Editor's note: Seeking Alpha is proud to welcome Data Science Partners as a new contributor. It's easy to become a Seeking Alpha contributor and earn money for your best investment ideas. Active contributors also get free access to the SA PRO archive. Click here to find out more »

*By Atanu Saha, Burton G. Malkiel, and Alex Rinaudo*

**Introduction**

There are generally two option writing, or selling, strategies: the first is a buy-write. It entails writing call options against a long position in a stock or a market index. The other is put-write, where the manager sells put options, while holding a portfolio of U.S. Treasury Bills to ensure that the writer can fulfill their contract obligation should the put buyer exercise the option. In both option selling strategies, the upside potential is capped even when the underlying asset price rises considerably higher than the strike price; however, when the underlying asset price falls, option writing cushions the losses to the extent of the cash received through the sale of options. As a result, the returns of option selling strategies tend to have lower volatility than that of the underlying asset.

Several prior academic studies have documented the attractive returns, especially risk-adjusted returns, of option writing strategies. In this article, we demonstrate that an investor can considerably improve their returns by deploying these strategies only during periods when anticipated volatility (as measured by VIX) is higher than usual. The economic intuition for our result stems from the observed differences in the volatility risk premium in different market environments. We show that the difference between implied volatility and realized volatility varies across VIX regimes. Implied volatility is based on the market's forecasts of future volatilities extracted from the prices of options written on the asset of interest. The difference between the implied and realized volatility is particularly pronounced when the VIX index, which reflects the market's implied volatility, is elevated. Thus, a strategy of selling options during high VIX regimes is expected to yield superior returns.

**The VIX**

The VIX is the most popular index purporting to measure the market's expectation of the next month's volatility of the stock market. The rules-based index is derived from the prices of a wide variety of put and call options on the S&P 500 stock index (henceforth S&P). Because of its tendency to rise during periods of unsettled declining stock prices, the VIX is often called the "fear index". The Chicago Board Options Exchange has created a historical record of the index dating back to 1990. Under the current methodology, the VIX is constructed using S&P 500 option prices for options expiring between 23 and 37 days in the future. As such, the VIX is intended to represent the 30-calendar day (approximately 21-trading day) forward volatility of the S&P 500 as a proxy for market volatility.

**The VIX and Market Volatility**

To characterize the relationship between the VIX and the S&P, we first look at the extent to which past market volatility (i.e., realized volatility) can explain the VIX, and then at the accuracy with which the VIX predicts future market volatility. Our analysis uses the daily closing values for the index for the nearly thirty-year period starting in January 1990 through June 2018. These three decades allow us to look at the relationship between the VIX and actual volatility in a variety of market conditions.

First, we regress the VIX on realized volatility, defined as the standard deviation of the S&P returns over the past 21-trading days. We find that, as expected, the VIX is highly correlated with past realized volatility, as demonstrated by a R-squared of 0.78, which implies about 80% of the movement in VIX is explained by realized volatility.

Next, we look at the relationship between the VIX and future volatility by regressing forward volatility on the VIX. We define forward volatility as the standard deviation of the S&P returns for the next 21-trading days. Results indicate that the VIX does a reasonable job of predicting future S&P volatility (R-squared of 0.61). By regressing forward volatility on realized volatility, we get a R-squared of 0.55; this implies that VIX does a better job than past volatility alone in explaining future volatility.

Consistent with findings of some prior studies, we also find that VIX tends to overstate both realized and forward volatility. In Table 1, we summarize this relationship between VIX and the two measures of volatility using data from January 1990 through June 2018. In this table, we show the difference between VIX and both realized volatility and forward volatility by VIX quartile. We find VIX levels are higher than both realized past volatility as well as the forward volatility over the next 21 trading days with an average overestimation of approximately 4 points. In fact, the overstatement is higher at higher levels of VIX.

Data Source: CBOE

This systematic overstatement is commonly attributed to the buy-sell dynamics of the underlying options upon which VIX is based. Because VIX has a negative correlation with stock prices, equity investors find the purchase of volatility-sensitive derivatives offers important insurance benefits. Investors who are long VIX realize gains when the market falls thereby offsetting negative equity returns. Such buying of volatility derivatives increases their prices and leads to a systematically larger prediction of future volatility than is actually realized.

What is particularly interesting is that the difference between VIX and observed volatility is larger at higher levels of volatility. For example, as shown in Table 2, in the lowest quartile of VIX values, VIX overstates forward volatility by 2.88 points; while in the highest quartile it overstates by 5.27 points. This observation will be important in motivating the conditional option-writing strategies we propose in this article.

**Traditional Option-Writing Strategies**

Option writing is then recommended as an optional strategy to take advantage of the possibility that people overpay for protection. Insurance companies that write fire-insurance policies profit from setting rates that are far higher than would be required on the basis of the actual probability that the insured houses would burn down. By analogy, the argument is that the writers (i.e., sellers) of put options will find that providers of volatility insurance would profit under most market corrections.

There are two kinds of writing strategies that are commonly employed. The first is to go long on an individual stock, or an ETF representing a market index, while simultaneously selling (writing) call options on the security or index. The sale is often made at the money - i.e., at the same price at which the security or ETF is trading. Writing puts typically involves selling put options at the money while depositing the margin in the form of safe U.S. Treasury bills with a maturity equal to the duration of the option.

Source: Data Science Partners

Chart 1 represents the payoffs from both strategies. The graph assumes that the index (or stock) sells at $40 and that the call and put options sell at $4 per share. The solid line represents the payoffs from buying the index or stock if the price rises or falls. The buyer of 100 shares benefits or loses in exact proportion to his investment as the price rises or falls. The investor who is long on the index and writes a $4 call gains 10 percent at any price above $40. While the call buyer exercises the call at any price above $40, the investor receives both the sale proceeds and the $4 option premium. If the price falls below $40, the option is not exercised and the investor is left holding a depressed stock. Their loss is reduced by the receipt of the option premium and they suffer a net loss only if the price goes below 36. The dotted line illustrates the payoff. The writer of the 100 puts is in exactly the same position. Neither calculations consider any dividends from the long holding or interest on the margin deposited by the put seller.

**Data on Option Writing Strategies**

The CBOE provides indices which represent the historical returns of both buy-write (BXM) and put-write (PUT) strategies. The CBOE provides historical data for these two indices using a consistent methodology going back to June 1986.

Both the BXM and PUT indices utilize a monthly roll. In the case of the BXM, this means that the index is constructed as if the investor held the S&P 500 and each month on the date of expiration of the prior monthly option contract the investor sells the relevant option at a weighted average price. Dividends paid on the component stocks underlying the S&P 500 Index and the dollar value of option premium deemed received from the sold call options are functionally re-invested in the covered S&P 500 Index portfolio. The PUT index follows a similar monthly roll process but holding risk-free assets instead of the S&P 500 index. Given this monthly roll feature of the BXM and PUT indices, we utilize monthly performance data to evaluate these strategies.

**Conditional Strategy Construction**

As discussed earlier, we observe that the difference between VIX (as a measure of implied volatility) and future volatility increases at higher levels of VIX. We therefore expect the returns of the BXM and PUT indices, which reflect the gains from selling options, to be higher at higher levels of the VIX. Table 2 shows the excess performance of the BXM and PUT indices over the S&P Total Returns by VIX quartiles.

Data Source: CBOE

The VIX quartiles are constructed such that they are free from hindsight bias. In particular, we determined the quartile cutoffs for the VIX based only on historical data - i.e., based VIX levels in the period prior to the current month. Therefore, as one moves forward in time, the strategies add one month of additional data to determine the VIX cutoff. To make sure there is a sufficient sample on which to base these cutoffs, we start in 1995 which provides us with a minimum of five years of prior history. We then use the median VIX level of the *prior* month to categorize the excess returns of BXM and PUT indices into VIX quartiles. The results in Table 2 show that the two option selling strategies provide positive excess returns in both the third and fourth VIX quartiles and underperform the market in the first two quartiles.

We utilize these results to construct two conditional option-writing strategies that seek to capitalize on this pattern. The conditional strategies are based upon a simple rule: invest in S&P 500 if VIX is below its historical median and engage in option writing if VIX is above the historical median.

For example, starting in January 1995, we determine the median historical VIX level, using data for the period January 1990 through December 1994. At the beginning of January of 1995, if the median VIX level in the prior month (i.e., December 1994) is higher than the historical median VIX value (i.e., using data between 1990 and 1994) than we enter the option selling strategy. If the median VIX is lower than the median value, we stay in the S&P 500. We make this same evaluation in each subsequent month by looking at the full VIX history up through the prior month to compute the historical VIX median and compare the median VIX level of the prior month to the historical median. Thus, each month, as we move forward in time from January 1995 onward, we have one additional month's data on VIX to compute its historical median. In each month, options are written if the VIX level of the prior month is above the historical median. By using only historical data in deciding whether or not to engage in option selling, we avoid any hindsight bias.

**Conditional Strategy Performance**

Table 3 compares the performance of these conditional strategies to the original strategies and the market. The results are clear. Both the conditional BXM and conditional PUT have higher returns than either the S&P Total Return or the respective unconditional option-selling strategies. Importantly, the conditional strategies offer meaningful improvements in both Sharpe and Sortino ratios over the market and over the unconditional returns of option selling in every period.

Data Source: CBOE

Chart 2 depicts the excess return (i.e., the excess over S&P Total Return) of the conditional put-write strategies to the S&P Total Return on an annual basis. In this chart, light gray areas show the years in which the portfolio stays in the S&P index. Out of the 23.5 years, there are seven years where this occurs (approximately 1/3 of the time). These years directly correspond with positive S&P 500 returns and low volatility environments.

This chart highlights the three different regimes for the strategy: years in which the strategy stays in the S&P index, years where the strategy shifts to option writing and outperforms the S&P 500 index and years in which the strategy shifts to option writing and underperforms the S&P 500.

The chart shows that in seven years the strategy outperforms the market. These years generally coincide with periods of negative (or low) market returns and higher market volatility. On average the outperformance during these seven years is approximately 9.7%. This more than compensates for the nine years in which the strategy underperforms as the average annual underperformance in those years is approximately 3.8%. These years of underperformance generally correspond with bull runs where the option premiums are insufficient to offset the capped upside of option selling.

Data Source: CBOE

Chart 3 shows the cumulative returns of the two conditional strategies and of the market. After an initial period of underperformance, both strategies consistently outperform the S&P after its first sustained decline and then continue to outperform over the remainder of the period.

Data Source: CBOE

Table 4 provides further insight into how the conditional strategies perform in market downturns.

Data Source: CBOE

Based on monthly returns from 1995 through 2018, there were five periods in which the S&P dropped by more than 5% below its prior peak. Note that during the two longer drawdown periods in 2000 and 2007, the conditional strategies peak later than the S&P resulting in a drawdown that is not only shallower in severity but also shorter in duration. These smaller losses in down markets largely explain the higher risk-adjusted returns of the conditional strategies.

**Concluding Comments**

In this article, we examined how buy-write and put-write strategies can be improved through a simple conditional strategy which sells options only when the VIX index is elevated. We started with an examination of market volatility. Consistent with prior studies, we found that implied volatility is consistently higher than future volatility. Furthermore, we show that this overestimation grows at higher levels of the VIX index. After observing that this extends to option writing indices which exhibit excess returns during periods of elevated VIX, we developed conditional option writing strategies that only write options when the VIX is elevated above its historical median.

We document that these conditional strategies outperform both the S&P 500 Total Return Index and the continuous option writing strategies. These findings suggest that portfolio managers who are utilizing option writing strategies should consider selectively deploying this strategy only in market conditions that are characterized by higher than normal level of volatility.

**Disclosure:** I/we have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours.

I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it. I have no business relationship with any company whose stock is mentioned in this article.