# A Simple Quantitative Analysis of Buffett’s Hedge Fund Bet

(This material was originally written for an entirely different context. However, the subject came up in casual conversation recently and I thought it was worth revisiting. Warren Buffett’s bet with a fund of funds firm has gotten a lot of press but little in the way of rigorous analytical treatment. That’s a shame in my view as the bet is a good jumping off point for a discussion of portfolio construction)

Sadly, there is not enough data (and doesn’t sound like there ever will be enough released publicly) to do a rigorous performance attribution for the funds of funds featured in the bet. But I did want to comment on a topic that stuck out to me, inspired by this passage:

The compounded annual increase to date for the index fund is 7.1%, which is a return that could easily prove typical for the stock market over time. That’s an important fact: A particularly weak nine years for the market over the lifetime of this bet would have probably helped the relative performance of the hedge funds, because many hold large “short” positions. Conversely, nine years of exceptionally high returns from stocks would have provided a tailwind for index funds.

Instead we operated in what I would call a “neutral” environment. In it, the five funds-of-funds delivered, through 2016, an average of only 2.2%, compounded annually. That means \$1 million invested in those funds would have gained \$220,000. The index fund would meanwhile have gained \$854,000.

Without more detail on how the funds of funds were allocated, it is difficult to confirm whether or not the market environment was actually “neutral” for them. I also believe at least one of the funds succeeded in creating some value despite trailing the index on an absolute basis.

Remember sitting in math class wondering why you would ever need to know to calculate things like standard deviation and correlation? Well, here is an opportunity to put all those seemingly wasted Stats classes to use.

With the help of some basic statistics we can build a simple attribution model to assess whether the hedge fund managers added value, as well as their risk exposures relative to the index fund.

I will not bore you with the specifics but trust me when I say we can use the annual return data from the Berkshire letter to calculate betas for all of the funds of funds. And since we can calculate betas, we can get an idea of how exposed the hedge fund portfolios were to the same systematic (read: market) risk factors as the index.

T-Bills, for example, have a beta of 0. This makes intuitive sense because T-Bills are not exposed to the same market risks as the stocks in the S&P 500. The S&P 500 Index fund has a beta of 1 to itself, which also makes intuitive sense because it is exposed to exactly the same market risks.

So what about the hedge funds?

Well, as is evident in the above table there are a range of betas, from .41 for FoF A to .69 for FoF E. We can use the betas to evaluate whether the managers trailed the market simply because they were less exposed to the market in a period whether the market did rather well (I would disagree with Mr. Buffett’s assertion that 2012 to 2016 have been “neutral” years for the market), or because the managers themselves destroyed value.

This one is a simple calculation. You simply multiply the beta by the index fund’s average return for the period:

FoF A = .41 * 9.1 = 3.71

FoF B = .55 * 9.1 = 5.00

FoF C = .53 * 9.1 = 4.82

FoF D = .65 * 9.1 = 5.91

FoF E = .69 * 9.1 = 6.28

The multiplication gives you the return you should expect from a hypothetical investment that does nothing more or less than match the hedge fund’s beta to the index. Compare this number to the actual average fund returns to get a rough idea of whether the manager has added or subtracted value on top of that.

For the funds in the table, most of them performed rather poorly even by this measure. As Buffet writes in his letter, this is because the managers weren’t able to add enough value to offset expenses, and on top of that probably made some mistakes. It is hard to say without knowing more about how the portfolios were built. We could expand our attribution model to try and get a more granular picture, but that is a topic for another day.

There is one exception among the funds. FoF C appears to add value. We can see this via the above comparison and also comparing its Sharpe ratio to the Sharpe ratio for the index fund. Note that FoF C delivered 67% of the return of the index with 65% of the volatility.

So why would I want to own FoF C instead of the index when it underperforms on a cumulative basis? Well, maybe I want an “equity-like” return with less risk (read: better risk-adjusted performance). And why would I want that? Maybe it aligns better with my risk tolerance or my goals as an investor (I may need a screwdriver instead of a hammer based on a particular problem I am trying to solve in a portfolio). Not everyone defines risk as permanent impairment of capital, and not everyone can withstand mark-to-market volatility. Also, there are very few investors who truly have a “long term” investment horizon.

How do you know if your horizon is truly long term?

If the market closed tomorrow and you could never trade again, would you keep the same portfolio? If so, you are truly a long term investor.

Most of us don’t meet that criteria, because we will need to draw down our portfolios to some extent to fund various living expenses somewhere over the next couple of decades. The point is this: if you are underperforming the broad market because you have made a conscious decision to be less exposed to the market, that’s not necessarily a problem. It depends on the bill of goods you’ve advertised to your investors.

Of course, I also might outperform the index at times simply by avoiding large drawdowns in periods of market stress. However, with a low net exposed fund I would definitely not hang my hat on absolute outperformance versus the index over a long time period.

### What Is The Point Of All This, Exactly?

Warren Buffett is perhaps the most misunderstood personality in finance. Though he may look the part, he is not simply some kindly old billionaire dispensing pearls of wisdom to the unwashed masses (he certainly excels at cultivating that image).

Warren Buffett is a value investor and should be viewed through that lens. If he finds value in an investment opportunity, he will pay for it. Even if it is nominally “expensive.” He admits as much in this very investor letter, writing:

And, finally, let me offer an olive branch to Wall Streeters, many of them good friends of mine. Berkshire loves to pay fees – even outrageous fees – to investment bankers who bring us acquisitions. Moreover, we have paid substantial sums for over-performance to our two in-house investment managers – and we hope to make even larger payments to them in the future.

To get biblical (Ephesians 3:18), I know the height and the depth and the length and the breadth of the energy flowing from that simple four-letter word – fees – when it is spoken to Wall Street. And when that energy delivers value to Berkshire, I will cheerfully write a big check.”

How do you reconcile this with his advice for other investors to index?

Warren Buffett knows most people, including a fair number of professionals, are profoundly awful at identifying good investments and good investment managers. He also may or may not believe that the trend toward indexing actually improves the opportunity set for a genuinely skilled investor (read: himself). That last bit is just idle speculation on my part.

In my view Buffett’s stance has more to do with his belief that most investors simply do not have a good understanding of how to identify “value,” whether in the context of an individual stock or an investment manager. He is also smart enough to realize most investors don’t need outperformance to achieve basic financial goals like funding their kids’ educations or saving for retirement. Cheap beta exposure (a.k.a “being in the market”) will get the job done.

For these investors there is little value to be had pursuing an active investment program, which they will almost certainly botch chasing 1, 3 and 5-year trailing performance numbers, all the while paying the higher cost of active management.

Put another way: these investors are better at wielding a hammer than a screwdriver.