Wednesday, July 1, 2009

Options as zero coupon bonds

The possibilities investors have with options are almost endless. Almost every view on the markets can be translated in an options strategy where call-options and put-options can be combined in various ways, and the options can be both purchased or sold. Many strategies have wonderful names like butterflies, condors, straddles and strangles, and are extensively described in books and articles. It is however less well known that options can be utilized as an instrument to generate income independently from any movement in underlying rates. The option transforms in a kind of interest instrument, where the investor can decide if he want to be on the paying or receiving end of the strategy. The strategy that I will describe here is essentially the equivalent of a zero coupon bond.

A zero coupon bond is a bond that does not make periodic interest payments, but only pays a certain amount of money, its face value, at a determined date in the future. One payment is followed by one redemption. The initial payment will obviously be lower than the face value and is determined by the required interest rate and the duration of the bond. By taking the actual value of a zero coupon bond, together with the remaining duration and face value, the effective yield to maturity of the bond can be calculated.

Options can also be used to create a cash flow pattern where initially a payment is made and a fixed amount of money is received at the expiration date of the options. This strategy can be set up with any underlying value and any expiration date, but my experience is that it is most efficient with index options on expiration dates with the highest trading volumes. Positions need to be taken with the highest and the lowest available strike prices. The advantage of index options is also that they are usually European style, which means that they cannot be exercised prior to the expiration date. With American style stock options there is always a risk that exercising the option may be efficient and therefore likely. This would obviously disrupt the strategy and influence the outcome.

As an example I use the AEX index options, expiring on December 12th 2012, which are listed on NYSE Euronext in Amsterdam. This exchange is very efficient for investors, with good liquidity and narrow spreads. Although in practice index options are always settled at the expiration date, I will assume in this example that the index is actually a deliverable underlying value. The result of this assumption is the same, but it makes it easier to describe the strategy.

By creating a combination of a purchased call-option and a sold put-option with the same strike price and the same expiration date, a position is created where with certainty the index will have to be purchased at the expiration date for the lowest available strike price, which in our example is 80. If the index is higher than 80 at the expiration date, the investor will exercise his right to buy the index at 80. If the index is below 80, the buyer of the put-option will sell for 80 to the investor. Because of the low strike price compared to the actual index value, the call-option will be very expensive, and will consist almost entirely of intrinsic value. The put option, which is far out-of-the-money will have a low value.
In a comparable way we can also create a position where with certainty the index will be sold at the expiration date of the options, by buying a put-option and selling a call-option, again with the same strike price, which in this case will be 640. When the index is below 640 on the expiration date, the investor will exercise his put-option right and sell the index for 640. If the index expires above 640, the investor will have to sell the index to the buyer of the call-option for 640. Either way, the index will be sold for 640. Because in this case the strike price of the put-option is well above the current index value, this option will have a high value, while now the call-option has a low value.

For this example I have taken the closing prices of Thursday June 25th, when the index closed at 254.12, and I have assumed that trading is possible at the mid prices between the bid and ask prices. The premiums are the following (all in Euro’s):

Buy call-option 80 -161.85
Sell put-option 80 +2.25
Sell call-option 640 +0.58
Buy put-option 640 -356.50

Net payable premium -515.52

On the expiration date at the end of December 2012, we will have a situation where with certainty the index will be purchased for 80 and sold for 640. This leaves a certain difference of 560.
Since we both know the initial cost of 515.52 and the final amount of 560, it can be determined what the effective return is on an annual basis. The implicit interest rate for the period of almost 3.5 years can be calculated to be 2.4% on an annual basis. An investor who believes that this is not an attractive return can decide to receive premium at the start of the strategy, which will give him an effective financing rate of 2.4%. However, this investor will need to have sufficient margin in his account and also needs to carefully consider how the received premiums are to be invested.

In Amsterdam, index options are listed until December 2013, which gives the possibility to calculate the strategy for 5 periods from 2009 to 2013. Through interpolation it is possible to determine a zero coupon yield curve for a 1-4 year period, which can be compared with the return on government bonds. The disadvantage of government bonds is that these normally can only be purchased, while the zero coupon curve of options can be both purchased and sold. The following graph shows how close both curves follow each other:

I find the zero coupon curve from options very useful, not just for trading purposes, but also as an information tool about the development of interest rates. Speculators with a certain view on the interest rate can also benefit from tracking the curve and trade accordingly. Investors who are interested in tracking these Euro interest rates, derived from options, can follow them through twitter, where I post actual calculated rates on a time schedule. The URL for these rates is

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