C7 - Quantitative Methods (10-20 Qs) SC Flashcards
A 6% bond is currently priced at £98.15. The bond is one year from maturity and will be redeemed at par
What is the internal rate of return (IRR)?
A) 1.1%
B) 1.9%
C) 6.0%
D) 8.0%
D - 8.0%
£98.15 = £106/(1+r).
Rearranged, R = (£106/£98.15)-1 = 0.07998 so 8%, or use trial and error.
If using T&E, go for one of the middle values and then adjust up and down from there, as will be less calculations
A repayment mortgage of £100,000 is taken out over 25 years
What is the annual repayment required at the end of each year if the rate of interest is fixed at 9%
A) £10,181
B) £11,233
C) £12,120
D) £13,204
A - £10,181
£100,000 = annual cash flow x annuity factor
Annuity factor = 1/0.09(1-(1/(1.09)^25)) = 9.8226
£100,000 = annual cashflow x 9.8226
Annual cash flow = £100,000 / 9.8226 = £10,181
Given the following data, what is the value of the 1st, 2nd and 3rd quartiles?
1 : 3 : 5 : 7 : 9 : 11: 17 : 18 : 20 : 22 : 23 : 26
A) 1, 7, and 17
B) 5, 11, and 20
C) 11, 20, and 26
D) 6, 14, and 21
D - 6, 14, and 21
25% of observations lie below the first quartile, 50% below the second quartile, 75% below the third quartile, and 100% below the forth quartile. BELOW not below or equal to.
With 12 observations, the first quartile will be a midway between the 3rd and 4th observations (5 & 7 = 6), the second quartile will be midway between the 6th and 7th observations (11 & 17 = 14) and the third quartile will be midway between the 9th and 10th observation (20 & 22 = 21)
The table below gives GDP figures for 5 consecutive years:
Year / GDP (£’s billions)
1 / 9.8
2 / 10.2
3 / 11.0
4 / 11.6
5 / 12.0
Taking Y1 as the base year, what is the index in Y5?
A) 102.2
B) 112.0
C) 122.4
D) 132.6
C - 122.4
12.0 / 9.8 x 100 = 122.4
What type of index is the Nikkei 225?
A) Weighted geometric
B) Unweighted geometric
C) Weighted arithmetic
D) Unweighted arithmetic
D - Unweighted arithmetic
The Nikkei 255 (stock market index for the Tokyo Stock Exchange) and Dow Jones Industrial Average (aka DJIA is a stock market index of 30 prominent companies listed on stock exchanges in the United State) are examples of unweighted arithmetic
Which of the following would demostrate most usefully the relationship between two variables?
A) Histogram
B) Scatter Diagram
C) Cumulative Frequency Graph
D) None of the above
B - Scatter Diagram
A scatter diagram shows the plot of two variables, giving a visiual representation of the relationship between them. Linear regression can be used to fit a straight line to summarise the relationship between the two variables by statistically minimising the error terms.
Calculate the sample variance of:
12, 34, 29, 54, 98 and 121
A) 1,723.6
B) 1,823.6
C) 1,895.3
D) 1,921.9
B - 1,823.6
Sample variance (s2) is a measure of the degree to which the numbers in a list are spread out. If the numbers in a list are all close to the expected values, the variance will be small. If they are far away, the variance will be large.
Computing sample standard variance:
Step 1: Get the MEAN (sum all and then divide by no of values) - for this question it is 58
Step 2: Take each observation (value) and deduct the MEAN, square and then sum = ((12-58)^2)+((34-58)^2) + … + ((121-58)^2) = 9,118
Step 3: Take solution from Step 2 and divide by the number of oberservations minus 1 to get the variance = 9,118/(6-1) = 1,823.6
Both MEAN and STANDARD DEVIATION can be computed using the calculator’s stats funcation
The FTSE 100 is a:
A) Weighted arithmetic index of stock prices
B) Unweighted arithmetic index of stock prices
C) Weighted geometric index of stock prices
D) Unweighted geometric index of stock prices
A - Weighted arithmetic index of stock prices
The FTSE 100 and FTSE 250 are market value weighted arithmetic indexes
The monthly interest charge on a shop credit card is 2.1%
What is the annual percentage rate (APR)?
A) 21.0%
B) 23.8%
C) 25.2%
D) 28.3%
D - 28.3%
Effective APR = ((1.021)^12)-1 = 0.2832 SO 28.32%
How does one derive values from a bar chart?
A) Frequency from height of bars
B) Width of bars equals number of sample
C) Height multiplied by the width equals frequency
D) Area of the bar equals sample population
A - Frequency from height of bars
The frequency of a variable is derived from the height of a bar chart.
(YEAR) X / Y
(1) 90 / 180
(2) 130 / 220
(3) 125 / 300
What is the geometric index value for X & Y for year 2, using Year 1 as base 100?
A) 113.86
B) 126.63
C) 132.87
D) 176.54
C - 132.87
Geometric indexes are constructed by multiplying the price relatives of the constituent stocks and raising the value o the power of 1/n, where n = the number of index constituents.
Price relative stock X = 130/90 = 1.4444
Price relative stock Y = 220/180 = 1.2222
Index = (1.4444 x 1.2222)^(1/2) x 100 = 132.8663 SO 132.87
If interest rates are fixed at 12% per annum, how much would you pay for an annuity (a financial contract between an annuity purchaser and an insurance company) of £8,000 payable at the end of each of the following five years?
A) £24,847.71
B) £27,973.32
C) £24,000.00
D) £28,838.21
D - £28,838.21
Present Value = £8,000 x annuity factor
Annuity factor = 1/0.12(1-(1/(1.12)^5)) = 3.6048
Present Value = £8,000 x 3.6048 = £28,838.21
What type of data are pie-charts most suitable for?
A) Categorical/discrete
B) Continuous
C) Time-series
D) Semi-long
A - Categorical/discrete
Pie charts give a visual representation for discrete data. Pie charts show the relative frequency of categories in the data set by dividing a circle into sections that are proportionate to the relative frequencies of each category. Pie charts are useful to gain a visual representation of how much the total data set that each category represents.
An investor buys 250 shares at £4 each. After 12 months a dividend of 30 pence per share is received, followed by a dividend of 50 pence per share at the end of the second year. The shares are then sold for £3.925 each at the end of year 2.
What is the internal rate of return on this investment
A) 10.02%
B) 9.73%
C) 8.52%
D) 9.00%
D - 9.00%
250 x £4 = £1,000 / 250 x £3.926 = £981.25
250 x £0.30 = £75 / 250 x £0.50 = £125
The only way of doing this is by trial and error: £1,000 = £75/(1+R) + ((£981.25 + £125)/(1+R)^2 = £999.92.
By trying each one, you will find 9% will get you closest to the purchase amount of £1,000.
IRR, or internal rate of return, is a metric used in financial analysis to estimate the profitability of potential investments. IRR is a discount rate that makes the net present value (NPV) of all cash flows equal to zero in a discounted cash flow analysis.
If small market capitalisation stocks outperform all other stocks, the difference between returns on the FTSE All Share Index and the returns on the FTSE-100 index will be:
A) Zero
B) Negative
C) Positive
D) Indeterminate
C - Positive
The FTSE All-Share is a broad market indicator capturing > 50% of the LSE listed firms and adroun 98% by market capitalisation. The FTSE 100 only represents the 100 biggest stocks (in terms of market capitalisation) on the LSE. If small cap stocks out perform large cap stocks, we would expect the FTSE All-Share to out perform the FTSE 100 Index (in this case FTSE All-Share - FTSE 100 performance woud be positive).
Which of the following are TRUE?
1. The Geometric Index may represent the value of an equally weighted portfolio of stocks
2. All major indices are total returns indices
3. Major world bond indices are total return indices
A) All of the above
B) 1 and 2 only
C) 3 only
D) 1 and 3 only
D - 1 (The Geometric Index may represent the value of an equally weighted portfolio of stocks) and 3 (Major world bond indices are total return indices)
A sample of 400 people were surveyed for their preference in hot drinks. The results were:
Coffee: 230
Tea: 120
Chocolate: 50
The data is to be presented on a pie chart, what angle would represent the tea drinkers
A) 30
B) 45
C) 108
D) 120
C - 108
120/400 = 30%, 360 x 30% = 108 degrees
What is the accumulated value of an investment of £1,000 invested at 1.2% per quarter for five (5) years and 3 months?
A) £1,264
B) £1,269
C) £1,275
D) £1,285
D - £1,285
5 years 3 months = 21 quarters
Future Value = £1,000 x (1.012)^21 = £1,284.67
Over the last 5 years an investors portfolio has grown at the following rates:
7%, 3%, -2%, -5%, and 4%
If the intial investment was £20,000, what is the portfolio worth after 5 years?
A) £21,341.95
B) £21,400.00
C) £22,550.75
D) £24,551.26
A - £21,341.95
£20,000x 1.07 x 1.03 x 0.98 x 0.95 x 1.04 = £21,341.9460
A share portfolio is bought for £20,000. It loses 15 per cent of its value in the first year. In the next year its value falls by 10 per cent and this followed bya 10 percentage fall in the third year
What is the value at the end of the third year?
A) £13,000
B) £13,270
C) £13,770
D) £15,000
C - £13,770
£20,000 x 0.85 x 0.90 x.0.90 = £13,770
Which of the following are examples of a secondary data?
1. The Bank of England Quarterly Bulletin
2. The International Monetary Fund’s International Financial Statistics
3. The annual society trends survey
A) 1 and 2 only
B) 2 and 3 only
C) None of the above
D) All of the above
D - All of the above
Primary data = the collection or generation of data.
Secondary data = existing data collected and distributed by an organisation.
Nine shares have the following percentage price change over the last two years =: 22%, 91%, -10%, 14%, 29%, 35%, 45%, 12%, and 82%
What was the median price change?
A) 33.6%
B) 22.1%
C) 35.0%
D) 29.0%
D - 29%
Median is the middle observation when they all the put into numerical order. SO
-10%, 12%, 14%, 22%, 29%, 35%, 45%, 82% and 91%
There are 9 observations, so the 5th observation (29%) is the Median
A portfolio of £100k gains 5% in the first year, loses 15% in the second before gaining 10% in each of the next three years
What is the value of the portfolio after 5 years?
A) £124,173
B) £118,792
C) £131,101
D) 127,210
B - £118,792
£100,000 x 1.05 x 0.85 x (1.1)^3 = £118,791.75
Which of the following stock indices can be regarded as a broad measure?
1. Nikkei
2. CAC40
3. Dow Jones
4. S&P 500
A) 2, 3 and 4 only
B) 1 and 4 only
C) All of the above
D) 1 only
B - 1 (Nikkei) and 4 (S&P 500) only
The Nikkei and S&P 500 re broad measures as they contain 225 and 500 securities. The Dow Jones Industrial Average contains 30 and the CAC contains 40, so not broad.
*Nikkei - Nikkei 225, a stock market index for the Tokyo Stock Exchange
CAC40 - CAC40 is a benchmark French stock market index
Dow Jones - Dow Jones Industrial Average, Dow Jones, or simply the Dow, is a stock market index of 30 prominent companies listed on stock exchanges in the US
S&P 500 - The Standard and Poor’s 500 is a stock market index tracking the stock performance of 500 of the largest companies listed on stock exchanges in the US
Estimate the mean and population standard deviation of the portfolio size from the data given below.
Portfolio Size (£’000) / No of Clients
20 and under 40 / 50
40 and under 80 / 160
80 and under 120 / 126
120 and under 200 / 35
200 and under 400 / 29
A) Mean = £95,000, SD = £66,652
B) Mean = £66,652, SD = £95,000
C) Mean = £95,000, SD = £44,425
D) Mean = £44,425, SD = £95,000
A - Mean = £95,000, SD = £66,652
Computing the GEOMETRIC MEAN:
Step 1: Compute mid point of each interval = £30, £60, £100 £160, and £300 (figures in £’000)
Step 2: Multiply mid-point by the frequency and sum = (£30 x 50) + (£60 x 160) + (£100 x 126) + (£160 x 35) + (£300 x 29) = 38,000
Step 3: Take solution from Step 2 and divide by the total number observations (in this case, clients) = 38,000/(50+160+126+35+29) = 38,000/400 = £95 adding back in the £’000 = £95,000
Computing the POPULATION STANDARD DEVIATION:
Step 1: Take each mid-point, deduct the mean and square, then multiple by the frequency and sum the results
= (((£30 - £95)^2) x 50) + (((£60 - £95)^2) x 160) + (((£100 - £95)^2) x 126) + (((£160 - £95)^2) x 35) + (((£300 - £95)^2) x 29) = 1,777,000
Step 2: Take the solution form Step 1 and divide by the number of observations to get variance = £1,777,000/400 = 4,442.5
Step 3: Take the square root of the vairance to arrive at SD = √4,442.5 (OR (4,442.5)^(1/2) ) = £66.652 adding back in the £’000 = £66,652
Note both geometric mean and SD can be computed using the calculators stats function…DATA > CLEAR MEMORY > STATS > LIST 1 ENTER MIDPOINTS > SELECT ONE FREQ > SELECT LIST 2 ENTER FREQUENCIES > SWITCH TO STATS MODE (2ND DATA 1) > 1-VAR > SELECT LIST 1 FOR DATA > SELECT LIST 2 FOR FREQUENCY > CALC > ANSWERS: n = VARIABLES / x = GEOMETRIC MEAN / Sx = SAMPLE SD / σx = POP SD
Unless stated sample SD is wanted, always use the population SD for answer
An analyst wishes to plot a graph of rates of change of share prices over time
Which of the following graphs would be most appropriate?
A) Scatter diagram
B) Bar chart
C) Histogram
D) Semi-log graph
D - Semi-Log Graph
When we wish to visually display the rate of change in a variable over time we plot the natural logarithm of the variable over time.
Which of the following are TRUE?
1. Indices show percentage change from base
2. Indices show actual change from base
3. Base is always 100
4. All components in an arithmetic index have the same impact on index value
A) All of the above
B) 1, 2 and 3 only
C) 1 and 4 only
D) 4 only
C - 1 (show percentage change from base) and 4 (All components in an arithmetic index have the same impact on index value)
Indexes show percentage change from the base, NOT actual change. The base value of the index can be anything but it is normally either 100 or 1,000.
An analyst predicts earnings’ growth for eight companies next year to be 10%, 8%, 20%, -5%, 6%, -25%, 30%, and 10%
Calculate the geometric mean predicted earnings’ growth.
A) 6.75%
B) 12.09%
C) 11.91%
D) 5.54%
D - 5.54%
(1.1 x 1.08 x 1.2 x 0.95 x 1.06 x 0.75 x 1.3 x 1.1)^(1/8) - 1 = 0.0554 i.e. 5.54%
While the arithmetic mean is based on adding and dividing values, the geometric mean multiplies and finds the root of values. Even though the geometric mean is a less common measure of central tendency, it’s more accurate than the arithmetic mean for percentage change and positively skewed data.
With a negatively skewed distribution:
A) The MODE will be greater than the MEDIAN and MEAN
B) The MEAN and MEDIAN are equal, but less than the MODE
C) The MEAN and MODE are equal, but greater than the MEDIAN
D) MEAN, MODE and MEDIAN are equal
A - The MODE will be greater than the MEDIAN and MEAN
A negatively skewed distribution is caused by the presence of large negative values of variable. With negative skew MEAN<MEDIAN<MODE (in a symmetrical distribution (MEAN = MEDIAN = MODE)
Which of the following is NOT true regarding index numbers?
A) The always reflect percentage changes since the base year.
B) They always reflect absolute changes since the base year
C) Extreme/Unusual values should be avoided when choosing a base year
D) They involve the rescaling to 100 of the base year value
B - They always reflect absolute changes since the base year
Indexes are designed to show percentage change in a vairable overtime NOT absolute chnages
A finance house finds that the distribution of the size of the deposits it holds as follows:
Deposits (£’000) / No Clients
0 to under 50 / 78
50 to under 100 / 97
100 to under 150 / 43
150 to under 200 / 50
200 and under 250 / 32
What is the population standard deviation of the size of the deposits in £’000s?
A) 65.99
B) 4355.10
C) 76.10
D) 14.61
A - 65.99
To get answer on calculator:
Step 1: Clear memory… DATA > DATA > 4
Step 2: Enter midpoints in List 1 (SO £25, £75, £125, £175, and £225)
Step 3: Enter frequencies into List 2 (SO 78, 97, 43, 50, 32)
Step 4: Switch to STATS MODE…. 2ND > DATA > 1(1-VAR)
Step 5: Select List 1 for DATA and press enter
Step 6: Select List 2 for FRQ and press enter
Step 7: Select CALC by hitting enter when it is flashing:
Step 8: Answers… 1:n = Variables (300), 2:x = Geometric Mean (101.83), 3: Sx = Sample SD (66.1024761) and 4:σx = POP SD (65.99221335)
It costs £5,000 to invest in a project, which generates a return of £13,500 in 5 years time
What is the net present value (NPV) of the project if the appropriate interest rate is 15%?
A) £1,417
B) £1,712
C) £2,835
D) £3,382
B - £1,712
-£5,000 + (£13,500/(1.15)^5) = £1,711.89
Calculate the MEAN and the MEDIAN of the following returns to a share:
-1.2, 2.8, 3.1, 4.1, 4.3, 4.4, 4.5, 6.7, 6.7, 5.2, and 12.2
A) Mean = 4.4, Median = 4.8
B) Mean = 4, Median = 4.4
C) Mean = 4.8, Median = 4.4
D) Mean = 4.8, Median = 6.7
C - Mean = 4.8, Median = 4.4
The MEAN is the sum of all the returns divided by the number of returns (SUM OF RETURN)/11 = 4.8
The MEDIAN us the central value after putting hem all in numercial order, so with the 11 numbers in numerical order the 6th number (4.4) is the median.
An investor puts £500 into a building society deposit account. The account earns 6% pa with interest being credited to the account on a 6-monthly basis
What is the value of the deposit after 3 years?
A) £589.25
B) £595.51
C) £597.03
D) £601.17
C - £597.03
This calculation must be done with semi-annual time periods. Three (3) years equates to six (6) semi-annual periods.
The semi-annual interest rate is 6%/2 = 3%
Future value = £500 x (1.03)^6 = £597.0261
A credit agreement quotes an annual percentage rate (APR) of 21%
What is the monthly rate?
A) 1.29%
B) 1.44%
C) 1.60%
D) 1.75%
C - 1.60%
Monthly rate = 1.21^(1/12) - 1 = 0.016 SO 1.6%
An index of prices in a commodity was originally based on 1989, then rebased on 1996. Express the 1997 value in terms of the 1989 base year.
YEAR / OLD INDEX / NEW INDEX
1989 / 100 / -
1995 / 135 / -
1996 / 150 / 100
1997 / ?? / 115
A) 115.00
B) 155.25
C) 165.00
D) 172.50
D - 172.50
The price index has increased by 15% from 1996 to 1997. Basing this on the old index price of 150 at 1996, the 1997 level would be 150 x 1.15 = 172.5
At the end of 6 years a deposit is worth £2,713 after it has accrued interest at the rate of 2.5% per quarter paid quarterly
What is the original deposit?
A) £1,600
B) £1,900
C) £1,873
D) £1,500
D - £1,500
The calculation must be done with quarterly time periods. Six (6) years equated to 24 quarterly periods.
Present Value (PV) = £2,713/(1.025)^24 = £1,499.95. £1,500 is the closest match to this figure.
The FTSE 100 is based on:
A) Market Capitalisation
B) Turnover
C) Market Share
D) Number of shareholders
A - Market Capitalisation
The FTSE 100 and FTSE 250 are market value weighted arithemetic indexes. FTSE100 being the 100 largest companies and FTSE250 being the NEXT 250 largest companies.
A security has annual rates of return over the last seven years of -9%, 12%, -19%, 22%, 28%, -5% and 2%
What is the GEOMETRIC MEAN return and the MEDIAN return?
A) 3.8 and 4.4
B) 3.8 and 2.0
C) 3.2 and 2.0
D) 3.2 and 4.4
C - 3.2 and 2.0
GEOMETRIC MEAN:
Geometric mean can be calculated by taking the seventh roof of ^7√(0.91 x 1.12 x 0.81 x 1.22 1.28 x 0.95 x 1.02) - 1 = 0.032 so 3.2
For TI-30XS calculator:
(0.91 x 1.12 x 0.81 x 1.22 1.28 x 0.95 x 1.02) ^(1/7) - 1 = 0.0554 i.e. 5.54%
MEDIAN:
-19%, -9%, -5%, 2%, 12%, 22%, and 28%
The median of an even number of items is:
A) The arithemetic mean of the middle two numbers
B) The geometic mean of the middle two numbers
C) The most common item
D) The arithemetic mean of the entire set of numbers
A - The arithemetic mean of the middle two numbers
Median = middle observation when data set is ranked from lowest to highest. With an odd number of observations there is only one middle obserbations, so this is the median. With even numbers of observations, there are two middle observations. The median is calculated by taking a simple mean average of the two middle values.
A project requires an outflow of £25,076 today and a further £2,000 in one years time. Thereafter it will generate inflows of £20,000pa for the next 2 years.
What is the internal rate of return of the project?
A) 16.45%
B) 17.57%
C) 24.07%
D) 25.62%
B - 17.57%
We need to find the discount rate that gives an overall NPV of zero. Trial and error is the only approach for this exam.
NPV = -£25,076 Year 1
- £2,000/ (1+R) Year 2
+ £20,000/(1+R)^2 Year 2
+ £20,000/(1+R)^3 Year 3
By trying each answer, you will find 17.57 is the discount rate that gets you closest to NPV of zero. Start with one of the two middle values offered and you will only need to do a max of 2 calculations.
A company invests in a new automated packing line at the cost of £500,000. The equipment is expected to last for 8 years and have a residual value of £40,000
What is the constant percentage rate of depreciation of the machinery (using the IRR approach)?
A) 11.5%
B) 12.5%
C) 25.3%
D) 27.1%
D - 27.1
£40,000 = £500,000 x (1-R)^8
Rearranged: R = 1 - ((£40,000/£500,000)^(1/8)) = 0.2707 SO 27.1%
The 1 - at the beginning is key!
The distribution of the market values of a sample of 500 quoted shares id:
Share Price (in pence) / No of Shares
Up to 50 / 80
51 to 100 / 120
101 to 150 / 200
151 to 200 / 100
The MEAN and STANDARD DEVIATION OF THIS SAMPLE are:
A) 107 and 46.3
B) 133 and 48.7
C) 107 and 48.7
D) 113 and 46.3
C - 107 and 48.7
To get answer on calculator:
Step 1: Clear memory… DATA > DATA > 4
Step 2: Enter midpoints in List 1 (SO 25p, 75p, 125p and 175p)
Step 3: Enter frequencies into List 2 (SO 80, 120, 200, and 100)
Step 4: Switch to STATS MODE…. 2ND > DATA > 1(1-VAR)
Step 5: Select List 1 for DATA and press enter
Step 6: Select List 2 for FRQ and press enter
Step 7: Select CALC by hitting enter when it is flashing:
Step 8: Answers… 1:n = Variables (500), 2:x = Geometric Mean (107), 3: Sx = Sample SD (48.7930479)and 4:σx = POP SD (48.74423043)
An investor puts £20,000 on deposit at a compound rate of 8%, and withdraws £600 at the end of each year
After 8 years, what is the value of the investment?
A) £30,637
B) £32,943
C) £25,412
D) £37,147
A - £30,637
Step 1: Compute the PV of the £600 annual deductions
PV = £600 x annuity factor
Annuity factor = 1/R(1-(1/(1+R)^Years)) = 1/0.08(1-(1/(1.08)^8)) = 5.7466
PV= £600 x 5.7466 = £3,448
Step 2: Compute net amount at at dates
NPV = £20,000 - £3,448 = £16,552
Step 3: Compound the net amount for 8 periods to get the terminal value
£16,552 x (1.08)^8 = £30,637
Which of the following are TRUE of total returns?
1. Total returns on a share consists of price changes and dividends received
2. The major stock market indices are total return indices
3. The major bond market indices are total return indices
A) All of the above
B) 1 only
C) 1 and 3 only
D) 2 and 3 only
C - 1 (Total returns on a share consists of price changes and dividends received) and 3 (The major bond market indices are total return indices)
Most stock market indexes focus on share prices (price return) and not total return (which includes any cash flow distributions). Most bond indexes reflect total returns over a period (coupons, price changes, and reinvestment income).
The annual bonuses for a group of fund managers at a major firm last year were as follows:
Bonus (£000) / No of Fund Managers
1-3 / 7
4-6 / 12
7-9 / 11
What are the MEAN and POPULATION SD of these annual bonuses?
A) 4.4 and 5.87
B) 5.4 and 5.24
C) 5.4 and 2.29
D) 6.4 and 5.40
C - 5.4 and 2.29
To get answer on calculator:
Step 1: Clear memory… DATA > DATA > 4
Step 2: Enter midpoints in List 1 (SO £2,000, £5,000, and £8,000)
Step 3: Enter frequencies into List 2 (SO 7, 12, and 11)
Step 4: Switch to STATS MODE…. 2ND > DATA > 1(1-VAR)
Step 5: Select List 1 for DATA and press enter
Step 6: Select List 2 for FRQ and press enter
Step 7: Select CALC by hitting enter when it is flashing:
Step 8: Answers… 1:n = Variables (30), 2:x = Geometric Mean (5.4), 3: Sx = Sample SD (2.328237457) and 4:σx = POP SD (2.289104628)
A share price increases by 20% in the first week, 25% in the second, 30% in the third week and 35% in the fourth week after issue.
The geometric mean return or the four weeks is:
A) 27.5%
B) 27.38%
C) 63.3%
D) 163.3%
B - 27.38%
Geometric mean return = (1.20 x 1.25 x 1.30 x 1.35)^(1/4) = 1.273773 SO 27.38%
Which of the following is TRUE about the inter-quartile-range?
A) A measure of distribution dominated by extreme values
B) A measure of distribution not dominated by extreme values
C) The variance of the range
D) It is a measure of central tendency
B - It’s a measure of distribution NOT dominated by extreme values
Range - Highest to lowest value in a data set. Median - midpoint of the dataset when arranged in numerical order (low to high). First Quartile - will be 1/4 through the data set (this can be described as the 25th percentile). Third Quartile will be 3/4 of the way through the dataset (i.e. halfway between the highest value and the median). Interquartile range is computed as the 3rd quartile value to the 1st quartile value. By definition the interquartile range will be the middle 50% of the dataset.
The annual returns are as follows:
Y1 -4.5, Y2 3.8, Y3 5, Y4 12, Y5 -2.0
What is the value of the index after 5 years
A) 114.54
B) 114.24
C) 114.00
D) 114.85
B - 114.24
(0.955 x 1.038 x 1.05 x 1.12 x 0.98) x 100 = 114.24
In order to ensure that each group within a population is represented in a sample, we should use:
A) Non-random sampling techniques
B) Random sampling techniques
C) Secondary data
D) Random numbers
A - Non-random sampling techniques
Non-random sampling increases the chance of ALL groups in a population being represented.
Consider the following statements:
1. A population is MOST of the members of a well-defined group
2. Primary data are collected with a specific task in mind
3. Non-random sampling does NOT involve judgements in selecting a sample
Which is/are correct?
A) All are false
B) 1 and 3 are true but 2 is true
C) 2 is true but 1 and 3 are false
D) Only 3 is true
C - Only 2 (Primary data are collected with a specific task in mind) is true
Population is ALL members of a well defined group and non-random sampling has judgements in selectings groups.
Calculate the arithmetic mean and median for the following series of stock returns:
7%, -7%, 3%, 9% and -2%
A) 9% and 3%
B) 3% and 2%
C) 2% and 3%
D) 2% and 2%
C - 2% (mean) and 3% (median)
(93 + 98 + 103 + 107 + 109)/5 = 102 - 100 = 2% for mean
When put in order, 3% is the middle number and therefore the median.
Calculate the geometric mean of the following bond returns: 20%, -5%, 2%, 9% and 11%
A) 7.4%
B) 8%
C) 9%
D) 7%
D - 7%
√ = suqare root
^5 √ (1.2 x 0.95 x 1.02 x 1.09 x 1.11) - 1 = 0.0706 so 7%
OR ((1.2 x 0.95 x 1.02 x 1.09 x 1.11)^0.2)-1 = 0.0706 so 7%
Select the CORRECT option to finish the statement:
If data have a positive skew…
A) …the mean is less than the mode is less than the median
B) …the median is less than the mode is less than the median
C) …the mode is less than the median is less than the mean
D) …the mean equals the mode equals the median
C - …the mode is less than the median is less than the mean
D is normal distribution (no skew). A and B are wrong as Median is ALWAYS in the middle.
- Positive skew = MODE < MEDIAN < MEAN
- Negative skew = MEAN < MEDIAN < MODE Tip - being mean to someone is bad (negative), so negative starts the chain when referring to LESS than
Which of the following statements is CORRECT?
A) The constant in a regression is always positive
B) The market model is a bivariate model
C) The dependent variable always explains the independent variables
D) Extrapolation and interpolation are both forms of regression analysis
B - The market model is a bivariate model
The market model relates to the return on a security to a constant and the return on the market
A bivariate model is a statistical model that examines the relationship between two variables. It can be used to identify patterns, make predictions, and understand how changes in one variable affect another.
Which of the following stock market indicies is an equally weighted GI?
A) FT30
B) FTSE 100
C) Dow Jones Industrial Average
D) S&P 500
A - FT30
The FT 30 (FT Ordinary Index or FTOI, not “FTSE 30”) is a now rarely used index that is similar to the Dow Jones Industrial Average. As an index of stocks to represent the real trends on the market, the FT 30 has been superseded by the FTSE 100, which was introduced in 1984. The FT 30 index was calculated using the geometric mean.[3][4] As Rowley states, this had the effect of understating movements in the index compared to using the arithmetic mean; and there are circumstances where this is undesirable.
Which of the following indicies is NOT calculated as an arithmetic market-weighted index?
A) CAC 40
B) DAX
C) Nikkei 225
D) FTSE 250
C - Nikkei 225
Nikkei is an unweighted arithmetic index
The Dow Jones Industrial Average is based on:
A) All US stock prices
B) The prices of all stocks traded on the NYSE
C) The prices of the 30 largest US stocks
D) The prices of a representative sample of 30 large US blue chip stocks
D - The prices of a representative sample of 30 large US blue chip stocks
The Dow Jones Industrial Average is a simple arithmetic aggregation of unweighted share prices of 30 major US industrial companies
What is the accumulated value of £150 invested for three years and three months when rate of interest is 0.5% per month?
A) £182.21
B) £181.19
C) £175.92
D) £160.05
A - £181.21
Three years and 3 months = 39 months
= £150 x (1.005)^39 = £182.2080905
If £100 is invested for two years at an interest rate of 2% per quarter, what is the difference between the compound and simple interest earned on this investment?
A) £1.17
B) £0.16
C) £1.12
D) £0.90
A - £1.17
2 years = 8 quarters
Compound:
£100 x (1.02)^8 = £117.17
SImple:
£100 + (8 x (£100 x 0.02) = £116
£117.17 - £116 = £1.17
What is the present value (PV) of £575 to be received at the end of ten years if the discount rate is 8.25% per annum?
A) £260.25
B) £251.95
C) £392.14
D) £1,270.42
A - £260.25
£575 / ((1.0825)^10) = £260.25
What is the future value of £100 invested at 1% per month for 5 years?
A) £170.91
B) £175.23
C) £180.96
D) £181.67
D - £181.67
5 years = 60 months
£100 x (1.01)^60 = £181.67
The annual percentage return (APR) on a loan is:
A) Total interest paid in a year divided by the initial balance
B) The same as simple interest
C) The annual discount rate
D) Twelve times the monthly interest rate
A - Total interest paid in a year divided by the initial balance
Although APR involves annualising a measure of return usually quoted on a monthly, quarterly, or semi-annually basisn by compounding, an alternative calculation involves summing the interest paid throughout the year and dividing by the initial amount.
If the discount rate is 9%, what is the net present value (NPV) of an investment costing £75 today, which will yield a single future cash flow of £100 at the end of two years?
A) £9.17
B) £0
C) £25
D) £16.74
A - £9.17
NPV = -£75 + (£100 / (1.09)^2) = £9.17
The present value (PV) factor for cash flow four years hence discounted at 7% per annum is:
A) 1.31
B) 0.76
C) 0.07
D) 0.28
B 0.76
1 / (1.07)^4 = 0.76
Which of the following is NOT true?
A) The internal rate of return (IRR) equates the present value (PV) of the cost of an investment with the PV of the cash flows coming from the investment
B) The IRR is the discount rate which sets net present value (NPV) to zero
C) The redemption yield on a bond is the bond’s IRR
D) The discount rate on an investment always equals the IRR
D - The discount rate on an investment always equals the IRR
The IRR equates the PV of the cost of an investment with the PV of the cash flows coming from the investment.
Which of the following discount rates give a NPV of zero to an investment costing £231.29 today and delviering cash flows of £100 at the end of Year 1 and £150 at the end of Year 2?
A) 4%
B) 4.5%
C) 5%
D) 5.5%
C - 5%
NPV = £0 = -£231.29 + (£100 / 1.05) + (£150 / (1.05^2))
In selecting the coefficients A and B in the bivariate linear regression, which one of the following criteria is used?
A) Maximise the errors
B) Minimise the absolute value of the erorrs
C) Minimise the average error
D) Minimise the residual sum of square error
D - Minimise the residual sum of square error
Linear regression calculate the value of coefficient by minimisign the residual sum of the squaref errors (Least squares method).
