Bill Johnson, Director of Education
at Options University
Ask Bill Your Question
|
Q: Could
you please explain more on "locked" option trades such
as box spreads?
A:
Generally
speaking, any time you hear the term “locked trade”
in
options, it is referring to a trade that has no risk. However, to be
thorough
in our answer, we really need to divide locked trades into two groups.
One group
contains true locked trades that have no risk. The other group has no
“theoretical”
risk and should really be considered “risk
arbitrage” or “pseudo arbitrage.” So
you must be careful of your interpretation of any strategy that is
lumped into
the nonspecific category of “locked” trades because
they may not be locked in
the truest sense of the word.
The box spread
belongs in the first group and is a true locked trade. The box spread
is made
up of a long call + short put at one strike and a long put + short call
at
another strike. All options have the same expiration date. For example,
if you
buy a $50 call and sell a $50 put and then buy a $55 put and sell a $55
call
you have entered a box spread.
To understand why
it is a locked trade, it’s best to break the trades down into
synthetic parts.
The long $50 call + short $50 put is a synthetic long stock position. A
synthetic position is one that behaves exactly like another in terms of
the
profit and loss profile. So if one trader buys the underlying stock for
$50
while another buys the $50 call and sell the $50 put then both have
effectively
done the same thing. On the flip side, if a trader buys the $55 put and
sells
the $55 call then he has entered a synthetic short stock position.
The box spread,
synthetically, is nothing more than a long stock position matched with
a short
stock position. If you are long and short the same stock, your account
value
will not change in any way regardless of the price of the underlying
stock.
Every dollar the stock rises for the long position will be exactly
offset by a
dollar loss in the short position and vice versa. Prior to computers,
brokers
had to manually calculate risks in customers’ accounts. To
make it easier, they
would draw a “box” around any long and short
position of the same underlying
since there was no risk. This was a way of eliminating the unnecessary
components
of risk in the account. For the same reason, the
“box” spread has no risk.
What is the above
box spread worth? If you have synthetically purchased stock for $50 and
effectively sold it for $55, then the box spread is guaranteed to be
worth $5.
If it is guaranteed, its value today must be the present value of $5.
To make
the calculation easy, if interest rates are 5% and you have a one-year
box, it
is worth $5/1.05 = $4.76 today. If you pay $4.76 for the box, it is
guaranteed
to grow to a value of $5 and you have earned exactly the risk free rate
which
is what you should earn for a position that has no risk. It is possible
for the
trader to earn more than $5 if he is assigned early on one of the short
positions but he will never earn less.
On the other hand,
we can enter another “locked” trade called a
reversal. A reversal consists of
short stock + long call + short put with the options having the same
strike
prices. Synthetically, the options make up a long stock position so,
again,
this appears to be a short stock position matched with a long stock
position so
should have no risk as well. However, during unusual circumstances, the
trader
may have to exit his short stock position during early thus exposing
him to
risk. So while this locked trade has no risk on paper, it certainly
does have
risk in the real world and is therefore a risk-arbitrage (or
pseudo-arbitrage).
Locked trades are
ways for the market makers to borrow or lend money to the market. They
are one
of the many ways to show that, despite their risky assumed nature,
options can
create risk-free positions. It all depends on how they are used.
Q: I
have a trading question that nobody could answer for me. My question
is about the collar (ATM Collar). Here is an example. Today,
2/28/07
,
the DIA is trading
at exactly 123. If I buy 100 shares of DIA and buy May 123 put for 2.70
and
sell May 123 call for 3.40, do I automatically lock in a profit of .70
at
expiration no matter what the price of the DIA will be? I really
appreciate
your answer. Thank you.
A: Yes,
you are correct that you would lock in the guaranteed 70-cent
profit by purchasing the stock, selling the call, and buying the put.
However,
before you get too excited about risk-free money, you must measure that
return
against other risk-free alternatives.
The
May options expire on
5/18/07
, which
is 79 days away from the
2/28/07
posting
date of
your question. Let’s find out what interest rate is necessary
to match the
70-cent return and then compare that rate to current market rates. If
you
invest $123 for 79 days, it would take an interest rate of about 2.6%
to yield
70 cents interest. We can find that by solving for i (interest rate) in
the
following equation: $123 * i * 79/360 = 0.70. If you solve for i,
you’ll find
that it is 2.59%.
Rather
than buy the DIA collar, the above equation shows that you
could, instead, take your $123 and place it in a money market for 79
days and
get the same guaranteed 70-cent return if your broker pays an interest
rate of
2.6%. With the Fed funds rate at 5.25%. I suspect that most brokerage
firms are
paying far more than 2.6%. However, even if they are, we must account
for
commissions. There is no cost for putting money in the money market but
there
are THREE commissions for the collar trade you referred to.
If
your broker charged you $1 for each of the three trades, you will have
effectively invested $126 to gain the 70 cents interest. If you solve
the
earlier equation by substituting $126 for $123, you’ll find
that the required
interest rate is now 0.25%, or one quarter of one percent. Because most
brokers
would definitely charge more than $3 for the above trades,
it’s safe to say
that you are better off in the money market.
Many
new traders think that risk-free trades in the options market are a
source of
“free money” but you must remember that the market
prices all assets according
to risk. If the trade is risk-free, you’re going to earn the
risk-free rate.
However, to accomplish this using the collar, you must pay three
commissions
and three bid-ask spreads and that’s why the resulting
interest rate is so low
thus making the money market alternative more attractive.
For
those who may be wondering why the collar is risk-free, it’s
easy to see if you
break it down into the resulting rights and obligations created by the
options.
To create a collar, the trader buys the shares, sells the call (has the
obligation to sell shares), and buys the put with the same strike (has
the
right to sell shares). In this example, if DIA is above $123 at
expiration, the
investor will be assigned on the short call and receive $123 cash. If
DIA is
below $123 at expiration, the trader will exercise the put and receive
$123
cash. No matter what happens to the price of DIA, the trader is
guaranteed to
receive $123 at expiration. Alternatively, the trader could place an
amount of
money into the money market and also be guaranteed to receive $123 at
expiration. In this example, the trader receives a net credit of 70
cents for
the collar so has effectively deposited $123 – 0.70 = $122.30
and will receive
$123 at expiration, which is synonymous with an interest rate of 2.6%. |
