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Investment Practice > Quantitative Methods > Flashcards

Quantitative Methods Flashcards

1
Q

How would you describe a set of data that had outliers with large values?

A

Positive Skew

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2
Q

What does positive skew suggest about the mean, median and mode?

A

Mean > Median > Mode

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3
Q

How would you describe a set of data that had outliers with small/negative values?

A

Negative Skew

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4
Q

What does negative skew suggest about the mean, median and mode?

A

Mean < Median < Mode

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5
Q

What is the difference between a flat periodic rate of interest and the effective annual rate (EAR)?

A

Periodic rate: the quoted rate of interest for a year.
EAR: the actual rate of interest per year, once compounded.
EAR = ( 1 + periodic rate)m^ -1
m = no. of compounding intervals per year

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6
Q

What is primary data?

A

The collection of new data in relation to a specific project/task.
May be obtained via: scientific investigation, research, observation, discussion, questionnaires, market research etc.

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7
Q

What is secondary data?

A

Existing data that has already been collected by others. Tends to obtained at a relatively low cost.

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8
Q

What does population represent?

A

All the members of a specifically defined group e.g. the electorate, all UK companies etc.

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9
Q

What does a sample represent?

A

A subset of the full population that has been selected for investigation e.g. in establishing the CPI, the prices of sample items are investigated as opposed to all available goods.

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10
Q

What is raw data?

A

Data that is presented as a sample list of figures/values that may or may not be ordered.

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11
Q

When is tabulated data used?

A

When summarising large volumes of discrete data (data that can only take certain values, such as whole numbers).

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12
Q

When is grouped data used?

A

When summarising continuous data (data that can take any value within a range).

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13
Q

What is the formula for finding the arithmetic mean for raw data?

A

X = ΣX/n

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14
Q

What is the formula for finding the arithmetic mean for tabulated data?

A

X = ΣXf/n

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15
Q

What is the formula for finding the arithmetic mean for grouped data?

A

X = ΣXm/n

where m = midpoint of the range

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16
Q

What is the relationship between the arithmetic and geometric mean?

A

The arithmetic mean is always greater than or equal to the geometric mean.

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17
Q

What are the four measures of dispersion regarding the median?

A

Range
Deciles
IQR
Percentiles

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18
Q

What are the measures of dispersion regarding the arithmetic mean?

A

Standard Deviation

Variance

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19
Q

How do you calculate the IQR?

A

Q3 - Q1

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20
Q

What does the IQR exactly measure?

A

The range over the central most 50% of the population and is more representative (as extremes are excluded)

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21
Q

How do you calculate Q1 and Q3? (to find the IQR)

A

Q1: 1/4 (n + 1)
Q3: 3/4(n + 1)

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22
Q

What is a normal distribution?

A

A symmetrical distribution that is specifically defined by a mean (expected return) and standard deviation (measure of risk).

  • Total area under the distribution = 1
  • Central values more likely than extreme values.
  • Distribution has a single σ.
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23
Q

Under normal distribution, what statistics are always the case which can be used for analysis of risk and return?

A

1 σ from mean = 68.26% of values
1.96 σ from mean = 95% of values
3 σ from mean = 99% of values

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24
Q

On what axis does the dependent variable go?

A

Y-axis

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25
Q

On what axis does the independent variable go?

A

X-axis

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26
Q

What is a correlation coefficient (r)?

A

A relative measure indicating how two variables move with respect to each other. It measures the direction and degree of linear association between two variables.
It will have any value between + 1 and - 1.
The meaning of the correlation coefficient can be best understood by considering the means.

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27
Q

What value does a perfect positive correlation have?

A

+ 1

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28
Q

What value does a non-perfect positive correlation have?

A

0 < r < 1

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29
Q

What value does a perfect negative correlation have?

A
  • 1
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30
Q

What value does an uncorrelated coefficient have?

A

0

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31
Q

What is interpolation?

A

Where we try to estimate the profits that will arise from sales within the already observed range.

32
Q

What is extrapolation?

A

Where we try to predict the profits that will arise beyond the observed range of sales.

33
Q

What is an index number?

A

A number that gives the value of something relative to some base value e.g. RPI

34
Q

Price Weighted Arithmetic Index

A

(Σ Current Prices / Σ Base Prices) x Base Index Value (usually 100)
ΣPn/ΣPo x Base Index Value

35
Q

Market Value Weighted Arithmetic Index

A

(Σ Current Market Cap / Σ Base Year Market Cap) x Base Index Value (usually 100)

This method reflects the relative size of companies and makes changes in values of large companies more important to the value of the index than small companies.

36
Q

How do you find the new index value if indices are rebased?

A

New Index Value = Old Index Value x (New Index when rebased / Old Index when rebased)

37
Q

What are the key characteristics of Benchmark Indices?

A
  • Specified and Unambiguous.
  • Appropriate to preferences of the fund.
  • Appropriate to currency of the fund.
  • Investable (similar investments to the fund).
  • Measurable.
  • Representative of achievable performance.
38
Q

What do share indices measure?

A

Appreciation in capital value - taking no account of any income generated. They compare capital gains.

39
Q

What indices are used for bond portfolios?

A

Total return indices that include both capital gain and income reinvested for bonds with particular characteristics.

40
Q

How do you calculate APR?

A

APR = Total interest per year / Starting Balance

41
Q

Net Present Value (NPV)

A

The sum of the present values of cashflows and cash inflows associated with an investment.
NPV = +ve, investment is worthwile.

42
Q

Internal Rate of Return (IRR)

A

The rate of interest that discounts investment flows to a NPV of 0. May be used as a method for assessing the total return of an investment.

43
Q

What assumption does the IRR make concerning reinvestment rates?

A

That surplus funds can be reinvested at a return equal to the IRR.

44
Q

How do you calculate the constant annual rate of appreciation (average growth)?

A

1 + r = n^√Vn/Vo

45
Q

How many shares does the FT Ordinary Share Index have?

A

30

46
Q

How many shares does the Dow Jones Industrial Average have?

A

30

47
Q

How much of the market value of UK listed shares does the FTSE 100 Index represent?

A

Approx. 70%

48
Q

What country is the stock market index CAC 40 from?

A

France

49
Q

What country are the stock market indices Nikkei 250 and Nikkei 300 from?

A

Japan

50
Q

What country is the stock market index Hang Seng from and how many shares in the index?

A

Hong Kong, 33

51
Q

What country is the stock market index CNX Nifty from and how many shares in the index?

A

India, 50

52
Q

What country is the stock market index DAX from and how many shares in the index?

A

Germany, 30

53
Q

How do you calculate the rate of return (for a FV) of a continuously compounded rate? i.e. the correct return rate for a given period of time

A

R = e ^(r x t) - 1

r = the rate of interest
t = time period (no. of days/365)
54
Q

How do you calculate the rate of return (for a PV) of a continuously compounded rate?

A

R = e ^(1/(r x t))

r = the rate of interest
t = time period (no. of days/365)
55
Q

What is the coefficient of variation?

A

The ratio of standard deviation to the mean of the population.

56
Q

What happens if the geometric index component goes to 0?

A

The value of the index also goes to 0.

57
Q

What are the three uses of stock market indices?

A
  • Used as an underlying instrument for a derivative.
  • A benchmark for investment performance.
  • Compare different asset classes.
58
Q

What is a example of an equally weighted geometric index?

A

FT-30

59
Q

What index is not calculated as an arithmetic market weighted index?

A

Nikkei 225

60
Q

What is the Dow Jones Industrial Average based on?

A

A simple aggregation of unweighted share prices of 30 major US industrial companies.

61
Q

How does linear (bivariate) regression calculate the value of coefficients?

A

By minimising the residual sum of the squared errors.

62
Q

What does the area of a histogram represent?

A

The number of items in the band

63
Q

Which type of data, by definition, is ranked data?

A

Ordinal data

64
Q

What is random sampling?

A

Each member of population having an equal (and known) chance of being selected.

65
Q

What is systematic sampling?

A

Often used instead of random sampling, every Nth record is selected from a list of population members, and as long as the list does not contain any hidden order, this sampling method is as good as random sampling.

66
Q

What is stratified sampling?

A

A probability based methodology that identifies characteristics of the population that are already known and then selecting a random sample to represent those characteristics in the correct proportion.

It is often considered superior to random sampling as it removes sampling error.

67
Q

What is convenience sampling?

A

Where a sample is selected out of convenience, without incurring the cost or time required to select a proper random selection.

68
Q

What is judgement sampling?

A

Similar convenience sampling, judgement sampling occurs when a researcher chooses a ‘good’ representation of the whole population.

69
Q

What is quota sampling?

A

Where the researcher identifies certain characteristics and their proportions and then selects the required number of subjects from each strata associated with the chosen characteristics.

70
Q

What is data mining?

A

Sorting through large amounts of information looking for anything that is relevant.

71
Q

What is the difference in the equation when calculating the sample variance/s.d. and the regular variance/s.d.?

A

Sample: Use n-1

72
Q

What is the disadvantage of the geometric index?

A
  • It cannot be used as a meaningful benchmark as it does not fairly reflect achievable portfolio returns.
  • It cannot produce a result with negative values.
73
Q

Which of the FTSE indices is a price-weighted index?

A

FTSE Ordinary. The index is made up of 30 UK shares representing the breadth of the UK industry. Size is not the primary consideration. It is, however, geometrically calculated.

74
Q

What does the term statistically significant mean, with regards to normal distribution?

A

If its observed average value is noticeably different from expectations.

75
Q

How do you calculate the standardised value (test statistic) when given an observed value and claimed value?

A

(Observed Value - Claimed Value) / Standard Error

Investment Practice (12 decks)

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