15-27 Forwards and Futures Flashcards
Formula for number of futures contracts needed to adjust beta of an equity portfolio
N(f) = (Bt - Bs) x Vp divided by Bf x Vf
where Vf is price of futures x multiplier
for S&P 500, multiplier for futures is 250
what is basis risk
basis risk is when risk adjustment is imperfect (hedged portfolio in numerator of formula is not a perfect match for the hedging vehicle in denominator of hedge formula) and as a result the relationship of the two change in unpredictable ways
typical reasons for basis risk
- number of contracts is rounded
- future and spot prices are not fairly priced based on cash and carry arb model
- numerator and denominator are not based on same item. e.g. stock portfolio hedged using a S&P500 or bond portfolio hedged with a T-bond contract based on single deliverable bond
- betas and durations used in hedge calculation don’t reflect actual subsequent market value changes of portfolio or contract (i.e., B and D aren’t accurate estimates)
- hedge results are measured prior to contract expiration and/or hedge is closed prior to contract expiration. alternatively, hedge may need to be extended after expiration of initial contract position (holding contracts to expiration reduces basis risk)
formula Effective beta
Effective beta = HPR on total portfolio including futures divided by market return
what is a synthetic position
- unleveraged position
- replicate same initial investment and ending results that would have occurred if replicated position had been owned
- based on same formulas using B or D to modify portfolio risk
- require buying futures and holding cash earning Rf to pay for the contracts at expiration. alternatively, hold underlying and short contracts to hedge position in such a way that hedged position earns Rf over hedging period
why create synthetic position
alternatives?
you expect S&P 500 market to rise and want to gain from it.
alternatives:
- own the stock portfolio - which is expensive and may have to make price concessions
- buy mutual fund - which requires money up front
- buy ETF - less expensive but still money up front
- buy futures contract - which is a leveraged position
- buy options, swaps etc …OR
- create unleveraged, synthetic position
formula for number of futures when equitizing cash
if creating equity from cash: same formula except Bt = Bf and Bs = 0. in effect the betas can be ignored and you are left with 1
if creating synthetic cash from equity: same except Bt = 0 and Bp = Bf. in effect the betas can be ignored and you are left with -1
when to use PV vs FV of a synthetic portfolio position when calculating number of futures?
FV:
wish to create $20m of synthetic S&P500 stock exposure for 3 months
formula PV of cash needed to invest today?
calculate number of futures and then multiply the rounded number of contracts by price of futures and multiplier, then divide the whole numerator by (1+Rf)^n
(Nf x F x m) / (1 + Rf)^n
formula for shares effectively purchased today
number of shares effectively purchased at maturity
=contracted number of shares discounted by dividend yield
= (Nf x multiplier) / (1+d)^n
at maturity:
number of futures contracts x multiplier
formula for number of futures used to adjust bond duration for bond portfolio
2 formulas
Nf = yield beta x (Dt - Dp) x Vp all divided by Df x Vf
where Vf = price of futures x multiplier
yield beta if not given is 1
Nf = (Dt - Dp) x Vp x CTD conversion factor all divided by Dctd x Vctd
How to adjust equity or bond allocations?
reduce alloc from one and increase in another
if reducing from one, target B or D would be zero
if increasing alloc to another, target B or D would be whatever is desired
what is preinvesting
no money now - money will be here in 5 days but within 5 days market will go up and want to gain from it.
preinvesting refers to buying contracts in anticipation of cash that will be received. buying contracts doesn’t require initial CF. is a type of synthetic position.
3 types of foreign exchange risk
which of the 3 types usually hedged with derivatives?
- transaction exposure (future CF hedged by forwards)
- economic exposure (when changes in currency values affect business competitiveness)
- translation exposure (not a real CF risk)
translation exposures
state position and action on following contractual agreements:
- receiving foreign currency
- paying foreign currency
- long position, sell forward contract
- short position, buy forward contract
