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Quizzes > Quizzes for Business > Finance

Test Your Quantitative Finance Knowledge Quiz

Sharpen Your Quantitative Finance Aptitude Today

Difficulty: Moderate
Questions: 20
Learning OutcomesStudy Material
Colorful paper art depicting elements related to a Quantitative Finance Knowledge Quiz.

Are you ready to test your command of quantitative finance? This interactive Finance Knowledge Assessment Quiz features 15 multiple-choice questions on risk modeling, derivative pricing, and portfolio optimization to stretch your analytical skills. Perfect for finance students and practitioners eager to master financial models and data-driven strategies. You can freely customize every question in our user-friendly editor to suit your learning path. Dive into more quizzes or explore advanced methods with the Quantitative Research Methods Quiz.

What is the expected return of a portfolio composed of 40% in Asset A with expected return 8% and 60% in Asset B with expected return 12%?
10.4%
9.6%
8.8%
11.2%
The expected return is the weighted average of individual returns: 0.4 - 8% + 0.6 - 12% = 9.6%. This uses basic portfolio weighting.
The Sharpe ratio of a portfolio is defined as which of the following?
(R_f - E[R_p]) / σ_p
(E[R_p] - R_f) / σ_p
(E[R_p] - σ_p) / R_f
(σ_p - R_f) / E[R_p]
The Sharpe ratio measures excess return per unit of risk, calculated as (portfolio return minus risk-free rate) divided by portfolio standard deviation.
Which relationship describes the put-call parity for European options on a non-dividend-paying stock?
C - P = S - K e^{-rT}
C + K e^{-rT} = P + S
C - P = S + K e^{-rT}
C + P = S - K e^{-rT}
Put-call parity states C - P = S - K e^{-rT} for European options on non-dividend-paying stocks, ensuring no-arbitrage between call and put prices.
In an AR(1) model X_t = φ X_{t-1} + ε_t, the process is stationary if which condition holds?
φ > 1
|φ| < 1
φ = 1
φ = 0
An AR(1) process is covariance-stationary only if the autoregressive coefficient φ has absolute value less than one, so shocks dissipate over time.
According to the CAPM, the expected return on a security is given by:
E[R_i] = α + β R_m
E[R_i] = E[R_m]
E[R_i] = R_f
E[R_i] = R_f + β_i (E[R_m] - R_f)
CAPM specifies the expected security return as the risk-free rate plus beta times the market risk premium, E[R_m] - R_f.
Given two assets with volatilities σ1 = 10%, σ2 = 20% and correlation ϝ = 0.5, what is the variance of a portfolio with equal weights?
0.005
0.04
0.025
0.015
Portfolio variance = w^2σ1^2 + w^2σ2^2 + 2w^2σ1σ2ϝ = 0.25 - 0.01 + 0.25 - 0.04 + 2 - 0.25 - 0.1 - 0.2 - 0.5 = 0.015.
Which assumption is fundamental to the Black-Scholes option pricing model?
Markets have transaction costs
Stock price follows arithmetic Brownian motion
Stock price has a log-normal distribution
Volatility is stochastic
Black-Scholes assumes the underlying follows a geometric Brownian motion, implying log-normal distribution and constant volatility in a frictionless market.
In a GARCH(1,1) model, the conditional variance σ_t^2 is typically given by:
σ_t^2 = α0 + α1 ε_{t-1}^2 + β1 σ_{t-1}^2
σ_t^2 = ε_{t-1}^2 + σ_{t-1}^2
σ_t^2 = α0 + α1 ε_t^2 + β1 σ_t^2
σ_t^2 = α1 ε_{t-1} + β1 σ_{t-1}
A GARCH(1,1) model uses past squared residuals and past variances: σ_t^2 = ω + α ε_{t-1}^2 + β σ_{t-1}^2, capturing volatility clustering.
What is the shape of the efficient frontier in mean-variance space for a set of risky assets?
Hyperbola
Parabola
Circle
Straight line
The efficient frontier of risky assets (without a risk-free asset) forms the upper branch of a hyperbola in mean-variance space.
Implied volatility is best described as:
The historical standard deviation of returns
The average forecasted volatility over the option's life
The realized volatility of the underlying security
The volatility input that makes the model price equal to the market option price
Implied volatility is the volatility parameter that, when plugged into a pricing model, yields the observed market price of an option.
Which test is typically used to check for cointegration between two non-stationary time series?
Johansen rank test
KPSS stationarity test
Ljung - Box Q-test
Engle - Granger two-step procedure
The Engle - Granger method first estimates a long-run regression and then tests residuals for stationarity to confirm cointegration.
The delta of a European call option on a non-dividend-paying stock ranges between:
-1 and 0
0 and 1
-2 and -1
1 and 2
Delta measures sensitivity to the underlying price; for a call on a non-dividend stock it lies between 0 and 1.
Calibration of a financial model typically involves:
Maximizing the volatility parameter
Calculating the analytical solution directly
Minimizing the difference between model and market prices
Maximizing historical fit only
Calibration tunes model parameters to minimize pricing errors relative to observed market data, ensuring better predictive performance.
Value at Risk (VaR) at 95% confidence is:
The maximum gain 95% of the time
The average loss in the worst 5% of cases
The loss level that is exceeded with 95% probability
The loss level that is exceeded with 5% probability
95% VaR is defined as the threshold loss which will be exceeded only 5% of the time, measuring extreme downside risk.
The Fama - French three-factor model includes all of the following factors except:
Size factor (SMB)
Market risk premium
Momentum factor
Value factor (HML)
Fama - French three-factor includes market, SMB (size), and HML (value); momentum is added in the Carhart four-factor model.
Which of the following is the correct Black - Scholes partial differential equation for a derivative price f(S,t)?
∂f/∂t + ½σ²S²∂²f/∂S² + rS∂f/∂S - rf = 0
∂f/∂t - ½σ²S²∂²f/∂S² + rS∂f/∂S - rf = 0
∂f/∂t + ½σ²S∂²f/∂S² + rS∂f/∂S + rf = 0
∂f/∂t + ½σS²∂²f/∂S² - rS∂f/∂S - rf = 0
The Black - Scholes PDE arises from delta-hedging and risk-neutral valuation: ∂f/∂t + ½σ²S²∂²f/∂S² + rS∂f/∂S - rf = 0.
In the Kalman filter, the Kalman gain K_t is computed as:
HᵀP_{t|t-1}H + R^{-1}
P_{t|t-1} + R
HP_{t|t-1}Hᵀ + R
P_{t|t-1}Hᵀ(HP_{t|t-1}Hᵀ+R)^{-1}
The Kalman gain balances model uncertainty and measurement noise: K_t = P_{t|t-1} Hᵀ (H P_{t|t-1} Hᵀ + R)^{-1}.
Which equation correctly describes the variance process in the Heston stochastic volatility model?
dv_t = κv_t dt + θ dW_t
dv_t = κ(θ - v_t)dt + σ√v_t dW_t
dv_t = α dt + β v_t dW_t
dv_t = σ² v_t dt + κ√v_t dW_t
Heston uses a mean-reverting CIR process: dv_t = κ(θ - v_t)dt + σ√v_t dW_t, ensuring positive variance and stochastic volatility.
In the Generalized Method of Moments (GMM), the optimal weighting matrix is proportional to:
A matrix of zeros
The covariance matrix of the moment conditions
An identity matrix
The inverse of the covariance matrix of the moment conditions
GMM attains efficiency when the weighting matrix equals the inverse of the moment-condition covariance, minimizing asymptotic variance.
Principal component analysis (PCA) of asset returns identifies:
Uncorrelated expected returns
Market-implied volatilities
Beta exposures to systematic risk
Orthogonal factors that sequentially explain maximum variance
PCA finds orthogonal linear combinations (eigenvectors) of returns that successively maximize explained variance, revealing key risk factors.
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Learning Outcomes

  1. Analyse risk-return trade-offs using quantitative models.
  2. Evaluate derivative pricing under stochastic frameworks.
  3. Apply statistical methods to financial time series data.
  4. Demonstrate portfolio optimization techniques and metrics.
  5. Identify key factors driving asset valuation processes.

Cheat Sheet

  1. Understand the risk-return tradeoff - Every investment is a balancing act between risk and reward. The higher the possible payoff, the more you're dancing on the edge of the financial cliff! Grasping this principle helps you pick the right assets for your comfort level. Read about the Risk-Return Tradeoff
  2. Learn the Black-Scholes model - This magical formula is the secret sauce for pricing European options, blending stock price, strike price, time, interest rates, and volatility into one neat package. Once you master Black-Scholes, you'll feel like a financial wizard decoding market spells. Dive into the Black-Scholes Equation
  3. Explore Monte Carlo methods - Imagine running thousands of "what-if" scenarios in the market - you're practically a financial fortune teller! Monte Carlo simulations model countless possible outcomes to price complex derivatives and measure risk. Explore Monte Carlo Methods
  4. Study modern portfolio theory (MPT) - Diversification is your best friend - mix a variety of assets to optimize returns for a given risk level. MPT shows you how to build a dream team of investments that work together like a winning sports lineup. Learn about Modern Portfolio Theory
  5. Understand stochastic discount factors - These factors help you discount future cash flows while accounting for risk, making sure you're not overpaying for tomorrow's money today. Mastering SDFs is like knowing the secret handshake of asset pricing. Discover Stochastic Discount Factors
  6. Familiarize yourself with the Capital Asset Pricing Model (CAPM) - CAPM connects systematic risk and expected return, giving you a formula to gauge whether an investment is worth its risk. It's like having a financial compass pointing you toward fair value. Check out the CAPM
  7. Learn about the Efficient Market Hypothesis (EMH) - EMH argues that markets are sharp-minded reporters, instantly reflecting all known info in asset prices. This implies beating the market consistently is as tough as catching lightning in a bottle! Read about the EMH
  8. Understand the concept of Value at Risk (VaR) - VaR calculates the worst loss you might face over a certain time frame at a given confidence level. It's your risk management GPS, warning you before you drift into dangerous financial waters. Learn more about Value at Risk
  9. Explore the Arbitrage Pricing Theory (APT) - APT says asset returns are influenced by multiple macroeconomic factors, not just the market as a whole. Think of it as building a multi-factor recipe for predicting returns. Explore the APT
  10. Study the role of machine learning in derivative pricing - From neural networks to random forests, machine learning is the new ace up the sleeve for pricing tricky derivatives. Get ready to code your way to sharper, faster pricing models. Discover ML in Derivative Pricing
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