Volume 1 - Quantitative Methods Flashcards
What are the 3 possible interpretations for a interest rate ?
An interest rate, r, can have three interpretations: (1) a required rate of return, (2) a discount rate, or (3) an opportunity cost. An interest rate reflects the relationship between differently dated cash flows.
An interest rate can be viewed as the sum of the real risk-free interest rate and a set of premiums that compensate lenders for bearing distinct types of risk: an inflation premium, a default risk premium, a liquidity premium, and a maturity premium.
r = Real risk-free interest rate + Inflation premium + Default risk premium +
Liquidity premium + Maturity premium.
What is A money-weighted return ?
A money-weighted return reflects the actual return earned on an investment after accounting for the value and timing of cash flows relating to the investment.
What is A time-weighted return ?
A time-weighted return measures the compound rate of growth of one unit of currency invested in a portfolio during a stated measurement period. Unlike a money-weighted return, a time-weighted return is not sensitive to the timing and amount of cashflows and is the preferred
performance measure for evaluating portfolio managers because cash
withdrawals or additions to the portfolio are generally outside of the control of the portfolio manager.
Gross return, return prior to deduction of managerial and administrative expenses (those expenses not directly related to return generation), is an appropriate measure to evaluate the comparative performance of an asset manager.
Net return, which is equal to the gross return less managerial and administrative expenses, is a better return measure of what an investor actually earned.
Annualizing periodic returns allows investors to compare differnt investments across different holding periods to better evaluate and compare their relative performance. With the number of compounding periods per year approaching infinity, the interest is compound continuously.
Real returns are particularly useful in comparing returns across time periods because inflation rates may vary over time and are particularly useful for comparing investments across time periods and performance between different asset classes with different taxation.
If USD 9,500 today and USD 10,000 in one year are equivalent in value, then USD 10,000 – USD 9,500 = USD 500 is the required compensation for receiving USD 10,000 in one year rather than now. The interest rate (i.e., the required compensation stated as a rate of return) is USD 500/USD 9,500 = 0.0526 or 5.26 percent.
An opportunity cost is the value that investors forgo by choosing a course of action. In the example, if the party who supplied USD 9,500 had instead decided to spend it today, he would have forgone earning 5.26 percent by consuming rather
than saving. So, we can view 5.26 percent as the opportunity cost of current
consumption.
What is The real risk-free interest rate ?
The real risk-free interest rate is the single-period interest rate for a completely risk-free security IF NO inflation were expected. In economic theory, the real risk-free rate reflects the time preferences of individuals for current versus future real consumption.
The sum of the real risk-free interest rate and the inflation premium is the nominal
risk-free interest rate
The nominal risk-free interest rate reflects the combination of a real risk-free rate plus an inflation premium:
(1 + nominal risk-free rate) = (1 + real risk-free rate)(1 + inflation premium)
In practice, however, the nominal rate is often approximated as the sum of the
real risk-free rate plus an inflation premium:
Nominal risk-free rate = Real risk-free rate + inflation premium.
Typically, interest rates are quoted in annual terms, so the interest rate on a 90-day government debt security quoted at 3 percent is the annualized rate and not the actual interest rate earned over the 90-day period.
Whether the interest rate we use is a required rate of return, or a discount rate,
or an opportunity cost, the rate encompasses the real risk-free rate and a set of risk premia that depend on the characteristics of the cash flows. All these premia vary over time and continuously change, as does the real risk-free rate. Consequently, all interest rates fluctuate, but how much they change depends on various economic fundamentals—and on the expectation of how these various economic fundamentals can change in the future.
The arithmetic mean return assumes that the amount invested at the beginning of each period is the same. In an investment portfolio, however, even if there are no cash flows into or out of the portfolio the base amount changes each year. The previous year’s earnings must be added to the beginning value of the subsequent year’s investment— these earnings will be “compounded” by the returns earned in that subsequent year. We can use the geometric mean return to account for the compounding of returns.
In general, the arithmetic return is biased upward unless each of the underlying
holding period returns are equal. The bias in arithmetic mean returns is particularly
severe if holding period returns are a mix of both positive and negative returns.
For reporting historical returns, the geometric mean has considerable appeal
because it is the rate of growth or return we would have to earn each year to match
the actual, cumulative investment performance.
The arithmetic mean is always greater than or equal to the geometric mean.
If we want to estimate the average return over a one-period horizon = we should use arithmetic, because it is the average of one-period returns.
If we want to estimate the average returns over more than one period = geometric, because the geometric mean captures how the total returns are linked over time.
The harmonic mean : sample of observations of 1, 2, 3, 4, 5, 6, and 1,000, the harmonic mean is 2.8560.
Compared to the arithmetic mean of 145.8571, we see the influence of the outlier (the 1,000) to be much less than in the case of the arithmetic mean. So, the harmonic mean is quite useful as a measure of central tendency in the presence of outliers.
Unless all the observations in a dataset are the same value, the harmonic mean is always less than the geometric mean, which, in turn, is always less than the arithmetic mean.
What is the trimmed mean ?
Both the trimmed and the winsorized means seek to minimize the impact of outliers in a dataset. Specifically, the trimmed mean removes a small defined percentage of the largest and smallest values from a dataset containing our observation before calculating the mean by averaging the remaining observations.
What is the winsorized mean ?
A winsorized mean replaces the extreme observations in a dataset to limit the
effect of the outliers on the calculations. The winsorized mean is calculated after
replacing extreme values at both ends with the values of their nearest observations,
and then calculating the mean by averaging the remaining observations.
What is the money-weighted return ?
The money-weighted return accounts for the money invested and provides the
investor with information on the actual return she earns on her investment. y. Amounts invested are cash outflows from the investor’s perspective and amounts returned or withdrawn by the investor, or the money that remains at the end of an investment cycle, is a cash inflow for the investor.
What is The internal rate of return ?
The internal rate of return is the discount rate at which the sum of present values
of cash flows will equal zero.
What are the 2 categories of Data and the 4 sub-categories?
1- Categorical: values that describe a quality or characteristic (must be mutually exclusive)
(N) Numerical: No logical order (Ex: Sectors of economy)
(O) Ordinal: has a logical order (no info about the distance between groups)
2- Numerical : Measured or counted quantities
(I) Integer/Discrete : Limited to a finite number of values
(R) Ratio/Continous : Can take any value within a range
What is Cross-sectional , Time-series and Panel Data ?
1- Cross-sectional : Multiple observations of a particular variable (stock prices of 60 companies)
2- Time-series : Multiple observations of a particular variable for the same observational unit over time (GM stock price in the last 5 days)
3- Panel Data : Cross-sectional + Time-series
What is structured and unstructured Data ?
1- Structured : Highly organized in a pre-defined manner
2- Unstructured Data : No organized form (social media, news) –> Also called alternative Data
In order to analyse Data, it must be transformed into structured data
For numerical data, how can we determine the interval width ?
Range (max - min) / K
K: number of intervals –> too few or too much can bring problems ; loss of info or too much noise