Thread by @Panoptic_xyz

1/12 In this series, we will look at different (financial) Greeks.

Most know about alpha, but what about beta? How can we compute it? How can we use it to hedge our investments?

Let's discuss! 🧵👇

2/12 First things first:

Beta (β) measures the risk of an asset or portfolio, S, against the risk of a reference market index, M.

See the mathematical definition below👇🤓

β(S; M)= correlation(S; M) x volatility(S) / volatility(M)

3/12 Beta increases w/correlation & relative risk (ratio of volatilities).

How can we interpret this? If:

- β = 1.5 ⇒ The asset S incr. 1.5% for each 1% incr. in the index M

- β = 0.5 ⇒ S incr. 0.5% for each 1% incr. in M

- β = -1.5 ⇒S decr. 1.5% for each 1% incr. in M

4/12 Let's take $ETH and $SPY as an example and compute daily returns using close prices.

We get:
correlation(ETH; SPY) = 0.33
volatility(ETH) = 0.037
volatility(SPY) = 0.013
⇒β(ETH; SPY) = 1.239

⚠️Spoiler alert: ETH is more volatile than the SPY

5/12 From 👆, a 1% price move in $SPY, implies a 1.2% price move in $ETH.

However, comparing ETH to SPY is like comparing apples to oranges!

Let's look look at token prices in UniV3 pools.

(Psst! here's a tutorial describing how to obtain these prices using Python and GBQ 😉)

https://twitter.com/Panoptic_xyz/status/1615373053705306112

6/12 We get the (1h) average token price of the following pools (all pools are at 0.3%)

LDO-WETH
UNI-WETH
WBTC-WETH
APE-WETH
MATIC-WETH
SHIB-WETH
WETH-sETH2
WETH-oSQTH

using ETH as the index M.

Note: All prices are converted to USDC using the USDC-WETH-0.3% pool price.

7/12 We obtain the following insights:

- Betas ranging from 0.587 (WBTC) to 1.914 (oSQTH)
- All betas considered are positive ⇒ prices (USD) positively correlated (see heatmap)
- β(SHIB; ETH) < 1, not bad for a meme coin 🤭

Note: 👆would change if we take a different index!

8/12 Ok, but how can we use this?

Investing in any asset entails 2 types of risk:

1. Unsystematic: related to the asset & industry
2. Systematic: related to market & macro factors

We can hedge against (1) by portfolio diversification.
We can use beta to hedge against (2).

9/12 How can we hedge against market risk (for a given M) ?

If we hold a portfolio S, shorting V * β(S; M) worth of M (with V = value of portfolio) would cancel out the market risk (see derivation below👇🤓)

Canceling out this risk means that our returns are independent of M!

10/12 Caveats:

- β measures risk wrt a market index M. Different markets = different β
- No SPY equivalent in DeFi means that we'd need to construct a given M when β-hedging cryptos.
-Can also use β to hedge options, but it's more complicated (we'll discuss this soon 😉)

11/12 Disclaimer:

None of this should be taken as financial advice. Please DYOR.

12/12 We hope you've found this thread helpful.

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