# Beta-Weighted

## Basic Points

- Beta weighting is a way to standardize all of one’s portfolio position by measuring their delta (directional exposure) to a single baseline as if it were all the same security.
- In this way, standardizing different securities (with varying percentage ranges and correlations) is “a means for investors to put all of their positions into one standard unit” (tastytrade, 2023).
- That standard unit is usually SPY deltas given that this represents the S&P 500 index which does a good job of representing the directional risk of most well-diversified equity portfolios. But some will opt to beta-weight their portfolio to QQQ if they are concentrated in tech. Likewise, in a portfolio concentrated with energy producers, perhaps they might want to beta-weight their portfolio to XLE (the energy sector).
- With a beta-weighting on SPY, which your broker would most likely use as a beta-weighting default, what happens is that each position gets translated into SPY delta. This reflects about how many shares of SPY each position would be worth. For those uncomfortable with thinking in deltas, each single delta has the same directional impact as a single share of SPY. That means 13 SPY deltas would have the same directional exposure as 13 shares of SPY.

## Advanced: Beta-Weighting Examples

If a security’s average percentage movement is greater than the SPY baseline, and it generally has a positive correlation (they usually move in the same direction), then it would have a higher beta (comparative measure of percentage range and correlation) than the S&P 500. As the CBOE puts it, “Beta weighted delta shows how much a stock will make or lose for every 1-point move in the referenced asset” (2022). Given that the baseline used for beta-weighting is always 1, if SPY is being used as the baseline then its beta will always be 1. It follows that if a stock’s beta is currently being measured at 2, then its beta-weighted deltas would be half of its normal deltas. Therefore, 40 shares of a stock (with a beta of 2) would be *beta-adjusted* so that they only have 20 beta-adjusted deltas. And the movement of this stock could be understood as if it were 20 shares of SPY, as opposed to 40 of its own deltas.

Applying this as an aggregation across the entire portfolio, beta-weighting makes it possible to understand the total directional risk. One might be holding 50 stock positions, all with different percentage ranges and correlations to SPY, meaning that they all have unique deltas. But by beta-weighting them all to SPY, we can approximate the entire directional exposure of a portfolio as if it were entirely composed of SPY. For example, if your portfolio has a total of 100 SPY deltas, and SPY drops 3 points, then your portfolio will lose about $300. But then if SPY moves up 5 points, then your portfolio will make about $500. Otherwise, with dozens of individual positions, the total expected profits and losses would be very unclear!

As another example, Interactive Brokers uses a metric called SPX delta, which is beta-weighted to SPX and applies to the entire portfolio. If it says that a portfolio has 10 SPX delta, then this means the global risk of the portfolio is about the same as being long 10 deltas worth of SPX. In terms of notional [cash] equivalence, 10 SPX deltas is the same as 100 SPY deltas. But as a pitfall to be aware of, these beta-adjusted metrics overlook items where the beta is unknown. As of March 2023, SPX delta ignores futures and mutual fund positions because they do not have a beta attribute.