You Can't Eat Sharpe

My brain is probably a little messed up from spending my whole career in trading. I don’t mean that it doesn’t work, I just mean that I often find little financial hacks that seem like a good idea at the time because the margins justify it. When I actually go ahead and do the trade, of course, it often becomes clear that I missed something crucial: You Can’t Eat Sharpe. Before we get into the dumb trade that I did, I want to do a bit of a primer on some basic theory that might be helpful.

If you already know what a Sharpe ratio is and you dream (nightmare?) of SOFR when you sleep, skip ahead to Fine Dining for the meat and potatoes

A Primer on the Sharpe Ratio

In 1966, William F. Sharpe wrote a paper on measuring “Mutual Fund Performance”^[1]. Plenty of people had tried this before (after all, the first U.S. based mutual fund started in 1924), but this paper has been cited so many times that it’s worth visiting even just to understand history.

The key idea that Sharpe explored is that comparing equity mutual funds of the 1960s was comparing apples to oranges. Technically all mutual funds are fruit, but there’s no guarantee that two portfolio managers have the same properties.

This creates a problem:

1. Ivan the Investor wants to invest in the best investment. He wants to make the most money possible, but he’s also scared of taking too much risk and losing the money he has scrimped to save
2. Ivan can invest his whole account in one of two funds, the Apple Always Allocation Fund (AAA) and the Buy Beanie Babies Fund (BBB)
3. assume the AAA fund returns roughly 10% per year, with 16% expected annual standard deviation
4. assume the BBB fund returns roughly 40% per year with 100% expected annual standard deviation
5. assume AAA and BBB are completely uncorrelated^[2]

Which fund does Ivan pick?

As it stands, the return maximizer with infinite holding horizon is of course going to pick the higher return despite the higher volatility - 40% per year sounds a lot better than only 10% per year. So BBB is the pick.

Which fund SHOULD Ivan pick?

In the real world, you can borrow money. In Sharpe’s idealized world, you get to borrow at the magical risk free rate. If you live in the United States, you can achieve something of a risk free rate by borrowing at the Securited Overnight Financing Rate (SOFR)^[3]. The point is that various repo counterparties borrowed/lent $3.15T overnight on May 5th at roughly 3.62% annualized (i.e. pay $1/day to borrow $10000). We’ll use this rate for our example but in reality you’ll probably pay some spread to SOFR.

Now which fund does Ivan pick? Let’s run through each of the 3 scenarios below

If Ivan just does Fund AAA or Fund BBB, he makes the same amount of money as expected ($10 on a $100 investment, or $40 on a $1000 investment).

On the other hand, if he lever up fund AAA by borrowing $525 for every $100 invested, he can eke out extra return just for paying a little bit of interest. By borrowing money, he also increases his risk - the same 16% volatility on $625 in assets is now $100 in volatility (or 100% of the initial investment).

The best part is that you don’t need to walk through this contrived example comparing the S&P 500 to spot Bitcoin (oops sorry I meant fund AAA and BBB) to be able to apply Sharpe’s work to other investments. You can simply compute the expected return minus the risk free financing rate and divide by expected risk. That number gives you a useful heuristic clean of the holy “risk adjusted return” that everybody on X seems to rave about.

A brief aside on leverage and risk managment

This is not investment advice. I happen to work somewhere where we do investing, but none of the views or opinions expressed here represent the views of my employer. These are solely my own opinions. I’d also broadly say that getting any kind of information from the internet is a bad idea. This is true if you’re going to commit your own capital to it, and even more true if you’re going to commit somebody else’s capital to it.

You may have noticed in the preceding example that Ivan levered up to 6.25x. For almost all traders, this is mostly a very bad idea because of margin calls and a magnified bankruptcy risk. Don’t do this.

The Fine Dining Experience

Now that we’re all roughly acquainted with how leverage can allow you to pick the better risk-adjusted investment we can get into why maximizing risk adjusted returns actually can’t be your only criteria.

I had the bright idea in February ‘24 to participate in a Tax Lien auction. The rough trade idea is very simple. People own property. Local governments in the United States levy property taxes on said property to pay for services that private property owners tend to benefit from (public roads for their cars, public schools for their children, hospitals, human services, etc.). Often times, property owners forget to pay their property taxes. Bidding on a tax lien certificate is effectively bidding on the right to collect the homeowners property taxes from them plus some penalty and some interest. You basically are fronting them the cash for their property taxes until they can pay it.

• 90% of the time, the owner has forgotten to pay and they pay the penalty and move on within a week.
• 8% of the time, they choose not to pay. You have to send them a letter and they pay the penalty and some interest within a month.
• 1.5% of the time, they can’t afford to pay because of circumstances in their control. For example, they bought a $2M house and then bought a Lambo the next month. This usually takes a while to resolve
• 0.5% of the time, there are unavoidable circumstances. Who am I to judge?^[4]

There’s relatively low (zero?) risk of this overcollateralized financial instrument (loan?) resulting in a loss, and the returns are generally decent (benchmark 6-7% annual coupon rate). Also the duration risk is relatively low given that most trades complete within a month or two and even the extended ones last max 2y.

This is exactly the kind of high Sharpe trade that should be massively levered, right?

This is where Sharpe isn’t the only metric that really matters at the end of the day

A Real Example

Below are the cashflows associated with the real auction that I did back in 2024. The IRR of almost 15% on fully collateralized notes with super-senior lien status is just absolutely mouthwatering. It’s also such a weirdly niche corner of finance that you don’t have a lot of institutional competitors crowding you out.

The main risk here is that the tax payer decides to never pay back and you need to foreclose and the lawyer fees are worth more than the house that needs foreclosure. As it turns out, all of these properties were worth more than 100x the lien, so that’s an unlikely issue.

On paper this is a sweet deal. It’s like picking up Sacagaweas off the floor in front of a steamroller except the steamroller is out of gas. I had fewer white hairs in my beard back then.

What’s the Problem?

You probably noticed that I only made $1241 after committing $8162 in capital for almost 2 years. Considering I financed 100% of this at SOFR, I basically clipped an IRR of 11.5% FOR FREE. Why not do this ad inifitum to make infinite money?

Turns out that high Sharpe just means that you have a capital efficient trade. The big problem with this investment is that the total market issuance is only about $25B a year across the continental United States. That’s every single municipality in the country. My $8k was only 0.5% of the bids in the auction I participated in. I won’t get into my pricing algorithm for placing bids, but it does mean that if I was looking to make meaningful money (call it $1M), that I would need to commit to bidding in 100+ municipalities with similar scale, or pricing tighter so I capture more of the auction (and reduce my implied yield to maturity).

It’s really really painful to navigate around even one township’s rules and regulations surrounding tax lien certificates. Don’t even get me started on expanding to hundreds.

Parting Thoughts

This could be an interesting trade for somebody that is willing to manage a whole portfolio of certs. If anybody has experience with similar-ish instruments feel free to reach out, I’m always interested to learn more and hear war stories.

Footnotes

[1] - The Journal of Business, Vol. 39, No. 1, Part 2: Supplement on Security Prices, pp. 119-138 JSTOR 2351741

[2] - ask Tyler Given if there’s a spurious correlation between Apple, Inc. and Beanie Babies

[3] - I won’t go into the mechanics of how you can put on this trade, it’s not important. Maybe for a future piece

[4] - these are the folks that I actually feel for. It can be a very harrowing experience and often times paying your property taxes is the last thing that gets dropped