Forward and Futures: Stock index futures

Question 1

What is the connection between a stock forward and a stock index forward?

Answer 1

The equation F₀ = (S₀ - I) * e^rt is true for both a stock forward and a stock index forward.

Question 2

What is the formula for the forward price of a stock index with dividends (assuming continuous dividends)?

Answer 2

F₀ = S₀ * e^{(r-q) * t}

Where r is the risk-free rate and q is the continuous dividend yiedl

Question 3

What are three example of European stock index futures?

Answer 3

1. Euro Stoxx 50 index future: 50 stocks from 11 Eurozone countries: Austria, Belgium, Finland, France, Germany, Ireland, Italy, Luxembourg , the Netherlands, Portugal and Spain.
2. Stoxx Europe 50 index future: 50 stocks from 17 countries (same 11 + Denmark, Norway, Poland, Sweden, Switzerland and UK)
3. Stoxx Europe 600 index future: 600 stocks from 17 countries (same as stoxx europe 50)

Question 4

What is the size of 1 future contract on an index?

Answer 4

F x multiple (determined for a specific index)

Question 5

What is the formula for implied dividend yield?

Answer 5

q_imp = r - (1/t) * ln(F_mkt/S)

Alternatively F_mkt = S * e^{(r-q imp) * t}

Question 6

What is a spread trading strategy?

Answer 6

• A spread trading strategy is a strategy which combines a long position on one asset and a short on another (very similar) asset, taking a view on the relative performance of the two assets.
  Two main examlpes with stock index futures
  1. Spread trading between maturitie
  2. Spread trading between similar indexes.

Question 7

What is basis risk?

Answer 7

Basis is the difference between spot & future (basis = S - F)
Since F = Se^{(r-q) * t}, basis converges to zero at maturity

Question 8

What is the hedge ratio for stock index futures?

Answer 8

h = ρ * (σ_V/σ_F) * V/F = β_V * (V/F)

Where V is stock, F is future and rho is correlation between the two

Question 9

What is the formula for a partial hedge?

Answer 9

Sell (β_V - β_target) * V/F