Brainscape's Knowledge GenomeTM

Browse over 1 million classes created by top students, professors, publishers, and experts.


See full index

cfa exam level 1 > Quantitative Methods > Flashcards

Quantitative Methods Flashcards

You may prefer our related Brainscape-certified flashcards:
CFA flashcards
1
Q

Annuity

A

A finite number of equal cash flows occurring at fixed intervals of equal length over a defined period of time (e.g., monthly payments of $100 for three years)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
1
Q

Lump Sum

A

A single cash flow. Lump sum cash flows are one-time events and therefore are not recurring

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
2
Q

Present Value

A

The value today of a cash flow to be received or paid in the future. On a timeline, present values occur before(to the left of( their relevant cash flows

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
3
Q

Future Value

A

The value in the future of a cash flowed received or paid today. On a timeline, future values occur after(to the right of) their relevant cash flows

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
4
Q

Perpetuity

A

A series of equal cash flows occurring at fixed intervals of equal length forever

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
5
Q

Discount Rate and Compounding Rate

A

The rates of interest used to find the present and future values

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
6
Q

Compounding or Compounding Values

A

When interest is earned or paid on interest

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
7
Q

Stated or Nominal Rate

A

the interest rate that is displayed on a loan agreement before any adjustments for compounding market factors.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
8
Q

Effective Interest Rates

A

The concept of compounding is associated with the related concept of effective interest rates

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
9
Q

Geometric Mean Return

A

A compound annual growth rate for an investment. The geometric mean return takes into account the effects of compounding. Smaller or equal to the arithmetic mean

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
10
Q

Discounting

A

Finding a present value by deducting interest from future value

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
11
Q

Ordinary Annuity

A

When cash flows are at the end of the period. It represents the typical cash flow pattern for loans, such as auto, home, furniture, fixtures, and business

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
12
Q

Annuity Due

A

Equal to the value of an ordinary annuity plus one period’s interest

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
13
Q

How to find the present value of an annuity due

A

Discount all future values and sum them up

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
14
Q

Perpetuity

A

A series of equal cash flows occurring at the same interval forever

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
15
Q

Present value of a perpetuity

A

Equals the periodic cash amount divided by the discount interest rate

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
16
Q

Population

A

The collection of all possible individuals, objects, measurements, or other items (e.g., the population of the US is all people who call the US their home country)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
17
Q

Sample

A

A portion or subset of a population that is used to estimate characteristics of the population (i.e., make inferences about)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
18
Q

Variable

A

An unknown quantity or measurement that can have different values

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
19
Q

Qualitative

A

A variable that measures attributes. These could include gender, religious preference, eye color, types of running shoe preferred, and place of birth

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
20
Q

Quantitative

A

A variable that is expressed numerically. These could include the average number of children in a typical household, the average height of American females, the percentage of people in the population with false teeth, or the average number of computers sold daily. Quantitative variables can be categorized as discrete or continuous

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
21
Q

Discrete

A

If the variable can only take on a whole number value from 1 to 10, it would be considered discrete

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
22
Q

Continuous

A

The variable can assume an infinite number of possible values

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
23
Q

Frequency Distribution

A

The tally of observations falling in equally spaced intervals. The frequency distribution shows how the data are scattered

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
24
Q

Frequency Distribution Histogram

A

A graph of a frequency distribution. A histogram illustrates how the data are scattered

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
25
Q

Mean

A

Just another word for average, or the center of the data

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
26
Q

Arithmetic mean

A

The most common measure of central tendency. sometimes the summation symbol E

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
27
Q

Central Tendency

A

A statistical term that refers to the typical or central value of a probability distribution. Measures of central tendency are often called averages. The most common measures of central tendency are the mean, median, and mode

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
28
Q

Median

A

The middle observation of the ranked data. The median finds the center of the distribution by number of observations. There are equal number of observations above and below the median, regardless of their values

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
29
Q

Difference between the Mean and Median

A

The median finds the center of the distribution by number of observations. There are equal number of observations above and below the median, regardless of their values.
The mean actually adds all the observations together and divides by the number of observations to find the mathematical center.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
30
Q

Mode

A

The observation that appears most often. The mode is the most common number that appears in your set of data. To find the mode count how often each number appears and the number that appears the most times is the mode.The mean, median, and the mode are all measures of central tendency

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
31
Q

Measures of Dispersion

A

Positive real numbers that describe how spread out a set of data is, or how homogeneous or heterogeneous it is. The value of a measure of dispersion is zero if all the data points in a set are the same, but increases as the data becomes more variable

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
32
Q

Range

A

The distance between the lowest and highest observed values.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
33
Q

Mean Absolute Deviation (MAD)

A

A measure of the dispersion of the sampe observations around the center of the distribution. It measures the average deviation from the mathematical mean.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
34
Q

Deviation

A

A deviation is measured as the distance from the mean to each observation
With a mean of 68.7”, the deviations for our sample are:

70.0” - 68.7” = 1.3”
71.0” - 68.7” = 2.3”
73.0” - 68.7” = 4.3”
66.0” - 68.7” = -2.7”
62.0” - 68.7” = -6.7”
70.0” - 68.7” = 1.3”

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
35
Q

Variance and Standard Deviation

A

Another way to measure the dispersion of a sample. Both variance and standard deviation are measures of dispersion of the data around the mean of the distribution.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
36
Q

Variance

A

Variance is the average of the squared differences between each data point and the mean

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
37
Q

Standard Deviation

A

The square root of the variance

38
Q

Normal Distribution

A

A type of continuous probability distribution that shows data points are symmetrically distributed around a central region, or mean. The distribution is bell-shaped and appears as a curve when graphed; in a normal distribution, the mean, median, and mode are equal.

39
Q

Perfect Symmetry

A
  • The center point of the distribution is the mean, median, and mode
  • 50% of all possible returns are to the right of (above) the mean
  • 50% of all possible returns are to the left of (below) the mean
40
Q

Empirical Rule

A

Also known as the 68-95-99.7 rule or three-sigma rule, a statistical rule that states that in a normal distribution, 68% of values fall within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations

41
Q

The effective interest rates depends upon?

A

The nominal rate and the number of compounding periods per year. As the number of compounding periods increases, the effective rate increases.

42
Q
  1. For a given present value and interest rate, the future value:
    a. Increases as the number of compounding periods per year increases
    b. decreases as the number of compounding periods per year increases
    c. remains the same as the number of compounding periods per year increases
    d. remains the same as the number of compounding periods per year decreases
A

A. increases as the number of compounding periods per year increases.

As illustrated in the equation

(1 + i/m)m

the effective interest rate increases as the number of compounding periods per year, m, increases. As the effective rate increases, the future value increases since you are compounding at a higher rate.

43
Q
  1. For a given present value and interest rate, the present value:
    a. increases as the number of compounding periods per year increases
    b. decreases as the number of compounding periods per year increases
    c. remains the same as the number of compounding periods per year increases
    d. remains the same as the number of compounding periods per year decreases
A

B. decreases as the number of compounding periods per year increases.

As the effective rate increases, the present value must decrease since you are discounting at a higher rate.

44
Q
  1. Jim Willson is planning to purchase a high performance sports car for $100,000. He will finance the purchase with a 5-year fully amortized loan at an interest rate of 5.0% with payments due at the end of each year. What is the interest portion of the payment in year three and the remaining principal balance at the end of year three?Interest Principle
    A. $5000 $42,948
    B. $3145 $30,708
    C. $5000 $30,708
    D. $3145 $42,948
A

D. $3145 $42,948

–100,000 = PV
5 = I/Y
5 = N
CPT PMT = $23,097

Interest in each year equal the interest rate (5.0%) times the principal balance at the end of the previous year. For the third year, the interest portion of the payment is 0.05 × 62,900 = $3,145. The principal portion of the payment is 23,097 – 3,145 = $19,952. Thus the principal balance gets reduced to 62,900 – 19,952 = $42,948 at the end of year three. The following amortization table demonstrates the interest, principal, and outstanding balance for each of the five years the loan is outstanding.

Year 0 = $100,000 Balance

Year 1 = $81,903 Balance ($100,000 - $23,097)

Interest pmt = $5,000 (100,000 x .05)
Principal pmt = $18,097 (23,097 - 5,000)
Year 2 = $62,900 Balance ($81,903 - $23,097)

Interest pmt = $4,095 (81,903 x .05)
Principal pmt = $19,002 (23,097 - 4,095)
Year 3 = $42,948 Balance ($62,900- $23,097)

Interest pmt = $3,145 (62,900 x .05)
Principal pmt = $19,952 (23,097 - 3,145)
Year 4 = $21,998 Balance ($42,948 - $23,097)

Interest pmt = $2,147 (42,948 x .05)
Principal pmt = $20,950 (23,097 - 2,147)
Year 5 = $0 Balance ($21,998 - $23,097)

Interest pmt = $1,100 (21,988 x .05)
Principal pmt = $21,988 (23,097 - 1,100)

45
Q

A client invested $1.5 million both in stocks earning 13% total return and in bonds earning 5%. Total earnings for the clients was $143,000. What percentage was invested in fixed income?

A. 17.2%.
B. 25.4%.
C. 43.3%.
D. 85.9%.

A

C

Set up two equations:

  1. x = equities
  2. 1,500,000 - x = bonds
  3. 0.13(x) + 0.05(1,500,000 - x) = $143,000
  4. .13x + 75,000 - .05x = $143,000
  5. .08x = 68,000
  6. 850,000 = equities
  7. 650,000 = bond

650,000 / 1,500,000 = 43.3%

45
Q

A student has $25,000 in her bank account, and the University charges a total of $500 per credit hour. How many credit hours can she purchase before she must borrow money?
A. 5.
B. 12.
C. 50.
D 150.

A

C

let n represent the number of credit hours (the unknown). We know that the number of hours multiplied by the cost per hour, $500, yields the total spent, which cannot be more than $25,000. We represent this in equation form as the following:

$500n = $25,000

n = $25,000 / $500 = 50

46
Q
  1. What are the range, mode, and median for the annual returns of Rector’s stock over the last 5 years?Range Mode Median
    A. 35% 10% 55%
    B. 55% 10% 35%
    C. 35% 55% 10%
    D. 55% 35% 10%
A

B

Multiplying both sides of the equation by c, we are left with the following:

15 = 3C

C = (15/3)

C = 5

47
Q

If p ≤ 25 / 5, which of the following represents the value of p?

A. L less than or equal to 5.
B. Greater than or equal to 5.
C. Equal to 5.
D. Equal to 25.

A

A

dividing 25 by 5, we are left with p ≤ 5. The ≤ sign indicates “less than or equal to,” so the interpretation of the equation is p is less than or equal to 5.

48
Q

In the equation 3(x + 5) = 45, which of the following represents the value of x?

A. 10.
B. 15.
C. 20.
D. 25.

A

A

First we multiply through the parentheses by 3 and are left with 3x + 15 = 45. We then subtract 15 from both sides and get 3x = 30. Dividing both sides by 3 leaves us with x = 10.

49
Q

If 4x + 4y = 24 and 2x + 3y = 24, which of the following statements is TRUE?
A. x = 6.
B. x = 12.
C. y = 6.
D. y = 12.

A

D

First set up the equations as simultaneous equations:

Equation 1: 4x + 4y = 24
Equation 2: 2x + 3y = 24
Sub one equation into another:

4x = 24 - 4y
x = 6 - y
Sub:
2(6 - y) + 3y = 24
12 - 2y + 3y = 24
12 + y = 24
y = 12
Sub:
4x + 4(12) = 24
4x + 48 = 24
4x = -24
x = -6

50
Q

If x = 2 – y and y = x – 4, which of the following relationships is TRUE?

A. x = 3.
B. x = 6.
C. y = 1.
D. y = 14.

A

A

First set up the simultaneous equations:

x = 2 - y
y = x - 4
Sub

y = 2 - y - 4
2y = -2
y = -1
Sub

x = 2 - (-1)
x = 3

51
Q

Jill invested $100,000 in stocks and bonds. Equities earned a total return of 12%, and the fixed income component earned 8%. If she had invested twice as much in equities, she would have made $1,800 more. How much was invested in equities?
A. $45,000.
B. $10,000.
C. $90,000.
DX. $55,000.

A

A

Define the variable, set up an equation based on the information, and solve for the variable.

x = amount of money invested in equities
$100,000 - x = amount invested in bonds
0.12x + 0.08(100,000 - x) + 1,800 = 0.12(2x) + 0.08(100,000 - 2x)

Left Side

Equity Rate of Return + Bond Rate of Return + Increased Amount
Right Side

Double Equity Rate of Return + Bond Rate of Return on Half of Bond Amount

52
Q
  1. Samantha Tyson must decide which of four investments are the most attractive in terms of future value. The details of each investment opportunity are as follows:

1: $1,000 annuity due with an interest rate of 7.1% and annual payments for three years.
2: $2,800 invested at an interest rate of 7.0% compounded monthly for three years.
3: $1,000 ordinary annuity with an interest rate of 7.1% and annual payments for three years.
4: $2,800 invested at an interest rate of 7.0% compounded semiannually for three years.

A

D Begin by calculating the future value of each investment as follows:

$1,000 annuity due with an interest rate of 7.1% and annual payments for three years.
Begin
Pmt = -1,000
I/YR = 7.1
N = 3
FV = $3,447
$2,800 invested at an interest rate of 7.0% compounded monthly for three years.
No Payment
PV = -2,800
I/YR = 7.0
N = 3*12 = 36
FV = $3,452
$1,000 ordinary annuity with an interest rate of 7.1% and annual payments for three years.
End
PMT = -1,000
I/YR = 7.1
N = 3
FV = 3,218
$2,800 invested at an interest rate of 7.0% compounded semiannually for three years.
PV = -2,800
I/YR = 7
N = 6
FV = $3,442
2,1,4,3

53
Q
  1. What is the value of $1,000 after 12 years at a semiannually compounded stated annual rate of 10%?
    A. $2,200.
    B. $3,138.
    C. $3,225.
    D. $3,600.
A

C

Future Value:

PV = -1,000
I/YR = 10%
N = 24
FV = $3,225

54
Q
  1. What is the value of $1,000 after 12 years at a quarterly compounded stated annual rate of 10%?

A. $3,271.
B. $3,304.
C. $2,200.
D. $3,385.

A

A

Future Value:

PV = -1,000
I/YR = 10%
P/YR = 4
N = 48
FV = $3,271

55
Q
  1. What is the value today for a lump sum of $1,000 to be received 5 years from now, using a 10% rate of interest?

A. $500.
B. $621.
C. $667.
D. $909.

A

B

Future Value

End or Beg
FV = 1,000
N = 5
I/YR = 10%
P/YR = 1
PV = 621

56
Q
  1. If $5,000 is deposited into an account paying 6%, compounded monthly, what is the expected effective rate of return?

A. 6.00%.
B. 6.17%.
C. 6.33%.
D. 6.50%.

A

B

Expected Effective Rate of Return:

End or Beg
PV = -1,000
I/YR = 6%
P/YR = 12
FV = 5,308.3891
(FV - PV) / PV = 6.17%

56
Q
  1. For any nominal rate of interest, when the number of compounding periods per year increases, the effective rate of interest:

A. increases.
B. decreases.
C. remains the same.
D. decreases at an increasing rate.

A

B. Decreases

57
Q
  1. Cliff Bernstein is about to inherit his grandfather’s estate. Over the next twenty years Cliff will receive $17,250 at the end of each year as part of the trust set up in his name by his grandfather. In addition, Cliff will receive two one-time payments of $250,000 six years from now and $675,000 thirteen years from now. What is the present value of Cliff’s inheritance using a 12% interest rate?

A. $425,660.
B. $528,117.
C. $224,740.
D. $410,198.

What if its a 1% rate?

A

$17,250 Payments

End
P/YR = 1
I/YR = 12%
N = 20
PMT = 17,250
PV = 128,848
$250,000 Payment

Beg or End
P/YR = 1
I/YR = 12%
N = 6
PV = 126,658
$675,000 Payment

Beg or End
P/YR = 1
I/YR = 12%
N = 6
PV = 154,693
Thus, the total value of the inheritance is $128,848 + $126,658 + $154,693 = $410,198.

What if its a 1% rate?

Note (17,250 x 20 = 345,000)

$17,250 Payments

End
P/YR = 1
I/YR = 1%
N = 20
PMT = 17,250
PV = 311,286
Note, larger present value because the discount rate is smaller than 12%
$250,000 Payment

End
P/YR = 1
I/YR = 1%
N = 6
PV = 235,511
Note, larger present value because the discount rate is smaller than 12%
$675,000 Payment

Beg or End
P/YR = 1
I/YR = 1%
N = 13
PV = 593,097
Note, larger present value because the discount rate is smaller than 12%

58
Q
  1. An investor plans to make five year-end deposits of $10,000 into an account paying 8%, compounded annually. At the end of five years (at the time of the last deposit) how much will be in the account?

A. $50,000.
B. $54,000.
C. $58,666.
D. $63,359.

A

End (it matters here)
P/YR = 1
PMT = $10,000
I/YR = 8%
FV = $58,666

59
Q
  1. An investor plans to make deposits of $10,000 into an account paying 8%, compounded annually. If she makes the deposits at the beginning of each year for the next five years, how much will she have in the account at the end of five years?
    A. $50,000.
    B. $54,000.
    C. $58,666.
    D. $63,359.
A

Beg(it matters here)

P/YR = 1

PMT = $10,000

I/YR = 8%

FV = $63,359

60
Q
  1. Suppose a 30-year, $200,000 mortgage loan is taken from a bank charging 6% interest, with annual compounding. What are the 30 year-end payments?

A. $6,667.
B. $7,067.
C. $13,707.
D. $14,530.

A

the present value of the payments must equal the amount borrowed.

Be sure your calculator is set to END .
Keystrokes:
PV = –200,000
I/YR = 6%
N = 30
CPT PMT = $14,529.78

61
Q
  1. An investment is expected to provide cash flows of $100 one year from today, $200 two years from today, and $500 three years from today. If the required return is 8%, the value of this investment today is closest to:
    A. $600.
    B. $661.
    C. $740.
    D. $800.
A

PV =

100 / (1.08)1 = 92.59
200 / (1.08)<span>2 </span>= 171.47
500 / (1.08)3 = 396.92
59 + 171.47 + 396.92 = 660.98
OR

Cash Flow

Flow 1 = 100
Flow 2 = 200
Flow 3 = 500
I% = 8%
NPV = 660.98

62
Q
  1. Mike will retire in 30 years and wants to have $2.0 million for his retirement years. Mike expects to earn 10% (compounded annually) on annual deposits to an investment account starting one year from today. How much should Mike deposit annually for each of the next 30 years to reach his goal?

A. $11,010.
B. $11,053.
C. $12,159.
D. $212,158.

A

C
End
P/YR = 1
N = 30
FV = $2,000,000
I/YR = 10%
PMT = $12,158.50

63
Q
  1. Ben purchased a computer on credit. The store will charge an annual interest rate of 15% compounded annually. Payments are made at the end of each year. The term of the loan is two years. The annual cost to Ben is $750. How much did Ben pay for the computer?

A. $1,154.
B. $1,219.
C. $1,304.
D. $1,500.

A

B
Be sure your calculator is set to END
Keystrokes:

PMT = 750
15 = I/YR%
2 = N
CPT PV = $1,219.28

64
Q
  1. Your money market account advertises a nominal rate of 2% with an effective annual rate of 2.0184%. Which of the following is the compounding frequency being used?

A. Annual.
B. Semiannual.
C. Quarterly.
D. Monthly

A

Effective Return = 0.02 = (1 + (i/m))m - 1 =

(1 + (0.02 / m))m - 1 =
To use trial and error, plug different choices for m:

Annual = 1, gives an effective rate of 2%, easy choise to eliminate
Semiannual = 2, gives an effective rate of 2.01%, not the correct answer
Quarterly = 4, gives an effective rate of 2.0151%, not the correct answer
Monthly = 12, gives an effective rate of 2.0184%, the correct answer

65
Q
  1. You are considering an investment with the following expected cash flows over the next 5 years (the first cash flow is 1 yr from today).
    Annual Cash Flow
    $10,000
    $12,000
    $14,000
    X
    $18,000
    The present value of the following cash flow stream is $44,381.54 and assumes a discount rate of 8%. Calculate the missing cash flow amount (denoted by X in the table).
    A. $2,000
    B. $4,000
    C. $8,000
    D. $16,000
A

A. $2000.00

66
Q
  1. If $5000 is invested today and $3000 is invested one yr from today, both at the annual interest rate of 6% compounded annually, the total amount in the account two years from today is closest to:
    A. $8000
    B. $8671
    C. $8798
    D. 8800
A

C.
FV = CF1(1 + i)2 + Cf2(1 + i)1
FV

67
Q
  1. Suppose your client owns a perpetuity with a present value of $1 million. What annual amount can your client withdraw every year, using an annual interest rate of 10%?

A. $100,000
B. $100,100
C. $500,000
D. $1,000,000

A

A. $100,000

The present value of a perpetuity equals the periodic amount divided by the interest rate.

PV = PMT/i
PV x i = PMT = $1,000,000 x 0.10 = $100,000

68
Q
  1. At a growth rate of 7.2%, approximately how long does it take a lump sum to double?

A. 5 yrs
B. 1 yr
C. 10 years
D. 8 years

A

C. 10 years

FV = PV(1 + i)n
Note if an investment doubles, the future value of each $1 will be $2. Therefore:
FV = 2 = 1(1.072)n
Use trial and error, plugging for n:
n = 1, FV = 1.072, too low – not the correct answer
n = 5, FV = 1.42, too low – not the correct answer
n = 8, FV = 1.74, too low – not the correct answer
n = 10, FV = 2.004, close enough! The correct answer is 10 years

69
Q

Cross-sectional analysis

A

Analysis that involves comparisons across individuals in a group at a point in time.

Differs from time-series analysis, which analyzes over time.

70
Q

Continuously compounded return

A

ln(1+HPR)

71
Q

Effective annual yield

EAY

A

An annualized return that accounts for the effect of compounding interest.

aka EAR

72
Q

Excess kurtosis

A

Degree to which the peakedness exceeds that of the normal distribution.

73
Q
  1. Assume you invest a lump sum of $100 today. Further assume your investment value grows to $210 in 5 years. What is your geometric mean annual return?
    A. 16%
    B. 20%
    C. 22%
    D. 25%
A
73
Q

Harmonic mean

A

A type of weighted mean computed by averaging the reciprocals of the observations, then taking the reciprocal of that average.

74
Q
  1. If returns for the last five years are at 2%, 15%, 17%, 19%, and 23%, which of the following represents the geometric mean?
A
74
Q

Use this table regarding Rector, Inc. to answer questions 24 -26

A

Year Return
20x5 35%
20x6 10%
20x7 5%
20x8 -20%
20x9 35%

74
Q

Year Return
20x5 35%
20x6 10%
20x7 5%
20x8 -20%
20x9 35%

  1. What is the arithmetic mean for the annual returns of Rector’s stock over the past five years?
A

[35% +10% + 5% + (-20) + 35%] / 5 = 13%

C. 13%

75
Q

Year Return
20x5 35%
20x6 10%
20x7 5%
20x8 -20%
20x9 35%

  1. What is the geometric mean for the annual for the annual returns of Rector’s stock over the past five years?
A

B. 11 %

(1.35 x 1.10 x 1.05 x 0.80 x 1.35) ^1/5 = 11%

76
Q

Year Return
20x5 35%
20x6 10%
20x7 5%
20x8 -20%
20x9 35%

26 What are the range, mode, and median for the annual returns of Rector’s stock over the past five years?

A

Range (high minus low) = 35% - (-20%) = 55%
Mode (most observations) = 35 %
Median (in the middle) = 10 %

77
Q
  1. All of the following are measures of dispersion EXCEPT:

A. mean average deviation
B. standard deviation
C. median
D. variance

A

C. Median is a measure of central tendency. Median is a descriptive statistic that measures the center of the distribution. Mean average deviation measures the average deviation from the mathematical mean. Average is calculated using the number of observations and deviation is measured as the distance from the mean of each observation. Standard deviation is the square root of the variance. Variance is the squared deviations from the mean.

78
Q
  1. All of the following are properties of the arithmetic mean EXCEPT:

A. The sum of the deviations of each value from the mean will always be zero
B. A set of data has only one mean
C. The mean is not affected by extremely large or small values
D. All values are included in computing the mean

A

C. Statistically described as outliers, these values have a distorting impact not only on the mean, but on all other descriptive statistics. Advanced statistical methods can be used to lessen the problem

79
Q

Null Hypothesis

A

One you want to reject in order to assume alternate is correct

80
Q

Two tailed vs. one-tailed

A

Two tailed is Ho = something

One-tailed is Ho > something

81
Q

Type I error

A

Rejection of null when it’s actually true

81
Q

Confidence interval (Z-test)

A

Sample mean - (standard error * critical z-value) < mean < sample mean + (standard error * critical z-value)

81
Q

Type II error

A

Failure to reject when it is actually false

82
Q

P-value

A

Prob of test stat that would lead to a type I error.

83
Q

T-Test

A

Use if population variance is unknown and either:

Sample is large
Sample is small, but distribution is normal

84
Q

Z-Test

A

Use if population is normal, with known variance or when sample is large and population variance is unknown

85
Q

Data mining

A

Searching for trading patterns until one “works”

cfa exam level 1 (11 decks)

Brainscape helps you reach your goals faster, through stronger study habits.
© 2024 Bold Learning Solutions. Terms and Conditions