Measuring Your Portfolio’s Bias 

By TradeSmith Editorial Staff

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Everyone holds different amounts of risk in their portfolio.

Some folks prefer low-volatility dividend payers, while others skew toward high-growth tech companies.

Looking at your portfolio as a whole, could you tell me your relative risk to the S&P 500? It’s a question most of us never really think about. Yet it’s one of the most crucial elements of investing.

Every investor must know the amount of risk and bias their portfolio holds in aggregate. So, how could you possibly quantify this?

Beta-weighted delta.

To start, you need two measures: beta and delta.

Investors can use beta to calculate the amount of risk and bias in their portfolio, which, coincidentally, are two sides of the same coin. And for this article, you can assume they are the same thing.

Delta helps you convert the risk into units.

I’m going to break down this concept into digestible bits to help you understand what beta and delta are and how to use them to calculate your portfolio’s risk and bias.

Beginning with Beta

On most days, if the SPDR S&P 500 ETF (SPY) rises, the Invesco QQQ Trust ETF (QQQ) rises.

In fact, the typical correlation between the two ETFs, meaning how often they move together, is 0.83.

For reference, correlation measures the movement of assets in relation to each other on a scale of -1 to 1, where -1 means the two assets move perfectly in opposite directions, 1 means they move perfectly in the same direction, and 0 means they move entirely independent of one another.

The thing about correlation is, it doesn’t tell you how much one asset is likely to move relative to another.

And that’s where beta comes in.

Crack a finance textbook and you’ll likely find beta defined as a measure of volatility or systematic risk relative to the overall market.

In other words, beta tells us how much a stock moves relative to a benchmark, which in most cases is the S&P 500.

Most finance websites will list a stock’s beta using the S&P 500 as the benchmark.

The problem is that many sites measure beta differently, choosing different time periods to calculate the beta value as well as whether it’s levered or unlevered, meaning whether the effects of the company’s capital structure are taken into account or not.

For example, if you look up Tesla (TSLA), you’ll get answers ranging from 1.42 to 2.05.

While I prefer calculations that only look back a year and incorporate levered information, you really just need to be consistent in how you calculate the beta across all your holdings. So pick one source and stick with it.

Digging Into Delta

If you trade options, chances are you have heard or learned about delta.

You can get a full rundown on delta from my previous newsletter.

As a refresher, delta is a measure of how much the price of an option changes for a $1 increase in the price of the underlying stock.

For example, the price of an option with a 0.40 delta would increase by $0.40 if the underlying stock increased by $1.

The other way we can think of delta is that it’s equivalent to the number of shares you control.

Using the same example, a 0.40 delta would be the equivalent of controlling 40 shares of the stock. Since each options contract controls 100 shares of stock, we multiply 100 x 0.40 to get 40.

This allows us to convert options into a similar measure to our stock holdings so that we can calculate our portfolio’s overall bias.

Combining the Two

Now for the good stuff.

We want to create what’s known as the beta-weighted delta for our portfolio, a concept coined by the folks at Tastytrade.

The formula is fairly straightforward.

We start by picking out the baseline. Most folks use the S&P 500 (SPX), or the SPY ETF. We’ll use SPY for this example.

Then we look up the delta for our options. The delta for a stock is always 1 for every share of stock that you own, or -1 for every share of stock you are short.

Then we plug in our values to the following formula:

Beta-Weighted Delta = Delta × Stock Price × Beta × (1 / Baseline Price)

Let’s see what that might look like for the sample portfolio below:

This made-up portfolio consists of various long stock positions, likely some puts on Amazon, as noted by the -0.60, and probably covered calls on AT&T, since the number of option contracts (10 contracts for 100 shares each) with a delta of -0.30 per contract matches up with the total number of long shares of AT&T’s stock (1,000 shares).

The total beta-weighted delta value of 93.32 says that for every one dollar increase in the SPY, the portfolio should increase in value by $93.32, all other things being equal.

This means the portfolio has a positive overall bias and risk because if the SPY were to drop by one dollar, we would expect the value of the portfolio to decline by $93.32, all other things being equal.

Beta-weighted delta is a great concept to help us calculate the net effect of a portfolio that includes stocks and options, with both long and short positions, to.

Keep in mind this analysis only gives you an idea of your bias. It is unlikely that your portfolio will move exactly as prescribed.

In fact, because of the nature of options, the deltas can and will shift as the price of the underlying asset moves around. This is what’s known as “dynamic” delta. Stocks will only ever have a delta of 1 for each share, which is why it’s referred to as “static” delta.

What I love about beta-weighted delta is how it lets you model individual positions and see the impact each one has on your overall portfolio.

It’s a fantastic tool that lets you take a portfolio of stocks and add in options strategies like call credit spreads to neutralize some of your directional risk.

So I have an assignment for you.

Download your portfolio into a spreadsheet like I modeled earlier and calculate your portfolio’s beta-weighted delta. Email me and let me know how it lined up with your expectations.

While I can’t answer your emails individually, I promise to read every one.