Vertical Spreads and Implied Volatility

One will commonly hear or read the following “rule of thumb” for options spread trading:

When implied volatility is high, sell credit spreads and when implied volatility is low, buy debit spreads.

Unfortunately, this is simply not true. The credit spread and its corresponding debit spread at the same strike prices will always have virtually identical returns on investment (ROI). This paper addresses the role of implied volatility in the vertical spread, both at initiation and over the course of the trade.

Background

Vertical spreads derive their name from the wall originally used to display option prices when they were first traded in Chicago many years ago. The months of expiration were displayed horizontally across the top of the board and the strike prices were displayed vertically along the left edge. Thus, spread trades using two options at two different strike prices in the same expiration month were in the same column and thus constituted a vertical spread. This includes bull call, bear call, bull put, and bear put spreads.

Similarly, horizontal spreads are created by buying and selling options from the same row – different months of expiration, but with the same strike price. Horizontal spreads are also known as calendar spreads or time spreads.

Diagonal spreads are created when different strike prices and different expiration months are used – thus, a diagonal line across the board between the option sold and the option purchased. An example would be buying the September $300 GOOG call and selling the July $320 GOOG call to create a diagonal bull call spread.

Vertical spreads either require a net investment to initiate (a debit spread) or we initially receive money into our account (a credit spread). For this reason, it is common terminology for us to say we are “buying a call spread” when establishing a debit spread and “selling a call spread” to refer to initiating a credit spread. Bull call spreads are created by buying a call and selling another call at a higher strike, or farther OTM (a debit spread). A bear call spread is created by buying a call and selling a lower strike price call, or farther ITM (a credit spread). Similarly, a bear put spread is established by buying a put and selling the lower strike price put that is farther OTM (a debit spread). And a bull put spread consists of buying a put and selling another put at a higher strike price, farther ITM (a credit spread).  

Credit or Debit?

There are many decisions made before we put on a trade, but for this discussion we will assume that a vertical spread strategy has been chosen as the optimal trading strategy for this situation. The next decision is whether to use a credit or a debit spread.  The maximum potential gain for the vertical spread, all variables held constant except the choice of calls or puts, will be indifferent to whether the trade is established as a credit or debit spread. For example:

GOOG closed at $310.71 on October 5, 2005.  If one were bullish on this stock, one could place an Oct $310/$320 bull call spread for a debit of $430 ($960 - $530) and a maximum potential gain of 133%, assuming expiration with GOOG trading above $320.

Similarly, one could place an Oct $310/$320 bull put spread for a credit of $560 ($1400 - $840) and a maximum potential gain of 127%, assuming expiration with GOOG above $320.

The small difference between the two returns is insignificant; we are using the closing bid and ask prices for these options, and the option prices are very fluid, so picking prices at any arbitrary point and getting exactly identical results would be unusual.  The conclusion is that any difference in returns between a credit and debit spread for the same underlying stock, strike prices, and expiration month will be small and temporary, because market forces will quickly adjust them to parity.

It is commonly taught that one should establish a credit spread when placing a trade with high implied volatility (IV) options and a debit spread with low IV options. But the previous example illustrated identical returns for the credit and debit spreads.  So, in that example, we would be indifferent to placing a debit or a credit spread. But let’s take it a step further.

We will use the Black-Scholes model to compute the theoretical prices of the GOOG $310 and $320 options from the previous example, but with IV boosted up to 60% (the actual IV values in the above example ranged from 33% to 34%). Now the spread values become:

The Oct $310/$320 bull call spread could be placed for a debit of $436 ($1613 - $1177) and a maximum potential gain of 129%, assuming expiration with GOOG above $320.

Similarly, the Oct $310/$320 bull put spread could be placed for a credit of $563 ($2058 - $1495) and a maximum potential gain of 129%, assuming expiration with GOOG above $320.

Thus, if we were considering placing a bullish vertical spread on Google, the returns would be virtually identical whether the IV was 34% or 60%, or whether we used a credit or debit vertical spread. The higher IV value increased the individual option values dramatically, but the spread values were unchanged. Higher IV does result in higher option prices, but in a spread, we are both buying and selling that high value.

I also computed these option values with IV adjusted to 20%. As we see below, at this very low IV, the returns for the credit and debit spread were still identical so there would be no advantage to placing the debit spread for this low IV stock as some have taught.

The Oct $310/$320 bull call spread could be placed for a debit of $381 ($580 - $199) and a maximum potential gain of 162%, assuming expiration with GOOG above $320.

Similarly, the Oct $310/$320 bull put spread could be placed for a credit of $623 ($1084 - $461) and a maximum potential gain of 165%, assuming expiration with GOOG above $320.

However, the returns for both spreads at IV of 20% are higher than we saw with the other examples with volatilities of 34% and 60%.  This is consistent with the overall financial laws of balancing risk and return, i.e., higher returns always carry higher risk. This example has us placing a bullish spread on a stock currently priced near the bottom edge of the price spread; the stock price must make a significant price move of over $9 before expiration for the spread to achieve maximum profitability.  However, the low implied volatility tells us the probability of a significant price move is low.  Therefore, the returns will be higher, commensurate with the lower probability of success, and therefore, a higher risk of loss.

These examples illustrate two important conclusions:

•    The returns for a credit spread and a debit spread placed at the same strike prices for the same equity or index will be identical. Any price differences seen in the marketplace will be transient, as arbitrage will quickly bring the prices back to parity.

•    The level of implied volatility (IV) is not a consideration when placing a vertical spread and deciding on a credit or debit spread. High IV does increase the individual option prices, but we are both selling and buying option premium in a spread, so the returns for the credit and debit spreads remain identical.

Changes in IV During the Trade

The maximum profitability of a vertical spread, once placed, cannot change due to changes in implied volatility after the trade was initiated.  The initial investment and the width of the spread are fixed; therefore, the maximum potential return is fixed.  This is equally true for both credit and debit vertical spreads.

However, the time decay curves of the spreads are affected by changes in implied volatility.  The value of the spread varies with time to expiration, implied volatility, and the price of the underlying stock.  Of course, interest rates and dividends will also affect spread values, but these will be less significant effects. Experienced spread traders know that even though the underlying stock price may have moved as predicted above or below the spread strike prices, the spread cannot be closed for a value close to the maximum theoretical profit until close to expiration. The value of the spread will gradually approach the maximum profit as the time value of the options decays away.

Increasing implied volatility (IV) during the trade results in the time decay curves being flattened so that the value of the spread approaches the ultimate value at expiration more slowly.  Therefore, the probability of closing the trade early for a majority of the maximum profit is reduced. We won’t illustrate it here, but the flattening effect on the time decay curves due to increasing IV during the life of the trade is identical for credit and debit vertical spreads.  Therefore, if one is expecting a large IV increase, such as in advance of an earnings announcement, there is no inherent advantage to either a credit or a debit spread.  But one should expect to have to carry the trade closer to expiration to achieve a majority of the potential profit if IV increases.

Vertical spreads have an inherent advantage over long or short option positions in that the ultimate profitability of the vertical spread is unaffected by IV changes while we are in the trade.  By contrast, if we buy a call option in anticipation of a positive earnings announcement, we may be disappointed in the results. Most likely, IV will decrease dramatically following the announcement, and this will drive down the value of our call option. This negative effect may be of equal or greater magnitude than the positive effect on our call option due to the increased stock price.

Decreasing implied volatility (IV) during a vertical spread trade results in the time decay curves spreading out so the value of the spread approaches the ultimate value at expiration more quickly. This effect on the time decay curves due to decreasing IV during the life of the trade is identical for credit and debit vertical spreads. The maximum profit available hasn’t changed, but the prospect of closing the trade early for a large portion of that maximum profit is now more probable.

Conclusions

The maxim to use credit spreads when implied volatility is high and debit spreads when implied volatility is low may be a confusion that arose out of long and short option positions.  It is indeed true that one should consider buying low volatility options and selling high volatility options. If we are considering a long call or put position, we would look for options with low implied volatility because these are inexpensive options. And similarly, we would target high IV options if we were considering a short call or put position.

However, when playing the stock’s directional move with a vertical spread strategy, the choice of a credit or debit spread is largely a personal preference.  Some prefer a credit spread because they can earn interest on the credit monies in their accounts while in the trade; another advantage of credit spreads is fewer trading commissions (assuming the spread is allowed to expire worthless).  Others prefer debit spreads because they have spent the maximum that can be lost on the trade; there is no possibility of an ugly surprise later if the trade turns against them (as there is for a credit spread).  

The returns for credit and debit spreads will be identical and IV levels will have no effect on the returns.  The effect of the volatility (either high or low) effectively cancels itself out by the opposite nature of the two legs of the spread.  Thus, vertical spreads are an excellent way to trade high volatility options when establishing a long or short option position would be both expensive and risky.

The change of IV during the course of the vertical spread trade will shift the time decay curves. Decreased IV will make it easier to exit the spread early for a large portion of the maximum profit, while increased IV during the trade will make it more likely one will have to take the spread into expiration.  But the ultimate profitability of the spread is unaffected by the change in implied volatility.