CFA & Investment Statistics Quick-Reference Guide:
Formulas, Concepts, and Key Practice Questions
Allen Jabber invested $400 at the beginning of the last 12 months in the shares of a mutual fund that
paid no dividends. Which Method will he correctly choose to calculate his average price per share from
the monthly share prices?
a) Arithmetic Mean
b) Harmonic Mean
c) Geometric Mean - ✔✔Harmonic Mean - The harmonic mean of the 12 purchase prices will be his
average price paid per share.
Colonia has 2 political parties, the Wigs and the Wags. If the Wags are elected there is a 32% probability
of a tax increase over the next 4 years. If the Wigs are elected there is a 60% probability of a tax
increase. There is a 20% probability the that the Wags will be elected. The sum of the (unconditional)
probability of a tax increase and the joint probability that the wigs will be elected and there will be no
tax increase is closest to:
a) 55%
b) 70%
c) 85% - ✔✔86.4% = C
The unconditional probability of a tax increase is: 0.2(0.32) + 0.8(0.6) = 54.4%.
The joint probability that the Wigs will be elected and there will be no tax increase is: 0.8(0.4) = 32%.
The sum is: 54.4 + 32 = 86.4%.
An analyst who wants to display the relationship between two variables graphically is most likely to use:
a) a histogram
b) a scatterplot
,c) a frequency polygon - ✔✔B = Scatterplot
Scatterplots illustrate the relationship between two variables.
Histograms and frequency polygons show the distribution of observations for a single variable.
Ralph will retire 15 years from today and has saved $121,000 in his investment account for retirement.
He believes he will need 37,000 at the beginning of each year for 25 Years of retirement, with the first
withdrawal on the day he retires. Ralph assumes his account will earn 8%. The amount he needs to
deposit at the beginning of this year and each of the following 14 Years (15 in all) is closest to:
a) 1350
b) 1450
c) 1550 - ✔✔B = 1450
Step 1:
Calculate the amount needed at retirement at t = 15, with your calculator in BGN mode.
N = 25, FV = 0, I/Y = 8, PMT = 37,000, CPT PV = -426,564
Step 2:
Calculate the required deposits at t = 0,1,.... ,14 to result in a time 15 value of 426,564, with your
calculator still in BGN mode.
PV = -121,000, N = 15, I/Y = 8, FV = 426,564, CPT PMT = -$1,457.21
The current price of Bosto shares is $50. Over the coming year, there is a 40% probability that share
returns will be 10%, 40% probability returns will be 12.5%, and a 20% probability share returns will be
30%. Bostos expected return and standard deviation of returns for the coming year are closest to:
a) E(R) = 15% Standard Dev = 7.58%
b) E(R) = 17.5% Standard Dev = 5.75%
a) E(R) = 17.5% Standard Dev = 7.58% - ✔✔A
E[R] = (0.4)(10) + (0.4)(12.5) + (0.2)(30) = 15%
, Variance = (0.4)(10 − 15)2 + (0.4)(12.5 − 15)2 + (0.2)(30 − 15)2 = 57.5
Standard deviation=√57.5=7.58%
Nikki Ali and Donald Ankard borrowed $15,000 to finance their wedding and reception. The fully
amortizing loan at 11% requires equal payments at the end of each of the next seven years. The
principle portion of the first payment is closest to:
A) 1500
B) 1530
C) 1560 - ✔✔B
The interest portion of the first payment is simply principal × interest rate = (15,000 × 0.11) = 1,650.
Using a financial calculator: PV = 15,000, FV = 0, I/Y = 11, N = 7, CPT PMT= $3,183
Principal = payment − interest = 3,183 − 1,650 = 1,533
Which of the following statements about probability distributions is least accurate?
A) Continuous uniform distributions have cumulative distribution functions that are straight lines from 0
to 1.
B) The probability that a continuously distributed random variable will take on a specific value is always
0.
C) A normally distributed random variable divided by its standard deviation will follow a standard
normal probability distribution. - ✔✔C
A standard normal probability distribution has a mean of zero, so subtracting the mean from a normal
random variable before dividing by its standard deviation is necessary to produce a standard normal
probability distribution.
Formulas, Concepts, and Key Practice Questions
Allen Jabber invested $400 at the beginning of the last 12 months in the shares of a mutual fund that
paid no dividends. Which Method will he correctly choose to calculate his average price per share from
the monthly share prices?
a) Arithmetic Mean
b) Harmonic Mean
c) Geometric Mean - ✔✔Harmonic Mean - The harmonic mean of the 12 purchase prices will be his
average price paid per share.
Colonia has 2 political parties, the Wigs and the Wags. If the Wags are elected there is a 32% probability
of a tax increase over the next 4 years. If the Wigs are elected there is a 60% probability of a tax
increase. There is a 20% probability the that the Wags will be elected. The sum of the (unconditional)
probability of a tax increase and the joint probability that the wigs will be elected and there will be no
tax increase is closest to:
a) 55%
b) 70%
c) 85% - ✔✔86.4% = C
The unconditional probability of a tax increase is: 0.2(0.32) + 0.8(0.6) = 54.4%.
The joint probability that the Wigs will be elected and there will be no tax increase is: 0.8(0.4) = 32%.
The sum is: 54.4 + 32 = 86.4%.
An analyst who wants to display the relationship between two variables graphically is most likely to use:
a) a histogram
b) a scatterplot
,c) a frequency polygon - ✔✔B = Scatterplot
Scatterplots illustrate the relationship between two variables.
Histograms and frequency polygons show the distribution of observations for a single variable.
Ralph will retire 15 years from today and has saved $121,000 in his investment account for retirement.
He believes he will need 37,000 at the beginning of each year for 25 Years of retirement, with the first
withdrawal on the day he retires. Ralph assumes his account will earn 8%. The amount he needs to
deposit at the beginning of this year and each of the following 14 Years (15 in all) is closest to:
a) 1350
b) 1450
c) 1550 - ✔✔B = 1450
Step 1:
Calculate the amount needed at retirement at t = 15, with your calculator in BGN mode.
N = 25, FV = 0, I/Y = 8, PMT = 37,000, CPT PV = -426,564
Step 2:
Calculate the required deposits at t = 0,1,.... ,14 to result in a time 15 value of 426,564, with your
calculator still in BGN mode.
PV = -121,000, N = 15, I/Y = 8, FV = 426,564, CPT PMT = -$1,457.21
The current price of Bosto shares is $50. Over the coming year, there is a 40% probability that share
returns will be 10%, 40% probability returns will be 12.5%, and a 20% probability share returns will be
30%. Bostos expected return and standard deviation of returns for the coming year are closest to:
a) E(R) = 15% Standard Dev = 7.58%
b) E(R) = 17.5% Standard Dev = 5.75%
a) E(R) = 17.5% Standard Dev = 7.58% - ✔✔A
E[R] = (0.4)(10) + (0.4)(12.5) + (0.2)(30) = 15%
, Variance = (0.4)(10 − 15)2 + (0.4)(12.5 − 15)2 + (0.2)(30 − 15)2 = 57.5
Standard deviation=√57.5=7.58%
Nikki Ali and Donald Ankard borrowed $15,000 to finance their wedding and reception. The fully
amortizing loan at 11% requires equal payments at the end of each of the next seven years. The
principle portion of the first payment is closest to:
A) 1500
B) 1530
C) 1560 - ✔✔B
The interest portion of the first payment is simply principal × interest rate = (15,000 × 0.11) = 1,650.
Using a financial calculator: PV = 15,000, FV = 0, I/Y = 11, N = 7, CPT PMT= $3,183
Principal = payment − interest = 3,183 − 1,650 = 1,533
Which of the following statements about probability distributions is least accurate?
A) Continuous uniform distributions have cumulative distribution functions that are straight lines from 0
to 1.
B) The probability that a continuously distributed random variable will take on a specific value is always
0.
C) A normally distributed random variable divided by its standard deviation will follow a standard
normal probability distribution. - ✔✔C
A standard normal probability distribution has a mean of zero, so subtracting the mean from a normal
random variable before dividing by its standard deviation is necessary to produce a standard normal
probability distribution.
