READING 32: RISK MANAGEMENT
APPLICATIONS OF FORWARD AND FUTURES STRATEGIES

32.1. HEDGING WITH FORWARD AND FUTURES

  1. Adjusting portfolio BETA
    =futures contract
  1. Hedging is RARELY perfect

32.2 MORE APPLICATION

Altering bond exposure using contracts

target duration
(applied for bond portfolio)

adjusting portfolio asset allocation

adjusting the equity allocation

preinvesting

32.3. SYNTHETIC POSITIONS

Construct a synthetic stock index fund using
cash and stock index futures (equitizing cash)

WHY future value is used in the synthetic call calculation?

32.4. HEDGING CURRENCY

HOW Forward contracts help to reduce the risk associated with future receipts and payment in a foreign CRY

Hedging limitation

Hedging market risk

changing % proportion among small-cap and mid -cap

among equity and bond

refers to buying contracts in anticipation of cash that will be received

a. should know


+ beta of futures contract
(not = 1, of S&P 500: ~1, but small- cap stocks: very different from 1)


+ beta of the equity portfolio

Recall the formula of beta


Beta = COV (i, m) / SD(m)^2


i = an individual stocks, equity portfolio or equity index.
COV (i,m) = covariance of returns of asset i with the market
SD (m)^2 = Variance of market returns

appropriate #contracts to sell or buy to hedge or leverage the position (reduce of increase beta)


#futures equity contract = [ (target Beta - Portf. beta) / futures contract beta ] / [ Portf. Value / (futures price x multiplier) ]

a. Basis risk
occurs when the item hedged is not perfect match for hedging vehicle

b. Reasons for basis risk

a. The numerator and denominator are not based on the same item

b. The betas and durations used in the hedge calculation do not reflect the actual subsequent market value changes of the portfolio or contract

c. The hedge results are measured/ The hedge is closed prior to the expiration of the contracts. => The hedge might need to be extended after the initial contract expires.

d. The number of contract is rounded

e. The futures and spot price are not fairly priced based on the cash & carry arbitrage model.

c. Effective beta of the position can be measured ex-post (after the fact)


Effective beta = % change in portf. value/ % change in the index

#futures bond contract

=[ ( yield beta) x (target MD - portf. MD) x Portf. value / (futures MD x Contract price)

#futures bond contract

in fixed income reading
=[target D - portf. D) x Portf. value x CTD Conversion factor / (CTD Duration x price of CTD)
+
*Price of CTD / CTD conversion factor = price of the futures contract

uses the same number of contracts formulas but requires multiple steps

Adjustments are often stated as percent allocations; however, the
calculations require dollar or other nominal amounts

Changing an allocation requires selling contracts to remove one exposure and buying contracts to create a different exposure

It is assumed the account has other assets that can be posted to meet margin requirements

Synthetic equity or bond
positions

require purchasing contracts and holding sufficient cash equivalents ( ie. might be cash or other types) earning risk free rate to pay for the contracts at expiration

synthetic cash positions

involve holding the underlying and shorting contracts to hedge the position in such a way that the hedged position "earns" the risk free rate over the hedging period.

the quantity to hedge (in the numerator of the hedging formula) is the FV of the amount to modify
(please remember to use to FV)

to COMPLETELY REPLICATE the beginning and ending results that would have been obtained if the desired synthetic position had been actually held.

View the contract price as price per share & number of contracts x contract multiplier = the number of shares

  • F0 is the FV of S0 minus the FV of any dividends to occur during contract life on the underlying.
  • The dividend yield is, therefore, already "priced" into the contract price.

03 types of FX risk

  1. Transaction risk: when CF of one CRY must be exchanged for another at a future date.
  1. Translation risk: when a FS in one CRY must be converted to different CRY
  1. Economic risks: less directly observable and affect the competitive standing of a business

perfect hedging CRY is unlikely

An equity investment in a foreign market has
both equity risk and foreign exchange risk

The two hedging strategies utilized by global portfolio managers

  1. selling forward contracts on the foreign market index (to manage market risk)
  2. selling forward contracts on the foreign currency (to manage the currency risk).
  3. They can choose to hedge one or the other, both, or neither
  1. If the manager shorts the appropriate amount of the index and it is perfectly correlated with the portfolio of investments, the return from the hedging strategy must be the foreign risk-free rate.
  1. If the same manager then chooses to hedge the currency risk, she knows the exact value of the foreign currency to hedge, and the return to the (double) hedging strategy must be the manager's domestic risk-free rate.

Hedging currency risk

An obvious problem faced when trying to hedge the foreign currency risk of a foreign investment is its uncertain future value.

  1. Hedging a minimum future value below which they feel the portfolio will not fall
  2. Hedging the estimated future value of the portfolio
  3. Hedging the initial value (i.e., the principal).