Quantitative Investment Methods Flashcards

Question 1

What does the time value of money principle state about cash received today versus later?

Accepted Answer

The time value of money principle states that a sum of money available today is worth more than the same sum received in the future, because today's money can be invested to earn a return. It also implies that future cash flows must be discounted to compare them with present amounts.

Question 2

How is the present value of a single future cash flow calculated?

Accepted Answer

The present value equals the future cash flow divided by one plus the discount rate raised to the number of periods, written as PV equals FV divided by (1 plus r) to the power n. A higher discount rate therefore produces a lower present value.

Question 3

What is the holding period return on an investment?

Accepted Answer

The holding period return is the total percentage gain or loss over the time an investment is held, calculated as ending value plus income received, minus beginning value, divided by beginning value. For example, buying at 50 and selling at 60 after receiving 2 in dividends gives a holding period return of 24 percent.

Question 4

How does geometric mean return differ from arithmetic mean return over multiple periods?

Accepted Answer

The geometric mean return is the compound growth rate per period, while the arithmetic mean is the simple average of periodic returns. Geometric mean never exceeds arithmetic mean, and the gap widens as volatility rises, so geometric mean better describes actual compounded wealth growth over time.

Question 5

What is the difference between time-weighted and money-weighted return?

Accepted Answer

Time-weighted return measures the compounded performance of the investment itself, removing the effect of the timing and size of cash contributions and withdrawals. Money-weighted return, often called the internal rate of return, reflects the actual experience of the investor, so it is affected by when money flowed in or out.

Question 6

What does annualizing a return over a shorter period involve?

Accepted Answer

Annualizing a return converts a return earned over a shorter period into an equivalent one year rate. For a return R earned over a fraction t of a year, the annualized rate is (1 plus R) raised to the power 1 divided by t, minus one. This assumes steady compounding.

Question 7

Why is a continuously compounded return often used in quantitative finance?

Accepted Answer

Continuously compounded returns equal the natural logarithm of one plus the simple return, so multiperiod log returns add together over time. This additivity and their convenient statistical properties make them popular in many quantitative models that assume returns are normally distributed.

Question 8

How is the internal rate of return defined for a series of cash flows?

Accepted Answer

The internal rate of return is the discount rate that makes the net present value of a series of cash flows equal to zero. It can produce multiple solutions when cash flows change sign more than once, and it implicitly assumes reinvestment at the same rate.

Question 9

What is the difference between a population and a sample?

Accepted Answer

A population includes every member of a group being studied, while a sample is a subset drawn from that population. Population parameters, such as the true mean, are usually unknown, so analysts estimate them with sample statistics. The reliability of these estimates depends on how the sample was selected and how large it is.

Question 10

What does the standard deviation measure in a set of returns?

Accepted Answer

The standard deviation measures the dispersion of returns around their mean, expressed in the same units as the returns. It is the square root of the average squared deviation from the mean, and in finance it is the most common proxy for total risk or volatility. A larger standard deviation indicates more variable outcomes.

Question 11

What is skewness and why does it matter for investment returns?

Accepted Answer

Skewness measures the asymmetry of a return distribution around its mean. Negative skew means large losses occur more often than large gains, while positive skew means large gains are more frequent. Ignoring skewness can understate downside risk, since a symmetric normal model may miss the tail losses that negatively skewed strategies produce.

Question 12

What is excess kurtosis and how does it relate to fat tails?

Accepted Answer

Excess kurtosis measures how heavily a distribution's tails are populated compared with a normal distribution, which has excess kurtosis of zero. Positive excess kurtosis indicates fat tails, meaning extreme returns occur more frequently than a normal model predicts, which raises the chance of large losses that standard volatility alone may not capture.

Question 13

What key characteristics define a normal distribution used in finance models?

Accepted Answer

A normal distribution is symmetric and bell shaped, with its mean, median, and mode all equal at the center. It is fully described by two parameters, the mean and the standard deviation, and its skewness and excess kurtosis are both zero. About two thirds of outcomes fall within one standard deviation of the mean.

Question 14

What is the difference between a discrete and a continuous random variable?

Accepted Answer

A discrete random variable takes countable values, such as the number of profitable trades in a month. A continuous random variable can take any value within an interval, such as a daily return measured precisely. For continuous variables, probabilities come from a density function, and the probability of any single exact value is zero.

Question 15

How does the central limit theorem help analysts draw conclusions about sample means?

Accepted Answer

The central limit theorem states that the distribution of sample means approaches a normal distribution as the sample size grows, regardless of the shape of the underlying population, provided its variance is finite. This lets analysts use normal based methods for inference about means even when individual returns are not normally distributed.

Question 16

What is a standard error and how does it relate to sample size?

Accepted Answer

The standard error is the standard deviation of a sample statistic, most often the sample mean, across repeated samples. For a mean, it equals the sample standard deviation divided by the square root of the sample size, so precision improves as the number of observations increases, though slowly.

Question 17

What is the null hypothesis in a statistical test?

Accepted Answer

The null hypothesis is the default claim that there is no effect, no difference, or no relationship in the population being studied. Analysts assume it is true and then check whether the sample data provide enough evidence to reject it in favor of an alternative hypothesis.

Question 18

What does a p-value represent in hypothesis testing?

Accepted Answer

A p-value is the probability of obtaining a test statistic at least as extreme as the one observed, assuming the null hypothesis is true. A small p-value suggests the observed data would be unlikely under the null, which is evidence against it. It is not the probability that the null hypothesis is true.

Question 19

What is the difference between a Type I error and a Type II error?

Accepted Answer

A Type I error occurs when a true null hypothesis is rejected, a false positive. A Type II error occurs when a false null hypothesis is not rejected, a false negative. The significance level sets the Type I error rate. Power equals one minus the Type II error rate.

Question 20

How does a t-test help determine whether an estimated mean return differs from zero?

Accepted Answer

A t-test compares the sample mean with a hypothesized value, usually zero, by dividing the difference by the standard error of the mean. The resulting t statistic is compared with a t distribution to find a p-value. A large absolute t statistic suggests the mean differs from zero.

Question 21

What does the slope coefficient represent in a simple linear regression?

Accepted Answer

The slope coefficient shows the expected change in the dependent variable for a one unit increase in the independent variable, in a model with no other variables. In finance, a market model slope estimates how much a stock's return tends to move with the market's return, which is often called beta.

Question 22

What is the R-squared statistic and what are its limitations?

Accepted Answer

R-squared is the proportion of the variation in the dependent variable explained by the regression model. A high value does not prove that the model is correct or that the relationship is causal, and it always rises when extra variables are added, so adjusted R-squared is often used to compare models.

Question 23

Why do analysts check regression residuals for autocorrelation and heteroskedasticity?

Accepted Answer

Residuals are the differences between observed and fitted values, and standard regression inference assumes they are independent with constant variance. Autocorrelation means errors are correlated over time, and heteroskedasticity means their variance changes across observations. Either problem can make reported standard errors and p-values misleading, so analysts test for them and adjust when needed.

Question 24

What is overfitting in a quantitative model and how can analysts reduce it?

Accepted Answer

Overfitting occurs when a model captures random noise in the historical sample rather than a stable underlying relationship, so it performs well in sample but poorly on new data. Analysts reduce it by using simpler models, testing on out of sample or holdout data, and requiring a sound economic rationale before including a variable.

Question 25

What is the expected return of a portfolio with several assets?

Accepted Answer

The expected return of a portfolio is the weighted average of the expected returns of its individual assets, with each weight equal to the fraction of total portfolio value invested in that asset. Unlike portfolio risk, expected return is a simple linear combination, so diversification does not change it directly.

Question 26

How is the variance of a two asset portfolio calculated?

Accepted Answer

The variance of a two asset portfolio equals the sum of each asset's weight squared times its variance, plus the same term for the second asset, plus twice the product of the two weights, the two standard deviations, and the correlation between the assets. Lower correlation reduces total variance, which drives diversification benefits.

Question 27

What is the efficient frontier in modern portfolio theory?

Accepted Answer

The efficient frontier is the set of portfolios that offer the highest expected return for each level of risk, measured by standard deviation. Portfolios lying below the frontier are inefficient because a better combination of return and risk is available. Investors then choose a point on this curve according to their risk tolerance.

Question 28

What is the capital allocation line and how does it differ from the efficient frontier?

Accepted Answer

The capital allocation line shows the combinations of a risk free asset and a risky portfolio that an investor can hold, starting at the risk free rate. Unlike the frontier, which contains only risky assets, the line adds borrowing and lending at the risk free rate.

Question 29

What is the Sharpe ratio and how is it interpreted?

Accepted Answer

The Sharpe ratio is the excess return of a portfolio over the risk free rate, divided by the standard deviation of that excess return. It measures return earned per unit of total risk, so a higher value indicates a better risk adjusted performance, and it is widely used to rank funds.

Question 30

How does the minimum variance portfolio differ from the tangency portfolio?

Accepted Answer

The minimum variance portfolio is the combination of risky assets with the lowest possible risk, regardless of expected return. The tangency portfolio is the risky combination that maximizes the Sharpe ratio, balancing expected excess return against risk. Only the tangency portfolio depends on expected returns and the risk free rate.

Question 31

What key assumptions underlie classical mean variance portfolio optimization?

Accepted Answer

Classical mean variance optimization assumes investors prefer higher expected return and lower variance, and that expected returns, variances, and covariances are known and stable over the investment horizon. It also commonly assumes returns are normally distributed, which can understate tail risk in practice.

Question 32

Why is the covariance matrix important for estimating portfolio risk with many assets?

Accepted Answer

The covariance matrix collects the variances of every asset and the covariances between each pair, and portfolio variance is computed from it using the asset weights. With many assets the number of pairwise estimates grows quickly, so small estimation errors can distort optimal weights, which is why analysts often use shrinkage or constrained estimation.

Question 33

What is a factor model and what role does it play in asset pricing?

Accepted Answer

A factor model explains asset returns using a small number of common drivers, called factors, plus an asset specific component. Its sensitivity to each factor is called a loading or exposure. Factor models help investors decompose performance, estimate risk, and identify whether returns come from systematic exposures or from security selection.

Question 34

What does the capital asset pricing model say about expected returns?

Accepted Answer

The capital asset pricing model states that an asset's expected excess return equals its beta multiplied by the expected excess return of the market portfolio. Only systematic risk, measured by beta, is rewarded, because unsystematic risk can be diversified away. The model rests on strong assumptions, including frictionless markets and homogeneous expectations.

Question 35

What do size and value factors add to the single factor market model?

Accepted Answer

Size and value factors capture systematic return patterns that the market factor alone does not explain. The size factor compares small firms with large firms, and the value factor compares firms with high book to market ratios against those with low ratios. Their premiums can vary and weaken over time.

Question 36

What is alpha and how is it measured in performance evaluation?

Accepted Answer

Alpha is the return a manager earns above what the strategy's risk exposures predict. It is estimated as the intercept in a regression of the fund's excess returns on the excess returns of one or more benchmark factors. A significant positive alpha may indicate skill, but it can also reflect omitted risks.

Question 37

What is the difference between in sample and out of sample testing?

Accepted Answer

In sample testing evaluates a strategy on the same historical data used to design or calibrate it, which tends to overstate its performance. Out of sample testing applies the fixed rules to data withheld from the design process, providing a more honest estimate of how the strategy might behave going forward.

Question 38

What is a backtest and what biases can make its results misleading?

Accepted Answer

A backtest applies a trading or investment rule to historical data to estimate how it would have performed. Results can mislead because of survivorship bias, which excludes firms that failed, look ahead bias, which uses information not available at the time, and data snooping, which tests many variations until one looks profitable.

Question 39

How do transaction costs affect the evaluation of a quantitative trading strategy?

Accepted Answer

Transaction costs, including commissions, bid-ask spreads, market impact, and taxes where relevant, reduce the net return actually available to an investor. A strategy that rebalances frequently may look attractive gross of costs yet become unprofitable once costs are deducted. Evaluations should therefore report results net of realistic trading costs and consider turnover.

Question 40

Why should an investor examine the risk adjusted performance of a quantitative strategy rather than raw returns alone?

Accepted Answer

Raw returns ignore the amount of risk taken to earn them, so a strategy with high returns and extreme volatility may be less attractive than a steadier one. Risk adjusted measures, such as the Sharpe ratio, alpha, or drawdown analysis, place returns in context and allow fairer comparisons across strategies with different risk profiles.

Quantitative Investment Methods Flashcards

1Time Value and Return Measurement

2Descriptive Statistics and Distributions

3Hypothesis Testing and Regression

4Portfolio Risk and Modern Portfolio Theory

5Factor Models and Strategy Evaluation

Learning Resources