RM Lecture 2

Question 1

What is the formula for delta-hedging a position V=f(X) with a hedging instrument H=h(X)?

Answer 1

Goal: Eliminate first-order risk (ΔV + a ⋅ ΔH ≈ 0)

Question 2

What is the formula for the optimal hedge ratio a* in minimum variance hedging?

Answer 2

Purpose: Minimize portfolio variance using correlated instruments.

Question 3

What is the remaining variance after applying the minimum variance hedge ratio a*?

Answer 3

Interpretation: ρ² (R²) quantifies hedge effectiveness.

Question 4

How does CAPM map portfolio risk to market risk?

Answer 4

Key: Portfolio returns depend on market returns (R_m) and idiosyncratic risk (ϵ).

Question 5

What additional factors does the Fama-French model include compared to CAPM?

Answer 5

Question 6

How is the beta (β) of a portfolio calculated?

Answer 6

β_portfolio = ∑(Value of asset i / Total portfolio value) * β_i

Example: For stocks with weights w_i, β = ∑w_i β_i.

Question 7

Is a delta-hedged portfolio risk-free under CAPM?

Answer 7

No. Residual idiosyncratic risk (ϵ_i) remains even after hedging market risk.

Question 8

What is basis risk in hedging?

Answer 8

Risk arising from imperfect correlation between the hedged position and the hedging instrument.

Question 9

How is the quality of a minimum variance hedge quantified?

Answer 9

Question 10

What happens to portfolio risk as N → ∞ under CAPM?

Answer 10

Idiosyncratic risk (ϵ) diversifies away, leaving only systematic risk (βR_m).