Quant Finance

Question 1

A portfolio with many different types of investment is less risky than a portfolio with only one type

Answer 1

Principle of diversification

Question 2

A dollar today is worth more than the promise of a pound tomorrow

Answer 2

Principle of the time value of money

Question 3

To earn a higher return on a investment you have to accept a higher level of risk

Answer 3

Principle of risk versus reward

Question 4

Measuring the degree and strength of the relationships between the returns on two different assets

Answer 4

Correlation and covariance

Question 5

Calculate the value in today’s terms of cash flows expected in the future

Answer 5

Discounting

Question 6

Calculate the variability of returns on investments based on historical data

Answer 6

Variance and standard deviation

Question 7

Possibility that actual returns will be different from expected returns

Answer 7

Risk

Question 8

A common way of measuring return on an investment

Answer 8

Holding Period Return (HPR)

Question 9

Purchase of a bond with exactly one year remaining untill maturity when the face value is repaid. The bond’s purchase price is 98 and its face value is 100. During the year, you received 5 in interest.

Answer 9

7.14%

Question 10

Purchase of a share in ‘Comeback plc’ on 1 April 2022 for 79.8p. It was then sold on 30 June 2022 for 101.5p. The company’s final dividend of 1.1p was paid to all shareholders in May 2022.

Answer 10

173.25%

Question 11

Simplest Way of measuring longer-term returns is to calculate the

Answer 11

Arithmetic Mean

Question 12

There are two main tools for measuring financial risk

Answer 12

Variance and Standard deviation

Question 13

A measure of how far a set of data points varies from the mean: the greater the range of possible returns, the higher the variance, and the greater the financial risk

Answer 13

Variance

Question 14

Examine the returns on a portfolio of shares over five years:
Year 1: 16%
Year 2: -32%
Year 3: 18%
Year 4: 4%
Year 5: 6%

Answer 14

Mean 0.02830610432

Question 15

Calculate the expected return:
Expected Return 11% Probability 50%
Expected Return 10% Probability 30%
Expected Return 9% Probability 20%

Answer 15

10.3%

Question 16

Calculate the difference between each annual return and the population mean:
Annual Return: 16% Mean 2.4%
Annual Return: -32% Mean 2.4%
Annual Return: 18% Mean 2.4%
Annual Return: 4% Mean 2.4%
Annual Return: 6% Mean 2.4%

Answer 16

Population Variance 325.44
Sample Variance 407
Standard Deviation 18.04

Question 17

The degree of potential variability from the expected returns from an investment

Answer 17

Variance

Question 18

Mathematical measure of the spread or dispersion of the individual observations of data around the mean result and is derived from variance

Answer 18

Standard Deviation

Question 19

Each constituent has an equal chance or probability of being included by using a table of random numbers to ensure that the selection is free from any bias

Answer 19

Random Sample

Question 20

Selection that is believed will select a more representative sample

Answer 20

Non-random Sample

Question 21

Analyzing the relationships between the movements of different assets - do they move in lane with each other or against each other, and by what degree?

Answer 21

Correlation and Covariance

Question 22

If 2 investments are moving in the same direction, their relationship is 1 what?

Answer 22

+1

Question 23

If 2 investments are moving in the opposite direction, their relationship is 1 what?

Answer 23

-1

Question 24

Consider the case of an investor who attempts to minimise risk. The investor has a choice of investing
in two out of three portfolios (assuming, for this example, that the investment will be 50/50 in each
portfolio). The possibilities are:
Portfolio A – invest in large, blue-chip UK companies; standard deviation is 14%.
Portfolio B – invest in large, blue-chip US companies; standard deviation is 12%.
Portfolio C – invest in emerging market companies; standard deviation is 29%

But, given that the correlation coefficients work out to be:
CORR(A,B) = 0.81
CORR(A,C) = 0.13
CORR(B,C) = –0.05.

Answer 24

the covariance of each of the three possible portfolios will be:
COV(A,B) = (0.14) x (0.12) x (0.81)
= 0.0136
COV(A,C) = (0.14) x (0.29) x (0.13)
= 0.0053
COV(B,C) = (0.12) x (0.29) x (–0.05)
= –0.0017

Question 25

What is the difference between PV of the inflows and PV of the outflows

Answer 25

NPV

Question 26

Assume the investor’s required annual rate of return is 10% and the principal or face value of the bond
is £1,000. Also, assume the company pays an annual coupon of 10% (ie, interest of £100) at the end of
each year.

Answer 26

Price = £1,000.00

Question 27

A company is considering undertaking an investment project that will require it to spend £75,000 this
year and which, in return, it expects to generate revenues of £20,000 in the first year and the same
amount in each of years two, three, four and five. The discount rate it uses is 10% (ie, 0.10)

Answer 27

NPV = £815.75

Question 28

An approach that establishes what the break-even rate of return is. It calculates the discount rate which implies an NPV of zero, where the percentage return is exactly equal to the percentage discount rate

Answer 28

IRR

Question 29

Method that takes a lower discount rate that produces a positive NPV and a higher discount rate that results in a negative NPV and then finds the rate between them that produces a zero NPV

Answer 29

Interpolation

Question 30

should only be used a way of establishing the break-even rate of return for investment projects

Answer 30

IRR