# Portfolio vega and equivalent long/short from levels

## Options trading skills tested :

Practical understanding of vega. Relationship between options, vega and profit and loss

## How to set up the training exercise

Load any Volcube simulation and make a few quotes and execute some trades against the broker in reasonable size. Aim to get your at-the-money Vega number in the Risk Detail showing a number at least long or short \$1000. Or click on the thumbnail image below to follow the example.

A delta-hedged short call spread position

Open up the thumbail which shows a Volcube simulation where we have sold 250 call spreads (that have been delta-hedged). You may want to print the image or at least have it in a place where you can read this and see the numbers in the image. We will use this as an example of how to perform this options training drill.

We can see that selling this call spread has generated an at-the-money vega position of minus \$1308. This is the number in the Risk Detail pane, in the vega row, directly below the 100 (i.e. the live Spot price). This tells us that the aggregate amount of vega in our whole position is short \$1308, versus the current spot price. The reason we are short vega is that we have sold the 100 – 109 call spread. In other words, we sold the 100 calls and bought the 109 calls, in equal amounts. We sold 250 of the 100 calls and bought 250 of the 109 calls (i.e. sold 250 call spreads). You can check this in the Inventory pane in the bottom left. Plus, you can check the Pricing Sheet and see that the 100 calls have more vega than the 109 calls. This makes sense because the 100 calls are at-the-money and the 109 calls are out-of-the-money. Hopefully this is clear enough. If you don’t understand any of the terms being used here, please check the Volcube Learning environment in the application for an appropriate video or article about vega or call spreads. Or check out the options articles on www.volcube.com here.

Also notice that selling this call spread has generated a theoretical profit of \$919 dollars. This can be seen from the Theo PandL row in the Risk Detail, under the current spot price.

Okay, so much for the basic set-up. After you have been through this example, generate your own situation or look at one of your previous Volcube trading sessions in Replay mode and you can pick out the equivalent numbers. Now for the training exercise!

Option traders will often look at these basic numbers and figure out the answer to the following question. Given my portfolio p and l and vega, where am I long or short implied volatility from, roughly? If you don’t understand the question fully; don’t worry. You will after you’ve played more Volcube games and once you understand the answer to the question! Let’s re-phrase the question slightly. Given the p and l and position vega, how far can implied volatility move before the position loses money? The trader in this case has \$919 dollars of theoretical profit. This means he has \$919 of real profit, if his theoretical option values are a fair reflection of the real market value of the options. He is short \$1308 vega. This means that for every 1% move in implied volatility, he makes or loses \$1308. Because he is short vega, he will make money if implied volatility falls and lose money if implied volatility rises. Remember also that by ‘a 1% move in implied volatility’,option traders typically mean from say 30% to 31%, not from 30% to 30.3%. So, we can say that if implied volatility rises by 0.7%, all of the theoretical profit and loss will vanish. (Remember the definition of vega: the change in option value for a change in implied volatility. So if implied vol here changes by 0.7%, the portfolio value will change by 0.7% times \$1308 = c.\$919).

This then gives the trader a very useful piece of shorthand information. In this case, he knows that he still has some profit unless implied volatility rises by more than 0.7%. This is the same as saying that the trader is synthetically short from 0.7% above the current level of implied volatility. So this is the answer to the question. Where is the trader synthetically short implied volatility from? 0.7% higher than its current level.

Try this for yourself. Generate a position in a Volcube game, hopefullly for a profit! Now, take the position vega. If you are long vega, you need to calculate how far implied volatility can fall before your profit and loss is wiped out. This tells you the level of the implied volatility from which you are long. Suppose you are net long \$1000 vega and have \$2000 in profit. Then, your profit will all be lost if the impied vol falls 2 vols. So this is where you are synthetically long implied volatility from. If at-the-money implied volatility is 30%, you could view yourself as long from 28%.

### Important caveats.

Remember this is just a shorthand and an approximation. The basic method makes all sorts of simplifying assumptions, such as that the vol curve will shift equally across the strikes or that position vega is not going to alter when other things alter. Nevertheless, this technique is still one that is used by option traders everywhere to get an approximate gauge as to the level of implied volatility they are long or short from. Make sure you can make this basic calculation (approximately at least) for any options portfolio in Volcube without using a calculator and in under 5 seconds.

These articles are for informational purposes only. They should not be regarded as an offer to sell or as a solicitation or an offer to buy any financial or derivative products.

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