Chapter 3 - Hedging Using Futures

Question 1

Basis Formula (Basis Risk)

Answer 1

Spot price - Futures Price

Question 2

Effect of basis strengthening and weakening on short and long hedger?

Answer 2

• Basis strengthening = spot ⬆️ relative to futures, so helps short hedger and hurts long hedger
• Basis weakening = spot ⬇️ relative to futures, so helps long hedger and hurts short hedger

Question 3

Minimum-Variance Hedge Ratio formula (Optimal Hedge Ratio) and meaning

Answer 3

h* = ρ * (σ_S / σ_F)
Where
σ_S = std dev of spot
σ_F = std dev of futures
Interpretation: fraction of exposure to hedge using futures

Question 4

Optimal number of futures contracts formula

Answer 4

N* = h* x (V_A / V_F)
V_A = exposure value
V_F = value per 1 futures contract

Question 5

Beta Hedging Formula (Equity Portfolios) and adjusting beta

Answer 5

N* = (beta) x (V_P / V_F)
Adjusting Beta: N* = (beta_target - beta_curr) x (V_P / V_F)

Question 6

How to choose a contract month

Answer 6

Futures closest to but later than hedge horizon

Question 7

Expected Returns from r, beta and Expected returns of market formula

Answer 7

• E(R_i) = R_f + β_i × (E(R_m) – R_f)
• Use to compute expected returns for portfolios or assets