MX Covered Straddle Writers' Index (MPCX)
(Since December 20, 1993)
MPCX – XIU
(Last 6 months)
Index value – MPCX
|May 6, 2013||May 7, 2013||May 8, 2013||May 9, 2013||May 10, 2013|
|Year high (March 15, 2013): 396.26||Year low (April 17, 2013): 372.44|
Introduction to covered straddle writing
A straddle involves the simultaneous purchase or sale of a close-to-the-money call and a close-to-the-money put. In order for a short straddle to be covered, the investor must hold the underlying security to cover the short call and must hold sufficient cash to meet the obligation of the short put.
An uncovered short straddle is a volatility trade. The straddle writer is not focused on where the underlying security is going, only that it remains within the boundaries of a trading range established by the straddle. In the XYZ example (see Covered Straddle Writing Strategy), the straddle writer will profit if XYZ remains between $41 ($50 strike price less $9 per share in premium income) and $59 per share ($50 strike price + $9 per share in premium income).
As for covered straddle writing, investors employ this strategy as a way to dollar average their way into a stock position. They do this by buying an initial position and setting cash aside to buy additional shares should the short put option be assigned.
Covered straddle writing should outperform a buy and hold strategy in a bear market. However, the strategy involves ownership of an underlying security and an obligation to buy more shares of the underlying security. In a bear market, the underlying security will decline in value and so too will the value of the covered straddle. It will not decline as far or as sharply as the buy and hold strategy, but it will move in the same direction.
Similarly, we would expect covered straddle writers to underperform in a strong bull market environment. The covered straddle writer is obligated to deliver the underlying security to the call buyer at a pre-determined price. In a bull market, that obligation acts as ceiling, limiting the full extent of a strong upside move.
MX Covered Straddle Writers' Index
The Montréal Exchange worked with Richard N Croft (President of R N Croft Financial Group Inc. Investment Counselors / Portfolio Managers, www.croftgroup.com) to construct a passive total return index based on writing close-to-the-money covered straddles. The MX Covered Straddle Writers' Index involves the simultaneous sale of a close-to-the-money call and a close-to-the-money put against a long position in the iShares of the CDN S&P/TSX 60 Fund and a cash position used to secure the short put option.
The near-term (i.e. one month) close-to-the-money call and put options are written each month, on the Monday following expiration, and are held until the following expiration. At expiration the written options are settled for cash, and on the following Monday, a new one-month close-to-the-money call and put option is written against the underlying iShares of the CDN S&P/TSX 60 Fund and cash. The cash component in the strategy earns interest at the prevailing market rate for 90-day Treasury bills.
Each time a new series of call and put options are written, they are assumed to be written at the reported bid prices, at the close of trading on the Montréal Exchange on the Monday following an expiration. The premiums collected from the sale of the call and put are added to the portfolio's total value. There is no guarantee that investors would be able to sell at the reported bid price on the Montréal Exchange, at the close of trading on the Monday following an expiration. Investors attempting to replicate the MX Covered Straddle Writers' Index (symbol MPCX) should discuss with their brokers possible timing and liquidity issues.
The MX Covered Straddle Writers' Index (symbol MPCX) is a benchmark designed to reflect the return on a portfolio that consists of a long position in the stocks in the S&P/TSX 60 Index plus cash, and a short position in an XIU close-to-the-money call and put options. The historical return series for the MPCX Index begins December 20, 1993 (the Monday following the December 1993 expiration), the first day that the Chicago Board Options Exchange published data for the Volatility Index.
MX Covered Straddle Writers' Index construction
While we have available data for the S&P/TSX 60 Index – the forerunner for the tradeable iShares – there was no data for the underlying options. In order to re-create the Index back to December 1993, we calculated a theoretical fair value (TFV) for the close-to-the-money options using the Black-Scholes option pricing model.
There are six inputs used in the Black-Scholes option pricing model:
Current price of index
iShares (or S&P/TSX 60 Index adjusted) daily prices were provided by the Montréal Exchange.
The strike price was assumed to be the option closest to the current price of the underlying security. For periods when the iShares were trading below $25 per share, strike prices were assumed to be a $1.00 intervals. For example, if the iShares were trading at $20 per share, we would assume strike prices of $19, $20 and $21.
For periods when the iShares were trading above $25 per share, we assumed strike prices at $2.50 intervals. If the iShares were trading at $28 per share, we would assume strikes prices at $25, $27.50 and $30.
In cases where slightly in-the-money options were the closest available strike to the current price of the underlying security, we employed a rigid methodology to determine whether slightly in-the-money or slightly out-of-the-money calls and or puts would be written. To that end, we did not write calls or puts where the strike price was 2% or more in-the-money.
For example, on March 20, 2000, the iShares closed at $56.625. The available April strikes were $55.00 and $57.50. Because the $55.00 strike price was 2.9% in-the-money, we sold the April 57.50 calls.
On March 20, 2000, the April 57.50 puts were slightly in-the-money, and were the closest put strike to the current price of the underlying index. We sold the April 57.50 put, because it was in-the-money by 1.5%, which was less than our 2% in-the-money threshold.
The risk free interest rate
For this input, we used the closing daily yield on 90-day Government of Canada Treasury bills.
We approximated the dividend yield on the S&P/TSX 60 Index (as well as the iShares), for use when calculating theoretical fair values for the various option series. For this purpose, the dividend yield was assumed to be 1.6% annually. There was no accounting for the tax implications of dividends versus interest income.
Although the MPCX Index is a total return index, it does not account for dividends that would have been received. Any comparisons between a buy and hold strategy for the iShares and the MPCX Index also excludes dividends.
Volatility was the most difficult input to ascertain. One approach was to simply use the historical volatility of the underlying security as our volatility input. However, historically, the experience in both Canada and the US, is that index options trade at implied volatilities that are generally higher than the actual historical volatility of the underlying index.
That trend can be quantified in the US markets by comparing the Volatility Index (symbol VIX) to the actual historical volatility of the S&P 100 Index (symbol OEX). Historical volatility is calculated as the annualized standard deviation of returns for the underlying security over the preceding 30 days (i.e. 20 trading days).
The CBOE Volatility Index, on the other hand, measures the implied volatility based on the actual prices for S&P 100 Index options. The CBOE Volatility Index has data back to December 1993. From December 16, 1993 to October 7, 2002, we counted 2,216 daily observations related to the actual historical volatility for the S&P 100 Index. There were also 2,216 available observations for the VIX. On 2,003 of those observations (90.39% or all observations), the VIX had a higher closing value than the actual historical volatility of the S&P 100 Index. On average, over that observation period, the VIX value was 1.45 times the value of the historical volatility as calculated for the S&P 100 Index.
Further studies showed that from December 1993 to October 2002, the S&P/TSX 60 Index had a positive correlation (0.75 correlation coefficient) with the S&P 100 Index. Suggesting that on average, both underlying indices tended to move in similar directions at the same time. There was however, some variance in the degree of daily moves when comparing the S&P/TSX 60 Index to the S&P 100 Index. Over the observation period, the S&P 100 Index was slightly more volatile on average, that the S&P/TSX 60 Index.
Given those observations, it was decided that the daily volatility input for the MX Covered Straddle Writers Index would be based on a multiple of the observed VIX implied versus actual historical volatility on the S&P 100 Index.
For example, on July 8, 1996, the annualized 30-day historical volatility on the S&P 100 Index was 15.9% (note on July 8, 1996, the S&P/TSX 60 Index had an implied volatility of 8.1%).
On that particular date, the VIX closed at 20.9%, or 1.3 times the level of the actual historical volatility for the S&P 100 Index. The 1.3 becomes the multiple used to calculate the TFV for the S&P/TSX 60 Index options on that day.
So, coming to full circle, we multiplied the actual 30-day historical volatility for the S&P/TSX 60 Index (i.e. 8.1%) by the 1.3 multiple as ascertained from the implied versus actual volatility for the S&P 100 Index to arrive at an implied volatility assumption for the S&P/TSX 60 Index of 10.6%. We input the 10.6% assumption in the Black-Scholes formula for that day, and utilized the same methodology for all other days until iShares S&P/TSX 60 Index began trading. Once iShares S&P/TSX 60 Index options began trading, we used the actual prices form the Montréal Exchange.
Time to expiration
The time to expiration is calculated as the total number of days between the Monday following a series expiration to the next expiration date. The expiration date for each option series is the Saturday following the third Friday of the expiration month.
When inputting these six factors into the model, the formula provides a TFV for the calls and the puts. Current daily index calculations are not determined by the model, but are based on the actual daily closing prices for the underlying index and the written option, as settled on the Montréal Exchange.
A new iShares covered straddle write is initiated on the Monday following each Friday expiration. The MX Covered Straddle Writers' Index is based on a portfolio of 2,500 shares of the iShares and the cash equivalent of 2,500 shares as of December 20, 1993. The beginning cash position was $54,145. Against that portfolio, we write 25 one-month close-to-the-money calls, covering the entire underlying share position plus 25 one-month close-to-the-money puts, which are secured by cash. The number of shares and cash was rounded to reflect a beginning portfolio value of $108,290.
The cash component in the MPCX Index is invested in Treasury bills and marked to the market daily, with the value based on the daily interest rate payable on 90-day Government of Canada Treasury bills. The MPCX Index does not account for transaction costs. Investors should recognize that trades in the Index occur every month and transaction costs can have a meaningful impact on the value of the Index.
A series of new indices
In recent years, the Montréal Exchange has received general interest from institutional and individual customers as to the performance attributes associated with various option strategies. MX has been encouraged to create passive benchmark indices to reflect these performance attributes. The Montréal Exchange believes that the introduction of the MX Covered Call Writers' Index (MCWX) and the MX Covered Straddle Writers' Index (MPCX) could lead to more long-term customer interest in and use of Montréal Exchange listed options.
Price levels of MX indices
Prices for the MX Covered Call Writers' Index (MCWX) and the MX Covered Straddle Writers' Index (MPCX) are available from this website and from quote vendors that provide options data. The price level for both MX Indices was set to 100 on December 20, 1993.
Tradeable, investable alternatives
In October 2002 the Montréal Exchange began disseminating MX Covered Call Writers' Index (MCWX) and MX Covered Straddle Writers' Index (MPCX) prices as a general indication of a hypothetical iShares option-based strategies. Based on theses indices, other products might be created such as ETFs, futures, hedge funds or mutual funds.
The Montréal Exchange does not provide specific recommendations for mutual funds, but investors interested in these strategies might research the returns and risks of mutual funds that engage in option writing strategies for a portion of their investment portfolios.
The added income from the covered calls in an option writing strategy has historically provided a cushion in times of flat to declining markets. When the underlying market is rising rapidly, option writing strategies generally underperformed a buy and hold approach for the iShares.
The most attractive feature in an option writing strategy is the marked reduction in the volatility of the overall portfolio. The daily standard deviation for all observations in the MX Covered Call Writers' Index was 0.83%, for the MX Covered Straddle Writers' Index it was 0.81% versus 1.15% for a buy and hold strategy using the iShares.
Covered straddle writing strategy
Assume a position where the investor holds 100 shares of XYZ at $50 per share and $5,000 in cash. The investor sells the XYZ six-month 50 call for a net premium of $5 per share ($500 per contract) and the XYZ six-month 50 put for a net premium of $4 per share.
In this example, the covered straddle writer has agreed to sell the 100 XYZ shares to the call buyer at $50 per share until the option expires. For agreeing to this, the call buyer will pay $5 per share in premium. The premium is retained by the straddle writer no matter where the stock ends up in six months.
With the short put, the covered straddle writer has agreed to buy an additional 100 shares of XYZ at $50 per share. The put buyer pays the $4 per share premium, and has the right to sell 100 XYZ shares to the seller anytime up to the options expiration.
The premium from the sale of the put is retained by the covered straddle writer, and sufficient cash (i.e. $5,000 cash to cover the potential purchase of 100 shares of XYZ at $50) is set aside to meet the purchase obligation. The cash earns interest at the prevailing rate until expiration. The covered straddle writer should be mildly bullish, or at the very least, neutral on the prospects for the underlying stock.
In the example cited, one of three outcomes will occur at expiration. XYZ can rise above $50 per share in six months. In that event, the call will be exercised, the call buyer will pay $50 per share, and the covered straddle writer will deliver the 100 shares of XYZ. In this scenario, the put option will expire worthless, and the covered straddle writer will also retain the premium.
XYZ can remain unchanged for the life of the option and close at exactly $50 per share. In this unlikely event, both the call and the put option will expire worthless. The straddle writer retains the cash, and the 100 shares of XYZ as well as the $9 per share premium received.
XYZ can decline below $50 per share between the time the options were written and the expiration date. In this case, the call option will expire worthless and the straddle writer will retain the premiums. The put option will be assigned and the covered straddle writer will buy an additional 100 shares of XYZ at $50 per share. At this point, the covered straddle writer will own 200 shares of XYZ.
The covered straddle establishes a set of parameters. In the XYZ example, the upside potential is limited to the strike price of the option, plus the $9 premium received. At the same time, the covered straddle writer has reduced the cost base of the initial stock purchase by the premium received.
Should the put be assigned and an additional 100 shares of XYZ be purchased, the covered straddle writer will own 200 shares of stock at an average cost of $45.50 per share. That is $50 per share for the initial 100 shares, plus a purchase of an additional 100 shares at $50 per share less $9 per share in premium income received at the time the straddle write was established.
Daily closing prices on the MPCX Index are calculated and disseminated by R N Croft Financial Group Inc. Changes in the value of the Index are based on daily changes reflected in the closing prices for the iShares and the written series of call and put options. Prices for MPCX Index are updated on the Montréal Exchange website weekly.