32.f Hedging with stock index futures

Let's break down the formula for hedging equity portfolios using index futures step-by-step:

1. **Hedge Ratio (HR)**: The hedge ratio, also known as beta (β), represents the sensitivity of the equity portfolio's returns to changes in the returns of the stock index futures. It measures the relationship between the two. A hedge ratio of 1 means the portfolio moves in perfect sync with the index, while a ratio of 0 indicates no correlation. The hedge ratio is calculated using regression analysis based on historical data.

   For example, if the hedge ratio (beta) is determined to be 0.7, it means that for every 1% change in the value of the stock index futures, the equity portfolio is expected to change by 0.7%.

2. **Value of Equity Portfolio (P)**: This is the total value of the equity portfolio that you want to hedge using index futures.

   For example, let's say the value of the equity portfolio is $1,000,000.

3. **Value of One Index Futures Contract (C)**: This represents the value of a single futures contract on the stock index. Each index futures contract covers a certain dollar value of the underlying index.

   For example, if the value of one index futures contract is $50,000, it means that one futures contract is based on the performance of $50,000 worth of the stock index.

4. **Number of Futures Contracts (N)**: This is the unknown variable we want to calculate using the formula. It represents the number of index futures contracts to be bought or sold to hedge the equity portfolio.

   Now, the formula for calculating the number of futures contracts required to completely hedge an equity position is:

   **N = (HR * P) / C**

   where:

   - N = Number of futures contracts

   - HR = Hedge Ratio (beta)

   - P = Value of the equity portfolio

   - C = Value of one index futures contract

   Substituting the values from our example:

   N = (0.7 * $1,000,000) / $50,000

   N = $700,000 / $50,000

   N ≈ 14

   So, to completely hedge the equity portfolio with a hedge ratio of 0.7, you would need to buy or sell approximately 14 index futures contracts.

It's important to note that the hedge ratio (beta) and the number of futures contracts needed to hedge may change over time due to market fluctuations and changes in the composition of the equity portfolio. Regular monitoring and adjustments are necessary to maintain an effective hedge.

Hedging With Stock Index Futures

You are a portfolio manager with a $20 million growth portfolio that has a beta of 1.4, relative to the S&P 500. The S&P 500 futures are trading at 1,150, and the multiplier is 250. You would like to hedge your exposure to market risk over the next few months. Identify whether a long or short hedge is appropriate, and determine the number of S&P 500 contracts you need to implement the hedge.

To hedge your $20 million growth portfolio with S&P 500 futures, you need to determine whether a long hedge or a short hedge is appropriate. Let's break down each scenario:

1. **Long Hedge**:

- A long hedge involves buying S&P 500 futures contracts to offset potential losses in your portfolio. This is suitable when you anticipate a decline in the market and want to protect your portfolio from potential losses.

- To calculate the number of S&P 500 contracts required for a long hedge, use the formula:

Number of contracts (N) = (Portfolio Value * Portfolio Beta) / (Futures Contract Value)

2. **Short Hedge**: - A short hedge involves selling S&P 500 futures contracts to protect against a potential increase in the cost of purchasing assets in your portfolio. This is appropriate when you expect the market to rise and want to lock in the current prices of your assets. - To calculate the number of S&P 500 contracts required for a short hedge, use the same formula as in the long hedge scenario. Now, let's calculate the number of S&P 500 contracts needed for both cases: Given data: - Portfolio Value (P) = $20,000,000 - Portfolio Beta (β) = 1.4 - S&P 500 Futures Contract Value (C) = $1,150 * 250 (multiplier) = $287,500 1. **Long Hedge**: Number of contracts (N) = ($20,000,000 * 1.4) / $287,500 = $28,000,000 / $287,500 ≈ 97.39 Since you cannot buy a fraction of a futures contract, you would need to round up to the nearest whole number. Therefore, you would need to buy approximately 98 S&P 500 futures contracts to implement a long hedge. 2. **Short Hedge**: Number of contracts (N) = ($20,000,000 * 1.4) / $287,500 = $28,000,000 / $287,500 ≈ 97.39 Similarly, since you cannot sell a fraction of a futures contract, you would need to round up to the nearest whole number. Therefore, you would need to sell approximately 98 S&P 500 futures contracts to implement a short hedge.

In this scenario, both the long and short hedges require the same number of contracts, which is approximately 98 contracts. The decision to choose between a long or short hedge depends on your market outlook and risk management strategy. If you expect the market to decline, a long hedge might be more appropriate. If you expect the market to rise, a short hedge could be more suitable to lock in your asset prices.

Sure! Here are some multiple-choice questions related to hedging with stock index futures:

Question 1:

What is the purpose of hedging with stock index futures?

A) To increase the exposure to market risk

B) To speculate on the direction of the stock market

C) To protect against potential losses in the portfolio

D) To maximize the returns of the equity portfolio

Answer: C) To protect against potential losses in the portfolio

Question 2:

Which hedge ratio (beta) would be preferred for a stronger hedge when using stock index futures?

A) 0.2

B) 0.8

C) 1.2

D) 1.8

Answer: D) 1.8

Question 3:

A portfolio manager has a $5 million growth portfolio with a beta of 1.5 relative to the S&P 500. The S&P 500 futures are trading at 1,300, and the multiplier is 200. If the manager wants to hedge the portfolio, how many S&P 500 futures contracts are needed for a long hedge?

A) 18

B) 25

C) 30

D) 35

Answer: B) 25

Question 4:

Which hedge strategy involves selling S&P 500 futures contracts?

A) Long hedge

B) Short hedge

C) Partial hedge

D) Uncovered hedge

Answer: B) Short hedge

Question 5:

In a short hedge, what is the purpose of selling S&P 500 futures contracts?

A) To increase potential losses in the portfolio

B) To speculate on the rise of the stock market

C) To lock in the current prices of assets in the portfolio

D) To eliminate all market risks from the portfolio

Answer: C) To lock in the current prices of assets in the portfolio

These questions cover the basics of hedging with stock index futures, hedge ratios, and the different hedge strategies. Make sure to thoroughly understand the concepts to answer these questions correctly.