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Illustrating the Cost of Leverage Effect on Returns
A couple of weeks ago, I presented a blog post called “The Effect of Crazy Time on Portfolio Allocations,” in which I pointed out that the effect of increasing volatility generally is to decrease the optimal portfolio allocations towards safer allocations. It was one of those posts where you initially say ‘well, duh’ but hopefully liked the fact that I ‘proved’ the intuition with the illustrations. While market volatility since then has been almost unbelievably low, it is hard for me to imagine that is sustained. It feels a little like a ‘deer in the headlights’ reaction from investors, as the Trump Train comes on so rapidly that all they can do is pull the shades.
I suspect that at some point, unless the Donald suddenly becomes a milquetoast business-as-usual kind of President, we will see those allocations shift.
But a few days ago I had another realization that called to mind the same old CFA-Level-I charts. I was explaining to someone who wanted me to leverage our really cool inflation-tracking strategy[1] that leveraging a mid-single-digits return makes a lot of sense when the cost of leverage is zero, but not so much sense when the cost of leverage was mid-single-digits. I’ve talked about this before – in October 2023 I published “Higher Rates’ Impact on Levered Strategies.”[2] I showed a table, but there’s a really simple way to illustrate the same thing.
I don’t really need the portfolio efficient frontier here. Maybe the optimizer spits out some share of the optimal portfolio that represents an investment in some hedge fund strategy you really like. Maybe it doesn’t. More likely, you don’t even use an optimizer. But if you really like that strategy, but want higher returns, you ask the manager ‘hey, can you lever that’? The manager says sure. But the manager can’t give you twice the returns for twice the risk – the leverage math doesn’t work that way. If the cost of leverage is 3% – which you can tell it is in this chart because that’s where the line hits the axis, at a risk-free rate of 3% – then your return for twice the risk is (2 x 4% – 1 x 3%) = 5%. So you pick up only 1% return for doubling the risk. And you can see that on the chart, because that’s the point the red line goes through: 5% return, 15% risk. For 3x risk, you get (3 x 4% – 2 x 3%) = 6%. And so on. The slope of the line is such that 7.5% additional risk gets you 1% additional return, no matter how many times you lever it.
So why do people ask for leverage? Well, because since 2008 the overnight rate was mostly at 0%.
If you can borrow at zero then levering simply multiplies risk and return simultaneously. At 2x leverage, your return is (2 x 4% – 1 x 0%) = 8%. You can see where this goes since 0 times anything drops out of the formula.
But this doesn’t work at higher costs of leverage. If the cost of leverage is equal to the expected return, then you just get more risk every turn of leverage you deploy. And if the cost of leverage is above the expected return, you make things worse every time you add leverage.
So it doesn’t make any sense to lever low-return strategies unless the cost of leverage is really low. And by the way, it doesn’t make much sense to lever high-return strategies unless they happen to be low risk. Because this math doesn’t just work with expected returns but also (and more importantly) with actual returns. Suppose you have a strategy that has a 6% expected return and a 15% risk. Say, an equity index. Now, you lever it 2x with the cost of leverage at 5% (by the way, if you use a levered ETF you’re not escaping the cost of leverage…but that’s for another day). Your expected return is now 7%, with 30% risk (check your understanding by doing the math).
Now, however, you get a 2-standard deviation outcome to the downside. Supposedly that happens only one year out of 40, but we know that there are fat tails in equity markets. But whatever the real probability, your unlevered return is now 6% – 2 x 15% = -24%. But now you’re riding the lightning and your return on the 2x leverage is (2 x -24% – 5%) = -53%. (Alternatively, you get to the same number if you just look at the new 7%ret/30%risk portfolio return as 7% – 2 x 30%).
Hedge fund managers understand this math…or should; if they don’t then get out…and it should change the numbers they report in forward-looking statements when interest rates are higher, for levered strategies. I will not comment on normal industry practice…
[1] To be clear, none of the red dots in this article represent the risk/return tradeoff for that strategy. I’m not trying to cagily present our fund’s performance because that would get me in trouble.
[2] This was a golden era for the blog. Right about the same time I also published one of my best posts in years, pointing out how the CME Bond Contract has shortened in duration and also has negative convexity again. “How Higher Rates Cause Big Changes in the Bond Contract.” How I loved that piece.
Growth. Does. Not. Cause. Inflation.
I am constantly amazed at certain articles of faith among the economics community. In my line of expertise, one of the most amazing to me is the absolute conviction with which the economics community believes that if the economy grows too fast, inflation will result and if it grows too slowly, disinflation or deflation will result. That this conviction is so strongly held is especially incredible, since there is essentially no evidence for that belief.
Theory says it is so. Growing too fast puts too much pressure on land, labor, and capital, which causes their prices to rise and therefore the price of the output. I mean, obviously.
Except that it doesn’t seem to have ever happened that way, at least for a long, long time.
Heck, let’s just take recent experience. In the last twenty years, we have had two global economic crises. The upheaval in 2008 was the largest since at least the Great Depression. The economic contraction in 2020 made the Global Financial Crisis look like a piker. So obviously, if we look at inflation it must have massively slowed down in those events, right?
Hmmm. Now, I’ve showed the Core CPI price level against GDP. If you squint, you can see a small deceleration in core CPI in 2010: it actually reached only +0.6% y/y at one point. We never even reached deflation, despite the fact that the GFC was triggered by housing and housing is by far the largest component of CPI. I don’t need to say anything about the COVID period because it is so recent. Core inflation vaulted higher, and continued to do so long after economic output had been fully restored to its prior level.
The other wonderful counterexample I like to show is the 1970s.
Notice there are several flat points here, where GDP was steady-to-lower and the price level kept on truckin’ (that’s a 1970s reference, kids). Notice that since I’m using core CPI, you can’t even say ‘well, the OPEC embargo caused energy prices to spike and that also slowed the economy.’ Yes, it did, but shouldn’t that slowing of the economy have taken pressure off of other non-energy prices? Well, it didn’t. Inflation was robust during the 1970s, despite growth that lurched forward and back in fits and starts.
Those are fun, visual aids but sometimes our eyes can deceive us and hide or exaggerate a relationship that is statistically present (or not). So here I did the economist thing and ran scatterplots at different lags. Each of these shows the y/y change in GDP on the x-axis (quarterly observations, since 1960 until 2024), and y/y changes in Core CPI on the y-axis. Chart A shows the y/y changes contemporaneously (1965Q1 vs 1965Q1, e.g.). Chart B lags the inflation one quarter, so we see if this year’s growth affected this year’s inflation but lagged a little bit. Chart C lags the inflation one year, so we see if this year’s growth affects the coming year’s inflation. And Chart D lags the inflation two years, so we see if this past year’s growth affects next year’s inflation.
The correlation coefficients, for your reference: -0.18, -0.13, 0.03, 0.14. That’s thin gruel on which to make a strong argument about growth causing inflation, in my mind.
Now, I’ve run these regressions since 1960 since the core CPI index only goes back to 1957. The same regressions with headline inflation show coefficients of -0.11, -0.05, 0.10, and 0.11. I’m actually surprised they’re not any better, because energy prices should be correlated with growth and flatter the relationship. The OPEC embargo does hurt that relationship, but even if we just run these regressions since 1980 the correlations between growth and headline inflation are just 0.13, 0.19, 0.16, and -0.09.
So where do we get the idea that growth causes inflation?
Well, if I look at GDP growth versus headline inflation, from 1929 until 1960, and I exclude 1946 when industry relaxed from its war footing and war-time price controls were removed, then I can coax a really nice correlation of 0.73.
Indeed, if you look at the correlation between 1929 and 1945, it becomes a whopping 0.88. That’s science, baby – fitting the data to the story! But now I think we get to the heart of the matter because something else momentous happened in 1948 and that was the publication of the first edition of the most-used textbook in history: Paul Samuelson’s Economics. It is no surprise, perhaps, that generations of economists learned this ‘fact’ based on a correlation of 0.88…that has been falling ever since.
Since that time, the correlation between core inflation and growth has been low, and sometimes even negative, over very long periods. If there is any causal relationship, it is completely swamped in exceptions. Decades-long exceptions. It is time to give up this idea. One unfortunate consequence of that is that the way the Federal Reserve operates is as if there is one dial it can turn and that is ‘the dial that increases growth until inflation gets hot, then decreases growth.’ The problem is that isn’t one dial, it’s two. In general, I think the Fed should keep its hands off the growth dial, but if it wanted to meddle on rare occasions it would do so by manipulating medium-term interest rates. To control inflation, it needs to moderate the growth of the money supply. Frankly, in my opinion the FOMC should simply focus on the latter mission and let growth, and markets, take care of themselves. They’re not good at any of these missions anyway.
Inflation Guy’s CPI Summary (January 2025)
We finished 2024 with a slightly soft reading, but we began 2025 with a hot reading. Now, my admonition last month about the volatility of December data applies also to January data, although less so in CPI than in some other indicators. However, averaging December and January is probably the right approach.
It still doesn’t look great even if you do that.
Let’s start with the market changes over the last month. You can tell from the table below that short inflation expectations as measured by the column on the far left have come up some, although not as much as you might have expected given all of the concern about tariffs. (For what it’s worth, in this table you can ignore the huge increase in 1-year breakevens – there really isn’t any such animal per se, and Bloomberg’s choice of bonds to use for the 1-year can change that a lot. Focus on the inflation swaps, which is a purer measure.)
The consensus estimates coming into today were for +0.30% on Core CPI and +0.29% on headline CPI. That represented an acceleration over the nice inflation data we saw in December (the best core inflation print since July!), but was expected to be attributable to one-offs such as wildfire effects. In fact, the number printed at an alarming +0.47% on headline and +0.45% on Core CPI, the worst since April of 2023. Here are the last 12 months.
But we are jaded these days because we’ve seen higher figures. Let’s back out a bit. Prior to COVID, we hadn’t seen a Core CPI number this high since 1992!
Okay, so some of these are one-off causes. And it is a January figure after all. Median CPI will be better. My calculation had it around 0.35%, but since the BLS changed weights for the new year in this report I am less confident in my estimate than usual. It should be close. And since last January was a big median print, that means the y/y median would drop to 3.66% or so on base effects. But there certainly doesn’t look to be any really marked improvement here.
Speaking of the reweighting of the CPI: this always sparks conspiracy theories even though the reweighting is very transparent. And the changes are pretty small year to year. Here are the changes from last January’s weights.
The BLS also announces categories that are being dropped or added or renamed. I never point those out because it’s really boring. At least, it is normally. This year, the BLS announced that the series for “Pet Food” has been renamed to “Pet Food and Treats.” Because who’s a good boy? That’s right, you’re a good boy.
Let’s look at some of the main culprits for the upside miss this month.
- Used Cars SA +2.19% m/m – We all expect some upward lift after the wildfires, but I am not sure this is due to that. New Cars CPI only rose +0.04%. But this is the highest m/m increase in Used Cars since 2023
A bigger concern with Used cars is the upward tilt in the overall price level. Remember that the spike during COVID (which happened thanks to the geyser of money that sprayed American consumers who had little else to buy, and few new cars being produced) was a big bellwether and/or driver (mathematically speaking) of the increase in core CPI post COVID. The unwinding of the spike in used cars pushed Core Goods inflation lower and lower, and dragged down Core CPI. But now it looks liked used car prices are again headed higher. This seems a good time to mention that M2 is also inflecting higher. The money supply is 40% bigger than at the end of 2019. Used car prices are only 32% higher. I think the deflation in used cars is over. (I’ve included M2 on this chart.)
AS a consequence of this, and despite apparel being -1.4% m/m (that’s one place tariffs could bite since we don’t produce any apparel in the US…on the other hand, there are lots of suppliers of apparel globally so absent a blanket tariff, we might not see a big effect), Core Goods CPI y/y went to -0.10% from -0.50%. As I’ve noted previously – ad nauseum, probably – to get inflation to 2% you need core goods inflation to stay negative, and pretty decently so. Core Services dipped to 4.3% y/y from 4.4% y/y, but obviously if that part is over 4%, and it’s the bigger part, you need Core Goods to stay flaccid.
- Health Insurance rose +0.74% NSA. Health insurance inflation jumps sometimes in January, so this is not something I’m worried about (plus, the health insurance number is really only calculated once a year and smeared out over the year). But it’s worth noting.
- Lodging Away from Home, +1.43% SA. Normally this is one of those categories that jumps around a lot and so we would expect a reversal next month, but with the wildfires in California I’d expect this to be buoyant for a while even if it is just the Western US being affected. But don’t forget that there are lots of people without homes still in North Carolina. On the other hand, if deportations ramp up a lot more than they currently are this is one place where pressure on prices could be relieved since many illegal aliens are housed in hotels at the expense of the local/state/federal government. That disinflationary effect, though, is months away at best, I think.
- Pharma had a huge month, rising 1.4% m/m SA. That’s the biggest monthly gain in decades. I suspect some of that is because pharmaceutical companies know that they are ‘on the X’ of President Trump’s ire after actively working against him in 2020. The President has recently been talking about how upset he is about US drug prices relative to the same drugs sold in other countries. This is a real threat – in his prior term, he talked about implementing a “Most Favored Nation” clause when it comes to pharmaceuticals (I wrote about it here: https://inflationguy.blog/2020/08/25/drug-prices-and-most-favored-nation-clauses-considerations/ ). So it strikes me as possible that pharmaceutical companies were raising prices in January partly so that they can cut them with great theatrics to show their ‘support’ for the President (and hold off most-favored-nation as long as possible). I do not expect to see this repeated next month, unless tariffs affect APIs (active pharmaceutical ingredients) in the near-term.
- Hospital Services were also high, at +0.95% m/m SA, but this is less unusual for that series which jumps around a lot like Lodging Away from Home. Still, that was the highest print since March.
On the good side – while Rent of Primary Residence was a little higher than last month (+0.35% vs +0.30%), OER was the same (+0.31%) and rents overall continue to decelerate. However, they are decelerating at a declining rate. It looks like the dip that I expected is never going to happen, as the growth rate of rents looks to be converging with our model in the high 3s. And it doesn’t need to be repeated, but I will anyway, that there is no sign of broad deflation in rents coming.
Food and energy were additive this month, although less than I expected. Food at home was +0.46% m/m, and I expected about double that. Eggs were +13.8% m/m (NSA), and +53% y/y, and are getting a lot of press. But that’s not an inflation thing, that’s a lack-of-chickens thing and egg prices will eventually come down (in, approximately, the time it takes a chicken to get to adulthood). Food away from home was relatively tame at +0.24%.
So what’s the big picture?
What we saw today was mostly the trend. I continue to think that the new ‘middle’ on Median CPI is the high 3%s, low 4%s area, with occasional forays above and below that level. Over the course of 2025, as tariffs are implemented, we are likely to see a slightly higher run rate. Tariffs are a one-off, and they aren’t a large effect unless applied in a blanket way to all imports. Remember (and review my recent blog https://inflationguy.blog/2025/01/29/trump-tactical-targeted-tariffs-a-reminder-of-the-impact-of-tariffs/ and podcast https://inflationguy.podbean.com/e/ep-131-how-tariffs-affect-you-three-things-you-maybe-didnt-know/ on the topic) that despite what some hyperventilating Congresspeople say, consumers do not usually pay the majority of a tariff except in narrow circumstances where demand for the good from that particular supplier is inelastic. If the Trump Administration imposes a blanket tariff of 20% on all imports, with no exceptions, it might cause an increase in inflation of 0.5%-1.0%. But that’s a one-time (level) effect unless tariffs keep being ramped higher, and the effect gets smaller the higher the tariff goes (a 1000% tariff will not raise prices any more than a 900% tariff, because at that point we aren’t importing anything). So, all else equal, we should expect slightly higher inflation in 2025 than we previously would have expected, and probably for the first part of 2026, but then the tariff effect will be over and the level of inflation we settle in at will be once again driven mainly by money growth.
On that score the news isn’t great, with M2 rising at a 5.8% annualized rate over the last quarter and 3.9% over the last year. 4% would get us to 1.5%-2% inflation in the long run, probably; 6% will get us into the high 3s, low 4s. Some think that if inflation ends up ratcheting a little higher, the Fed might raise interest rates again. But monetary policy has very little control over inflation that is caused by tariffs and it would make no sense to reverse course for that reason. This just accentuates how bad the box is that the Fed got itself into by making a nakedly political ease in the middle of last year. Tightening because of tariffs has no economic justification; it would look nakedly political again. I would be surprised if overnight rates went higher from here. Of course, I’d also be surprised to see them going lower especially since tariffs are also good for domestic economic growth.
So there will continue to be lots of economic volatility from here, but stasis appears to be high 3s, low 4s. Still.
The Effect of Crazy Time on Portfolio Allocations
I am continually fascinated by how many second-order ‘understandings’ are missed, even by those people who have a really good first-order understanding of finance. For example, every financial advisor understands that bonds are less volatile than stocks. Most financial advisors understand that stocks and bonds in a portfolio together also benefit because they’re not correlated. Some financial advisors, and most CTAs, understand that diversifying a portfolio works because when you add uncorrelated assets together, the risk of the whole is less than the sum of the risks because of the offset from the correlation effects. Those are all coarse understandings that any financial professional should ‘get.’ However, it is fairly unusual for advisors or even CTAs to understand that the correlation of stocks and bonds undergoes a state shift when inflation get above about 2.5% for a few years, and become correlated, and that means more risk for the same combination of stocks and bonds. Here’s that chart I love to show, updated through the end of the year.
While that’s an example of a ‘second-order understanding’ that isn’t widely known, it isn’t what I want to write about today. Actually, for a change what I want to discuss is something that has nothing directly to do with inflation, and that is the effect of volatility on asset allocation.
This is an important discussion right now, because whether or not you have gotten the message yet that President Trump is going to be much more Machiavellian in his approach to the global world order than prior Presidents have been – and whether you think that’s a good thing or a bad thing – you surely must have noticed that the volatility of the markets under this regime is likely to be somewhat higher than under Sleepy Joe and also higher than it was during Trump’s first term. And that leads to the second-order understanding about what that implies for markets. Hang with me here; if you’re not a finance person this gets a little hairy.
The next chart shows Modern Portfolio Theory on one chart.
The blue line is the Markowitz efficient frontier: every point on the line represents a portfolio of assets that is the least-risky for that level of expected return. So, the highest vertical point is a portfolio of 100% in the asset with the highest expected return…you can’t get more return without leverage.[1] In this case, let’s assume that is equities. As you go down the curve, you allocate more to other less-risky assets and give up some portfolio return. Because assets are not 100% correlated, you can always get a portfolio that has at least as good (and usually better) returns for a unit of risk than any single asset – that’s the benefit of diversification. As you get to very low expected returns, you get to the part of the curve you’d have to be irrational to be on because you get higher risk and lower returns, and so we usually ignore that part of the curve that bends back.
The red line is popularly called the “Capital Asset Line.” Assuming there is some zero-risk instrument (that’s not already in the assets we’ve considered, so there’s some hand-waving here) and you can both borrow and invest at that rate, you can think of a portfolio that is the ‘best’ portfolio on the blue curve, either combined with the zero risk instrument (sliding down the red line to the left) or levered at the zero risk instrument (moving up the red line to the right). The ‘best’ portfolio here is defined as the place where the red curve is tangent to the blue curve.
A lot of times you’ll just see those two lines, but it doesn’t answer the question of which portfolio an actual investor prefers. It turns out that investors do not have linear risk preferences…that is, if I make my portfolio 10% more risky, perhaps I require 1% more return but if I make it another 10% risky, I’m going to need more than 1% additional return. I’m not only risk averse, but I get more risk averse the larger the potential risks. [Lots of experimental data on this. If I offer you a bet where you pay me $1 and on the basis of a coin flip I will either pay you $2 or $0, you are much more likely to take that bet than if I offer you a bet where you are risking $10,000 for the chance at $20,000…or zero]. So the purple dotted line is a hypothetical ‘investor indifference curve’. I just made up that term because I can’t remember what the theoreticians call it. The curve represents all of the combinations of risk and return that make the investor equally happy. So, the best portfolio for this investor is where the purple line – the highest purple line we can find, indicating the MOST happiness – touches the red line.
With me? Now consider the next chart. All I have done here is to increase the risk of every asset and shift the whole portfolio efficient frontier to the right.
What happens? The Capital Asset Line (red) now flattens out. And that means that the prior purple line no longer has a point of tangency. We have to go to a lower purple line, and since the purple line is concave upward the red line becomes tangent to the purple line at a point further to the left (the slope of the red line is flatter, and the flatter parts of the purple line are to the left). I’ve put the new ‘optimal portfolio’ as a dot in purple.
The implication is this: if overall risk in markets is perceived to have permanently increased, then rational investors will move from portfolios with more risky assets to portfolios with fewer risky assets.
You probably could have guessed that without all of the curves. If I am comfortable with a certain amount of risk, and the overall risk of things goes up, then it stands to reason that I’d work to reduce my overall risk. The second-order understanding here is, then, that if President Trump is perceived by investors to increase the overall volatility in markets and individual country and company outcomes, we should expect investors to lighten up on equities.
And that brings me to the final chart. This is the Baker, Bloom and Davis news-based Economic Policy Uncertainty Index, which counts the number of articles in US-based news sources that contain a set of predefined terms that indicate uncertainty about economic policy. The dotted lines below show weekly data; the heavy red line shows the 12-week moving average to get rid of the noise.
Notice the three prior spikes on the chart are during and immediately following the end of the internet/stock market bubble in the early 2000s, the end of the housing bubble and the Global Financial Crisis in 2008-09, and the COVID crisis. All three of those episodes were associated with significantly lower markets, although you could argue that harsh bear markets might trigger some policy uncertainty (that certainly happened after 2008). The jump on the right is the Trump jump, and it is already higher than any other period on this chart other than COVID.[2] Volatility we have. Uncertainty we have. And even if you like the President’s policies, the volatility means that we should not be surprised to see investors pull some chips off the table.
[1] If you take this best-returning asset and leverage it, you basically get a straight line going up and to the right forever; the slope of the line depends on the cost of leverage.
[2] Incidentally, the index goes back to about 1985 and although I didn’t show it there are two more bumps that are similar to the leftmost two on this chart: around the 1993 recession, and around the time of the stock market crash in 1987. They are all lower than the Trump jump.
