Conversion Arbitrage
by John Summa
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Table of Contents
1) Conversion Arbitrage: Introduction
2) Conversion Arbitrage: What Is It?
3) Conversion Arbitrage: How Does It Work?
4) Conversion Arbitrage: Forward Conversions
5) Conversion Arbitrage: Reverse Conversions
6) Conversion Arbitrage: Dividend Risk And Reward
7) Conversion Arbitrage: Interest Risk And Reward
8) Conversion Arbitrage: Other Risk Factors
9) Conversion Arbitrage: Conclusion
1) Conversion Arbitrage: Introduction
Conversion arbitrage does not typically find its way into books about options trading. It
is not surprising, given that the term alone would cause most eyes to glaze over. With a
little extra effort, however, this stock and options combination strategy should not be too
difficult to fully understand.
To help demystify conversion arbitrage, we begin with an uncomplicated model of
conversions, making some simplifying assumptions to get at the core concept. Later, as
we proceed through other sections of this tutorial, assumptions are dropped as more
complex relationships are introduced into the picture.
While understanding conversion arbitrage does not require an advanced degree in
finance or being a veteran market maker, it will require a basic understanding of put and
call options (both buying and selling), familiarity with stock buying/shorting and
knowledge of the stock dividend process. Conversions incorporate these elements, and
a few others, in their cost and profitability structures and in the dimension of risk
assessment, so you should brush up on them before getting started. (To learn more,
read Put-Call Parity And Arbitrage Opportunity, When To Short A Stock and How And
Why Do Companies Pay Dividends?)
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Market Efficiency, or Lack Thereof
When we speak of arbitrage of any kind, it is always associated with the idea of taking
advantage of some sort of marketplace mispricing - pricing that is out of line with
theoretical or fair value. The textbook story is one where the arbitrageur is supposed to
play the role of keeping prices efficient by seizing opportunities when prices deviate
from fair values, and thus driving them back to efficient levels.
In the options markets, it is the process of conversion and reverse conversion that helps
keep put and call prices efficient. If an arbitrage opportunity appears for the options
strategist seeking to lock in a potential profit using a conversion strategy, the purchase
and sale of conversions act ultimately to remove that opportunity for profit.
Conversions have a long history, which is usually associated with market makers or
floor traders who have a trading edge as a result of being on the trading floor, operating
with lower margin requirements and having much lower transaction costs.
These key advantages - plus earning interest on short sales in reverse conversions helped give this approach its reputation of not being for the retail guy. In today's more
level playing field for trading, however, conversion opportunities may be available for
any astute trader. (Arbitrage is no longer just for market makers; find out more in
Arbitrage Squeezes Profit From Market Efficiency.)
If prices are efficient, there is no way to extract a profit from conversion arbitrage above
the risk free rate of interest. You would be better off buying a Treasury bill or CD and
save yourself the trouble – not to mention the transaction costs.
As you will see, it is possible to find profitable conversions, especially when
incorporating dividend payments and interest earned on credit balances (for reverse
conversions). It is absolutely essential to fully understand exactly how to cost-price
these strategies before jumping into positions. Otherwise, you may ultimately make
money on the trade only to learn that you could have made just as much, or more, by
plunking your money down and buying a CD. Or worse, you may actually experience a
loss due to not properly understanding the hidden risks. (To learn more, read Don't Let
Stock Prices Fool You.)
With this in mind, the availability of efficient online trading tools, deep discount
commissions and new margin rules offer traders a better opportunity for finding
conversions providing potential profits above a CD rate or risk-free rate of
interest. Hopefully this tutorial will encourage you to further explore this approach.
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2) Conversion Arbitrage: What Is It?
Conversions involve combining three legs in a complex options strategy that can best
be understood in terms of the concept of time value spreading, which is explained
below. Typically, conversions are explained in terms of their cost (purchase price) for
establishing the position (stock price plus put price minus sale of call). Here we speak of
a forward conversion (reverse conversions are discussed below). Throughout this
tutorial, we will refer to forward conversions simply as conversions and reverse
conversions as reversals. The price paid for a conversion is the amount you pay to
establish the position, thus entailing a net cash outlay (debit to the trading account).
Locking in a Time-Premium Credit
A conversion is created by buying or holding a position in a company's stock, then
selling call options and buying put options at the same strike price and expiration date
as the call options. If this can be executed for a net time-premium credit on the call and
put options, you will have locked in a profit no matter where the stock trades before
expiration day. You can think of it as a synthetic short (same strike short call/long put)
hedged with a long stock position. (Learn more about arbitrage in Put-Call Parity And
Arbitrage Opportunity.)
While we are abstracting from some complicating factors, this simplistic model does
provide a way to grasp the basic idea in order to get started. Often the conversion idea
is presented in terms of the price of buying the options (debit cost) in relationship to the
strike of the options. If the cost (purchase price) is less than the strike price, then an
arbitrage profit is established. This amounts to the same thing as locking in a time-value
credit across the two options, as will be demonstrated in subsequent parts of this
tutorial. In the section of this tutorial specifically addressing conversions, some
examples are presented to make the idea of locked-in profit more tangible.
The related strategy of reverse conversions (reversals) involves exactly what the name
implies, the reverse of a conversion. Here the arbitrageur will be selling the stock short,
and then buying calls and selling same-strike, same-month calls. As with a conversion,
if this can be executed for a net time-premium credit between the call and put options,
there is a locked-in profit for the strategist no matter where the stock trades by options
expiration day. Again, we are abstracting from some complicating factors to be
addressed later.
Adding Dividends to the Story
As the reader will see, when moving to a more complex understanding of the
conversion and reversal, dividends can play a key role in determining potential profit
and loss, and while it is possible to remove or at least reduce the dividend risk from the
strategy, it will alter the profit potential.
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Additionally, the cost of carry is a feature of this strategy that will be incorporated as we
move closer to the full model without any oversimplifications. Cost of carry comes into
play in conversions, but not reversals. Reversals create a credit balance and are thus
free of a cost of carry (interest paid on debit balance). In fact, reversals are strategies
that allow for capturing interest payments on the cash proceeds of the short sales in the
reversal itself. These interest earnings are then factored into the equation for
determining ultimate profitability. (Learn more about interest rates in How Interest Rates
Affect The Stock Market.)
However, like dividend payments in conversions, there is no guarantee that interest
payments will remain fixed, thus opening a degree of potential risk to the reversal
arbitrageur. If the arbitrageur, however, is establishing conversions or reversals by
taking the proper steps regarding dividend risk and interest rate risk, it is possible to
minimize these potential pitfalls, as will be demonstrated in subsequent sections of this
tutorial. (To learn more, check out The Importance Of Dividends.)
Conclusion
Conversions involve locking in an arbitrage profit with a long stock purchase combined
with short sale of a call and purchase of a same-strike put with the same expiration
date. Reversals involve selling stock short, selling a put and purchasing a same-strike
call with the same expiration date. We've just gone over the general idea of conversions
and reversals. In the following segment, we look at the pricing structure of a conversion
and what makes it work as an arbitrage trade.
3) Conversion Arbitrage: How Does It Work?
In the previous section of this tutorial we saw that conversions and reversals are threelegged strategies combining stock and options positions. Still remaining with the
simplified model, the workings of the conversion strategy will be explained in more
detail.
Because a conversion trader buys stock, sells calls and buys same-strike puts (with the
same expiration dates), directional risk is removed from the equation. Actually, a
conversion is a long stock position combined with a synthetic short stock position, which
is created from the short sale of the call and purchase of a same-strike put. (Read more
in Short Selling Can Be Similar To Buying Long.)
Synthetic Short Stock Combined with Long Stock
As an example, if we constructed an at-the-money conversion, the deltas would be -50
(short call) and -50 (long put), or -100 deltas taken together, and would be exactly
opposite the long stock position of 100 shares. This offers a perfect hedge, as gains and
losses are offsetting. It is displayed in Table 1.
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As mentioned previously, if this can be executed for a net time-premium credit (extrinsic
value collected from selling the call is greater than the extrinsic value of the put), an
arbitrage profit is available. (Learn more about options strategies in Gamma-Delta
Neutral Option Spreads.)
Conversion Long Stock Short Call
Long Put
Stock Up
Loss
Gains
Loss
Stock
Loss
Gain
Gain
Down
Figure 1: Any long stock gains are offset by short
call/long put losses, leaving a net time-value credit
for the conversion arbitrageur. Meanwhile, any long
stock losses are offset by short call/long put gains,
but also leaving the same net time-value credit for
the arbitrageur.
Expiration Day Outcomes
Now we'll break this down for expiration day. If the stock traded higher by options
expiration day, the short call expires in the money (ITM) with zero time-value and the
put expires out of the money (OTM) (assuming the conversion was done using at- or inthe-money calls). The put time-value is lost and the call time-value becomes profit. The
difference between the two is the profit on the trade. The call gets exercised and the
stock is called away leaving the trader flat all legs, left with just his or her arbitrage
profit.
If the stock trades lower by expiration (again making the assumption of a conversion
done at the money) the call expires OTM with zero time-premium and the put expires
ITM (also with zero time-premium). The put is exercised and the stock is put to sellers of
the puts, leaving the trader flat, with the initial time-value credit turned into a profit. (Help
increase your success when trading options; read Stock Option Trading Cycles.)
Reversals
Regarding reversals, the same is true in terms of the net time-value (extrinsic value)
credit conditions outlined above. Recall that the reverse conversion involves selling the
stock short, selling puts and buying same-strike calls (with the same expiration date).
Here we have a synthetic long created with the short put/long call options, and this
perfectly hedges the short stock position.
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Reversal Short Stock Short Put
Long Call
Stock Up Loss
Gain
Gain
Stock
Gain
Loss
Loss
Down
Figure 2: Any short stock up losses are hedged by
the short put/long call gains, leaving a net time-value
credit for the conversion arbitrageur. Any short stock
down gains are offset by short put/long call losses,
leaving the same net time-value credit for the
conversion arbitrageur.
As displayed in Figure 2, if the stock trades lower by the time of the expiration of the
options, the short put expires ITM with zero time-premium, and is exercised thus
removing the short position. The call expires worthless, out of the money. Again, if the
reversal was established for a time-value credit (put extrinsic value > call extrinsic
value), this will leave a profit (assuming no commissions, as we do throughout this
tutorial) equal to the size of the time-value credit.
Finally, if the stock trades higher by expiration date of the options, the long call expires
in the money with zero time-value and is exercised, thus removing the short stock
positions. When you exercise a call you get a long stock position. Since you are already
short stock, this flattens out the short stock position. (Try a new approach to covered
calls, read An Alternative Covered Call: Adding a Leg.)
Summary
In this tutorial section, general outcomes for conversions and reversals were
summarized. For a conversion where you are long stock, we looked at the results of a
stock trading higher or lower by expiration. For reversals where you are short stock, we
walked through the same two scenarios. We explained that the resulting profit would
depend on the size of the time-value credit obtained in the initial setup of the strategies.
In the next section, we will begin working with an example of a conversion with actual
prices to demonstrate why this occurs.
4) Conversion Arbitrage: Forward Conversions
With a forward conversion (herein, referred to as a conversion), it is possible to achieve
a risk-free profit if same-strike calls and puts are priced out of line (defined here as time
value not equal). This means that a call can be sold and a put purchased at the same
strike and in the same month, but at different time values (call time value > put time
value). The different time values on the call and put options offer an opportunity to lock
in a profit by use of a conversion. Here we will look at an example to illustrate the point.
(To read more about time value, check out The Importance Of Time Value.)
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Let's take a look at a forward conversion on a stock we will call ABC. The inner
workings of the strategy will be revealed when we start working with some numbers.
However, we will keep the example simplified (leaving out dividends, interest and a few
other issues) until later.
Forward Conversion Example
Suppose ABC stock last traded at $73.95 with an ask price of $74.10. Meanwhile,
ABC's December 75 calls and puts were showing a bid and ask respectively of $4.95
(call) and $5.80 (put). At the bid/ask pricing of the options, a conversion could be
purchased for $74.95. Recall that there are two ways to assess whether a profit exists
at these prices. We will now walk through both.
First, the quickest way to look at the pricing is to ask if the purchase price for the
conversion, $74.95, is less than the strike price, $75. If it is, then a conversion profit
exists. If you fill it for 5 cents under the strike price, there would be a profit of $5 per
conversion. (Learn about other investing strategies in Profit On Any Price Change With
Long Straddles.)
Let's take a second look from our time-value perspective. Another way to think of this
conversion is to compare time value (extrinsic value) on the call and put options. Figure
3 provides a breakdown of the two types of value in options. There is both intrinsic and
extrinsic value in each option, the latter being the basis for potential arbitrage profit with
a conversion.
Option
Month
Option Option Option Intrinsic Time
Type Strike Price Value
Value
December Short
Call
75
4.95
(bid)
0
4.95
December Long
Put
75
5.80
(ask)
.90
4.90
Net
Time
$.05
Value=
Figure 3: ABC stock last traded at $73.95, with an
ask price of $74.10. The example above uses the
ask price for the purchase price of the stock. As can
be seen, this produces a 5 cent net time-value credit
per share, which translates into $5.00 per
conversion (buy 100 shares, sell Dec. 75 call and
buy Dec. 75 put).
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If the price of ABC stock at the expiration of December options is $100, the profit on the
position is $5.00. And if the price of the stock at expiration of the December options is
$50, the profit is still $5.00. This is presented in Figure 4. For example, at the price of
$100, the Dec. 75 call would lose $20.05, the Dec. 75 put would lose $5.80 (total loss of
$25.85), but the stock position would gain $25.90, leaving a 5 cent per share
gain. Figure 5, furthermore, presents the profit/loss payoff diagram of this conversion at
all prices, showing $5.00 in profit at any price. (Learn more in Stock Option Expiration
Cycles.)
Conversion Position Settlement Position Position
Legs
Entry
Prices @ Gain/Loss Gain/Loss
Price
100/50
@ 100
@ 50
Dec 75
Short Call
4.95
(sale)
25/0
-20.05
4.95
Dec 75
Long Put
5.80
(buy)
0/25
-5.80
19.20
100/50
25.90
-24.10
Long Stock 74.10
(buy)
74.95 <
$.05
$.05
75
($5.00)
($5.00)
Figure 4: Calculation of profit/loss with stock price at
$50 and $100. The table above shows the gains and
losses at the two assumed expiration prices for ABC
stock and the associated same outcomes for the
three legs of the conversion.
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Figure 5: Profit/loss diagram for ABC stock December 75 conversion
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Again, this outcome results from having an initial net time-premium credit (extrinsic
value collected from selling the call is greater than the extrinsic value on the put) that
amounts to an arbitrage profit.
In the ABC stock example, Table 5 shows an alternative calculation to determine
profitability of a conversion. The purchase price we know must be less than the strike
used in the conversion. But here, we see that the strike price plus call price minus the
stock price plus put price arrives at the same 5-cent per share profit. This is seen in
both the time-value based calculation and the purchase-price-greater-than-strike-price
calculation.
Conversion Profit Calculation
(Strike Price
+ Call Price)
(Stock
Price +
Put Price)
75 + 4.95 =
$79.95
Minus(-) 74.10 +
Profit=$0.05
5.80 =
$79.90
Figure 6: Conversion profit assumes carrying costs
and no dividend payment.
In the calculation in Figure 6, the conversion profit assumes no carry costs or dividend
payments. The reality of trading is not so simple and actual profitability includes such
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things as dividend payments (if any), interest paid on debit balances (carrying costs)
and any transaction costs (commissions/fees).
Conclusion
This section of the tutorial provided an example of a December 75 conversion on a
hypothetical stock, which was used to flesh out the bare bones approach with which we
began. By selling the December 75 call for more time premium, then spent on
purchasing the December same-strike put, a small arbitrage profit was secured, but
here we saw two additional calculation methods used to arrive at this same outcome.
Before relaxing key assumptions in our simple conversion story, let's take a closer look
at a reversal to examine its inner workings.
5) Conversion Arbitrage: Reverse Conversions
The related strategy of reverse conversions (or reversals) involves exactly what the
name implies, the reverse of a conversion. Here the arbitrageur will be selling (instead
of buying) the stock short, and then buying a call and selling a same-strike, same-month
put. (Read more about arbitrage in Trading The Odds With Arbitrage.)
As with a conversion, if this can be executed for a net time-premium credit between the
call sale and put purchase, you will have locked in a profit no matter where the stock
trades before expiration day. To remind you, at this level we are abstracting from some
complicating factors to provide a way to better grasp the basic idea.
Just as a conversion involves three legs in the strategy, so too does a reversal. The rule
of thumb for determining profitably applies with one minor alteration. Recall that
conversions can be explained in terms of the cost of establishing the positions (stock
price plus put price minus sale of call), which is a debit price. Here we look to compare
a credit price (received for the reversal) to the strike price used in the trade to look for
potential profitably.
When speaking of conversions, as long as the debit sale price is less than the strike
price, a conversion profit exists (leaving aside the complicating factors we will turn to in
subsequent sections). With a reversal, on the other hand, the same rule of thumb
applies but the credit received for establishing the position must be greater than the
strike price for a potential arbitrage profit to exist. (Learn more about options in Do
Option Sellers Have A Trading Edge?)
Using Reversals to Capture Time-Value Credit
Unlike the conversion, where you have to pay for the position with a net cash outlay, a
reversal involves selling short the stock and the put, which brings in a credit to the
account. Leaving aside the interest earnings potential on this credit balance for now, the
size of the credit must exceed the strike price for a reversal profit to be established. This
reduced form model should allow for grasping the core concept of the reversal without
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overwhelming you with complicating details.
While a reversal involves selling stock short and then buying a call and selling a samestrike and same- month put, it must be executed for a net time-premium credit. This is
simply stating, in a different way, that the overall pricing conditions (overall credit
received from sale of reversals > the strike price) need to lock in a profit. Above we
mentioned that the credit from the reversal must exceed the strike price, so we are
simply boiling all this down to show that it amounts to establishing a net time-value
credit between the put sold and call purchased.
Figure 7 shows some hypothetical prices (altered from our previous actual example) for
ABC stock to illustrate the idea of a December 75 reverse conversion's potential
arbitrage profit as a time-value credit.
Option
Month
Option Option Option Intrinsic Time
Type Strike Price Value
Value
December Long
Call
75
4.90
(ask)
0
4.90
December Short
Put
75
5.85
(bid)
.90
4.95
Reversal
Profit
Net
Time
$.05
Value=
Figure 7: ABC's stock has an assumed ask price of
$74.10 and options prices slightly altered to show
how a reversal would generate a small arbitrage
profit. The 5 cent net time-value credit translates into
$5 per reverse conversion, which requires selling
100 shares short at $74.10, selling a December 75
put at $5.85 and buying a December 75 call at
$4.90.
Often the reversal is presented in terms of the price of selling the stock (credit cost) in
relation to the strike of the options. If the credit received from selling it is greater than
the strike price, then the arbitrage profit is established, as seen in Figure 8, where the
position entry price shown is $75.05, which is greater than the strike of $75 by 5 cents.
For example, at the price of $25, the December 75 long call loses $4.90 and the
December 75 short put loses $19.15 (for a total loss of $24.05), but that is offset by a
gain of $24.10 on the short stock, leaving a per-share gain of 5 cents. As was seen in
Figure 7, we arrived at the same profit we saw above by showing how this is simply the
same as collecting a net time-premium (or extrinsic value) credit.
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Reversal Position Positions Position Position
Legs
Entry
Settlement Gain/Loss Gain/Loss
Price
Prices @ @ 100
@ 50
100/50
Dec 75
Long
Call
4.90
(buy)
25/0
20.10
-4.90
Dec 75
Short
Put
5.85
(sell)
0/25
5.85
-19.15
Short
Stock
74.10
(sell)
100/50
-25.9
24.10
75.05 (>
$.05 ($5) $.05 ($5)
75)
Figure 8: Here we demonstrate the same profit of $5
is available at any price for this reversal. We take
only two prices, however, to simulate the outcomes
(it would be true for any prices on the scale). We
calculate results based on an assumed stock price
of $50 and $100 for the stock at options expiration
day. The table above shows the same gains at the
two assumed expiration day prices for ABC stock.
Reversal Profit Calculation
(Stock Price
+ Put Price)
(Strike
Price - Call
Price)
74.10 + 5.85 = Minus(-) 75.00 +
Profit=$0.05
79.95
4.90 =
$79.90
Figure 9: Reversal arbitrage profit in this model
assumes no carrying costs and no dividend paid or
received. Here you can see that the position
establishes a $5 arbitrage profit as was
demonstrated in the other calculation methods
shown in Figure 7 and Figure 8.
As the reader will see, when moving to a more complex understanding of a conversion
and reversal, dividends can play a key role in determining potential profit and loss.
While it is possible to reduce the dividend risk from the strategy through the proper
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assessment of trades, it will remain a potential risk.
Additionally, the cost of carry is a feature of this strategy that will be incorporated as we
move through the different parts. It comes into play in the conversion but not the
reversals. Reversals create a credit balance and are thus free of a cost of carry (defined
as the interest paid on a debit balance).
In fact, reversals are strategies than allow for capturing interest payments on the cash
proceeds of the short sale (put plus short stock) in the reversal itself. These interest
earnings are then factored into the equation for determining ultimate profitability.
However, like with dividend payments in conversions, there is no guarantee that these
variables will remain fixed once in a conversion or reversal, thus opening a window of
risk to the arbitrageur. (Learn more in Using Options Instead of Equity.)
Conclusion
Reversals on stocks involve selling the shares short, selling a put and buying a samestrike call with the same expiration dates. Here we demonstrated how such a strategy
could make a profit if the sale price of the reversal is above the strike price used. When
this condition is met, there is a locked in time-value credit that represents an arbitrage
profit. However, we are still excluding the possibility of dividends in the equation, a
subject to which we now turn.
6) Conversion Arbitrage: Dividend Risk And Reward
Up to this point we have been concerned with a simplified conversion model, where
there are no carrying costs, interest earnings on credit balances, dividend payments or
payouts to be concerned with as an arbitrageur. Now we will begin to relax some of
these assumptions. While not all stocks a conversion arbitrageur is following will pay
dividends, those that do can substantially alter the equation. For the conversion
arbitrageur this can potentially be a source of additional profit, but with it comes some
associated risk. (Find out more about the risk/reward payoff in Naked Options Expose
You To Risk.)
When dividends become part of the equation, the dividend payment can be earned by
the arbitrageur because he or she is long in the stock. Provided that the ex-dividend
date (ex-date) for the stock is between entry date and expiration date of the conversion,
it is possible to add to any conversion profit that has been locked in by the amount of
the dividend to be paid. Like most things, more profit means more risk and often the
option pricing for a conversion contains the expected dividend payment, or part thereof,
and there is no guarantee that a dividend is going to be paid. (Find out more in How
Dividends Work For Investors.)
Let's not get ahead of ourselves. First, let's add dividend payments into the conversion
profit equation so that is clearly understood.
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Figure 10 contains the profit calculation for a conversion with dividend payment. As
shown, using the April 100 ABC stock conversion (the April options are used here
because the expiration date must be later than the ex-dividend date in order to capture
the dividend). ABC stock is scheduled to pay a dividend of 40 cents in March
2009. Therefore, the conversion price actual cost is reduced by this amount. Suppose
we have a price of $101.08 for the April conversion.
April 100 Conversion Profit Calculation w/
Dividend and no Carry Costs
(Conversion Price Dividend)
Profit=$0.32
$101.08 - $.40 =
$99.68
Figure 10: Conversion profit assumes no transaction
or carrying costs but now includes a dividend
payment of $.40 per share on ABC stock. Here April
100 '09 strikes are used.
This price is eight cents above the strike price. Therefore, the conversion itself is not
profitable because the purchase price $101.08 is greater than the strike price, as we
demonstrated in the previous sections on conversion profitability determination. But
when we factor in the receipt of a dividend payment of 40 cents, the cost drops to
$99.68, leaving room for a profit of 32 cents per share or $32 for each conversion. This
looks great provided that the dividend is not canceled or lowered. (Learn more in Is
Your Dividend At Risk?)
Leaving aside carrying costs, the conversion could not lose provided that the dividend is
not cut by more than $32. Recall that it is possible for a surprise dividend cut to be
announced or, on the plus side, a dividend increase, which would add to the potential
profitability of the conversion.
Reversals and Dividends
When doing reversals, it should be made clear that the short stock position in the trade
means that the strategy carries dividend risk. If you are short stock going into an exdividend date, the reversal strategist will need to pay the dividend, not earn it.
(Understanding the dates of the dividend payout process can be tricky. We clear up the
confusion in Dissecting Declarations, Ex-Dividends And Record Dates.)
Therefore, when pricing reversals it is important to factor that payment into the equation,
or to avoid dividend-paying stocks to sideline that risk factor in the pricing. The reversal
strategist brings in a credit balance with the sale of the put and stock short sale.
Therefore, interest is earned on this balance. We take up this aspect in the following
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section, along with the interest costs for conversions.
Summary
In this part of the conversion tutorial, the simple model of a conversion with no dividends
was relaxed. While dividends ultimately lower the cost of the conversion, they carry with
them potential risk. For reversals there is dividend liability, but interest earnings on short
sale proceeds help offset that cost. Profit that essentially amounts to a dividend capture
can be realized with a conversion strategy, although not without certain risks.
7) Conversion Arbitrage: Interest Risk And Reward
In the previous section, the concept of dividend payout was introduced. Now we take
another step closer toward reality by introducing additional elements of reward and risk:
interest rates and cost of carry. Recall from the previous part of this tutorial that there
was a dividend profit potential of $32 in the April 100 conversion (see Table 10).
Note that on its own, the conversion itself is not profitable because the purchase price
$101.08 is greater than the strike price, as we demonstrated in the previous sections on
conversion profitability determination. But when we factor in the receipt of a dividend
payment of 40 cents, the cost drops to $99.68, leaving room for a profit of 32 cents per
share or $32 for each conversion. This looks great provided that the dividend is not
canceled or lowered. But what about a change in carry costs?
Suppose now that there are carry costs of 0.48 % (just under one half of one percent
annually). This position would cost $21 in interest charged to hold open with a debit
balance for the 158 days of life to the options. (To learn about minimizing carry costs,
read Don't Let Brokerage Fees Undermine Your Returns.)
April 100 Conversion Profit Calculation w/
Dividend and No Carry Costs
(Conversion Price Dividend)
Profit=$0.32 per share
(or $32)
$101.08 - $.40 = $99.68
Figure 11: Conversion profit assumes no carrying
costs but now includes a dividend payment of 40
cents per share on ABC stock. Here April 100 '09
strikes are used.
In Figure 12, this would leave just 11 cents per share of conversion/dividend profits, or
$11 per conversion. The debit balance is $101.08 x 100 = $10,108, to which is applied
the cost of carry charge ($10,108 x .0048/360 x 158 days in the trade = $21).
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April 100 Conversion Profit Calculation w/
Dividend Minus Carry Costs
(Conversion Price Dividend)
Profit=$0.11
$101.08 + $21 - $.40 =
$99.89
Figure 12: Conversion profit assumes total carrying
costs of $21 and includes a dividend payment of 40
cents per share on ABC stock. Here April 100 '09
strikes are used.
Conversion
Outcomes
Dividends
Interest
Profit
Profitable
$33 earned
$23 paid
$10
Breakeven
$23 earned
$23 paid
$00
Loss
$23 earned $33 paid
-$10
Figure 13: Three scenarios are presented for the
conversion strategist. Profitable, breakeven and
loss, which depend on dividend costs and interest
rates paid on credit balances. Here we assume that
the credit balance is equal to the strike price of the
reversal. Therefore, there is no arbitrage profit per
se, simply a potential profit that the dividend
generated over interest charged.
In this scenario, carry costs could increase or dividends could be cut or eliminated, thus
eliminating this small profit or both could occur at the same time. Figure 13 shows the
effects of changes in these two variables on a conversion. In Figure 13, a conversion
profit of $10 goes to zero and then to a loss of $10 when dividends are cut by $10 to
$23 from $33 (breakeven) followed by a $10 rise in cost of carry, leaving an overall loss
for the position.
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Reversal
Outcomes
Dividends
Interest
Profit
Profitable
$23 paid
$33 earned $10
Breakeven
$33 paid
$33 earned $00
Loss
$33 paid
$23 earned -$10
Figure 14: Three scenarios are presented for the
reversal strategist. Profitable, breakeven and loss,
which depend on dividend costs and interest rates
paid on credit balances. Here we assume that the
credit balance is equal to the strike price. Therefore,
there is no arbitrage profit per se, simply a potential
profit from interest earned over the dividend paid.
Reversal, Dividend Risk and Interest Earnings
Reversals have potential profit arising from interest earnings on credit balances, which
are above any locked-in arbitrage profit on the three-leg strategy. Taking a look at Table
13, here we see that a dividend to be paid by the reversal strategist during the life of the
strategy is first $23, with interest earned on the credit balance $33, leaving a profit of
$10 per reversal. If the dividend is increased while in the trade, the dividend cost rises,
resulting in a change of$10 (from $23 to $33), thus erasing the potential for a profit on
this trade. Finally, in the third scenario, the dividend is increased and the earned interest
on credit balances falls by $10 to $23 from $33 (this could result from changes in
market conditions that fluctuate over time), leaving the strategist with a loss of $10
overall. (Read Managing Interest Rate Risk to find out more.)
Currently, we are leaving out compound interest calculations, which at high interest rate
levels might make a material difference. We are also assuming that there are no
transaction costs. Given the rates earned on interest are known for the day, and the
dividend cost is available to the strategist on that day, it is possible to know if the
reversal is making money on any given day. Obviously, if a surprise dividend increase
occurs during the life of the trade, it will most likely turn the trade into a loss. The
interest earned will not be sufficient to cover the dividend costs. On the other hand, a
surprise dividend cut would add profit to the position, as would rising rates.
Basically, the interest potential is a source of profit and the dividend payment is the
cost. Depending on how much interest can be earned on the credit balances (depends
on prevailing rates and strategist status), it is possible to establish a reversal that is
known to be earning a profit each day. We will return to the issue of credit balances and
interest earned in the following section covering issues related to interest costs and
profits. (Discover the issues that complicate dividend payouts, read Dividend Facts You
May Not Know.)
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Summary
Interest rates impact both carry costs and earnings on credit balances, two important
factors in conversions and reversals, respectively. We have just looked at their potential
to impact profitability in both strategies, showing that a rise in carry costs will reduce a
conversion profit and improve performance of a reversal. Meanwhile, a fall in interest
rates will have the opposite impact, when other things remain the same (ceteris
paribus).
8) Conversion Arbitrage: Other Risk Factors
While called arbitrage, conversions should not be construed as trades that never have
any risk. Nevertheless, after identifying some major risk factors, we will present here
some important steps toward reducing or even eliminating these factors. (Just because
you're willing to accept a risk, doesn't mean you always should; check out Risk
Tolerance Only Tells Half The Story to find out why.)
Assuming that a conversion strategist is able to lock in a small profit from buying the
conversion (i.e, debit price is less than strike price), and that a reversal strategist is able
to secure an arbitrage profit from sale of a reversal (i.e., credit price is greater than the
strike price), we can now isolate the potential risks to this so-called arbitrage profit.
Dividends
As we saw in part 6 of this tutorial, dividends are a source of potential profit for the
conversion strategist and a cost for the reversal strategist. Since dividends are never
guaranteed (they can be cut or increased by company decision), the strategist cannot
control this risk factor unless a policy of avoiding dividend paying stocks is adopted.
Obviously, by not applying conversions and reversals to dividend-paying stocks, there is
no risk for the conversion strategist. However, if a company announces it will begin
paying a dividend and the declared dividend date falls before the reversal expires, the
reversal strategist is going to have costs rise, and if these costs are greater than the
initial arbitrage profit, this will result in a loss(unless interest is enough to offset that
cost).
Dividends are a great source of potential profit for the conversion strategist, so it may
make sense to do the proper research on dividend-paying stocks and try to capture that
dividend payment in addition to any pure conversion profit. If risk is diversified and
proper research is conducted, it may be possible to enhance potential gains well
beyond the simple conversion arbitrage profit level in exchange for taking on dividend
risk. However, keep in mind that conversion strategists earn more if a surprise dividend
increase is declared. (Learn more in Dividends, Interest Rates And Their Effect On
Stock Options.)
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Early Assignments
If there is an early assignment, resulting in the long stock position in a conversion being
removed, no dividend will be earned and a conversion strategy dependent on earning
that dividend may experience a loss. If the conversion was put on at exactly break even
(strike price = debit charge to buy conversion), then the loss will be equal to the carry
costs, which could be significant depending on when the early exercise occurs. If the
conversion was established with enough profit to cover carry costs to term then there
would be no loss (ignoring commissions, which we've done throughout this
tutorial). There is also the issue of the left-over long put, which might have a little time
premium left. If the long put is left open, it does have the potential to gain more value, or
it could be liquidated to lock in what little value is left on it once the early assignment
takes place. (Get more info in Profiting From Stock Declines: Bear Put Spread Vs. Long
Put.)
One way to minimize this risk is to establish conversions that have substantial time
value on the short call, which can be done by using options that expire well past the exdividend date (ex-date). But here, of course, there is a trade off because the longer you
remain in the position past the ex-date, the larger your cost of carry. However, it may be
possible to close the conversion following the ex-date and take a profit at that point, or
hold the position open past another ex-date. If the call options are trading below parity
before ex- date, there is a good chance they will be exercised. Any time value on the
option (meaning it is above parity) when the stock goes ex-dividend, on the other hand,
will likely prevent it from being exercised. (Find out how to keep your dividends out of
the tax man's hands. Read Make Ex-Dividends Work For You.)
Reversals suffer from early assignment as well. Here, the short puts would be assigned
thus removing short stock, credit balances and interest being earned daily. Depending
on whether the position was established with a dependence on interest earnings for a
profit, it could experience a loss, especially if a dividend risk was already incurred. If the
interest earned was a substantial portion of the targeted profit, covering dividend fixed
costs, then an early assignment might turn the trade into a loser. There is a left-over
long call, which might gain value if held until expiration, one offsetting factor, if not
closed.
Carry Costs
We explored the subject of carry costs in the previous part of this tutorial. For
conversion strategists, this takes the form of interest charged on debit balances, and
this cost is not fixed. Each day, there are changes in market rates of interest and the
benchmark rates used to compute a broker's carry charge for a conversion debit
balance. Therefore, the conversion strategist has little control over this variable. (Learn
which tools you need to manage the risk that comes with changing rates, read Manage
Interest Rate Risk.)
Obviously, it's a good idea to allow room for carry rate increases in order to achieve an
arbitrage profit. You may want to take on some dividend risk to buffer against expected
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rate increases when setting up a conversion. Here you might be adding dividend
reduction or elimination risk, but if that seems less likely than a rate increase for your
carry costs (usually these are tied to Fed funds rate), then this might make sense. Some
strategist might hedge rising rates risk by shorting financial instruments that fluctuate
with the Fed funds market to lock in a carry cost for the life of the trade. Meanwhile, the
reversal strategist is not subject to carry costs and therefore avoids this risk.
Interest Rates
There are no carry costs for reversal strategists. Instead, in their profit calculations,
reversal strategists depend on the interest paid on credit balances. The best way to
minimize this risk is to minimize the dependence on interest earned for the profitability
of the strategy. If interest earned falls, it will reduce profit, but may not eliminate it.
Another approach might be to invest (assuming you have that option) in interest-bearing
instruments like CDs or Treasuries to lock in a rate on the credit balances, instead of
letting them fluctuate throughout the life of the trade. Alternatively, if rates are expected
to move higher over the life of the trade, it would be advantageous to not lock in a rate
on interest earned on credit balances, so that with a rise in interest rates there would be
additional profit potential on credit balances.
Expiration Day
One last issue is the expiration day level of prices for the stock position, in either a
conversion or reversal. If the price is well above the short call in the conversion, it is not
an issue as the call is deep in the money (ITM) and will be automatically exercised, thus
taking away the long stock position. Meanwhile, the long put expires out of the money
(OTM). This is also not an issue if the call is out of the money and the put in the money.
The put will be exercised and this removes the stock position. All is fine as long as you
know one side will be in the money at expiration. (Learn more in Stock Option Expiration
Cycles.)
9) Conversion Arbitrage: Conclusion
As we have seen, conversions and reversals involve combining three legs in complex
options combination strategy aimed at establishing an arbitrage profit. We have
demonstrated that at a stripped-down level of the options, it is simply a way to lock in a
net time-value credit.
In practice, this is a positive theta (time-value decay rate) trade where time-value decay
works in our favor, as the options premium declines to zero at expiration. As long as we
are not net buyers of time premium, with a conversion or reversal, we can have our
profit, at least in the simplified model used in the tutorial. (To learn more about
arbitrage, check out Trading The Odds With Arbitrage.)
The simple model we initially worked with abstracted from carry costs and other cost
and risk factors so we could isolate the core idea. Once that was done, we moved to
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adding in additional variables, namely dividends, interest rates and cost of carry. Here
we saw that we need to pay special attention to the carry rates of interest, as well as
dividends that might be paid (for conversions) or charged (for reversals) to our trading
account.
Conversions are a buying strategy and reversals are a selling strategy, which creates
some interesting differences not apparent on the surface. Reversals, we showed, have
potential to earn interest on their credit balances. Conversions, meanwhile, provide a
way to capture dividends, and this too can be a sizable portion of potential profitability.
Both, of course, are not risk free and may turn arbitrage profits into losses.
Last, we looked at various risk factors that both conversions and reversals carry with
them, and as a result saw that the simple model can get quite complex in terms of
different determinants of the outcomes to these combination strategies. (Read more in
Do Option Sellers Have A Trading Edge?)
For conversions, the key risks include: surprise cuts to or elimination of dividends,
interest rate increases, early exercise and strike price proximity to the underlying on
expiration day. Key reversal risks include: surprise dividend increases or declarations of
a dividend to be paid on a stock not paying a dividend, interest rate decreases, early
exercise and proximity of the underlying to the strike price of the reversal on expiration
day. (Check out Going Long On Calls to learn how to buy calls and then sell or exercise
them to earn a profit.)
While an entire book could be written on this topic, the core concept of a conversion and
reversal can be grasped with this tutorial. For additional reading on the topic, one might
wish to read Larry McMillan's Options As A Strategic Investment, which provides
discussion on the topic of conversions and related strategies.
Keep in mind that this approach to trading options requires attention to a number of
variables and is not a guarantee of profit. Even with an arbitrage profit on the position, it
is possible to lose money with these trades. Yet with responsible management of the
strategy, and putting in the time to do proper research, these risks can be minimized
and made manageable.
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