A sharp decline is the case where the value of an asset in your portfolio drops quickly and then stabilizes to a new baseline value.
This graph illustrates a sharp decline and then stabalization. The white line is the price of a single asset in a portfolio. The orange line is the value of the portfolio if the HODL strategy is used from beginning the end. The blue line is the value of the portfolio if a rebalance was performed at the white dot. Result: rebalancing and HODL produce similar results for this type of sharp decline.
HODL of an asset which has a sharp decline simply results in the reduction of portfolio value directly proportional to its own value decrease over time.
The results for this situation are the same as those of HODL. While the single asset crash resulted in a net decrease for the portfolio, a rebalance at the dot does not introduce any additional loss in funds. Rebalancing anywhere along the decreasing line before the dot would result in additional loss (See “Slow Death”).
Both rebalancing and HODL perform the same in this instance when looking at the complete portfolio value. Rebalancing at the dot will accumulate more of the asset which had a sharp decline, however, the stabilizing price afterwards means no additional loss in portfolio value is observed.