D.30 Quantitative investment concepts and measures of investment returns

Question 1

Which of the following measures is not commonly used to evaluate investment returns?

A. Internal rate of return (IRR)
B. Net present value (NPV)
C. Total shareholder return (TSR)
D. Gross domestic product (GDP)

Answer 1

D. Gross domestic product (GDP)

D.30 Quantitative investment concepts and measures of investment returns

Question 2

Which of the following investment performance measures takes into account the timing and amount of cash flows?

A. Time-weighted return (TWR)
B. Money-weighted return (MWR)
C. Both TWR and MWR
D. Neither TWR nor MWR

Answer 2

B. Money-weighted return (MWR)

D.30 Quantitative investment concepts and measures of investment returns

Question 3

What is the formula for calculating the holding period return (HPR)?

A. (Ending value - Beginning value) / Beginning value
B. (Ending value - Beginning value) / Ending value
C. (Ending value + Beginning value) / Beginning value
D. (Ending value + Beginning value) / Ending value

Answer 3

A. (Ending value - Beginning value) / Beginning value

D.30 Quantitative investment concepts and measures of investment returns

Question 4

Which of the following measures is a common way to adjust investment returns for risk?

A. Standard deviation
B. Sharpe ratio
C. Treynor ratio
D. Sortino ratio

Answer 4

B. Sharpe ratio

D.30 Quantitative investment concepts and measures of investment returns

Question 5

Suppose you invested $10,000 in 100 shares of stock that paid a dividend of $1 per share and sold it one year later for $12,000. What is your holding period return (HPR)?

A. 11%
B. 21%
C. 31%
D. 41%

Answer 5

B. 21%

HPR= [(Ending Value+Dividends)−Initial Investment] / Initial Investment

HPR = [(12,000 + 100) - 10,000] / 10,000
HPR = .21 or 21%

D.30 Quantitative investment concepts and measures of investment returns

Question 6

What is the formula for calculating the Sharpe ratio?

A. (Portfolio return - Risk-free rate) / Standard deviation
B. (Portfolio return - Risk-free rate) x Standard deviation
C. (Risk-free rate - Portfolio return) / Standard deviation
D. (Risk-free rate - Portfolio return) x Standard deviation

Answer 6

A. (Portfolio return - Risk-free rate) / Standard deviation

The Sharpe ratio measures the excess return of an investment relative to the risk-free rate per unit of total risk.

D.30 Quantitative investment concepts and measures of investment returns

Question 7

Which of the following measures is used to evaluate the performance of a mutual fund manager?

A. Information ratio
B. Tracking error
C. Alpha
D. All of the above

Answer 7

D. All of the above

Each of the options mentioned can be used to evaluate the performance of a mutual fund manager, albeit in different ways:

• Information Ratio: This measures the excess return of the portfolio relative to the return of the benchmark, divided by the tracking error. A higher information ratio indicates better portfolio management performance when adjusted for the risk taken relative to the benchmark.
• Tracking Error: It measures the standard deviation of the difference between the portfolio’s returns and its benchmark’s returns. A lower tracking error indicates that the portfolio closely follows the benchmark.
• Alpha: This is a measure of the excess return of an investment relative to the return of a benchmark index. A positive alpha indicates that the fund has outperformed its benchmark on a risk-adjusted basis, while a negative alpha suggests underperformance.

D.30 Quantitative investment concepts and measures of investment returns

Question 8

You are evaluating the performance of two investment portfolios: Portfolio A has an average return of 10% per year, and the risk-free rate is 3%, and a standard deviation of 15% Portfolio B has an average return of 12% per year, and the risk-free rate is 3% and a standard devication of 20%. Given this information, which portfolio has a higher Sharpe ratio?

A. Portfolio A
B. Portfolio B
C. Both portfolios have the same Sharpe ratio
D. Cannot be determined without more information

Answer 8

A. Portfolio A

The Sharpe ratio is calculated as follows:

Sharpe Ratio = (Portfolio Return - Risk-Free Rate) / Portfolio Standard Deviation

Given the risk-free rate of 3% for both portfolios, we can now calculate the Sharpe ratios:

For Portfolio A:
Sharpe Ratio for Portfolio A = (10% - 3%) / 15% = 0.47

For Portfolio B:
Sharpe Ratio for Portfolio B = (12% - 3%) / 20% = 0.45

Comparing the Sharpe ratios, Portfolio A has a higher Sharpe ratio (0.47) compared to Portfolio B (0.45). Therefore, Portfolio A has a higher risk-adjusted return, indicating that it provides better returns relative to the risk taken compared to Portfolio B

D.30 Quantitative investment concepts and measures of investment returns

Question 9

You are evaluating the performance of a mutual fund manager who achieved an alpha of 2% and a tracking error of 3% relative to its benchmark. What is the information ratio?

A. 0.67
B. 0.83
C. 1.00
D. 1.50

Answer 9

A. 0.67

The information ratio is calculated as the excess return of a portfolio relative to its benchmark per unit of active risk. In this case, the excess return is the alpha (2%), and the active risk is the tracking error (3%). Therefore, the information ratio is 2% / 3% = 0.67.

D.30 Quantitative investment concepts and measures of investment returns

Question 10

You invested $5,000 in a stock that paid no dividends and sold it one year later for $6,000. During that year, inflation was 2%. What is your real rate of return?

A. 11%
B. 15%
C. 18%
D. 20%

Answer 10

A. 11%

D.30 Quantitative investment concepts and measures of investment returns

Question 11

You invested $10,000 in a mutual fund that charged a front-end load of 5%. The fund has an average annual return of 8% for the next five years, and you reinvested all dividends and capital gains. What is your total return on investment (ROI) at the end of the five years?

A. 31.67%
B. 35.67%
C. 39.67%
D. 43.67%

Answer 11

B. 35.67%

The front-end load reduces the initial investment to $9,500. Then, the average annual return of 8% for five years compounds to a future value of $13,572.70. Adding back the initial investment, we get a total future value of $23,072.70. The ROI is therefore ($23,072.70 - $9,500) / $9,500 = 1.4267, or 35.67% when converted to a percentage.

D.30 Quantitative investment concepts and measures of investment returns

Question 12

You are a financial planner, and your client has come to you with information regarding an investment they’re considering. They’re interested in a bond with the following characteristics:

Initial investment: $20,000
Annual coupon rate: 5%
Maturity: 10 years
Face value: $25,000
Required rate of return: 4%
Given these details, which of the following is closest to the bond’s current market value?

A. $21,058.82
B. $22,500.00
C. $23,750.00
D. $27,027.72

Answer 12

D. $27,027.72

To solve for the bond’s current market value, you’ll want to find the present value of the bond’s future cash flows, which consist of the annual coupon payments and the face value returned at maturity.

Using the HP 10bII+ calculator:

Turn on the calculator.
To clear previous data, press [C ALL].
Enter the number of periods (years): [10] [N].
Enter the discount rate (required rate of return): [4] [I/YR].
Enter the future value (face value of the bond): [25,000] [FV].
Enter the annual coupon payment: (0.05 x 25,000 = 1,250). Input [1,250] [PMT].
Compute the present value by pressing [PV]. This will give you the bond’s current market value.
The calculator should display a value close to $27,027.72

D.30 Quantitative investment concepts and measures of investment returns

Question 13

You are evaluating the performance of a portfolio that consists of 50% stocks with an average return of 12% and a standard deviation of 20%, and 50% bonds with an average return of 6% and a standard deviation of 10%. What is the portfolio’s expected return and standard deviation?

A. Expected return of 9%, standard deviation of 15%
B. Expected return of 10%, standard deviation of 15%
C. Expected return of 9%, standard deviation of 10%
D. Expected return of 10%, standard deviation of 10%

Answer 13

C. Expected return of 9%, standard deviation of 10%

The expected return of a portfolio is the weighted average of the expected returns of its components, and the portfolio’s standard deviation is the square root of its variance, which is the weighted sum of the variances and covariances of its components. Using the formula for expected return and standard deviation of a portfolio, we get:

Expected return = 0.5 x 12% + 0.5 x 6% = 9%
Standard deviation = sqrt[(0.5 x 20%)^2 + (0.5 x 10%)^2 + 2 x 0.5 x 20% x 10% x 1] = 10%

D.30 Quantitative investment concepts and measures of investment returns

Question 14

You bought a call option on a stock with a strike price of $50 for a premium of $3. The current stock price is $55, and the option expires in three months. What is your breakeven stock price?

A. $53
B. $53.50
C. $56
D. $56.50

Answer 14

A. $53

The breakeven stock price for a call option is the sum of the strike price and the premium paid. In this case, the breakeven stock price is $50 + $3 = $53.

D.30 Quantitative investment concepts and measures of investment returns

Question 15

Jane, a Certified Financial Planner CFP®, sold a put option on XYZ stock with a strike price of $40 and received a premium of $2. The current stock price is $45, and the option expires in six months. If the stock price drops significantly, what is Jane’s maximum potential loss per contract?

A. $38
B. $40
C. Unlimited
D. $2

Answer 15

A. $38

When you sell (or “write”) a put option, you agree to buy the stock at the strike price if the option is exercised. The maximum loss occurs if the stock price falls to $0. In that case, you would have to buy the stock at the $40 strike price even though it is worthless.

Calculating the maximum potential loss:
Maximum Loss=(Strike Price−Premium Received)×100
= ($40 - $2) x 100
= $38 x 100
= $3,800

D.30 Quantitative investment concepts and measures of investment returns

Question 16

You want to invest $50,000 in a mutual fund that has a sales charge of 5.75%. The fund has an expense ratio of 1.5% and an average annual return of 10%. How much will you have after 10 years?

A. $106,549
B. $130,524
C. $135,700
D. $138,950

Answer 16

A. $106,549

Sales Charge = (Sales Charge Percentage / 100) * Initial Investment
Sales Charge = (5.75% / 100) * $50,000
Sales Charge = 0.0575 * $50,000
Sales Charge = $2,875

Now, deduct the sales charge from the initial investment:

Initial Investment after Sales Charge = Initial Investment - Sales Charge
Initial Investment after Sales Charge = $50,000 - $2,875
Initial Investment after Sales Charge = $47,125

Future Value = $47,125 * (1 + 0.10 - 0.015) ^ 10
Future Value = $47,125 * (1.085) ^ 10

Now, calculate the future value:

Future Value ≈ $47,125 * 2.26
Future Value ≈ $106,549

D.30 Quantitative investment concepts and measures of investment returns

Question 17

Michael, a Certified Financial Planner CFP®, is helping his client, Alice, evaluate the performance of her investment portfolio. They are considering various measures to assess the returns of individual investments. Which of the following measures is least likely to be relevant to their evaluation?

A. Internal rate of return (IRR)
B. Net present value (NPV)
C. Total shareholder return (TSR)
D. Gross domestic product (GDP)

Answer 17

D. Gross domestic product (GDP)

When evaluating individual investment returns, measures such as IRR, NPV, and TSR are relevant because they provide insight into the financial performance and value of the investment.

A) IRR represents the discount rate at which the NPV of a series of cash flows is zero and helps in determining the profitability of an investment.
B) NPV shows the difference between the present value of cash inflows and outflows over time.
C) TSR measures the return received by shareholders from holding a company’s stock and includes both capital appreciation and dividends.

GDP is a broad economic indicator that measures the total value of goods and services produced in a country over a specific period. It is not typically used to evaluate the returns of individual investments.

D.30 Quantitative investment concepts and measures of investment returns

Question 18

Which of the following investments has the highest Sharpe Ratio if all have a risk-free rate of 2%?

A. Investment A: Expected return of 8% and standard deviation of 10%
B. Investment B: Expected return of 10% and standard deviation of 12%
C. Investment C: Expected return of 12% and standard deviation of 15%
D. Investment D: Expected return of 6% and standard deviation of 5%

Answer 18

D. Investment D: Expected return of 6% and standard deviation of 5%

The Sharpe Ratio is calculated using the formula: (Expected return - Risk-free rate) / Standard deviation. Higher ratios indicate better risk-adjusted returns. Calculation:

Investment A: (8% - 2%) / 10% = 0.60
Investment B: (10% - 2%) / 12% = 0.67
Investment C: (12% - 2%) / 15% = 0.67
Investment D: (6% - 2%) / 5% = 0.80

D.30 Quantitative investment concepts and measures of investment returns

Question 19

A client invested $10,000 in a mutual fund five years ago. Today, the investment is worth $16,105. What is the Compound Annual Growth Rate (CAGR) of the investment?

A. 5%
B. 10%
C. 15%
D. 20%

Answer 19

B. 10%

D.30 Quantitative investment concepts and measures of investment returns

Question 20

An investor has a portfolio that includes a stock with a beta of 1.5. Considering the market’s expected return is 8% and the risk-free rate is 3%, what is the expected return of the stock according to the Capital Asset Pricing Model (CAPM)?

A. 7.5%
B. 10.5%
C. 12.0%
D. 10.0%

Answer 20

B. 10.5%

D.30 Quantitative investment concepts and measures of investment returns