0.91
C)
Fund C: correlation coefficient = 0.00
D)
Fund B: correlation coefficient = +0.65
a According to modern portfolio theory, total portfolio risk, as measured by standard deviation, is lowered by combining securities in a portfolio so that individual securities have negative (or low positive) correlations between each other’s rates of return.
LO 6.2.4
Based on the information provided, identify the stock that should be acquired if the investor’s objective is to minimize the relative total risk per unit of expected return.
Stock A
Standard deviation 12.49%
Beta 1.07
Expected return 4.65%
Stock B
Standard deviation 23.51%
Beta 1.98
Expected return 10.40%
Stock C
Standard deviation 14.43%
Beta 1.40
Expected return 8.75%
Stock D
Standard deviation 17.98%
Beta 1.56
Expected return 9.63%
A)
Stock A
B)
Stock B
C)
Stock C
D)
Stock D
c Coefficient of variation (CV) is a relative measure of total risk (as measured by standard deviation) per unit of expected return. Use the coefficient of variation to solve for the best investment alternative:
Stock A: 12.49 ÷ 4.65 = 2.6860
Stock B: 23.51 ÷ 10.40 = 2.2606
Stock C: 14.43 ÷ 8.75 = 1.6491
Stock D: 17.98 ÷ 9.63 = 1.8671
The stock with the lowest CV has the least amount of total risk per unit of expected return.
LO 6.2.3
You want to recommend two mutual funds to a new client and have narrowed your selections to the following three funds. The expected returns and standard deviations of each fund are approximately equal. The correlations between the funds are as shown in the following table.
Correlation of Returns
Large-cap Fund
Mid-cap Fund
Small-cap Fund
Large-cap fund
+1.00
Mid-cap fund
+0.67
+1.00
Small-cap fund
+0.41
+0.23
+1.00
Which two funds should you recommend, assuming that your goal is to recommend the two funds that will provide the lowest total portfolio risk and that the portfolio will be equally weighted in the two funds you select?
A)
None, since no fund is negatively correlated with another fund
B)
The large-cap fund and the mid-cap fund
C)
The mid-cap fund and the small-cap fund
D)
The small-cap fund and the large-cap fund
c A negative correlation is not necessary; low positive correlations are adequate to lower the standard deviation of a portfolio. The fund combination that should be selected, given the objective and the fact that all other factors are equal, is the combination with the lowest correlation—the mid-cap fund and the small-cap fund.
LO 6.2.4
Bobby has these securities in his portfolio: ABC common stock, XYZ common stock, PQR mutual fund (domestic small cap), DEZ mutual fund (foreign small cap), 30-year Treasury bond, and 5-year Treasury note. Point out the risk that should NOT concern Bobby.
A)
Reinvestment rate risk
B)
Default risk
C)
Financial risk
D)
Systematic risk
b The answer is default risk. Treasuries are considered default risk-free. Financial risk is the uncertainty introduced from the method by which a firm finances its assets (i.e., debt versus equity financing). Reinvestment rate risk is the risk that as cash flows are received they will be reinvested at lower rates of return than the investment that generated the cash flows. Systematic risk is the risk that all securities are subject to and typically cannot be eliminated through diversification.
LO 6.1.2
An analysis of the monthly returns for the past year of a mutual fund portfolio consisting of two funds revealed these statistics:
Fund A Fund B
Total return 18% 11%
Standard deviation 23% 16%
Percentage of portfolio 35% 65%
Correlation coefficient (R) 0.25
What is the coefficient of determination (R2) of Fund A and Fund B?
A)
84.64%
B)
6.25%
C)
50.00%
D)
21.49%
b The answer is 6.25%. The coefficient of determination is the square of the correlation coefficient (0.25)2 = 0.25 × 0.25 = 0.0625, or 6.25%.
LO 6.2.5
Which of the following statements concerning a knowledge of the risk/return relationship is CORRECT?
Future risk/return relationships are not guaranteed to match past risk/return relationships.
Chances are that past relative relationships will not continue into the future.
A reduction in risk also means a reduction in the possible return on the investment.
The smaller the dispersion of returns, the greater the risk associated with a particular investment.
A)
II, III, and IV
B)
I and III
C)
I only
D)
II and III
b Chances are that past relative relationships will continue into the future. The smaller the dispersion of returns, the lower the risk associated with a particular investment.
LO 6.1.1
If two stocks have positive covariance, which of these statements is CORRECT?
A)
The two stocks must be in the same industry.
B)
The rates of return tend to move in the opposite direction relative to their individual means.
C)
If one stock doubles in price, the other will also double in price.
D)
The rates of return tend to move in the same direction relative to their individual means.
d The answer is the rates of return tend to move in the same direction relative to their individual means. If one stock doubles in price, the other will also double in price is true if the correlation coefficient = 1. The two stocks need not be in the same industry.
LO 6.2.4
