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By Lawrence G. McMillan

This article was originally published in The Option Strategist Newsletter Volume 4, No. 14 on July 26, 1995. 

We have written about portfolio protection using options in the past, but with the relatively large number of questions coming from subscribers about this topic, it appears to be time to revisit it. We will go through an example using a small, but highly volatile portfolio. This is the type that seems to be worrying individual investors the most; they are, of course, happy with the profits that have built up in the tech stocks, but are nervous about how to protect those profits.

The Simple Way: Use Stock Options

The easiest and most efficient way to hedge your portfolio is to buy slightly out-ofthe- money puts against the individual issues that you own. If you own 2000 shares of Microsoft, selling at 93, then you might want to buy 20 Microsoft October 80 puts (price: about 2½) as protection. Or if you desire greater protection, then buy 20 October 85 puts or even October 90's. If you think the puts are too expensive, you could defray some of the cost of the puts by selling out-of-the-money Microsoft calls (for example, the October 110 calls bring in 3¼). The main problem with this latter addition to the strategy is that you are cutting off your upside potential by selling the call, and not everyone is comfortable with doing that.

You could buy puts individually for each stock in your portfolio (assuming that the stock has listed options trading). Then, when you were done, you would have a "perfect" hedge. We use "perfect" in the sense that the puts will increase in value at the same rate your stocks fall, if they fall far enough. Thus, no matter what happens to each stock individually, your puts will provide protection below their respective striking prices.

Using Index Options

Most holders of larger portfolios prefer to use index options to hedge their positions, because of the large number of orders and commissions involved in buying puts on each individual stock in the portfolio.

The main problem with using index options is that the index may not perform like your stocks do. For example, if you buy OEX puts to hedge your portfolio of high-tech stocks, you may find that your portfolio collapses while OEX barely goes down at all. That is called "Tracking Error".

So, you must try to select an index that will perform more or less like your portfolio of stocks if you decide to use index puts as protection. If you have a broad-based portfolio, then you can almost always use OEX or SPX (S&P 500 Index) puts as protection. If you have a more specific portfolio, you may be better served by using puts on a Sector Index. Using only some arithmetic, you can determine how many puts to buy.

Figuring Your Portfolio's Volatility-adjusted Worth

It's a simple matter to value your portfolio in terms of net worth, but when one is attempting to use index puts as protection — assuming he doesn't own exactly the stocks that comprise the index — then he must first calculate the volatility-adjusted worth of his portfolio.

Suppose that one owns 2000 Microsoft, 1000 Intel, 500 Texas Instruments, and 500 IBM. Furthermore, suppose that he wants to hedge this portfolio. His first calculation would be the volatility-adjusted net worth, which is merely the sum, by stock, of the net worth of that stock times the stock's volatility.

                     (a)        (b)     (a × b)       (c)           (a × b × c)
Stock              Quantity    Price   Net Worth   Volatility   Volatility-adjusted
                                                                    Net Worth
Microsoft            2000       93      186,000       55%           $102,300
Intel                1000       65       65,000       60%             39,000
Texas Instruments     500      150       75,000       40%             30,000
IBM                   500      107       53,500       32%             17,120
Totals                                  379,500                      188,420

Determining Which Index Puts To Use

Now that we have computed the volatility-adjusted net worth of the portfolio, we can compare it to any index we want, merely by using the volatility of that index. For example, if we wanted to use OEX to hedge this portfolio (an action which I would not actually recommend, based on the makeup of this portfolio), we would divide OEX's volatility of 12% into the volatility-adjusted dollars to determine how much of OEX to use to hedge this portfolio:
Number of "do=lla 1rs8"8 ,o4f2 O0E / X0 .n1e2e =d e1d,5 t7o0 h,1e6d7ge this portfolio

One way to view this would be to note that even though the small portfolio is only worth $389,000, we need over $1.5 million worth of OEX to properly hedge it, because the portfolio is so much more volatile than the OEX Index.

Using that same philosophy, we can compare this portfolio with other indices that might have better tracking. The table on the top of page 3 shows how many "shares" of various indices would have to be used to hedge this portfolio.

Index              Index      "Dollars" of
                 Volatility   Index Needed
                                to Hedge
OEX (S&P 100)       0.12       $1,570,167
SPX (S&P 500)       0.11        1,712,909
SOX (Semiconductor) 0.39          483,128
NDX (NASDAQ-100)    0.35          538,342
XOC (OTC 100)       0.29          785,083

Since this portfolio is so oriented with high-tech stocks, it would probably be best to use one of the last three indices as a hedge. We need to use fewer of the SOX Index puts because SOX is the most volatile of the three. However, these puts are going to be more expensive in terms of absolute dollars for the same reason — it's the most volatile index on the list.

The final calculation that one needs to make is which put to buy. Let's say, for the purposes of this example, that we intend to use the Semiconductor Index puts. With SOX at about 275 (after its split — see article below), one might choose to use the 250 puts as a hedge since this strike is approximately 10% below the current SOX price. The number of puts to use is easily determined by taking the number from the last table for SOX — 483,128 — and dividing it by 250, the strike. This results in 1932 "shares" worth of SOX. Since the puts are for 100 shares, we divide by 100 and get 19.32 puts. So one would buy 19 or 20 SOX puts to hedge this portfolio.

The actual cost of 20 of the SOX December 240 puts is $26,000 since the puts are selling at 13. This $26,000 represents 6.85% of the actual net worth of the portfolio (which was $379,500). Thus, one would have to decide if he wants to spend almost 7% of the value of his portfolio in order to protect it after a 10% decline, out to December — five months from now. That decision can only be made by the stockholder, of course.

In summary, a few arithmetic calculations can be used to help one determine how many puts to buy to construct protection at a certain strike with a specific index. However, the portfolio owner must make the final decision as to whether or not the protection is worth the cost, much as he would need to do with any form of insurance.


This article was originally published in The Option Strategist Newsletter Volume 4, No. 14 on July 26, 1995.  

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