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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.
Higher Rates’ Impact on Levered Strategies
I am old enough (fortunately??) to be able to remember when interest rates were last at this level. Even higher – I can remember in my first job, at technical analysis firm Technical Data, being tasked with updating the point-and-figure chart of the 10 3/8 – 2012 as it rallied from 9%! I mention this because, as interest rates have headed back higher I have noticed that a lot of people don’t remember some of the investment implications of higher rates. So, I want to review one of them today. Next week, I’ll write about how the rise in rates will tend to make bond futures negatively convex after years of positive convexity…there aren’t many bond basis traders left, because it’s been years since there has been a shift in bond deliverables, but it makes a lot of things more interesting and I suspect will resurrect some old relative-value trades that haven’t been seen in a dog’s age.
But today, I want to point out one big effect on the hedge fund industry: higher interest rates leads to lower hedge fund risk-adjusted returns, directly and significantly. If you’re a hedge fund, you already know this. If you’re an allocator, you may or may not realize that you need to carefully monitor any changes in the risk-taking of your existing hedge fund portfolio, and start to ask tougher questions of hedge funds touting high returns.
The dirty little secret of hedge fund returns is that you can make a good edge look like a fantastic return if leverage is cheap enough and if you lever enough. If I buy a bond yielding 5% with $100, and then borrow $90 at a 0% borrowing rate, by pledging that bond as collateral…and invest in another bond yielding 5%, then magically I have turned a simple bond-buying strategy into one that yields 9.5% (5% on 100, plus 5% on another 90, divided by the 100 in unlevered principal). Yes, I have almost doubled my risk but I have created a return that looks really nice.
But if instead of borrowing at 0% I am borrowing at 2.5%, then levering to buy that bond doesn’t add as much. The $90 spent on that 5% bond now costs me 2.5%, for a net 2.5% return on that piece. I still have the risk, but my return has gone down to 7.25%. If I can borrow another 90, and do the trick again, I’ll get back to my 9.5% return but now I’m 3x levered instead of 2x. (Naturally, most hedge fund strategies are more complex but this is the basic concept).
Now, for small changes in financing rates this is of course a small effect. And for decreases in financing rates, it’s a positive effect. But when you have large increases in interest rates, it has a big effect on returns:
Yes, I know this is overly simplistic but the easiest way to think about this is with a bond strategy where you’re leveraging up a simple yield. The significance of a change in the cost of leverage, though, is felt across many hedge fund categories. There’s an exception with many CTA strategies because there is no money required to hold the natural underlying. The longs and shorts are exchanging daily P&L, and no one actually needs to hold the underlying instrument because there isn’t any. Similarly, long/short bond and equity strategies, in principle, only care about the spread between the financing of the long position (which is paid) and the financing of the short position (which is earned) rather than its level, assuming equal notionals on long and short. But most long/short strategies – including fixed-income arbitrage, weirdly – are highly correlated to stocks, which suggests that in most cases there’s net long exposure. Here are charts of the CS long/short equity hedge index, and the Bloomberg Fixed-Income Arb index, against the S&P 500.
Managed futures, not so much, although there’s a decent correlation to commodity indices (not as much as in the above examples relating long/short returns to equity returns).
If a futures strategy or a long/short strategy holds unencumbered cash, they should get some benefit from higher rates…but most such strategies don’t tend to have a lot of unencumbered cash. In the same way, commodity futures indices such as the Bloomberg Commodity Index or the Goldman Sachs Commodity Index (and many others) get some benefit in expected returns because they earn more on the collateral they hold against futures positions, and they do hold a lot of cash and Tbills.
However you slice it, the sharply higher financing rate environment we are now in is likely to have a meaningful effect on the returns (and the risks, if more leverage is used to chase a higher return) of many hedge fund strategies. All else being equal, this will be a lower penalty on less-levered strategies; which means investor money should flow to less-levered strategies for a better risk-reward tradeoff.
