Question 35 of 50

Which statement correctly links normal and lognormal variables?

If X ~ N(mu, sigma^2) and Y = exp(X), what is the expected value E[Y]?

Why is the lognormal distribution often used to model asset prices?

If daily continuously compounded returns have sample standard deviation 0.012, what is the approximate annualized volatility using 250 trading days?

Which expression correctly links a price PT to current price P0 and continuously compounded return r0,T?

Under i.i.d. one-period continuously compounded returns with mean mu and variance sigma^2, what is Var(r0,T) for T periods?

Which of the following is NOT a typical use of Monte Carlo simulation in investments?

Which sequence lists the main steps of a Monte Carlo simulation as described in the chapter?

In a Monte Carlo simulation for a one-year horizon with monthly steps (K = 12), which variable is drawn K times per trial for a single-factor geometric model?

You simulate 1,000 trials for a contingent claim and find 654 trials produce payoff zero. What does the histogram of simulated payoffs likely show?

Which is a key limitation of a Monte Carlo simulation noted in the chapter?

What does bootstrapping treat as the empirical population?

When performing bootstrap resampling, how is each resample created?

What is a primary advantage of bootstrap over analytical standard-error formulas according to the chapter?

If you draw B = 1,000 bootstrap resamples and compute the mean for each resample, which formula gives the bootstrap estimate of the standard error of the sample mean?

Which statement best contrasts Monte Carlo and bootstrap as described in the chapter?

A practitioner wants to estimate the one-day 95 percent VaR using the analytical variance-covariance method under normality. How does Monte Carlo relate to this approach as described in the chapter?

Which of the following is an instance where block bootstrap (noted indirectly by the chapter) would be more appropriate than standard bootstrap?

You run a Monte Carlo with I = 50,000 trials. Which action reduces simulation error without changing the underlying model assumptions?

Which formula from the chapter gives the variance of a lognormal random variable Y = exp(X) where X ~ N(mu, sigma^2)?

Which of the following best describes the role of the error term epsilon_i in the linear regression Yi = b0 + b1 Xi + epsilon_i?

How are the OLS slope and intercept estimates computed in simple linear regression as given in the chapter?

In the regression example ROA = 4.875 + 1.25 CAPEX, how would you interpret the slope 1.25?

Which diagnostic plot is emphasized in the chapter to check linear regression assumptions?

Which assumption is violated when residuals cluster into two groups with very different variances (regimes)?

A residual plot shows a strong seasonal cyclical pattern. Which regression assumption is likely violated according to the chapter?

Which statistic is equal to the square of the Pearson correlation in simple linear regression per the chapter?

Given SST = SSR + SSE, if SSR = 120 and SST = 200, what is R^2?

Which regression test uses an F-distributed statistic as explained in the chapter?

Which measure equals the square root of the mean squared error in a regression and indicates the average distance of observed Ys from the fitted line?

When should a practitioner prefer parametric Monte Carlo over bootstrap according to the chapter's recommendations?

Which of these is the correct interpretation of the parameter sigma in the lognormal mean formula E[Y] = exp(mu + 0.5 sigma^2)?

In Monte Carlo pricing of a lookback option (payoff = final price - minimum price during life), what additional path statistic must you track compared with a European option?

Which of the following best characterizes jackknife resampling mentioned in the chapter?

You want to bootstrap the sample median of monthly returns for a rarely traded stock with only 12 months of data. What does the chapter suggest about this approach?

Which of the following is true about the relationship between continuously compounded returns and simple holding-period returns as used in the chapter?

If one-period log returns are not normal but i.i.d., what theorem does the chapter invoke to justify approximate normality of the T-period log return as T grows?

You fit a simple linear regression and find the residual mean equals zero. Which statement aligns with the chapter's treatment?

Which of these is a practical recommendation the chapter gives when using Monte Carlo or bootstrap?

If you model asset prices with a lognormal distribution implied by normal log returns, which of the following is true regarding the median of Y relative to exp(mu)?

Which statement concerning resampling-based confidence intervals in bootstrap is supported by the chapter?

In the sample Monte Carlo valuation of an Asian-style contingent claim, what effect does increasing the number of subperiods K (e.g., months per year) generally have, holding trials constant?

Which of the following is a reason to prefer bootstrap over a Monte Carlo parametric simulation per the chapter?

What effect does increasing sigma (variance of ln Y) have on a lognormal variable's skewness and mean according to the chapter?

Which of these statements about implementation of Monte Carlo is emphasized in the chapter?

When comparing Monte Carlo and analytical methods for an option that has a known closed-form price (e.g., Black-Scholes), the chapter suggests:

Which of the following best describes the reason practitioners log-transform prices when modeling returns, per the chapter?

Which diagnostic indicates residuals might be non-normal and hence t-based inference may be unreliable for small samples, according to the chapter?

According to the chapter, which is a valid reason to prefer analytical methods over simulation when available?