AIFA AIFA Quantitative Methods & Financial Modeling 1 — Questions and Answers
Question 1: A US investor deposits $50,000 into an account earning 6% annual interest compounded monthly. What is the approximate future value after 5 years?
- $66,911
- $67,443 (Correct answer)
- $67,898
- $65,000
Correct answer: $67,443
Using FV = PV × (1 + r/n)^(n×t) = $50,000 × (1 + 0.06/12)^60 ≈ $67,443.
Question 2: In a discounted cash flow (DCF) model, which rate is used to convert future cash flows to present value?
- Internal rate of return
- Weighted average cost of capital (WACC) (Correct answer)
- Dividend yield
- Return on equity
Correct answer: Weighted average cost of capital (WACC)
The WACC is commonly used as the discount rate in DCF models because it reflects the blended cost of both debt and equity financing.
Question 3: Which statistical measure describes how much individual data points in a dataset deviate from the mean on average?
- Median
- Variance
- Standard deviation (Correct answer)
- Skewness
Correct answer: Standard deviation
Standard deviation measures the average dispersion of data points around the mean and is expressed in the same units as the original data.
Question 4: A bond with a face value of $1,000 pays a 5% annual coupon and matures in 10 years. If the required yield is 6%, the bond is trading at a:
- Premium to par
- Discount to par (Correct answer)
- Par value
- Cannot be determined
Correct answer: Discount to par
When the required yield exceeds the coupon rate, the bond trades below par (at a discount) because its cash flows are worth less when discounted at the higher rate.
Question 5: What does a correlation coefficient of -1.0 between two assets indicate for portfolio construction?
- The assets are perfectly positively correlated
- The assets move completely independently
- The assets move in exactly opposite directions, offering maximum diversification (Correct answer)
- The assets carry equal risk
Correct answer: The assets move in exactly opposite directions, offering maximum diversification
A correlation of -1.0 means the assets move in perfectly opposite directions, which theoretically allows a portfolio to eliminate unsystematic risk entirely through diversification.
Question 6: Which financial model estimates the value of a company's equity by discounting expected future dividends at the required rate of return?
- Capital Asset Pricing Model (CAPM)
- Gordon Growth Model (Dividend Discount Model) (Correct answer)
- Arbitrage Pricing Theory
- Black-Scholes Model
Correct answer: Gordon Growth Model (Dividend Discount Model)
The Gordon Growth Model (a form of DDM) values equity as D1 / (r - g), where D1 is next year's dividend, r is the required return, and g is the constant dividend growth rate.
AIFA AIFA Quantitative Methods & Financial Modeling 1
A US investor deposits $50,000 into an account earning 6% annual interest compounded monthly.
What is the approximate future value after 5 years?