Since Central Banks announced last year that they were going to increase interest rates, I (for once) acted responsibly and asked myself this question: should I reduce the leverage in my portfolio?
The cost to borrow money represents a hurdle rate: the return I get from investing has to be higher than its cost. This is the point that is missing in any discussion about leverage, which is usually debated in absolute terms. Leverage is bad. No, it depends.
It is also why you should hurry to repay your credit card debt, which usually has an interest rate cost higher than 20%, but you should have a strong motive to consider pre-paying your 2% mortgage. It is really hard to find an investment that consistently (I should say in the long-term) returns more than 20% but rather easy to find one that pays higher than 2%.
If and when you should borrow money to invest is hard to define for a basic reason: you know TODAY how much it costs to borrow but you will only know IN THE FUTURE the return generated by your investments initiated today (and given the probabilistic nature of this game, even knowing that specific return might not give you the correct answer).
Me and leverage
I started using a margin account with Interactive Brokers around mid-2020. I had the willingness to use leverage for a loooooong time (here is an example) but I found out about IB only around that date. At the time, interest rates were at or around 0% basically everywhere in the Developed (in the financial sense) World, an objectively trivial hurdle rate to beat. It was an easy decision. It is also not funny to realize that, while rates were at 0 for a decade, I implemented my strategy just before inflation decided to come back and Central Banks to enter in a new hiking cycle. Never ever lucky.
As Silicon Valley Bank CFO, at first I did not expect Central Banks to be so aggressive, to hike so much, so fast. In my head, I was planning to have an ‘internal discussion’ about leverage only after rates would have been higher than 3%…which I thought would have been in like 2024. I was already a father but I still remembered when CBs were hiking at a pace of 25bps per quarter, you know?
[This feels like the right point to clarify something: my borrowings are roughly distributed 66% in USD and 34% in EUR, with some residual amount in GBP from time to time. This is related to IB rules: I fund my account mainly with GBP (sometimes with EUR) and I invest in a lot of USD-based ETFs. I do not love IB rules but I have to admit they also prevent me to take a huge FX risk. I could also cheat the rules by sending USD to IB via Revolut instead of GBP but…let’s say I am too lazy to do it]
I think it is valuable, even for a sort of entertaining purpose, to provide you with my considerations in chronological order, instead of going straight to what I think is the right conclusion (given the information I have today).
In Q2-22, given the rates outlook, I thought it was time to at least start to think about what I should do. I did not have the time to do any sort of deep research but leverage was definitely not a foregone conclusion like the year before.
A margin loan on IB costs CB rate plus 1.5%. As you can see from the below graph, taken from Credit Suisse’s (R.I.P.) 2023 Yearbook, in the long-term stocks and bonds (WLD = World Index) beat my cost of funding (Bills returns should be 20 to 30bps higher than CB rates).
This should be a conservative analysis, given that my stock portfolio has factors’ tilts and my bond portfolio includes Corporate and High Yield Debt. The hope is that my choices would not, at least, destroy value compared to the very simple, market-weighted, standard indexes.
If you are asking yourself “wait, shouldn’t this punk have checked this stuff before using leverage?”…your question is 100% legit. And I did. But this is a great example of how putting down a plan in Excel is one thing, seeing the incoming trouble in real life is another. My convictions did not feel that solid anymore, I had to check and re-check.
I should also precise that IB let me leverage only up to 1.35x (and not be harassed by frequent soon-to-be margin call emails, I keep my leverage around 1.3x). Even if in theory my portfolio should generate gains in the long term, there is always the risk that a big market drop would prompt a margin call and consequently an asset sale at the bottom. I have two back-stops to prevent this scenario:
- I add fresh funds to the portfolio on a monthly basis and reset the leverage (admittedly, this process f*&ks up the dollar-cost-averaging because I buy a bit less when the portfolio is down and a bit more when it is up. This ‘risk’ is taken care of by how the portfolio is constructed, i.e. the focus on uncorrelated assets)
- I have a ‘reserve’ invested in my stock ISA that I can move over to IB. This process was designed when the capital gain allowance in the UK was at 12k, now that is lower…I do not care anymore because I am leaving the bloody island 🙂
I am still experimenting with this margin account and I can do it because the amounts involved are not too large compared to what I have invested elsewhere (mainly because this type of investment was highly tax-inefficient in the UK; once I am in Switzerland, I will have to design a different plan but I am not sure to go 100% on IB anyway). I (strongly) suspect that IB calculates available daily margins based on volatility: in 2022 I had to dial down the leverage to around 1.27x because of that.
What about future expected returns?
Now that I know I am pretty confident that the strategy worked in the past, and in the long run, the next question I asked myself was more tactical in nature. Is there a level where it makes sense to pause leverage?
I will use bonds in this example because their mechanics are more intuitive to grasp. Based on CS data, a strategy that goes long bonds and short bills would have generated positive returns. The issue with the strategy is when the interest rate curve inverts, when the bond portfolio yield is lower than the bills yield. The portfolio yield is based on purchases I made in the past, when I locked returns for multiple future years; the bill’s yield is based on what the FED is doing right now.
If I buy a 10-year bond today and I hold it until maturity, I will earn 4%/year for 10 years (if the issuer does not default); in this strategy, the returns on the investment part are certain but the cost on the borrowing side is not. Let’s assume my capital is 100% invested and I do not have any excess capital to add to the strategy. If I stop the strategy when the curve inverts (I sell the bonds to close the borrowing), I have two issues:
- the current price of my bond portfolio might be lower than the purchase price: I would simply trade a probable future loss for a certain one today
- if I wait to re-enter the strategy when the curve normalizes, at that point the 10-year yield might be already too low
The moment when I should have stopped the strategy was around 2021, just BEFORE the bills’ rate started to rise. This is kind of…obvious: it is a market timing issue and well, if I have the ability to time the market, I would use it in a more profitable way.
There cannot be a profitable strategy based on the simple rule if the current 10-year yield>bill yield then go long, flat otherwise, because the market would have arbitrage that away. And if I stop the strategy too early, or jump back in too late, then my strategy would diverge from the long-term data published by CS, most likely in a detrimental way. In other words, the 4% yield on a 10 year bond I am renouncing today because the FED rates are at 5% is the same yield that contributes to the long term performance of the strategy.
When you add stocks to the equation, the problem becomes more complex because it is way harder to estimate what would be their future 10-year return. Valuations can give a hint but they are a terrible market timing tool. A market with a P/E of 30 is expensive but it can stay so for a long time; it can even go to 40 or 50 before coming down.
The CS paper includes the following graph with their estimated future return for the 60/40 portfolio:
Is that estimate valid for where stocks and bonds were at the end of 2021 or it is still valid today when stocks and bonds are down 10 to 20%? The decision of selling the portfolio today to close the borrowing is more related to my (and your) OUTLOOK for the FED funds than where the FED funds are today.
I decided to suck it up and keep leverage as it was.
Breaking The Market
Fast forward to early March 2023, when a reader sent me a few links related to the blog breakingthemarket.com with some questions about those posts. One link was this one, a post on how to balance a portfolio made of cash and a risky asset to maximise long-term returns. It builds on the importance to distinguish between the average and the geometric return of an asset; Kris-Moontower wrote few posts about this topic in the previous months so you can understand why I was already sold on it 😉
I do not want to repeat here the whole mixing methodology: in short, it suggests that when the Risky Asset Bottom Range (Average Return – Variance) is higher than the Risk-Free return, I should use leverage. The amount of leverage is given by the formula: Leverage = (RF return – Bottom Range) / (Range)
I went to PortfolioCharts and created a proxy of my portfolio (I kept the US as Home Country because that’s how the tool works best IMO; as long as I keep USD as cash for this exercise and my real portfolio does not have an FX exposure coming from the use of leverage, I am fine with the result):
Moving from a portfolio of assets to a single risky asset with the same characteristics (return and volatility) as the portfolio is a big leap. Already using historical volatility for a single asset as a proxy of future volatility is quite wrong. Here I am making big assumptions on the correlation between the portfolio assets as well, based on what happened in the past. This analysis can only be illustrative at best but…this is the amount of time I can dedicate to it 😉
The tool uses real returns, net of inflation. My portfolio average return is 5.9% with a standard deviation of 12%, meaning the geometric return is 5.18% and the bottom range is 4.46%. According to PC, cash real return is 0.8%, which is materially higher compared to the CS paper.
In any case, using the above inputs, the optima leverage comes out at 2.5x!!
Even using CS data for US stocks (6.4% real return, 20% stdev, 0.8% cash return), the optimal portfolio of stocks and cash is a 100% stock portfolio levered 1.4x. The amount of leverage I am using for my portfolio is lower than that…
What about today?
When I first saw the model I thought “great, now that I have a relationship between cash (cost of borrowing) and the risky asset, I can see where is the optimal point as of today”. Unfortunately, it is not that easy. I know what cash earns today but I do not know what’s the prospective return for my portfolio given today’s bond yield and stock prices.
Assuming that stocks always return their average (8.3% nominal, 20% st dev), I should bring leverage to 0 when cash returns more than 4.3% (or to 3.8% considering the 1.5% IB spread). According to Research Affiliates, today’s CAPE is a bit above average, so future returns should be lower than average, meaning I should have removed leverage even earlier:
But this model is clearly sensitive to volatility (and correlation). Choose a mix of assets that are not correlated, and the threshold to remove leverage increases materially.
At that point, my head was exploding. I thought that anyway, the future return of any risky asset class should eventually (eheheh) be priced above the risk-free rate. I had only a timing mismatch, soon enough risky asset returns will pick up with cash and I will be fine again.
To note, my Model Portfolio is levered 1.3x and yet its performance does not seem to be over-penalised by high borrowing rates, at least so far:
Ben Felix
Last week I listened to Ben Felix’s interview on Mr RIP YouTube channel. Imagine my joy when, around 1:30:00 here, Giorgio asked if the cost of leverage going up means leverage should decrease and Ben replied that expected returns should always stay on top of the risk-free rate.
YAY!!!
Or..not..
Immediately after, he conceded that as rates go up, expected returns might go down and cited a recent paper on the topic (link):
In Expected Stock Returns When Interest Rates Are Low, published in the July 2022 issue of The Journal of Portfolio Management, David Blitz examined whether the theory that the equity risk premium is a reward that investors earn on top of the prevailing risk-free return was supported by the long-term historical data—all else equal, total expected stock returns should increase with the level of the risk-free return.
Blitz’s data was monthly U.S. equity market returns and risk-free Treasury bill returns over the period January 1866-June 2021. He defined the equity excess return as the total equity return minus the return on risk-free Treasury bills, and the equity risk premium as the long-term average equity excess return. Blitz also examined international data from 16 developed countries with the start date of the series varying between 1870 and 1900 for the various countries and ending in 2021. He stated: “If equities offer a fairly stable risk premium, then we would expect to observe a similar-sized risk premium for all levels of the risk-free return and total returns that are clearly increasing with the level of the risk-free return.” However, as shown in the chart below, the actual picture looks very different, with similar-sized total returns for all levels of the risk-free return and an inverse relation between the equity risk premium and the risk-free return. In addition, when the risk-free return was more than 6 percent, the average total return on equities was not sufficient to obtain a positive average risk premium.
Using the longest sample period for which all variables were available, February 1881 to June 2021, Blitz regressed monthly equity returns minus the risk-free return (Rm − Rbills) on the prevailing risk-free return (Rbills) and earnings yield (inverted CAPE). If the equity risk premium was independent of the level of the risk-free return, we would expect the estimated coefficient for the risk-free regressor to be indistinguishable from zero. However, if total equity returns were similar regardless of the level of the risk-free return, we would expect the estimated coefficient to be about −1, to offset the subtraction of the risk-free return from the equity returns on the left-hand side of the regression.
Blitz found that the estimated coefficient for the risk-free return was strongly negative, −2.07 (t = −3.59)—rejecting the hypothesis that the equity risk premium is independent of the level of the risk-free return. In fact, he explained, “because the estimated coefficient for the risk-free return is well below −1, it seems that there is even an inverse relation between total expected equity returns and the level of the risk-free return,” as seen in the above chart. As a test of robustness, using international data he found similar results: “For most countries the total stock returns are flat or even inversely related to the level of the risk-free return, implying a very high equity risk premium when the risk-free return is low, and a very low equity risk premium when the risk-free return is high.”
Blitz concluded: “It is important to realise that we do not propose a market timing strategy. We find that the equity risk premium tends to be larger when the risk-free return is low and that the equity risk premium tends to be smaller when the risk-free return is high. However, we do not identify scenarios in which the equity risk premium is strongly negative, which would be needed to justify short positions. Thus, when used as a tactical asset allocation strategy, our signal would be long 100% of the time. We see the application of our insights more at the strategic asset allocation level, such as asset liability management studies.”
To be honest, I am not 100% sure I understand the underlined part (I did not have access to the whole paper) but it seems to me to suggest that leverage, if applied to stocks, should not be static but vary with the cost of cash.
So….back to square one?
What I think is clear is that, apart from maybe the not-so-reliable valuation metrics like CAPE, we should always expect stocks to deliver their average geometric return (even if I remember a post from Ben Carlson where he demonstrated that, each year, stocks deliver anything BUT average returns).
Maybe the correct solution is the most simple one: when I dial down leverage, I am effectively investing at the leverage rate, so it makes sense to reduce it if the expected return of the portfolio is lower than the cost of leverage. But if equity total returns are constant, irrespective of where the risk-free rate is, my portfolio returns could also be constant (bonds should indeed just lag cash for the most part). So with my estimated nominal geometric returns at 7.18% to 8.18%…hopefully the cost of leverage will never get there 🙂
[Hopefully one day I’ll have some time to play around the more complex model created by BreakingTheMarket]
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