An introductory article on how beta impacts the volatility of a portfolio, how to beta weight, and how to calculate beta on your own.

# Bumpin’ with Beta: or, How I Learned to Love Portfolio Volatility

## Why is my Portfolio Imbalanced?

Hello there, crypto readers! Are you ready for a friendly fireside finance chat? For our need-to-know finance tidbit today, we’ll be playing around with a concept you may or may not be familiar with: **beta**. To start us off, picture this: you’ve taken up positions in three different altcoins; coin X, coin Y, and coin Z. The market is doing well, and, as it often is, the altcoin market is highly correlated to Bitcoin. The price of BTC increases 2%, and because of that correlation, your entire portfolio increases too. However, your three altcoins don’t all act the same. Coin X increases 2%, coin Y only increases 1%, and coin Z increases 6%. What’s going on? Shouldn’t they all increase equally because of their correlation with Bitcoin?

Introducing **beta**.

## What is Beta?

So, if beta is the culprit behind this tomfoolery, then what exactly is it? Let’s investigate. We’re all intuitively familiar with the concept. When Bitcoin moves violently up or down, the entire altcoin market reacts in lockstep. You might hear talk about specific altcoins having relative strength in a downturn. Sometimes, word on the “tweet” centers on altcoins that outperform a bullish Bitcoin. All these discussions refer to the concept of **beta**.

**Beta** measures the overall volatility of an individual asset against the overall market, or whatever benchmark is used. In the example above, we’re using Bitcoin as the benchmark since it is generally accepted that the broader crypto market is heavily influenced by “The King.”

While you might typically hear about beta in terms of volatility, I’d like to instead view beta through the lens of systematic risk. So, what is systematic risk and how does it help us analyze our portfolios?

Systematic risk describes risk across the board – a type of risk that you expose yourself to by simply entering the market. If Bitcoin plummets 10% in 10 minutes, any positions you hold across the entire market will undoubtedly be adversely affected. We call this “undiversifiable risk,” because there’s no way to avoid it – this type of liquidation cascade is difficult to perfectly anticipate in advance, and whether your holdings are diversified into 10 or 100 altcoins, your portfolio won’t be safe from the ensuing overwhelming market shock. As we dive deeper into **beta**, keep systematic risk in mind.

## The Building Blocks of Beta?

Now, let us examine the core components that make up **beta** and what the raw values mean in the context of systematic risk.

**1.0 ->** For beta readings, our baseline is 1.0. The benchmark beta value will always be 1.0 – for the rest of our fireside chat today, Bitcoin will be the benchmark to compare against altcoins.

If an altcoin has a beta of 1.0, it then has the same volatility of Bitcoin (1% BTC price increase = 1% Altcoin price increase), moves in the same direction, and has the same systematic risk (your portfolio would be as exposed to the market as just holding Bitcoin).

**0 to 1.0 ->** Values between 0 and 1.0 indicate decreased sensitivity across the board.

If an altcoin has a beta of 0.5, it is 50% less sensitive to BTC (1% BTC price increase = 0.5% Altcoin price increase), it still moves in the same direction, and it has less systematic risk (your portfolio would have some resistance to surprising moves from Bitcoin).

**Over 1.0 ->** Values greater than 1 are a magnifier in every respect.

If an altcoin has a beta of 2, that means it is 100% more volatile than BTC (1% BTC price increase = 2% Coin price increase), it still moves in the same direction, and it also greatly increases your systematic risk (your portfolio would now have extra exposure to any surprising moves from Bitcoin).

**Note**: because overly positive values act as an amplifier, altcoins with these values can be viewed as leveraged positions. This is important to note especially if you are already trading with leverage because if you long an altcoin with 5x leverage that has 2.0 beta, you are then potentially **twice as leveraged** and twice as exposed to the market!

**0 ->** Zero beta means the coin is not exposed to Bitcoin.

If an altcoin has a beta of 0, it moves randomly or not at all relative to BTC, so its volatility is not determined by any of Bitcoin’s price movements, and thus it carries no systematic risk (your portfolio would be perfectly hedged against surprising moves from BTC). In reality this is rarely a realistic situation in crypto unless you are holding a Stablecoin or a coin that temporarily moves in and out of correlation with Bitcoin. Even though an altcoin can sometimes (rarely) show 0 or near 0 beta readings, this can quickly change as a market experiences shock, and a coin that was previously showing low beta readings can suddenly jump to positive readings. Don’t necessarily trust a 0 beta reading!

**Negative beta ->** Negative readings mean the coin is acting as a “safe haven” against BTC.

If an altcoin has negative 1.0 beta, it moves in the opposite direction of BTC (1% BTC price decrease = 1% Altcoin price increase), is still volatile and related to BTC, and carries no systematic risk (your portfolio is not only hedged but benefits against BTC market shocks).

This is an exceedingly rare relationship that typically only shows up in “alt-season” where BTC pullbacks are met by a growth in altcoin prices across the board. There are cases in which a severe BTC downmove has one-off altcoins showing negative beta, but that relationship rarely lasts long.

**Important note**: Beta only measures the **historical** relationship of the asset to its benchmark! So while a long-term relationship can give us clues as to how an asset may respond to market stress, beta values can quickly change, potentially rendering your portfolio plan obsolete.

## Beta Weighting Your Portfolio?

Now that we have established an understanding of the underlying concepts behind **beta** and how the raw values can be interpreted, we’ll re-examine the first example in our mock portfolio and learn how to apply the concept of **beta weighting**.

In an advancing bullish Bitcoin market, you have three coins in your portfolio posting different returns. We understand that beta influences this factor, so we look at the values.

**Coin X = 0.5 = 50% less volatility**

**Coin Y = 1 = Same volatility as BTC**

**Coin Z = 4 = 3x as much volatility as BTC**

Armed with this information, we might make some adjustments. We could choose to be aggressive and overexpose ourselves to the market by shifting more funds to **Coin Z**, since it is outperforming Bitcoin, effectively entering a 4x leveraged position. This has benefits like freeing up capital for other positions and allowing you to capitalize on a fast-moving altcoin. However, if we want to be more conserative and we believe that **Coin X** can shelter us against a Bitcoin downturn, we could instead weigh our portfolio to this less risky asset.

Once we’ve chosen a position, calculating portfolio beta is easy. For ease of calculation, let’s look at an account size of 1 BTC.

- Add up all positions as shown in column A.
- Convert position sizes to percentage of total account.
- Fill in beta of all coins in portfolio.
- Multiply percentage size by each coin’s beta to find
**weighted beta**value. - Total portfolio beta = sum all of weighted beta.

To find your portfolio beta, you first add up all of your positions, as shown in column A. Next, convert those position sizes to a percentage of your total account to find out how much each position size occupies relative to your entire account. After you fill in the beta of all the coins you are currently holding, remembering that the benchmark is always equal to 1, multiply the % size by the coin’s beta. The result will be the **weighted beta**. The sum of all the weighted beta readings results in your **total portfolio beta**.

In this example portfolio, we have allocated a total of 20% to altcoins, with 10% allocated to the riskier Coin Z, which has a beta of 4 (300% more volatile!). The remaining 80% of the portfolio remains in BTC. After summing the weighted beta values, we get **1.275 beta**. That tells us that this portfolio is **27.5% more volatile** than bitcoin, or **1.275x leveraged**. We can also confidently say this portfolio does have systematic risk, because whether bitcoin moves up or down, our holdings’ gains and losses are amplified by beta.

Again, it’s very important to note that beta is a **historical lookback**, and as such we can measure **beta** with different lookback periods to get a different perspective on the historical sensitivity of an altcoin. For example, below is a measurement captured on March 4th, 2021, of 1-day, 7-day, and 30-day beta measured against BTC.

On the 1-day lookback, Cream is effectively neutral with BTC, Dot is 49% less reactive to BTC, and Uni is 252% more reactive. 1-day readings give us a very short term impression on how these altcoins are behaving, but when we observe the long term data, we can see that overall these coins have acted as leveraged positions compared to BTC.

## Simple Maths and Calculating Beta in Excel/Sheets

I am no swanky mathematician. There are plenty more sources that will take you on much more intricate journeys into the mathematics of beta, so I’ll only lightly touch on it here.

**Beta = Covariance of altcoin and of the benchmark (Bitcoin) / Variance of benchmark (Bitcoin)**

In plain english, beta looks at how an altcoin and Bitcoin move together, and compares it against how Bitcoin moves relative to its mean.

**Note**: you can substitute Bitcoin for any number of other benchmarks that you are interested in measuring, for example: a privacy coin against a privacy index, a DeFi coin against a DeFi index, an exchange token against an exchange index, and so on. I find FTX’s indexes to be especially useful here as a guide for identifying different sectors upon which to build beta readings, but you could potentially identify any number of unique categories that could prove useful.

For those of you interested in calculating beta on your own in Excel or Sheets, I recommend using the =slope(x,y) function as follows, where x is the return % window of the altcoin and y is the return % window of the benchmark (Bitcoin):

In this example I have captured the last six 4-hour candles (24hour window) of Uni and BTC to calculate 1-day beta.

**=slope(C3:C8, F3:F8)**

Column C3:C8 is the altcoin’s return % (using the last 6 periods to capture a 24-hour window), and column F3:F8 is Bitcoin’s return %.

Uni-USDT is 182% more volatile than BTC-USDT over the last 24-hours.

## Closing Thoughts

We have come to the end of our journey together, crypto friends. I hope that some of the descriptions and examples of beta discussed within have sparked a creative interest in the applications of beta for some of you. I know it has for me.

Now before I send you back into the wilds of the marketplace, let’s remember some of the key points we’ve learned here today.

Beta is a historical lookback and not a predictor of future systematic risk, but can be an important tool to ballpark the level of portfolio risk you are assuming anytime you open or close an altcoin position.

Beta can be furthermore used as a tool to find market leaders and outperformers you might prefer to leverage up on in a bull market, as well as an indicator to risk-off if you’re too overly exposed during a pullback. It can also be used to find relative strength on a short-term basis, or seek out longer term investments that continue to outperform the market.

There are endless iterations of categorizing and creating your own benchmarks beyond just looking at the obvious market leader Bitcoin, though when creating and monitoring other benchmarks like a DeFi or Privacy basket, I always find it helpful to link their beta and correlation back to Bitcoin, because, as we all know, at the end of the day:

Bitcoin is king.