From Gerd Kommer and Daniel Chancellor
This post was updated in August 2024.
To finance investments with borrowed capital - to leverage or, in modern German, to leverage [1] – appears attractive if the achievable loan interest rate is lower than the historical average return of the investment, be it stocks, real estate, gold or cryptocurrencies. This has probably been the case for stocks four-fifths of the time in the last 100 years.
In principle, the return on equity of an investment can be increased indefinitely through leverage.
In view of this ultimately banal statement, in this blog post we attempt to give a new answer to the old investor question: “How sensible does it make sense to partially finance equity investments with credit or credit leverage in order to increase the return on the equity capital invested?”
Leveraging or, less elegantly, “debt-funded investing” can occur at both the corporate and household levels. In this blog post we will focus primarily on leverage at the household level, but will also address corporate leverage. If you want to arrive at a meaningful assessment of the advantages and disadvantages of leverage, the two fields cannot be separated.
We'll look at the following aspects of leveraged investing below:
- How does the credit leverage effect work?
- Leverage as a cause of financial ruin
- Empirical studies on the return effect of leverage for companies and private investors
- The “financial mathematical margin call problem” when analyzing leveraged investments
- The problem of negative interest rate differentials in leveraged investments
- The myth of debt invalidation through inflation
- Practical advice for anyone considering leverage
(1) How does the credit leverage effect work?
Readers familiar with the mechanics of credit leverage can skip this first section.
A case study: Lisa invests 100,000 euros in an MSCI World stock ETF. She finances 40,000 euros of this (40%) through a securities loan, and 60,000 euros comes from herself as equity. We imagine two scenarios. In scenario 1, the MSCI World rises by 30% during the observation period, while in scenario 2 it falls by 30%.
What effect does the two scenarios have on the return on Lisa's equity (EK)?
In scenario 1, Lisa's equity return is 30,000 euros ÷ 60,000 euros = plus 50% (profit from equity), in scenario 2 the equity return is -30,000 euros ÷ 60,000 euros = minus 50%. (We ignore the cost of debt and any tax effects here for the sake of simplicity.)
Without leverage, equity returns would have been plus 30% and minus 30%. (Where there is no leverage, the return on equity and return on total capital are identical.)
We see that leverage symmetrically increases both the opportunity (the upside) and the risk (the downside).
In general, leverage results in increased equity returns for a given period, be it six months or 20 years, when the debt expense (absolute or percentage) is lower than the total investment return (absolute or percentage). The general formula for calculating return on equity is:
EKR = GKR + (GKR – FKZ) × (FKA ÷ EKA)
Explanation of abbreviations: EKR = return on equity, GKR = return on total capital, FKZ = interest rate on debt, FKA = share of debt in percent or absolute, EKA = share of equity in percent or absolute.
A numerical example. We use Lisa's investment in scenario 1 and a loan interest rate of 3%: EKR = 30% + (30% - 3%) × (40% ÷ 60%) = 48% (rounded).
With leverage you can also lose more than 100% of your equity. A numerical example: Lisa again invested 100,000 euros in a leveraged way in an MSCI World stock ETF, this time with only 30,000 euros equity and 70,000 euros FK. Now the global stock market collapses by 40% within a few months (like in the Corona crash at the beginning of 2020). Lisa has now lost her entire equity of 30,000 euros and owes the bank another 10,000 euros. In percentage terms, your loss is –40,000 ÷ 30,000 = –133%
So we have seen that leverage symmetrically increases both upside potential and downside potential.
For the theoretical proof that corporate leverage does not produce a systematic advantage in terms of risk-weighted return on equity (ignoring any tax advantages), the two economists Franco Modigliani and Merton Miller received the Nobel Prize in Economics in 1985 and 1990, respectively. [2]
(2) Leverage as a cause of financial ruin
In the past 200 years, there is probably no other single factor that has led to the economic ruin of private households, companies and states more often than leverage. A small library could probably be filled with books about losses and bankruptcies through debt-financed investing. For reasons of space, we will not mention specific cases and will limit ourselves to quoting an experienced, successful investor - Warren Buffett:
"As we all learned in third grade - and some of us learned again in 2008 - any series of positive numbers, no matter how impressive, evaporates when multiplied by a single zero. Financial history teaches that leverage, unfortunately, often produces zeros, even when practiced by clever people." (Warren Buffett, Letter to the Shareholders of Berkshire Hathaway 2010)
To the extent that leverage is undertaken voluntarily, the motives are usually one or more of the following three considerations:
(a) Increase the return on equity (“get rich faster”) through the credit leverage effect.
(b) Benefit from the tax deductibility of borrowing costs (only for commercial investments).
(c) Exploit the “theory” that inflation reduces the burden of credit.
Involuntary leverage (involuntary borrowing) is naturally the result of a lack of equity or liquidity. In most cases, involuntary leverage is likely to worsen the relevant returns on equity.
In this blog post we will primarily deal with argument (a) and briefly with argument (c). We ignore the tax argument (b) because it is probably well known to our readers anyway and because it is rarely the dominant pro-leverage argument when it comes to debt financing of assets for private investors.
(3) Empirical studies on the return effect of leverage for companies and private investors
Although leverage is an extremely practical phenomenon, there are fewer scientific studies on it than on many other influencing factors in investing. This probably has to do with the particularly big challenges in statistically analyzing the impact of credit leverage. Having said this, we briefly summarize the literature in this section.
(a) After over 50 years of empirical financial market research on this fascinating topic, there is no convincing scientific evidence that leverage has a systematic positive return effect on companies (i.e. at the immediate company level). Rather, the opposite is true: the majority of existing scientific studies show that companies with higher levels of debt do not have systematically better business profitability indicators and often even have worse ones. Leverage at the company level also appears to have, on average, a negative impact on shareholder returns - on the absolute and even more so on the risk-adjusted shareholder return (the return-risk combination), e.g. B. in the form of the Sharpe ratio. [3] We know from so-called “quality companies” (“quality” in the sense of the statistical “factor premium quality”) that they statistically outperform the overall market in the long term. Quality companies are defined, among other things, by the fact that they have particularly low debt in comparison. We list a selection of scientific studies on the negative or at least ambivalent return effects of leverage at the end of this blog post.
(b) For real estate companies and real estate funds, it has been particularly clearly demonstrated that high leverage leads to worse absolute or risk-adjusted returns than low leverage or no leverage. This is surprising given that in parts of the private real estate community there is a sometimes cult-like belief in the advantages of credit leverage in the real estate sector. Because this misconception is so common with regard to both rental properties and owner-occupied residential properties, we have addressed the topic Credit leverage of real estate investments dedicated a separate blog post (here).
(c) The fact that private investors who actively trade in the capital market underperform a correctly selected passive benchmark has been confirmed in new studies for over 20 years (Barber et al. 2000, Bhattacharya 2016, Barber et al. 2022). If you look even more closely and differentiate these traders into those who work with and those without leverage, it becomes clear that leverage statistically further worsens performance (Davydov 2022, Heimer 2022).
(d) In the case of so-called leveraged stock ETFs (the debt financing is here at the product level, so it is “built in”), the risk-adjusted returns (Sharpe ratio) are statistically worse over long periods of time than with similar non-leveraged ETFs (Subrahmanyam 2021, Davydov 2022, Frazzini et al. 2022). This means that although the absolute returns of these products may be higher over long periods of time and especially in good stock market phases than the returns of conventional, non-leveraged product alternatives, the risk-weighted returns (e.g. the Sharpe ratio) are worse in most cases. The volatility of leveraged ETFs is often twice as high and the maximum drawdown is over half as strong. Even the longest “zero return periods” are longer than with corresponding unleveraged products. Whether leveraged ETFs are meaningful products for private investors due to their complex technical properties, the so-called “path dependency”, and whether they are sufficiently understood by the majority of their buyers is doubted in the specialist literature (Pessina et al. 2022).
All in all, we can conclude from existing scientific studies that highly leveraged investments in stocks rarely produce higher risk-adjusted returns. In other words: the investor receives less return for the risk taken than with the non-leveraged alternative.
(4) The “financial mathematical margin call problem” in the analysis of leveraged investments
For an investment financed purely from equity, the maximum loss is known to be 100%. With a partially leveraged investment, however, the maximum loss is higher, both theoretically and practically. It can far exceed 100%.
A calculation example: Investment X is financed with 40% equity and 60% debt. The value of the investment now drops by 50%. In this case, the calculated equity loss is minus 125%. The investor has lost his entire investment and also owes the lender an additional 25% of the original equity.
In practice, however, securities investments will rarely result in a loss exceeding 100% because a margin call (an additional payment obligation) is made by the lending bank beforehand.
Typically, banks only lend up to 50% on stock investments. The so-called loan to value (LTV) is a maximum of 50%. If the LTV rises above this limit due to a negative return on the mortgaged investment, the bank requires the investor to reduce it below this limit. This can be done in three ways.
(a) The investor provides additional funds financed from equity as additional collateral (cash or new shares).
(b) The investor partially repays the loan from his own funds external to the depository.
(c) The investor sells a certain amount of shares from the portfolio and uses the proceeds to repay part of the loan. Losses then occur in a statistically particularly unfavorable phase.
If the investor does not respond in time with one of the three measures, the bank will carry out (c) independently - even without the investor's consent. It is entitled to do this based on the provisions of the loan and pledge agreement. In some private investor constellations it is even the case that the bank takes measure (c) without prior notice or warning at the moment the LTV threshold is breached. The investor should have reacted beforehand, but failed to do so.
Could the investor (a) or (b) problem-free (instead of through the involuntary liquidation of other investments), the question arises as to why he took out a loan of this size in the first place and did not use less debt and more equity right from the start.
With regard to the methodically clean analysis of the return and risk of a leveraged portfolio, measures (a) and (b) represent a problem because they make the portfolios in question financially incomparable with the other portfolios. In order to solve this basic analytical problem, every leveraged portfolio would have to have a fictitious cash investment in the amount of the loan attached to it from the start. Any margin call would then be serviced from this low-interest cash investment.
If you do this, the returns on equity of all leveraged portfolios will decrease, if correctly calculated including the cash reserve.
However, if the fictitious cash reserve is not taken into account in the calculation, the leverage portfolios with the worst returns are no longer financially comparable with the other portfolios and their equity returns are calculated incorrectly (too high).
Anyone who believes that the margin call issue is only relevant in relation to securities loans from banks and their margin calls is mistaken. In a broader sense, the margin call problem generally represents various types of rights of the lender to intervene in the investment decisions of the borrower (investor) - regardless of whether it is a securities investment or another investment. Every commercial loan will give the lender such rights of intervention that are potentially dangerous for the investor, often even in the case of loans within the family without a written loan agreement. The mere pledging of the shares to the lender represents a fundamental, far-reaching right to intervene.
Only in the case of private real estate financing through banks are the lender's rights of intervention comparatively limited for legal and perhaps historical-cultural reasons. Private households that finance owner-occupied real estate, and to a lesser extent other real estate borrowers, can be happy about this.
In general, anyone who leverages their investments is subjecting themselves to partial external control. Loan financing means less control or giving up part of your control - always and without exception. This can go so far that a leveraged investment that would have been successful in the long term is prematurely “killed” by the lender because the lender causes a “gameover event” through a margin call or other intervention at its discretion. Then a potential recovery of the investment later on will no longer be of any use to the investor. An example of this is the bankruptcy of the then famous US hedge fund LTCM 1998. The heavily leveraged fund was liquidated by its banks through a margin call in September 1998 due to high book losses in its speculation in emerging market bonds. There was a 100% loss for the equity investors (the fund investors). However, without the margin call, the fund would have recovered some time later because its investment strategy was correct in the long term.
Ergo: The stronger the leverage, the shorter the measurement and decision-making intervals for success or failure, forced termination or continuation of the investment. This “law” is also indirectly expressed in Buffett’s quote above. Being right in the long term is no longer enough to be profitable with a leveraged investment.
Our following historical simulation shows how quickly a margin call can occur from a statistical perspective, even with a highly diversified stock investment such as an MSCI World ETF stock investment: We look at the monthly returns of the MSCI World Index from January 1970 to August 2022 (52.7 years) in DM or euros. For our evaluation, we assume an initial level of debt financing of 40% and - in line with market practices in private customer business - a maximum permissible loan to value of 50% (the investment can therefore fall by 20% until an MC occurs). We take standard market credit costs of 2.5% p.a. a. above the money market interest rate and, for the sake of simplicity, ignore outflows for taxes and investment costs. We look at 513 individual cases. These are all complete ten-year periods, each starting on the first of the month between January 1st, 1970 and September 1st, 2012. This date allows for the last full 10-year period to end available return data on August 31, 2022.
Across these 513 cases, a margin call occurred in 44% of all cases (all ten-year periods). When there was a margin call, it only took an average of 24.3 months to occur. In only 49% of cases there was no margin call and the equity return was higher than without leverage.
However, this balance sheet basically still presents the situation too positively. Taking the following three factors into account would further worsen the results for the leveraged investor:
(a) If we had based our analysis on daily returns instead of monthly returns to make it even more realistic, the results would be less favorable for the leveraged investor. There would have been a margin call in moderately more than 44% of cases and on average this would have come a little earlier. (It would have been much more difficult for us to calculate daily returns.)
(b) A less diversified investment than the MSCI World with higher volatility would also have degraded the results from the leveraged investor's perspective - probably significantly so in the case of a less diversified portfolio, even if its average return would have been slightly higher than that of the MSCI World.
(c) Finally, taking costs and taxes into account would have adversely affected the results (but in turn greatly increased the complexity of the calculation).
According to our intuition, these are numbers that overall speak little for leverage.
(5) The problem of negative interest rate differential transactions in leveraged investments
In our consulting practice, we occasionally come across the situation in which a private investor household is considering a leveraged stock portfolio and would unknowingly enter into a “negative interest differential transaction” (NZDG). An NZDG exists when a household (or a company) holds low-interest cash balances or cash-like, low-risk bonds somewhere and at the same time takes out a loan somewhere else where the interest on the expense is higher than the interest on the cash investment. This amounts to a systematic loss-making transaction. We dealt with the NZDG phenomenon, which is often overlooked among private households, in an earlier one Blog post concerned.
Anyone considering leverage should first understand the topic of the NZDG well. With a few restrictions, leverage only makes economic sense if the household in question previously eliminated all of its NZDGs. This means shifting low-risk investments into risky investments and thus increasing the risk level of the asset allocation - which would also happen to an even greater extent through leverage. Some people who plan to invest in leveraged investments abandon this plan after realizing the impact of the NZDG elimination on their asset allocation.
(6) The myth of debt devaluation through inflation
A common pro-leverage argument is that inflation is beneficial to borrowers because it devalues loan debt over time. From the perspective of a debtor, the majority of this argument is unfortunately wrong, but from the perspective of a creditor it is fortunately wrong.
We have addressed this issue, which is important for borrowers, in our own blog post (here) dealt with in detail. There is No Free Lunch – not even for credit defaulters.
The situation can be summarized as follows:
(a) No debtor benefits from inflation to the extent that it was expected (anticipated) by the market when the loan agreement was concluded, i.e. it is priced into the market interest rates - neither in terms of the interest rate nor in terms of the obligation to repay the capital amount itself, which is not directly influenced by inflation expectations. This ultimately even applies to states that supposedly "easily" get out of debt through inflation.
(b) Market expectations for inflation are, from what we know, neither systematically too low nor too high in the long run.
(c) If expected inflation subsequently proves to be too high for a given period, debtors are thereby economically penalized and creditors rewarded.
Inflation is a two-way street to economic advantage for debtors. Because inflation and thus nominal interest rates fell relatively continuously in most countries from the beginning of the 1980s to the end of 2021, debtors are likely to have suffered an economic disadvantage during these four decades due to the existing but falling inflation. No trace of “debtor advantage”.
Despite its limping legs, the strange theory of debt inflation will probably be spread or parroted for many decades to come in financial advice books, print articles, blogs, YouTube videos and in the recommendations of real estate bankers on loan financing of real estate and other investments. Reasons: Conflicts of interest, wishful thinking or lack of expertise.
(7) Practical advice for anyone considering leverage
As the foregoing suggests, the authors of this blog post are, by and large, “leverage skeptics” when it comes to household stock investing. In our opinion, if a risk-taking and risk-bearing household still wants to partially finance its stock investments with debt, it should ensure three things:
First, the asset allocation of the investor's budget should before At the beginning of the leveraged investments, you must have already reached an aggressive (risk-taking) level of a “100/0” asset allocation. “100” stands for the percentage of all investments that are risky and that, conversely, cannot be classified as low-risk. “0” stands for “low-risk investment” and means investments with the lowest possible volatility, the lowest possible risk of default, very high liquidity and no exchange rate risk. In practice, for private households living in Germany, these are low-risk bonds in euros with short remaining terms and a high credit rating or bank balances within the statutory deposit insurance.
Second, the budget should ensure relatively low volatility in the portfolio through diversification. Leveraging is more dangerous the more volatile the underlying investment is. Leveraging a portfolio of a few individual investments in stocks with more than 20% leverage is close to kamikaze.
Third: The probability that a margin call will occur must be low. This means leveraging only moderately. In practice, this only works for a securities loan for a globally diversified stock portfolio with a maximum LTV of 50% specified by the bank if the LTV on “day 1” is 20%, meaning a 60% loss can occur before a margin call is triggered.
If these three criteria for rational leverage are addressed, the following advice can be helpful at the implementation level: A more attractive debt financing option for private households than a securities loan from a bank is to take out a loan on a property that is completely or largely debt-free - if one exists. This approach has three advantages: Normally there cannot be a margin call (because these are unusual in private real estate financing), long-term fixed interest rates are also possible (which is not typically the case with a securities loan) and the interest rate is likely to be around one percentage point lower than with a securities loan. Under these circumstances, a slightly higher degree of leverage would probably be possible than recommended in the previous paragraph.
Conclusion
Empirically, leverage works worse for businesses and households overall than most of us assume. On average, leverage has a negative effect on the risk-adjusted return on equity (the return-risk combination) and often on the absolute return on equity. Therefore, only investors who have high expertise and a high risk capacity should attempt leverage.
Correctly calculating the statistical return effect of leverage and methodically benchmarking it with non-leveraged investments is not easy due to the margin call effect. The return effect of margin calls or generally of coercive measures by the lender (reduction of control for the investor) is not only difficult to measure historically, it is also difficult to model and therefore estimate forward for an individual investor, for example in an Excel sheet.
Anyone considering credit leverage should first be clear about the problem of negative interest rate differentials and its consequences for their own asset allocation.
The fact that inflation is a reliable supporter of the borrower is a false but impossible legend. This dubious argument should not play a role when weighing up whether or not to leverage an investment.
For risk-taking households with a largely or completely debt-free property, lending against that property could be a smarter way to leverage an equity investment (moderately) than a traditional securities loan.
Endnotes
[1] “Lever” = leverage, “Leverage” = leverage effect.
[2] Modigliani, Franco/Merton Miller (1958): “The cost of capital, corporate finance, and the theory of investment”; In: American Economic Review; 48; 1958
[3] The Sharpe ratio is defined as the average excess return of an investment over the observation period compared to the risk-free interest rate divided by the standard deviation (the risk) of this excess return.
literature
(a) Scientific papers demonstrating that leveraging equity investments for private investors does not have a systematic positive effect on absolute or risk-weighted equity returns
Barber, Brad et al. (2022): “Leveraging Overconfidence”; July 26, 2022; Internet reference here
Barber, Brad/Odean, Terrance (2000): “Trading is Hazardous to Your Wealth: The Common Stock Investment Performance of Individual Investors”; In: Journal of Finance; April 2000; 55; No. 2
Bhattacharya, Utpal et al. (2016): “Abusing ETFs”; In: Review of Finance; 2016; 21; No. 3
Davydov, Denis/Jarkko Peltomäki (2022): “Investor attention and the use of leverage”; October 3, 2022; SSRN; Internet reference here
Frazzini, Andrea/Lasse Pedersen (2022): “Embedded Leverage”; In: The Review of Asset Pricing Studies; 2022; Vol. 12
Heimer, Rawley/Alex Imas (2022): “Biased by Choice: How Financial Constraints Can Reduce Financial Mistakes”; In: Review of Financial Studies; 2022; 35; Issue 4
Pessina, Colby/Robert Whaley (2020): “Levered and inverse ETPs: Blessing or curse?” September 25, 2020; SSRN; Internet reference here
(b) Scientific papers proving that leverage does not have a systematic positive effect on shareholder returns or on the economic return of companies
Adami, Roberta et al. (2015): “How does a firm’s capital structure affect stock performance?” In: Frontiers in Finance and Economics; 2015; 12; No. 1
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Ivanova, Maria/MariaKokoreva (2016): “The Puzzle of Zero Debt Capital Structure in Emerging Capital Markets”; In: Journal of Corporate Finance Research; 10; No. 4; 2016
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Strebulaev, Ilya/Baozhong Yang (2013): “The Mystery of Zero-Leverage Firms”; In: Journal of Financial Economics; Volume 109; Issue 1; July 2013
Subrahmanyam, Avanidhar et al. (2021): “Leverage is a Double-Edged Sword”; December 8, 2021; SSRN; Internet reference: here
Zhang, Jasmin/Xiao-Jun Zhang (2022): “Off-Balance Sheet Assets, Financial Leverage, and Stock Returns”; Sept. 2022; Internet reference here