Question

Discuss the amount of leverage in futures trading.

Discuss the three theories of futures pricing.

Discuss the simplicity of hedging a portfolio with stock index futures.

Answer 1

1) Leverage can seem risky, but when used properly it is a game changer. Leverage is the ability to control a large contract value with a relatively small amount of capital. In the futures market, that capital is called performance bond, or initial margin, and is typically 3-12% of a contract's notional or cash value.

2) Relationship between arbitrage arguments and expectation

The expectation based relationship will also hold in a no-arbitrage setting when we take expectations with respect to the risk-neutral probability. In other words: a futures price is a martingale with respect to the risk-neutral probability. With this pricing rule, a speculator is expected to break even when the futures market fairly prices the deliverable commodity.

Contango and backwardation

The situation where the price of a commodity for future delivery is higher than the spot price, or where a far future delivery price is higher than a nearer future delivery, is known as contango. The reverse, where the price of a commodity for future delivery is lower than the spot price, or where a far future delivery price is lower than a nearer future delivery, is known as backwardation.

Arbitrage arguments

Arbitrage arguments ("rational pricing") apply when the deliverable asset exists in plentiful supply, or may be freely created. Here, the forward price represents the expected future value of the underlying discounted at the risk free rate—as any deviation from the theoretical price will afford investors a riskless profit opportunity and should be arbitraged away.

3) The idea behind hedging risk is to mitigate an investor’s exposure to the volatility of stock prices. If an investor owns a portfolio of stocks, his exposure is to a downward move in stock prices. Hedging can be accomplished with many different types of financial instruments -- including a stock index that represents a proxy for a portfolio of stocks.

Investors who want to hedge their portfolios need to calculate the amount of capital they want to hedge and find a representative index.