A part of classical portfolio theory has always bugged me. It treats levered strategies fundamentally the same as ones that don’t borrow. I think that inherently everyone knows they are very different.
Before we dive in, think about this question:
Modern Portfolio Theory
Modern portfolio theory says the logical investment strategy is to invest at the tangency portfolio and then scale up or down with leverage or cash to meet either your desired risk level or return level.
On paper this all makes since. If you follow these principles, you will theoretically receive the best return for whatever risk level you choose.
But in implementation, this strategy doesn’t always lead to a comfortable portfolio selection.
Levering the Tangency
Many times the market looks like the following: one where the benefit on paper to levering up the tangency portfolio is real, but small.
In this instance the tangency portfolio — the portfolio with the best Sharpe ratio — is conservative with 50% bonds and 50% stocks. Bonds are calm and negatively correlated (-0.3), so the “bullet’s nose” sticks out a good bit. The return premium from bonds isn’t much above the risk-free rate (1/2%). So the unlevered efficient frontier rises nearly as fast as the levered tangency portfolio.
The green dot is the 50% bonds/ 50% stocks portfolio levered up 2 times. This investor own 100% stocks, then take out a loan and buys 100% bonds as well. But notice, that doing this produces a portfolio that is very similar to owning just stocks alone.
Is small gain worth the “risk” of levering a portfolio 2X?
Leverage Aversion
I explored this question on twitter:
People clearly don’t like leverage.
Classical theory is likely indifferent to this choice. I think it makes perfect sense to not want leverage here. On paper there isn’t any benefit to doing so when expected return and volatility are equal.1 I totally get why nearly everyone chose to avoid leverage. I feel the same way.
So what are the preferences when leverage provides a slightly better return, similar to the chart above?
Even when providing slightly more return, people’s choices barely moved. Seventy three percent still chose to give up an expected return to avoid using leverage.
Should this be called leverage aversion?
How Much Aversion?
I kept pushing the levered returns higher to try and find a tipping point.
An extra two percent return doesn’t do the trick. Most people still chose to avoid leverage.2
What about the same return, but less volatility, and only 1.5X leverage?
Closer, but still more people avoid the leverage, preferring the higher volatility to employing leverage.
Ok, let’s push harder. What about both: 2% lower volatility, and 2% higher return from 1.5X leverage?
Finally, more people are willing to employ leverage. But still, even here nearly a third of respondents preferred to stay away from leverage.
This is Logical
Some followers understood the existence of leverage represented a hidden unaccounted for risk.
People grasp that leverage itself contains extra risks which don’t show up in modern portfolio theory.
- Leverage magnifies errors made in portfolio construction.
- Magnifying these errors can be disastrous.
I agree with these sentiments, but I don’t fully know how to quantify them yet. I’m still exploring this.
Crossover Point
Now there is certainly nothing scientific about these polls. But my own intuition tells me that all things being equal, I would rather not use leverage. And all things nearly equal, I would still not use leverage.
But at some point when a levered portfolio provides enough benefit, I would flip and be perfectly happy using leverage. Where is this point though?
Judging by my twitter followers, my personal flipping point is earlier than most. But this may be because I envision levering a well diversified portfolio with simple components. Riskier assets would increase my fear of leverage.
It’s OK to Dislike Leverage
Modern portfolio theory’s view of leverage isn’t entirely flawed. Many times the efficient frontier curve makes leverage advantageous. The leverage line can be steeper. And if you’re targeting very high returns, leverage is a must. Foundationally the concept is fine.
But ultimately the concept of levering the tangency portfolio is incomplete. It doesn’t acknowledge that leverage has it’s own risks which stem from parameter estimation errors and personal investment criteria. These are real risks and real inputs that are very difficult to quantify.
Inherently I think we all know this at some level. I use the term “aversion” here a bit tongue and cheek as I don’t think there is anything wrong with this. Academics may say this “fear” of leverage is irrational. But it’s not. It’s just very hard to quantify.
So if you dislike leverage, don’t worry, it’s perfectly understandable. And if you’re building a portfolio with leverage, confirm it’s providing a benefit that warrants the amount of leverage employed.
1-There actually is an argument why you might want to choose leverage and it involves taxes. Depending on your situation, the interest from the margin may be tax deductible, and could make leverage preferable. Hat tip for Brandon Koepke for bringing taxes into the discussion.
2-This is an interesting answer to the question. Investing in both strategies, as an ensemble may produce a superior result.
off the top of my head, we quantify the following:
1. disutility from downside (costs of financial distress from leverage gone wrong)
2. utility from upside (extra return)
ratio of these (1 versus 2) will give you the leverage aversion.
potential curveball: they might be non-linear functions instead of linear functions or point estimates.
https://elmfunds.com/george-costanza-at-it-again/
This problem discussion is related to the Tiger Woods articles describing the safe play and possibility of incorrect input estimates.
Yes, very much so.
I am prsonally comfrtable using leverage. But I can think of 2 additional risk elements that it adds to a portfolio:
1) Leverage costs make it harder to recover from a long downtrend
– The lesser one is that the fixed and recurring cost of leverage amplifies the impact of low performance periods – over a long period with no sustained moves upward your capital is depleted further than without leverage. When the statistically-predicted upside returns finally do come in you’re starting from a lower relative base than an unleveraged portfolio.
2) Leverage changes your distribution pattern away from “normal” –
With leverage there is a hard and fixed downsidei nthe form of the borrwed funds thta much we repaid, not a tail that slopes away forever. SImplistically, if you lose 50% of a 2:1 leveraged portfolio and you will be called in and wiped out. The distribution for a leverage portoflio looks more like a fat-tailed Chi- squared distribution than a bell curve.
Both strong reasons to follow your earlier advcie and “lean left” with leveraged portfolios!
Historical volatility looks like future volatility until suddenly it doesn’t.
Heavy losses can kill you levered, while you live to fight another day
unlevered. There is a large negative fat tail potential with the levered option
that may not show up in backwards looking statistics.
What if you did’t call it leverage? What if you called it super fun booster? There is an aversion to the word, not the fact! If you call something equity then people will like it! Equity usually has significant embedded leverage. If you call something private equity then people will LOVE it! Private equity has even more leverage.