Delta

All deltas are not the same. This is because delta is not weighted. You can be long 100 deltas of AAPL and long 100 deltas of Bank of America (BA), yet the exposure is different because of the price and volatility of each stock. This is where the concept of beta weighting comes into play. Beta weighting a portfolio to a base index is key. This is a practice engaged in by many trading firms, including some of the largest market making firms in the world. So how do you beta weight?

The first step is to pick the right index to beta weight a portfolio against. Most active traders’ portfolios are best weighted to the S&P 500. The SPX has the most active futures and most traders do not specialize in only one sector. The alternative is to beta weight to a different index, potentially the NDX or RUT; the NDX (NASDAQ-100 Index) is a good choice if you trade a lot of the major tech stocks, or you can choose RUT (Russell 2000 Index) if you specialize in small cap names. If you have a smaller portfolio, you could weight to the ETF of the index instead of the index (SPY, QQQ, or IWM). There are brokerage platforms that have beta weighting already programmed and others that do not. However, the concept is the same.

It is not hard to find beta weighting based on historical deltas; it simply involves comparing historical volatility of the underlying to the weighted index. By beta weighting, you are able to gauge the exposure of a portfolio due to a move in a major index like the S&P 500.

Gamma

The effect of beta weighting on gamma is much the same as the effect beta weighting has on delta. Because gamma is how the delta changes with a one point move, when a portfolio is beta weighted gamma, it will also convert and can be calculated in similar fashion.

Change gamma by the same adjustment made to delta. Thus, a stock with delta of 110 and gamma of 100 would see its gamma converted, relative to the SPX, by the same effect: 100 deltas convert to 4.8 deltas and has a beta multiplier of .048. Applying this to gamma converts 100 gamma to a gamma of 4.8 as well.

Essentially, to convert gamma:

While not exact, this will be better than a back of the envelope conversion for those using a spreadsheet to calculate a beta weighted portfolio.

Theta and Vega

Unlike delta and gamma when beta weighting, theta and vega are already weighted.

Theta

Theta represents the amount a position costs or produces with a daily passage of time. Because this number is derived from premium paid or collected, it is already weighted if you sell premium at the same delta. A single contract sold at 3.00 with 32 days to expire will, if it goes out worthless, produce $300 of decay and a similar theta number to a contract with delta sold at 0.30 10 times. It does not matter if it was SPX or a $30 stock; $300 of premium at a given delta sold in SPX will have a similar rate of decay (theta) compared to the same amount of premium sold in a $150 stockl. An example can be seen in the AAPL options vs. SPX options in Figures 13.1 and 13.2.

The two options, with similar expirations and deltas have the same amount of theta.

In Figures 13.1 and 13.2, the two sales collected similar premium, while the AAPL options produced slightly less theta (the result of a slightly higher delta); the two options produced similar risk, and more importantly, similar theta levels.

Vega

Much like theta, vega is derived from premium collected. In its raw form, vega is already weighted. 1000 vega in AAPL is the same, in raw terms, as 1000 vega in SPX; although the former would need more contracts to create that much volatility exposure. The more premium, the more vol exposure, regardless of price. However, a couple attributes of vega take the analysis a step further. For example, how do you analyze volatility?

Weighted Vega

Vega has a gamma to it, in that as the underlying moves, vega also changes. The closer to expiration, the more the volatility of the option. This can be seen in the price action of VIX futures. While every VIX future represents 1000 vega notionally, in actuality they do not act that way. A near-dated VIX future will have much lower implied volatility than a long-dated VIX future. Figure 13.3 shows a future with X days to expire that has much lower implied volatility than a longer-dated vol future. March is lower than April and April is lower than May, etc.

However, that is not the whole story. Because of the near dated nature of short term futures, they have a higher actual volatility (vol of vol) than longer dated futures. A move in VIX will cause near-dated futures to move more than long-dated futures. Take a look at how futures reacted to the French elections of 2017 (Figure 13.4). As the election got closer, VIX rallied, but the VIX futures did not move in unison; near-dated futures rallied harder over the 2 weeks heading into the election than long-dated futures:

Futures with less time to expire moved at a much greater relative speed than long-dated futures and, in some cases, long futures didn’t move at all.

Because near-dated volatility is so much more active than long-dated volatility, it becomes important to take this movement into account. Traders generally weight the volatility of their portfolio. By weighting a portfolio, you are able to give more emphasis to volatility in near-dated options than premium held in longer-dated options. There are several ways to calculate weighted vega.

Professional shops run correlation by days to expirations. This means that a professional group has run the correlation of volatility of an option within a single name or index that has 20 days to expiration against how its vol moves against options with expirations from one day to well over a year to expiration. These correlations probably are too much work for an independent managing a small book.

For the independent trader, it makes more sense to use a simple squaring function to calculate weighted vega. To calculate weighted vega, first come up with a base number of days to expiration, a simple standard duration of the portfolio. To do this, take the square root of the standard days to expiration over the days to contract expiration. Thus:

1000 vega with 60 days to expire with a standard duration of 30 days would have a weighted vega of:

1000 * SQRT(30/60)

which becomes:

1000 * 0.707 or a weighted vega of 707.

With a weighed vega of 707, I should expect to make about 0.70 on the dollar relative to my raw vega in the event that volatility increases. Thus, while in theory I am long 1000 vega, if the VIX moves up 1 point, I am likely only to make 707 dollars. This is important because if I have a vol spread long, a short in a near-dated month and long in a further dated month, I am not going to make money on a movement in volatility created by the overall market (something like a market sell off) the way I am expecting. If I am counting on vega to produce profit against the losses in being short gamma on a calendar spread, and if I only looked at raw vega, I am not going to get the results I want.

Using weighted vega will give a portfolio manager a better idea of how the portfolio will perform in a VIX spike than will raw vega alone. Weighted vega is a huge step toward portfolio management, but does not answer the vega question entirely. The next step is to use vol vega.

Vol Vega

Vol vega is a concept I learned at Group One Trading. I had to ask current CEO Jon Kinahan (at the time, head of training and head trader) what it was. He described it this way:

“If you own 1000 vega of a biotech, it is not the same as owning 1000 vega in an industrial. Vol vega adjusts for it.”

He then walked through the calculation. Vol vega multiplies how much more volatility the underlying has than the base index has. Thus, if I am long 1000 vega in SPX and at the same time long 1000 vega in AMGN, vol vega adjusts for the differences in the stock’s volatility. So if AMGN is two times as volatile as the SPX, SPX would have a vol vega of 1000 and AMGN would have a vol vega of 2000.

Vol vega is one of the most important calculations for anyone trading a wide range of stocks and indexes. It allows you to piece together what your real vol exposure is in the event that volatilities start to move, so that you are prepared for how dramatically the individual components may start to move.

Additionally, and this is the far more important case for vol vega, it is great for volatility pair traders (traders that sell volatility in one stock, or month, against another). Imagine I am trying to set up a pair trade between XLF (the Financial Select Sector Spyder Fund) and IBB (a biotech ETF)—yes I know there would never be a pair trade here that is why I used these two. While the two are both index ETFs, they are in very different sectors. If I buy 1000 vega in XLF because I think the vol is cheap, and sell 1000 vega in IBB because I think the vol is too expensive, even if I am right I might not win on volatility because IBB vol can move so much more. Using vol vega allows you to put a vol pair trade together that will make money because of volatility.

As an example, suppose XLF has volatility of 19. IBB has volatility of 27. If volatility increases by 10% in IBB and 15% in XLF, if I am long 1000 vega in both do I actually win?

In IBB, I would lose:

1000 * (27 * 0.10), or 2700

In XLF, I would make:

1000 * (19 * 0.15), or 2850

$150, not bad for a vol trade. But when you consider the capital involved, there were likely better trades. Next, adjust for vol vega.

27/19 is 1.42. Thus, if I traded on vol vega terms, I would go long 1400 vega in XLF for every 1000 vega in IBB. Thus my vega trade would look like this:

1000* (27 * 0.1), or 2700

versus

1400 * (19 * 0.15), or 3060

The end result is more than double the P&L. That is how strong vol vega is in a volatility pair trade.

Managing a Book

Now that we dug into the how to actually value a book of trades, how should you manage the book? It’s easy. Manage each trade individually. This make sense in particular if you are carrying fewer than 10 positions. However, when deciding to add to a book, you need to look at net Greeks to develop a portfolio. In the last chapter, we discussed ranking your trades based on the positions carried. In setting up a book to be beta weighted, vega weighted, and with some touch of vol vega, you can rank each trade against the whole portfolio.

Look at each trade on its own merits; if it is a good trade it should be considered, but once you have established positions on more than a few stocks and indexes, you need to start rating trades against the book. If the book is short gamma and short vega, you should be actively trying to find trades that are opposite the existing position. It’s easier to evaluate the value of the trade against a book if you are weighting properly.

Weighting will allow you to trade smaller or larger depending on the circumstances of the portfolio. For a portfolio after weighting, you should know which way you are leaning in buying or selling. If you have a clear idea of the net of your portfolio, you can set up a hedge based on movement.

The final attribute of portfolio management is how to manage severe global risk. You can set up a constant hedge or you can engage in crisis alpha management. Crisis alpha is a system of going for volatility when it is needed and ignoring it when its unneeded. This is the topic of the next chapter.