Beta weighted delta

Entering my sophomore year of high school, I decided to relinquish three weeks of summer vacation to take a course in "International Markets and Finance" at Brown. Despite doing what any fourteen-year-old would cringe at, I actually had a lot of fun and learned from my intelligent peers and professor. It was a great introduction into the world of finance and definitely gave me a new perspective at the trading world.  

During our coursework, we were assigned a paper trading project in order to make some virtual dough. After competing with other teams in our class, we were going to be evaluated on performance and strategy by our professor. 

Our class duration of three weeks was a tiny time frame to measure any kind of performance or skills, because success inevitably laid in selecting stocks and hoping it rallied. What was worse,  we couldn't short stocks or trade options, futures, or any derivatives. Given these shortcoming, I dipped into my bag of tricks and tips that I learnt from my trading gurus at TastyTrade and picked 'beta-weighting delta'.

So what exactly is 'beta-weighting delta'? 

Beta-weighting delta on a portfolio is  one number that can tell us as to how much our portfolio can move up if the index moved up 1 point -- or much our portfolio would move down if the index lost 1 point. While this didn't necessarily help in picking lucky stocks, it did help us watch the impact any of our picks made on our portfolio. While our team didn't win the stock-picking competition, our unique approach to portfolio management won us some accolades from my professor.

In a past post,  I previously discussed the important Greek metric: delta. Deltas of an option are the measure of how much the option price would move for a $1 move in the price of stock. While a bit different, the concept of the 'beta weighted delta' of a portfolio remains the same: it answers the question as to how much your portfolio would gain (or lose) for a $1 gain (or loss) in the index that you are beta-weighting against.

So what is beta? Beta is a measure of volatility for a specific stock. This is computed by your trading platform based on historic relations with the index. Different stocks have different betas.  Listed below are a few betas:

As you can see, Amazon's (AMZN) beta is 1.48 while that of Facebook (FB) is 0.71. The benchmark index SPY is 1.
Beta of the stock helps us infer the volatility of the stock compared to the index. So Amazon's at 1.48 means it is about 48% more volatile than SPY and if the index rallies up one point, Amazon could rally up 48 points. 

Using beta, we can beta weight all of our stocks against the index which in essence would compare a diverse group of stocks into some sort of equivalence using the index.  The formula and calculation of the beta weighted delta is as follows:​

Consider for example a simple FANGs portfolio in which we have short 30 delta put (that is, we have long bias in the four stocks). Here we have found the beta weighted delta for all four stocks 

So if you sum up all the beta weighted deltas of individual stocks, you get the beta weighted delta of your portfolio -- in our example it's 347.05.

This single number gives us a bird's-eye view of the risk in our portfolio .  Using this information, we can strategically position ourselves to neutralize our deltas and reduce risk.  We could hedge our portfolio against a downturn by selling about 347 deltas worth of SPY which can be done by either straight selling 357 SPY stocks or selling say about 7 ATM calls of SPY (each ATM call is 50 delta).

Note that the beta weighted deltas constantly fluctuate with price so any and all adjustments should be made with the current prices. Most good trading platforms (like TastyWorks) provide these calculations for free so traders can focus on trading and not crunching numbers. Having a basic understanding of this concept will go a long way in managing your portfolio.

Thank you for reading! :)