Conversion Arbitrage: Interest Risk And Reward
By John Summa
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 Figure 11).
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).
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.
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 lockedin arbitrage profit on the threeleg strategy. Taking a look at Figure 14, 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.)
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).

Derivative
A security with a price that is dependent upon or derived from ... 
Security
A financial instrument that represents an ownership position ... 
Series 6
A securities license entitling the holder to register as a limited ... 
Internal Rate Of Return  IRR
A metric used in capital budgeting measuring the profitability ... 
Board Of Directors  B Of D
A group of individuals that are elected as, or elected to act ... 
Strike Width
The difference between the strike price of an option and the ...

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