Derivative and currency mgmt 15-17 Flashcards
put-call parity
so+po = x + xe^(-rt)
synthetic long forward
long call +short put with same strike
synthetic short forward
long put + short call
synthetic call
long call = asset + put
synthetic put
long put = call - asset
covered call
stock + short call
max profit = (x-so)+co
breakeven= So-Co
Max loss = unlimited
protective put
buying insurance
upside potential with limited downside risk
stock + long put
max profit = unlimited
breakeven So+Po
Max loss = S0-x +P0
Implied volatility
value of unobservable volatility variable that equities the result of adoption pricing model
Delta
change in option price/change in underlying
call +
put -
Gamma
change in delta/change in underlying value
largest at the money near S0
call/put +
Vega
change in value of option / change in volatility of underlying
call/put +
Theta
time decay, sensitivity of option’s price o passage of time
call/put -
benefit of covered call
a. yield enhancement
writing covered calls is cash generating in anticipation of limited upside moves in the underlying
b. reducing a position at a favorable price
call premium = time value + intrinsic value
= time value + max(0, s-x)
sell ITM call option
c. target price realization (hybrid of a+b)
write OTM calls with K near the target price for the stock
Collar
acquire downside protection through protective put but reduce cash outlay by writing a covered call
protective put + covered call
Long stock + long put Xl - call XH
buy int rate floor + selling int rate cap
zero - cost collar buy put + sale call with same premium net cost=0 BEI=S0 max gain = St-So max loss = S-x
sacrifice the position part of the return distribution in exchange for the removal of the adverse position
- narrow the distribution of possible investment outcomes, risk is reduced return is limited
- economically intermediate b/w pure equity and FI exposure
cash secure put
for bullish view
acquire shares at a particular price
write a call and simultaneously deposit same amount of money equal to the exercise price in a designated account
bull spread
buy XL, short XH
when price increase spread increase more value
bull call
long call L + short call H (less expensive) debt spread
profit = max(0, St-XL) - max(0, St-Xh) -CL + CH
Max profit = XH-XL +CH-CL
Max loss = CH-CL
BEI = XL-net premium
bull puts
long put L + short put H (more expensive) credit spread
profit = max (0, XL-S) - max(0, XH-S)
BEI between two strike
bear spread
Short XL, buy XH
when price decrease spread increase more value
bear call
short call L + long call h
bear put
short put L + long put H
spread are classified in 2 ways
market sentiment
by direction of the initial cash flow
debt spread
long
long option value > short option value
credit spred
short
the short option value > long option value
Tactical adj. for option trader
adding a short leg to a long position (bull call)
spread and dealt (change in market view)
Long straddle
short
long put + long call with same x and exp. date
short put + short call
two BEI X+/- (C+P)
MAX LOSS = -P-C
calendar spread
sensitive to implied volatility
take advantage of the time decay
time decay is more prominent for a short term option
long (stable market/increase in implied volatility)
long more distant call and sell near call
short (decrease implied volatility)
long near term call and sell the long-daed call
credit spread implied volatility decrease
Themat for ITM call may provide motivation for a short calendar spread.
implied volatility BSM
Std(month%) = std(annual %) / sir(252/21)
if an investor buy an ATM one-month (21)day straddle using puts and call, in order to be profitable, price must move up/down by at least by the implied volatility
volatility smile
when the implied volatility priced into both OTM puts and calls trade at a premium to implied volatility of ATM options, the curve is U-shaped
volatility skew
implied volatility increase for OTM put
decrease for OTM calls as the strike price move away
OTM put typically command higher implied volatility than ATM or OTM calls due to “fat tail”
skew depend on investor sentiment
when implied volatility is significantly higher for put
with X below S
an imbalance in the supply and demand for option
a sharpe increase in the level of skew, accompanied with a surge in the absolute level of implied volatility
an indicator market sentiment is turning bearish
higher implied volatility for call with X > s
indicate investor are bullish
demand for OTM calls to take an upside exposure is strong
Delta hedge
delta-neutral position of 0
price lead to implied volatility change
std increase, long straddle/strangle buy ATM CALL/PUT
std decrease, short straddle/strangle sell ATM call/put
take a long or short position in a risk reversal
when Std PUT >std call
long risk reversal by selling the OTM put
buy the same exp. OTM call
term structure of volatility
often in contango F near term
when in stress/de-risk, demand ST option to push up the prices
term structure of volatility to invert
implied volatility surface (3-dimensional plot)
joint influence of maturity (x) and strike (y)
the shape of the volatility skew reflects varying degrees of market participants’ fear about future market stress
advantage of derivatives
- cheaper
- leverage
- liquidity
outlook on the trend of underlying asset
bearish
implied volatility decrease
write calls
unchanged
write call and buy puts
increase
buy puts
outlook on the trend of underlying asset
unchanged
implied volatility decrease
write straddle
unchanged
calendar spread
increase
buy straddle
outlook on the trend of underlying asset
bullish
implied volatility decrease
write puts
unchanged
buy calls and write puts
increase
buy calls
bullish view not sure treading up/down
call bull spread
bearish view not sure treading up/down
put bear spread
interest rate swap
- convert b/w floating and fixed exposure
2. alter the duration of a fixed-income portfolio
buyer swap
makes a series of fixed-rate pmt and receive a series of floating rate ptm
basis risk/spread risk
basis point value BPV = mv * md *0.01%
price discrepancy b/w price of cash and FI futures
= spot cash price - futures price * CF
<0 BUY BASIS BUY BOND, SHORT FUTURES
>0 short basis buy futures, short bond
assumption:
change in value of bond p portfolio can be approx. by using the concept of modified duration, old curve inflation, and it is affect only by parallel shift
portfolio and derivative contract used to hedge are prefect substitute
MPp(MDVRp) + Ns(MDVRs) = MVp(MDVRt)
MDVRs MD of swap
measure change in value of swap
mdvrt md of combined portfolio
change in p
= Ns*change in S
Ns
(MDVRt - MDVRp)
/ MDVRs
MDVRt - MDVRp <0 fixed rate payer
MDVRt - MDVRp >0 fixed rate receiver, floating rate payer
interest rate forward & futures
FRN
FRA will settle only the discounted difference between the rate agreed and the actual rate prevailing at the time of settlement, applied on the NP
HEDGE Future ST borrowing/lending rate
FRA borrower long FRA
FRA lender
short fRA
Interest rate future borrower
short futures
interest rate futures lender
long futures
fixed income futures
hedge duration risk for longer maturities
Duration of a future contract is usually consistent with the forward behavior of the cheapest to deliverable bond
will reflect the duration of the CTD bond
price sensitivity of bond future will reflect the duration of the CTD bond
low coupon, long maturity
long duration CTD bond
if market yld > notional yld of FI futures
high coupon, short maturity
short duration CTD bond
if market yld < notional yld of FI futures
hedge ratio change of value of FI futures=
change in p/change in CTD * conversion factor
BPVHR=
- BPVP/BPVctc * CF
=bpvt-bpvp/bpvctd * cf
np=
$change in duration /2
hedging result are imperfect because:
the hedge is done with the cheapest to deliver bond
duration of futures contract can change
- the relationship b/w interest rate & bond prices is not linear, owing to convexity
- the term structure of interest rates often changes via non-parallel moves
currency swaps
hedge against the risk of exchange rate fluctuation to achieve better rate outcomes
cross currency basis swap
exchange NP because the goal of the transaction is to issue at a more favorable funding rate and swap the amount back to the currency of choice
advantage equity swap vs. physical stock
pay equity return
and get index return
gain exposure to equity when participation in physical market is restricted or equity is liquid
avoid tax in physical ownership
avoid custody fees on physical ownership
avoid the cost of monitoring physical positions, which may increase due to corp. actions
equity swap required collateral
swap are iliquid
swap doesn’t convey voting rights
equity futures
exchange traded, standardized, require margin
have low transaction cost, and are available on indexes and single stocks
enable:
1. implement tactical allocation decision
selling futures decrease equity exposure
- achieve portfolio allocation
- gain exposure to international markets
- make directional bets on the direction of the market
Nf =
Bt-Bs/bf *(s/f)
beta of portflio
% change in portfolio /% change in index
cash equalization/cash overlay
cash = security - future
boost returns by finding ways to equities uninvested cash holdings
beta s=0 with cash holding
volatility and stock index negative correlated
variances spread has a valuable convesity feature as realized volatility increase
contago
negative yield curve
S>F
backwardation
positive yield curve
s>f
Variance swap
used for taking directional bets on implied vs. realized volatility for speculative or hedging purpose
realized variance > swap’s variance X
long payoff >0 swap seller pays buyer
settlement amount = variance N (realized variance - variance strike)
is convex
variance notional
vega notional / 2* strike price
settlement about = N variance * ( variance - x^2)
probability of a Fed rate hike of short-term US interest rates.
implied fed fund effect rate - current target rate
/ size of rate change
2.825% (= 100 – 97.175).
avg(2.50%– 2.75% ) = 2.625%
2.75-2.5=0.25%
prob: (2.825-2.625)
/0.25 =80%
federal fund rate
int rate the deposit institution charge others for loans in overnight interbank market
federal funds effective rate
weighted avg of interest rate charged on overnight interbank loans
federal fund target rate
rate set by FOMC meeting 8times/yr
base currency hierachy
EUR GDP AUD NZD USD
return decomposition Rdc =
(1+Rfc)(1+Rfx)-1
volatility decomposition Variance (Rdc) =
variance (rfx) + variane (rdc) + 2std* std * correlation
variance rfx = (1+rfc)*rfx
hedge/not hedge
not hedge
- fx rates revert to historical means to their fundamental value
- No LT gains after netting out mgmt and transition costs
- negative correlation help portfolio diversification
hedge in ST only
-FX rates to international trade and capital inflows
central banks, gove’t agencies and retail traders can have a larger impact on fx
-fx and FI move with interest rates, currency exposure provides little diversification benefit to FI portfolios and currency risk should be hedged
- optimal hedge ratio seems to depend o market conditions and LT trends in foreign currency bond portflio
forms trading expenses/cost with currency management
bid-ask spread
currency option premiums
overhead costs
opportunity cost
100% hedge forgo any possible favorable currency rate moves
<100% ex-ante dilemma
passive hedging
rule based and typically matches the portfolios currency exposure to that of the bak used to evaluate the portfolio’s performance.
require period rebalancing to maintain this match
goal is to eliminate currency risk relative to the benchmark
The following will shift the portfolio towards more passive currency management:
A short time horizon for portfolio objectives
High risk aversion
Lack of concern with regret at missing opportunities to add value through discretionary currency management
High short-term income and liquidity needs
Significant foreign currency bond exposure
Low hedging costs
Clients who doubt the benefits of discretionary management
discretionary hedging
allow the manager to deviate modestly from passive hedging by a specific percentage
goal to decrease currency risk while allowing the manager to pursue modest incremental currency returns relative to the bak.
active currency mgmt
allow manager to have greater deviation from bmk currency exposures
goal: to create incremental return (alpha) not to reduce risk
currency overlay
out sourcing of currency mgmt purely seeking currency alpha, not risk reduction
- . use outsources currency overlay manager to passively hedge their fx position
- for a active fund = separate the alpha and hedging mandate
- engage multiple currency overlay manager if the manager’s use different active mgmt strategy
factors shifts strategic decision formulation toward a benchmark neutral or fully hedged strategy are:
- short term investment objective of the portfolio
- high risk aversion
- client who’s concerned with the opportunity cost os missing positive currency return
- high st income and liquidity needs
- significant foreign currency bond exposure
- low hedging costs
- -clients who doubt the benefits of directional mgmt
active currency mgmt base on economic fundamentals
converge to fair value
real exchange rate = real ppp between 2 countries
LT equilibrium level for th real exchange rate is determined by PPP
ST: movement in real exchange rate reflect real int.rate diff
All else equal,
base currency’s real fx should appreciate if there’s an upward increase movement in :
1. long run equilibrium real fx
2. either its real/nominal int. rate which should attract foreign capital
3. expect foreign inflation, which should cause the foreign currency to depreciate
4. foreign risk premium, which should make foreign asset less attracted compare with the base currency nation’s domestics asset
technical analysis
market reflect future expectation
historical data incorporate all relevant information on future price movements and that such movements have a tendency to repeat.
- in a liquid freely traded market the historical price data can be helpful in projecting future price movement
- historical patterns have a tendency to repeat and provide profitable opportunities
- technical analysis does not attempt to determine where mkt prices should take but we’re they will trade
carry trade
= buying currencies selling at a forward discount
and sell currencies trading at a forward premium
currency with higher relative int rate tend to attract capital and appreciate in value
borrowing in low yield currencies and invest in high yield currencies
strangle
ohm call/put similar to straddle but less payoff
when relative currency increase
decrease the hedge (short position) or increase long position
relative currency depreciate
increase hedge or decrease long position in the currency
market condition stable
carry trade
market condition crisis
discontinue the carry trade
forward contract vs. futures
- futures are standardized, settlement dates and contract size may not be appropriate
- minor currency futures may not be available
- futures require initial margin and margin maintenance
- OCT forward are more liquid
static hedge with forward contract
avoid transaction cost, but will also end to accumulate unwanted currency exposure as the value of foreign currency asset change because market value of foreign currency assets will change with market conditions, create a mismatch between market value of foreign currency asset and the nominal forward contract.
solution: use dynamic hedging
purely currency risk
dynamic hedge with forward contract
require rebalancing periodically
increase transaction cost
roll-yield/return
> 0 ibIp
F/S-1
negative roll yield, increase hedging cost
do no hedge if negative
positive roll yield, decrease hedging cost
encourage hedging
reduce hedging cost
1. over-or under hedge with forward contract
base currency appreciate decrease hedge ratio
base currency depreciate increase hedge - positive convexity gain>loss low cost strategy
reduce hedging cost
2. buy ATM put option
highest initial cost but no opportunity cost
eliminate downside risk and return all upside potential
ATM option is relative expensive and has only time value, no intrinsic value
reduce hedging cost
3. buy oTM put option
reduce initial cost of hedging but does not eliminate all downside
offer loss downside protection limited to x of puts
reduce initial cost of hedging but does not eliminate all downside
reduce hedging cost
4. collar
further reduce initial cost but limit upside potential
some downside protection while decrease cost than ATM put
sale of OTM call removes some upside potential but generate premium
reduce hedging cost
5. put spread
decrease initial cost and reduce downside protection
buy OTM put in base currency
sell put that are further OTM
downside protection but if base currency fall below XL, protect is lost
decrease initial cost and reduce downside protection
reduce hedging cost
6. seagull spread
= buy call spread + Short OTM PUT
= buy XL sell XH + short OTM put
exotic option
knock-in-out feature
plan vanilla option that only comes into existence if underlying 1st reaches some prespecified level
disadv:
the stock price could rise to the level that causes the expiration of the knock-out, and then decline, resulting in unprotected losses.
exotic option
digital option
pay fixed amount that does not vary with diff. in price b/w x and underlying price
cross hedge - currency
occurs when a position in one asset is used to hedge the risk exposure of a different asset
moves the currency risk from one foreign currency to another foreign currency
likely most efficient for the emerging market currencies (to reduce transaction costs) but not necessary for widely traded currencies such as the USD, EUR, and GBP.
proxy hedge
removes the foreign currency risk by hedging it back to the investor’s domestic currency
macro hedge - for EM currencies
a type of cross hedge that address portfolio-wide risk factors rather than the risk of individual portfolio asset
uses a derivatives contract based on a fixed basket of currencies to modify currency exposure at a macro (portfolio) level.
minimum-variane hedge ratio
from regressing foreign market return in domestic currency vs. foreign currency value
riskier
determine the optimal cross hedge ratio
cov(Y,x)/var(x) = correlation(y,x) * (std(y)/std(x))
does not applied to direct hedge
used to jointly optimize over changes in value of rfx and rfc to minimize the std of rdc
strong positive correlation between Rfx and Rfx increase the volatility of Rdc
hedge ratio >0 reduce vol of rDC
Strong negative correlation between Rfx and Rfc decrease volatility of rdc hedge ratio <0 volatility decrease
BASIS RISK
Rdc=
a+b(%change in Sa/b)+ error
other unique challenges EM currencies/foreign exchange hedging face
- EM currencies are thinly traded, causing higher transaction costs
- underlying foreign currency asset in EM can be illiquid and lack derivative products
- increase likelihood of extreme market event and severe liquidity under stressed mkt condition
Em currencies return distributes are non-normal with higher probabilities of extreme events, negative skew of returns
higher yield of em currencies will lead to large forward discount (negative roll yield)
tail risk, gov’t intervention
non-deliverable forwards
cash settled “bet” on movement in the spot rate of these currencies
gov’t frequently restrict movement of their currency in/out of the control to settle normal derivative transaction
benefit:
lower credit risk only the gains to one party are paid at settlement
full repricing method
use of spot rates (zero coupon cubes)
most accurate measure of price changes in securities.
-require more data than duration based approach.
Risk involved in carry trade
- high yielding currencies are typically from high-risk countries
- in times of global financial crisis, there is a rapid movement from high-risk currencies to low-risk currencies, resulting in unwinding of carry trade.
- large-scale losses can be incurred quickly due to the large amount of leverage involved with a carry trade
hedge return ~=
rf + (id-if)
id-if >0 domestic currency depredate
cashless collar
buying a put and selling a call
buy low sell high
forward conversion option
buy put and sale a call with same strike and expiration date.
= synthetic short position.
the riskless position can be used as collateral for a loan at favorable terms, generating liquidity.
direct hedge
widely-traded currencies such as the USD, EUR, and GBP.
However, because the portfolio contains some emerging market currencies, those currencies are not likely to be efficiently hedged using direct hedges due to high transaction costs and the potential non-existence of an appropriate hedging contract.
hedging cost
trading costs
opportunity cost
speculative volatility trades
markets are stable:
net short volatility
when volatility increase
long volatility
hedger of volatility
net long volatility, long option as if they are paying insurance premium
buy protection from unanticipated price volatility
bear call
modest stock price decline is expected and there is very limited potential for a price increase.
equity swap risk
- return paid on equity index maybe more than the return earned on the stocks held, making a loss
- counterpart risk
