READING 32: RISK MANAGEMENT APPLICATIONS OF FORWARD AND FUTURES STRATEGIES
READING 32: RISK MANAGEMENT
APPLICATIONS OF FORWARD AND FUTURES STRATEGIES
32.1. HEDGING WITH FORWARD AND FUTURES
Adjusting portfolio BETA
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) ]
Hedging is RARELY perfect
occurs when the item hedged is not perfect match for hedging vehicle
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
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.
of the position can be measured ex-post (after the fact)
Effective beta = % change in portf. value/ % change in the index
32.2 MORE APPLICATION
Altering bond exposure using contracts
(applied for bond portfolio)
#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
adjusting portfolio asset allocation
among equity and bond
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
adjusting the equity allocation
changing % proportion among small-cap and mid -cap
refers to buying contracts in anticipation of cash that will be received
It is assumed the account has other assets that can be posted to meet margin requirements
32.3. SYNTHETIC POSITIONS
Construct a synthetic stock index fund using
cash and stock index futures (equitizing cash)
Synthetic equity or bond
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
of the amount to modify
(please remember to use to FV)
WHY future value is used in the synthetic call calculation?
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
the FV of any dividends to occur during contract life on the underlying.
The dividend yield is, therefore, already "priced" into the contract price.
32.4. HEDGING CURRENCY
HOW Forward contracts help to reduce the risk associated with future receipts and payment in a foreign CRY
03 types of FX risk
Transaction risk: when CF of one CRY must be exchanged for another at a future date.
Translation risk: when a FS in one CRY must be converted to different CRY
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
selling forward contracts on the foreign market index
(to manage market risk)
selling forward contracts on the foreign currency
(to manage the currency risk).
They can choose
to hedge one or the other, both, or neither
Hedging market risk
If the manager shorts the appropriate amount of the index and it is
with the portfolio of investments, the return from the hedging strategy must be the
foreign risk-free rate.
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.
a minimum future value
below which they feel the portfolio will not fall
estimated future value
of the portfolio
(i.e., the principal).