Financial Markets and Products 3

Arguments against hedging

1. Hedging can lead to less profitability if the asset being hedged ends up increasing in value 2. Questionable benefit that accrues to shareholders because they can hedge risk easier on their own than the company 3. Nature of the hedging company's industry - prices in an industry frequently adjust for changes in input prices and FX

Sources of Basis Risk

1. Interruption in the convergence of the futures and spot prices 2. Changes in the cost of carry 3. Imperfect matching between the cash asset and the hedge asset

Assumptions of CAPM

1. Investors care only about the expected return and standard deviation of the return from an asset 2. The returns from two assets are correlated with each other only because of their correlation with the return from the market. This is equivalent to assuming that there is only one factor driving returns 3. Investors focus on returns over a single period and that period is the same for all investors 4. Investors can borrow and lend at the same risk-free rate 5. Tax does not influence investment decisions 6. All investors make the same estimates of expected returns, standard deviations of returns, and correlations between returns

Characteristics of Stock Indices

1. Settled in Cash, not by delivery of the underlying asset 2. All contracts are marked to market to either the opening price or the closing price of the index on the last trading day 3. Positions are deemed to be closed

2 types of risks associated with the return in CAPM

1. Systematic risk is risk related to the return from the market as a whole and cannot be diversified away 2. Nonsystematic risk is risk that is unique to the asset and can be diversified away by choosing a large portfolio of different assets

Reasons why Perfect Hedges are rare

1. The asset in the existing position is often not the same as the asset underlying the futures 2. Hedging horizon may not match perfectly with the maturity of the futures contract.

Hedging is not straightforward because of the following reasons:

1. The asset whose prices is to be hedged may not be exactly the same as the asset underlying the futures contract 2. Hedger is uncertain of the date when the asset will be bought or sold 3. The hedge may require the futures contract to be closed out before its delivery month

Choice of Contract

1. The choice of the asset underlying the futures contract 2. The choice of the delivery month

Hedging and Competitors

A company that does not hedge can expect its profit margin to be roughly constant. However, a company that does hedge can expect its profit margins to fluctuate.

Perfect Hedge

A hedge that completely eliminates the risk

Tailing the Hedge

A small adjustment that is made to allow for the impact of daily settlement when futures are used for hedging. Va = is the dollar value of the position being hedged Vf = is the dollar value of one futures contract (futures price times Qf)

Systematic risk

According to CAPM, which risk should the return be dependent on?

Basis

Basis in a hedging situation: Basis = Spot price of asset to be hedged - Futures price of contract used

Hedge Effectiveness (R^2 - in stat, goodness of fit of a regression)

Can be defined as the proportion of the variance that is eliminated by hedging Measures the variance that is reduced by implementing the optimal hedge. Independent variable - change in futures price Dependent variable - change in the spot price

Stock index futures

Can be used to hedge the systematic risk in an equity portfolio

Rule of thumb when choosing the delivery month

Choose delivery month that is as close as possible to, but not later than, the expiration of the hedge.

Cost of carry

Cost of carry includes storage and safekeeping, interest, insurance costs

No daily settlement

Daily settlement only has a small effect on the performance of a hedge

Minimum Variance Hedge Ratio

Depends on the relationship between changes in the spot price and changes in the futures price

Relationship between basis risk and time difference between the hedge expiration and the delivery month

Direct relationship - as the the time difference between the hedge expiration and the delivery month increases, basis risk also increases

Interruption in the convergence of the futures and spot prices

Example is position is unwound prior to maturity

Maturity / Duration Mismatch

Example is treasury notes to hedge mortgages. Basis risk arise when interest rates fall and mortgage prepay faster

Calculating effective price gained

Final Spot (S2) + Gain on the Future (F2-F1), or Initial Futures Price (F1) + Final Basis (B2)

Calculating effective price paid

Final Spot (S2) - Gain on the Future (F2-F1), or Initial Futures Price (F1) + Final Basis (B2)

Beta

From the capital asset pricing model is the slope of the best-fit line obtained when excess return on the portfolio over the risk-free rate is regressed against the excess return of the index over the risk-free rate

10

Futures multiplier of Dow Jones

Alternative definition of Basis

Futures price - Spot Price, particularly when the futures contract is on a financial asset

Cross Hedging

Hedger's exposure is different from the asset underlying the futures contract and it leads to an increase in basis risk

How to minimise Basis risk

Hedgers should select the contract on an asset that is most highly correlated with the spot position and a contract maturity that is closest to the hedging horizon

Long Hedge

Hedges that involve taking a long position in a futures contract. Is used when the hedger knows it will have to purchase a certain asset in the future and wants to lock in a price now

Liquidity mismatch

Hedging an illiquid asset with a more liquid asset would result in basis risk Basis risk is inversely proportional to the liquidity of the hedged asset

Optimal number of contracts

Hedging of equity portfolios using futures contracts on stock indices

2. One is $10 times the index and the other $5 times (Mini DJ Industrial average

How many futures contracts does CME Group trade in Dow Jones?

2 futures contracts. One is $100 times the index, the other is on $20 times the index (Mini Nasdaq100)

How many futures contracts does CME Group trade in Nasdaq-100?

2. One is $250 times the index and the other is $50 times (Mini S&P 500)

How many futures contracts does CME Group trade in S&P 500?

A hedge ratio different from 1 may be appropriate

How to minimize the variance of a position?

Zero Basis

If the asset to be hedged and the asset underlying the futures contract are the same, the basis should be zero

Short Hedge

Is a hedge that involves a short position in futures contracts. Hedger already owns an asset and expects to sell it at some time in the future. Can also be used when an asset is not owned right now but will be owned some time in the future

Capital Asset Pricing Model (CAPM)

Is a model that can be used to calculate the expected return from an asset during a period in terms of the risk of the return

US Dollar Index

Is a trade-weighted index of the values of six foreign currencies: euro, yen, pound, canadian dollar, swedish krona, swiss franc

Russell 1000 index

Is an index of the prices of the 1000 largest capitalization stocks in the US

Nasdaq 100

Is based on 100 stocks using the National Association of Securities Dealers Automatic Quotations Service

Dow Jones Industrial Average

Is based on a portfolio consisting of 30 blue-chip stocks in the US. The weights given to the stocks are proportional to their prices

Standard & Poor's 500 Index

Is based on a portfolio of 500 different stocks: 400 industrials, 40 utilities, 20 transportation companies, 40 financial institutions. The weight of the stocks in the portfolio at any given time are proportional to their market capitalizations

Hedge ratio

Is the ratio of the size of the position taken in futures contracts to the size of the exposure Is the ratio of the size of the futures position relative to the spot position

Optimal hedge ratio

Is the slope of the best fit-line obtained when changes in the spot price are regressed against changes in the future price **Beta of spot prices with respect to futures prices is equal to the hedge ratio

Stack and Roll

Rolling the hedge forward by closing out one futures contract and taking the same position in a futures contract with a later delivery date

Relationship of basis and hedger's position

Short hedge Basis Strengthens —> Hedger's position improves Basis Weakenens —> hedger's position worsens For a long hedge, the reverse holds

R^2

Square of the correlation coefficient (p^2) between spot and futures prices

Basis Risk

The hedge risk is the uncertainty associated with b2 at maturity of the hedge Defined as the change in Basis over the hedge horizon

Basic principle of hedging risk using futures markets

The objective is usually to take a position that neutralizes the risk as far as possible

Return on the Market (Rm)

The return from the portfolio of all available investments and is usually approximated as the return on a well-diversified stock index such as the S&P 500

Hedging and Shareholders

The size of futures contracts makes hedging by individual shareholders impossible in many situations

Credit risk mismatch

The widening and narrowing of credit spreads constitutes another form of basis risk

Total Return Index

This is calculated by assuming that dividends on the hypothetical portfolio are reinvested in the portfolio

Stock index

Tracks changes in the value of a hypothetical portfolio of stock. **Dividends are usually not included in the calculation so that the index tracks the capital gain/loss from investing in the portfolio

Hedge-and-Forget Strategies

We assume that no attempt is made to adjust the hedge once it has been put in place

Implication of Beta

When Beta = 1, the return on the portfolio tends to mirror the return on the index; When Beta = 2, the excess return on the portfolio tends to be twice as great as the excess return on the index. <— twice sensitive so use twice as many contracts to hedge the portfolio When Beta = 0, an asset's return are not sensitive to returns from the market

Weakening of the Basis

When futures price increases faster than the spot prices over the hedging horizon

Rollover Risk

When rolling a hedge forward, the hedgers are not only exposed to the basis risk of the original hedge but also to the basis risk of the new position

Hedge ratio of 1

When the asset underlying the future contract is the same as the asset being hedged. Using this hedge ratio is not always optimal

Choice of delivery month

When the expiration of the hedge corresponds to a delivery month, the contract with that delivery month is chosen

Strengthening of the Basis

When the spot price increases faster than the futures price over the hedging horizon

Locking in the Benefits of stock picking

You should short beta x Va / Vf index futures contracts where Beta is the Beta of your portfolio, Va is the total value of the portfolio and Vf is the current value of one index futures contract. If your portfolio performs better than a well-diversified portfolio with the same beta, you will make money