Quantitative Methods & Statistics Flashcards

An analyst runs a multiple regression with 3 independent variables on 50 observations. The F-statistic tests:

Answer: Whether the overall regression model explains a significant portion of variation in Y

The F-statistic tests the joint null hypothesis that all slope coefficients are simultaneously equal to zero, assessing overall model significance.

In a Monte Carlo simulation, the Law of Large Numbers implies that as the number of trials increases:

Answer: The simulated mean converges to the true expected value

The Law of Large Numbers states that the sample average converges to the population expected value as the number of independent trials grows.

Which statement about the p-value is most accurate?

Answer: The p-value is the smallest significance level at which H₀ can be rejected

The p-value is the probability of obtaining a test statistic as extreme or more extreme than observed, assuming H₀ is true—equivalent to the minimum α at which H₀ is rejected.

A bond's price changes from $1,000 to $980 over one period. Using the holding period return formula, the return is:

Answer: −2.00%

HPR = (980 − 1000)/1000 = −20/1000 = −2.00% (assuming no coupon income).

If X and Y are independent random variables, which expression equals Var(aX + bY)?

Answer: a²·Var(X) + b²·Var(Y)

For independent variables, Cov(X,Y) = 0, so Var(aX + bY) = a²Var(X) + b²Var(Y).

Historical simulation for Value at Risk (VaR) estimation differs from parametric VaR because it:

Answer: Uses actual historical return data without assuming a specific distribution

Historical simulation replays actual past returns to build an empirical distribution, making no parametric assumptions about return shape.

An analyst finds that adding a new variable to a regression increases R² but decreases adjusted R². This most likely indicates the new variable:

Answer: Does not add sufficient explanatory power to justify the additional degree of freedom used

Adjusted R² penalizes for each additional variable; if it falls when R² rises, the variable's marginal contribution does not compensate for the lost degree of freedom.