MCQ Quiz

Question 1 of 35

If a normal random variable X has mean $\mu$ and variance $\sigma^{2}$, the mean of Y = exp(X) is most likely:

$\exp(\mu)$.
$\exp(\mu + 0.5\sigma^{2})$.
$\exp(\mu - 0.5\sigma^{2})$.

Question 2 of 35

A share price rises from EUR 100 to EUR 110 over one period. The continuously compounded return is most closely expressed as:

$(110 - 100)/100$.
$\exp(110/100)$.
$\ln(110/100)$.

Question 3 of 35

In Monte Carlo simulation, specifying the method for generating the data most likely requires the analyst to:

avoid any parametric assumptions entirely.
make distributional assumptions for key risk factors.
rely solely on observed historical records of returns.

Question 4 of 35

Compared with Monte Carlo simulation, analytic methods most likely:

provide more insight into cause-and-effect relationships.
always require historical observations of returns.
cannot be used to value options.

Question 5 of 35

If the current stock price is $P_{0}$ and the continuously compounded return from 0 to T is $r_{0,T}$, the future stock price $P_{T}$ is most likely:

$P_{0} \times \ln(r_{0,T})$.
$P_{0} \times \exp(r_{0,T})$.
$P_{0} \times (1 + r_{0,T})$.

Question 6 of 35

In Monte Carlo simulation, the final estimate of value is generally obtained by:

using only the result of a single representative trial.
solving an exact analytic equation at the end.
averaging outcomes across the specified number of trials.

Question 7 of 35

In bootstrap resampling, each item drawn from the original sample is most likely:

removed permanently so it cannot be drawn again.
replaced before the next draw.
redrawn only after every other item has been selected.

Question 8 of 35

Which investment task is Monte Carlo simulation most likely to support?

Valuing securities with complex embedded options.
Eliminating all statistical uncertainty in pricing.
Producing exact cause-and-effect relationships.

Question 9 of 35

A Monte Carlo simulation is most accurately characterized as a technique that:

generates many random samples from specified probability distributions.
derives an exact closed-form price through algebraic manipulation.
relies only on a single observed historical path of returns.

Question 10 of 35

In a bootstrap resample, individual observations from the original sample most likely:

appear multiple times or not at all.
each appear exactly once.
are excluded from every resample by rule.

Question 11 of 35

A recognized strength of bootstrap resampling is that it is:

guaranteed to provide exact numerical results.
simple to perform.
free of any statistical uncertainty in its estimates.

Question 12 of 35

The core idea of the bootstrap is to:

treat the observed sample as if it were the population.
fit an analytic distribution to the sample before resampling.
discard the sample and draw directly from the true population.

Question 13 of 35

The first step when implementing a Monte Carlo simulation is most likely to:

draw the final set of random numbers.
specify the quantity of interest.
compute the terminal summary statistic across all trials.

Question 14 of 35

Bootstrap resampling most likely draws each new sample from:

the original observed sample.
the true population directly.
a specified theoretical probability distribution.

Question 15 of 35

A common feature of both Monte Carlo simulation and bootstrap resampling is that they:

rely only on closed-form analytic solutions.
require the population distribution to be known in advance.
build on repetitive sampling to produce estimates.

Question 16 of 35

A contingent claim whose payoff at maturity depends on the average price of the underlying over its life is most accurately described as:

an Asian option.
a lookback option.
a plain vanilla European option.

Question 17 of 35

A standard lookback contingent claim pays the greater of zero and the difference between:

the average price and the initial price.
the final stock price and the minimum price during its life.
the initial price and the final price.

Question 18 of 35

In a bootstrap simulation of a contingent claim, the random stock price changes are most likely drawn from:

the empirical distribution of observed price changes.
a specified normal distribution with chosen mean and variance.
a lognormal distribution with known analytic parameters.

Question 19 of 35

In a Monte Carlo simulation, dividing the calendar horizon into K subperiods primarily defines the:

number of distributions required per trial.
number of independent risk factors in the model.
time increment $\Delta t$.

Question 20 of 35

If one-period continuously compounded returns are i.i.d. with variance $\sigma^{2}$, the variance of the T-period continuously compounded return is most likely:

$\sigma^{2}/T$.
$\sigma^{2} \times T$.
$\sigma^{2}$.

Question 21 of 35

The shape of a lognormal distribution is most accurately described as:

symmetric around its mean.
skewed to the left with a long left tail.
skewed to the right with a long right tail.

Question 22 of 35

The lognormal distribution is often preferred to the normal for modeling asset prices primarily because:

asset prices cannot take negative values.
asset prices are always symmetric around the mean.
asset returns cannot take negative values.

Question 23 of 35

For i.i.d. one-period continuously compounded returns, the T-period continuously compounded return is most likely equal to:

the sum of the one-period returns.
the product of the one-period returns.
the average of the one-period returns.

Question 24 of 35

A recognized weakness of bootstrap resampling is that it:

cannot be performed without an analytic z-statistic.
provides only statistical estimates, not exact results.
requires the population distribution to be fully known.

Question 25 of 35

A random variable Y is most likely said to follow a lognormal distribution when:

ln Y is normally distributed.
Y is uniformly distributed.
Y is normally distributed.

Question 26 of 35

A recognized limitation of Monte Carlo simulation is that it:

cannot use any probability distributions as inputs.
is incapable of performing sensitivity analysis.
provides only statistical estimates, not exact results.

Question 27 of 35

A key application of Monte Carlo simulation in investment management is to:

provide exact valuations with no statistical uncertainty.
replace analytic solutions that are already known in closed form.
test a model's sensitivity to changes in key assumptions.

Question 28 of 35

A lognormal distribution is completely described by how many parameters?

Two.
One.
Three.

Question 29 of 35

Bootstrap resampling is most appropriate when an analyst:

has access to the complete population data.
has only one sample and no knowledge of the true population.
knows the exact analytic sampling distribution of the statistic.

Question 30 of 35

A key distinction between bootstrap simulation and Monte Carlo simulation is that bootstrap:

requires the analyst to specify a theoretical probability distribution.
cannot be implemented using repeated sampling.
draws random values from the observed empirical distribution.

Question 31 of 35

If the natural logarithm of a random variable is normally distributed, the variable itself most likely follows which distribution?

Uniform.
Normal.
Lognormal.

Question 32 of 35

Monte Carlo simulation is most useful for valuing securities when:

the security already has a simple closed-form price.
no analytic pricing formula is available.
historical price observations are unavailable.

Question 33 of 35

In bootstrap resampling, the size of each resample most likely equals:

half the size of the original sample.
the size of the unknown population.
the size of the original sample.

Question 34 of 35

If the daily volatility of continuously compounded returns is 0.01, the annualized volatility assuming 250 trading days is most closely:

$0.01 / \sqrt{250}$.
$0.01 \times 250$.
$0.01 \times \sqrt{250}$.

Question 35 of 35

The lognormal distribution is bounded from below by a value of:

1.
0.
-1.

Simulation Methods (Katas)

First Principles Thinking: mean of lognormal

First Principles Thinking: definition of continuously compounded return

First Principles Thinking: distributional inputs

First Principles Thinking: analytic vs simulation

First Principles Thinking: price from continuously compounded return

First Principles Thinking: aggregating simulation output

First Principles Thinking: sampling with replacement

First Principles Thinking: Monte Carlo and complex payoffs

First Principles Thinking: defining feature of Monte Carlo

First Principles Thinking: composition of resamples

First Principles Thinking: advantages of bootstrap

First Principles Thinking: bootstrap rationale

First Principles Thinking: simulation workflow

First Principles Thinking: source of bootstrap draws

First Principles Thinking: shared foundation

First Principles Thinking: payoff structure identification

First Principles Thinking: lookback payoff rule

First Principles Thinking: bootstrap data source for simulation

First Principles Thinking: time grid construction

First Principles Thinking: variance scaling under independence

First Principles Thinking: skewness of lognormal

First Principles Thinking: why lognormal fits asset prices

First Principles Thinking: additivity of continuously compounded returns

First Principles Thinking: output quality of bootstrap

First Principles Thinking: definition of lognormal

First Principles Thinking: nature of simulation output

First Principles Thinking: sensitivity analysis via Monte Carlo

First Principles Thinking: parameters of the lognormal

First Principles Thinking: when bootstrap helps

First Principles Thinking: bootstrap vs Monte Carlo inputs

First Principles Thinking: log-to-level mapping

First Principles Thinking: when Monte Carlo adds value

First Principles Thinking: resample size rule

First Principles Thinking: annualizing volatility

First Principles Thinking: support of the lognormal