Deriving the Stock Drawdown That Triggers Portfolio Rebalancing

Summary

The document derives the decline in stocks that would move a portfolio away from its target stock allocation far enough to trigger a rebalance. It assumes stocks begin at allocation X₀, bonds remain unchanged, and the trigger occurs when the stock share of the portfolio falls to a specified allocation X. After a stock decline, the new stock weight is calculated as the reduced stock value divided by the combined reduced stock value and unchanged bond value. Solving this relationship yields the drawdown threshold.

For a drift band expressed as a percentage below target, the response substitutes the lower boundary, X multiplied by one minus the drift allowance, for X in the formula. This addresses an allocation drift trigger rather than a portfolio drawdown target. The answer notes that the original interview question is ambiguous and qualifies its proposed interpretation; it does not discuss transaction costs, changing bond prices, or implementation details.

Key ideas

• A stock decline changes its portfolio weight even when bond value remains constant.
• The rebalance trigger can be found by solving for the stock decline that brings its weight to the threshold allocation.
• For a proportional drift band, use the lower allocation boundary as the trigger weight.
• The derivation assumes unchanged bond returns and a particular interpretation of the question.

Tags

# How to answer this interview programming question about drawdowns?


# How to answer this interview programming question about drawdowns?












I saw this question as an interview, and to be honest, I have no idea what it's even asking for:

> Write a function (in R or Python) that finds the stock drawdown which will trigger a rebalance, if given: an X% stock (vs bond) target allocation; and a Y% drift threshold from target allocation.

Do I pick a drawdown figure (20%?) and then calculate how much stocks need to fall to hit 20% portfolio DD given x% in stocks?

Do bond returns stay constant?

Same thing with the 2nd question, I just don't seem to understand what they are asking?

Any help appreciated!

## Answer by Karim L (score 1)

https://quant.stackexchange.com/a/22550

Say X0 is the % of stock at the peek

For 1), assuming the bond return stays constant, we will trigger a rebalance when:

$\frac{X_0(1 - DD)}{X_0(1-DD) + (1 - X_0)} = \frac{X_0(1-DD)}{1-X0.DD} = X$, and solving for DD gives $ DD = \frac{X_0 - X}{X_0(1 - X)} $

For 2), I would say same answer replacing $X$ by $ X(1 - Y) $

Not sure if this the correct answer, question formulation is weird.

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