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Protecting A Stock Portfolio
By Lawrence G. McMillan

This article was originally published in The Option Strategist Newsletter Volume 15, No. 6 on March 30, 2006. 

As our regular subscribers know, the CBOE recently listed cash-based options on its Volatility Index ($VIX). We have published several recent articles describing the details of these options, so we’ll review those only briefly in this article.

Clearly, these options can be used by speculators trying to predict whether $VIX will rise or fall over the lifetime of the options. However, perhaps a more broad-based approach is to use them as a stock portfolio hedge against a declining stock market. That will be the focus of this article.

The Basics of $VIX Options

These options settle, at expiration, at the value of $VIX. Since they are cash-based options, the difference between the striking price and the price of $VIX (if that difference is positive) becomes a credit in one’s account. The CBOE has recently received permission to list more expiration months for $VIX options (and for Volatility and Variance futures as well), so that there are currently $VIX options and futures extending out to Feb ‘07.

Expiration dates are a bit difficult to determine: each month’s expiration date is 30 calendar days prior to the following month’s $SPX options expiration date. So, for example, April $VIX options expire 30 days prior to the last trading day of regular May $SPX index options. $SPX May options expire on 5/19/06, so April $VIX options expire 30 calendar days prior to that – on April 19th. As a result of this seemingly arcane procedure, $VIX options always expire on a Wednesday – either the one immediately preceding or the one immediately after regular option expiration. This expiration date – 30 days prior to the next month’s $SPX option expiration – is necessary in order for market makers and arbitrageurs to be able to establish riskless hedges. Without the potential for arbitrage, an option market cannot attain large liquidity.

Other than that, $VIX options are very similar to any other index options – calls and puts are listed, a one point move is $100, and various striking prices are offered for both puts and calls (currently, the striking price differentials are 2.5 points, but hopefully approval will be forthcoming fairly soon to reduce that to 1-point differentials).

A fair amount of debate arose as to how to properly price $VIX options, using the Black-Scholes or any other option model. This is because $VIX trades in a range – rarely going below 10 and (although it’s been several years since it’s been highly priced) rarely going above 45. Therefore, no one wants to buy the 10 strike puts, for example, and lots of people would want to own calls at that strike. This relationship seems to be imbedded in the Volatility Futures as well, so a shortcut that seems to be working so far is to price each different month of $VIX options using that month’s futures price as the underlying price – not the price of $VIX itself. This is a departure from the way that other index options – $SPX, $OEX, $DJX, etc. – are priced.

Protecting A Stock Portfolio With Derivatives

Since the inception of listed derivatives – especially index derivatives – traders have striven to design low-cost or low-risk hedges that protect against a market collapse. Some of these have worked better than others.

The simplest strategy is merely to buy puts on the exact stocks that one owns. This is usually the most costly way of constructing a hedge, but it is an accurate hedge – if the stock drops, the hedge will work.

A similar, and generally less expensive, approach is to buy index puts as a hedge against a portfolio of stocks that presumably behaves similar to the index itself. Generally, broad-based portfolios use $SPX or $OEX puts for this purpose. These hedges, too, are expensive, since so many traders are buying or bidding for the same or similar puts. Another problem with using index options is called tracking error – your portfolio will not likely perform exactly the same as the index you’ve chosen.

Either of the above strategies is called a protective put purchase. Traders often attempt to reduce the cost of buying puts as a hedge by simultaneously selling out-ofthe- money calls – using the call proceeds to pay for part (or sometimes, all) of the cost of the puts. This is called a collar. The problem with a collar is that it caps the profit that can be made on the upside, if the underlying stock(s) should rally strongly. The best way to counter that is to use the longest-term options possible in constructing the collar – that will allow for the call strike to be as high as possible, thereby allowing for the most upside stock movement possible.

Futures can also be used as a hedge, although they have their own set of problems. Futures do not have a striking price, so their values grow or shrink proportionately to the rise or fall in the underlying stock or index. In other words, if you were to sell S&P 500 futures as a hedge against your stock portfolio – assuming you sold a quantity designed to hedge the whole portfolio – you would effectively eliminate the chances for any gains or losses. Any gains in the stocks would be offset by losses in the futures, and vice versa. As a result, it is rare to use the futures as a complete hedge for a stock portfolio (although an arbitrage-like strategy, called swapping is often practiced by large portfolios resembling the $SPX Index).

One ill-fated strategy involving futures was popular in the mid-1980's, called portfolio insurance. In this strategy, a large holder of stocks sold a few futures against his portfolio. Then, if the market rose, he did nothing else. If, however, the market fell, he sold more futures against the portfolio. If the market fell far enough, then a full “load” of futures would be sold against the stocks. In theory, this worked much better than buying puts, for the seller of futures was earning time premium rather than paying. In reality, though, when the market began to unravel just before and especially during the Crash of ‘87, the strategy proved to be unworkable. The futures marketplace was not liquid enough to handle all of the futures that needed to be sold – at least at “fair value.” So the futures sellers drove the futures down to deep discounts in order to get their hedge on. These deep discounts in the futures equated to massive sell programs in stocks which may not have caused the Crash of ‘87, but certainly exacerbated it. This strategy is probably still practiced today, especially since $SPX futures and options are so much more liquid than they ever were, but most institutions who got burned (and even investigated) in 1987 want no part of it.

Using Volatility Products As A Hedge

Due to the ever-evolving nature of the derivatives markets, a new class of products has been created in the last two years – Volatility Products. At first there were just the volatility futures, then variance futures, and now we have volatility ($VIX) options as well.

When the volatility futures were listed, a theoretical paper was circulated that showed that a 10% hedge in $VIX futures would perform quite admirably as a low-cost, but effective, hedge for a broad-based portfolio of stocks. In other words, if the portfolio was worth $10 million, then one would buy $1 million worth of $VIX futures as a hedge. As the value of the portfolio moved up and down, the quantity of futures would also be adjusted – in order to keep the hedge at the desired 10% level. The strategy works because $VIX generally moves up when the market moves down – so that a long position in $VIX futures would be making money even though the long stocks in the portfolio would be losing.

In theory, this was a tremendous strategy – much more cost effective than buying puts, which are a wasting asset. However, the original data used to backtest the strategy used the price of $VIX as the hedge, for the futures didn’t exist at that time. In reality, when the prices of the futures were available, the time value premium in them was so large that the strategy was ineffective – and actually more costly than collars or protective puts.

Admittedly, $VIX has been very low-priced since the futures were introduced, and the futures have a larger premium when that is the case. Had $VIX been near 30, the futures might have been trading at a discount and therefore been a good hedge. But, so far, they have not. It should be kept in mind, though, that when $VIX becomes high-priced –as it is sure to do someday – the purchase of $VIX futures as a 10% hedge may indeed be a viable strategy.

Which now brings us to the concept of using $VIX options as a hedge for a portfolio of stocks. The concept is to be “delta long” $VIX against a portfolio of long stocks. There are two basic ways to be delta long: owns calls and/or sell puts.

Buy $VIX Calls As A Hedge

Let’s start out simply: buy $VIX calls as a hedge for long stocks. In theory and in practice, this could be a superior strategy to buying $VIX futures as a hedge. For example, with a call purchase, you know exactly what your dollar risk is. That is, the cost of your hedge is fixed. That’s not true with the futures contract.

However, how many calls should be bought? This is a difficult question to answer, especially if you are looking for a definitive hedge. The suggestion in futures was a 10% hedge, and a similar percentage might be applied to an option hedge. However, one can also control the cost and effectiveness of an option hedge by the striking price he chooses.

If the hedge is to be 10%, it should be determined using the striking price as the notional amount of the hedge, not some other factor such as the delta of the options.

Example: $VIX = 11.58
Feb (‘07) 17.5 call = 2.00

In this case, the stock portfolio owner is willing to accept the risk in the market if a mild decline develops, but that decline does not cause $VIX to rise above 17.50. However, if a major correction or bear market develops, $VIX should increase substantially above 17.5 and so the hedge would take effect.

Suppose that $1 million worth of stock is owned. A 10% hedge would mean that $100,000 worth of “$VIX” should be purchased. Using the 17.50 strike, each option represents a strike value of $1,750.

# of calls to buy = $100,000/$1,750 = 57

Thus, the purchase of 57 Feb 17.5 calls at $200 apiece would construct a 10% hedge once $VIX rose above 17.50. The cost – $11,400 – is about 1.1% of the entire portfolio’s value of $1 million. That is far, far cheaper than a put hedge or a futures hedge.

Of course, the hedge is not perfect. First, it doesn’t take effect until $VIX rises above 17, and second, there is no guarantee just how far $VIX will rise during a market correction. We haven’t seen a 10% correction in three years (second longest hiatus in history), but there is a historical period that might be similar to today – the 9.7% correction that took place from a low-volatility environment in Feb-March 1994. $VIX rose from 10 to 17 as the correction took place, then briefly spiked to 24 and back over a couple of days. Without that spike, the 17.5 calls wouldn’t have been very beneficial. Perhaps the 15 strike would be more useful, although it would involve paying more for the calls (2.90 at current prices) and buying a larger quantity (67 calls).

As for how far $VIX increases when the market declines, a cursory examination of past data shows that $VIX increases about 12 - 15 points when the broad market falls by 10%. And in a more severe decline, such as the 35% market drop from March – July, 2002, $VIX rose from 18 to 45. In a decline of that magnitude, the wisdom of owning $VIX calls is clear.

Selling $VIX Puts As A Hedge

Another approach that creates some “delta long” $VIX would be to sell puts. This is not a very effective hedge because the puts only offer a hedge to the extent of the premium received for the put. In a severe market correction, that would not be a meaningful hedge against the losses in a stock portfolio.

If one buys calls and sells puts with the same terms, that is equivalent to owning that month’s futures – so that’s a strategy we won’t pursue, because it was discussed above.

However, if we separate the strikes of the put and the call, we have something akin to a collar protecting the stock portfolio, but this type of collar has unlimited profit potential (and large risk if $VIX should fall).

$VIX Feb (‘07) 17.5 call: 2.00
$VIX Feb (‘07) 12.5 put: 0.70

Using the same arithmetic as before, we would want to buy 57 calls and sell 57 puts. The net cash outlay for this hedge would be $130 x 57 = $7,410 – considerably less percentagewise than buying the calls outright for $11,400.

There could be additional risk, though. If $VIX fell to 10 at expiration, there would be an additional cost of $250 to buy back the 57 puts at expiration (although the hedge could be rolled to a later month or year).


Those stock owners looking to create an effective volatility hedge for a portfolio of stocks should consider the use of $VIX options, rather than futures. The absolute dollar cost of the hedge is likely to be smaller than that of buying index or equity puts as protection, and is also likely to be much less than the time value premium expense of a $VIX futures hedge.

Moreover, the flexibility that the $VIX options can offer in terms of striking prices and expiration dates allows the hedger to construct a hedge to fit his capacity for risk (the use of higher $VIX strikes means he is willing to accept more short-term risk and only wants to hedge against a large increase in $VIX – which would normally occur only during a large market decline).


This article was originally published in The Option Strategist Newsletter Volume 15, No. 6 on March 30, 2006.  

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