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Leverage, Borrowing Costs, and Long-Run Portfolio Value

Article Quant Q&A · Author: Dorky
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Summary

The question compares the long-run behavior of leveraged exchange-traded funds with a buy-and-hold portfolio using borrowed money, especially when the underlying asset ends a period near its starting price. The replies challenge the claim that leveraged funds must always fall to zero: a price path can be constructed in which a leveraged fund and a similarly leveraged portfolio continue to rise.

A separate reply points out that borrowing costs can erode a leveraged portfolio even when the underlying is unchanged, since financing has a cost. The exchange provides competing observations rather than a general result or a worked calculation. Outcomes depend on the path of the underlying, leverage mechanics, financing costs, and the particular product; the brief discussion does not quantify these effects or establish that a leveraged portfolio will inevitably reach zero.

Key ideas

  • A leveraged fund does not necessarily decline to zero under every possible underlying price path.
  • A leveraged buy-and-hold portfolio can rise if the underlying path supports gains after leverage.
  • Financing costs can reduce the value of a leveraged portfolio even when the underlying ends unchanged.
  • Long-run outcomes depend on price paths, leverage structure, and borrowing costs.

Tags

Risk managementPosition sizingEquities
Full text
# Leverage on ETF the same effect as on portfolio?


# Leverage on ETF the same effect as on portfolio?












While we know that leveraged ETFs do decline in value to zero given infinity, can we also say the same with our portfolio value if we use leverage in our trading activity and seeing our portfolio value fluctuating in close correlation to the underlying asset price times leverage, with a net decline in value over time, while the underlying asset price remain unchanged by the end of the same time period, even though we commit to just 1 trade (buy-n-hold) within this time period?

Edition: It's okay. I've found the answer. This question is considered resolved but with no relevant answer given I would want to delete the question but don't know how.

## Answer by 6595 (score 1)

https://quant.stackexchange.com/a/17892

I'd question the assertion in your question, what proof do you have that leveraged ETFs must go to zero? A plausible price pattern can easily be constructed that leads to a leveraged ETF that climbs forever. That same leveraged portfolio would climb forever as well.

## Answer by vega (score 0)

https://quant.stackexchange.com/a/18447

I may not have fully understood your question, but I assume you are asking what will happen on a leverage portfolio over time if the underlying price stays the same.

A leveraged portfolio would likely eventually go to zero (and below) simply because of the cost of leverage. At minimum, you are borrowing at the risk-free rate. An ETF would just go to zero.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.