Quant Finance Flashcards
7 Questions
A portfolio with many different types of investment is less risky than a portfolio with only one type
Principle of diversification
A dollar today is worth more than the promise of a pound tomorrow
Principle of the time value of money
To earn a higher return on a investment you have to accept a higher level of risk
Principle of risk versus reward
Measuring the degree and strength of the relationships between the returns on two different assets
Correlation and covariance
Calculate the value in today’s terms of cash flows expected in the future
Discounting
Calculate the variability of returns on investments based on historical data
Variance and standard deviation
Possibility that actual returns will be different from expected returns
Risk
A common way of measuring return on an investment
Holding Period Return (HPR)
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.
7.14%
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.
173.25%
Simplest Way of measuring longer-term returns is to calculate the
Arithmetic Mean
There are two main tools for measuring financial risk
Variance and Standard deviation
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
Variance
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%
Mean 0.02830610432
Calculate the expected return:
Expected Return 11% Probability 50%
Expected Return 10% Probability 30%
Expected Return 9% Probability 20%
10.3%
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%
Population Variance 325.44
Sample Variance 407
Standard Deviation 18.04
The degree of potential variability from the expected returns from an investment
Variance
Mathematical measure of the spread or dispersion of the individual observations of data around the mean result and is derived from variance
Standard Deviation
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
Random Sample
Selection that is believed will select a more representative sample
Non-random Sample
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?
Correlation and Covariance
If 2 investments are moving in the same direction, their relationship is 1 what?
+1
If 2 investments are moving in the opposite direction, their relationship is 1 what?
-1
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.
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
What is the difference between PV of the inflows and PV of the outflows
NPV
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.
Price = £1,000.00
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)
NPV = £815.75
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
IRR
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
Interpolation
should only be used a way of establishing the break-even rate of return for investment projects
IRR
