In Praise of High-Volatility Alternatives

Perspective

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Topics - Alternative Investing Portfolio Construction Portfolio Risk and Performance Volatility

In Praise of High-Volatility Alternatives

Everyone knows that it’s compound returns over time that matter, and everyone knows that volatility (“vol”) is a drag on compound returns. E.g., 30% up and then 30% down is 9% down; 50% up and 50% down is 25% down. 3 And, to go to extremes, one -100% means compound returns are -100% forever (there’s no compounding your way out of Hades 4 ). But there’s a caveat that often gets left out. What everyone knows is true is only true if we are discussing an investor’s whole portfolio. If anyone believes that only compound returns matter for the components (I’ll call these “line items”) of the whole portfolio, particularly modest-sized line items, particularly diversifying ones, then they are actually wrong. 5 This is a particular issue for alternative investments, since they are indeed often modest-sized components of a portfolio, are there to provide diversification, and often can be delivered in a wide range of targeted volatility. 6

Now, high vol, even on small components of the portfolio, doesn’t make life easy. Many, certainly including me, talk about the practical difficulties of sticking with an individual investment through periods of large losses, which obviously are more likely the higher the targeted vol. 7 Even a great investment can be spoiled if you can’t stick with it through its tough times. This is a particular problem when those losses are coming from unconventional investments. 8 Alternatives, if they’re done right, are inherently unconventional. One of the most common ways to combat this problem is to shy away from very volatile (at least if marked-to-market) investments. Indeed, at AQR we often offer less-volatile options as in truth many cannot stand the heat and will redeem from the kitchen at the worst time when invested at higher vol. Even at modest vol we do think alternatives can help. But this note argues that good higher-vol alternative investments, 9 that are indeed often very hard to stick with, can be important tools in constructing the best overall portfolio, and if (a big if) investors can stick with them are often a more effective tool than their lower-vol cousins. 10 Basically, I think they are underutilized.

Some Basics on Vol and AlternativesI’m going to explain this using one of the most basic true alternatives I can think of; long-short market-neutral equities.

The return on a $1 long, $1 short portfolio 11 of individual equities is roughly: 12 , 13

Cash Return + [Return on Longs - Return on Shorts]

The volatility of this return over the risk-free rate will be the volatility of the [Return on Longs – Return on Shorts] component. Call that volatility ∑. Now imagine instead of $1 long and $1 short you lever the portfolio L times. That is, you’re now $L dollars long and $L dollars short proportionately in the same stocks. Now the return is:

Cash Return + L * [Return on Longs - Return on Shorts]

And the volatility of the portfolio is L * ∑. The Sharpe ratio of the portfolio is the same. 14

Our First Strategy at AQR

Let me tell you about launching our first strategy at AQR in mid-1998 as the story is relevant. 15 At Goldman Sachs our group (7 of us who started AQR came from our 13 person group at Goldman) ran a suite of strategies including alternative investments striving to be uncorrelated by being equally long and short, and traditional investments trying to beat a benchmark by over- and under-weighting securities (both used the same models for what they liked and didn’t like). So, what did we launch first at AQR? An uncorrelated alternative, of course. 16 But not just any. Nope, nothing mundane for us. We launched with one of similar volatility to our most aggressive strategy at Goldman. By design, using our own risk estimates, we were taking north of 20% annualized volatility. In complex mathematical terms that’s a boat-load of uncorrelated return, and more important for this discussion, uncorrelated risk! 17

While traveling the world for six months launching this strategy, one of my co-founders David Kabiller and I got asked many times something like “hey, we like this, but we don’t need to try to shoot the lights out, how about you do ½ or ¼ that aggressiveness?” 18 I responded every time, in a kind of flip manner (if you can imagine that from me), “sure, just give us ½ or ¼ the money.” I was mathematically correct. In dollar terms, which is all that should matter, investors would get ½ or ¼ the return for the commensurately lower risk. In fact, it was fair in another important way as the fixed fee would be reduced by ½ or ¾ (the performance fee adjusts most or all the way, depending on any hurdles, on its own). One of the more deceptive, uncool things an active manager can do is to start out aggressive at high fees, do well, then lower the aggressiveness over time, but not lower their high fixed fees (essentially giving less of their strategy for the same fee without stating it up front — i.e., just sneakily raising their effective fee). Nope, none of that for us. Giving us less money at the normal high vol was a clean solution and the fee adjustment was fair.

I will never agree that I was wrong on the math. That is a hill I will still die on. But I was wrong in every other way that mattered – particularly making this our sole offering. We had a terrible start from near minute one. 19 Our first 19 months we were down in the mid to high 30s (it’s very bad to start a strategy that is largely based on rational investing minutes before the dot com bubble really takes off). Now, to a quant geek that’s a bad initial result, but not super shockingly bad when you run at north of 20% vol (especially in a fat-tailed and sometimes trending world). So, to me, I was a little surprised this was such a big deal to people. That’s how freaking naïve I was. Nobody else was surprised. To seemingly every single other person on Earth it was obvious that OMG, this is horrific! 20 Thankfully we had a strong explanation for why it occurred and some serious evidence that we’d soon come to reverse that early bad start. 21 That led to us retaining a fairly gratifying fraction of our clients (some even added). But we still lost a lot of investors who just couldn’t take it despite my babbling about “uh, we hate this start, but in standard deviation terms we expect this occasionally and it looks great from here…” They couldn’t take it despite this statistical argument and despite the reason for our pain, and likely bright future, being rather (IMHO) obvious. So, when I discuss the virtue of high vol below, please be assured I have seen the other side of the argument, and, as I’m guessing most of my readers know, twenty years later I would live (barely) to see it all again.

So, nowadays, unlike my stubborn flip dismissal back in 1998 of “give us half the money” we offer both low- and high-vol alternatives as we do bow to practical reality. 22 But I would like to tilt at this windmill again, arguing one more time for the virtues of the higher-vol versions.

Compound Returns Are Overrated

OK, again, the above header is totally false at the overall portfolio level. But it can be true at the line-item level (line-item means each part of the portfolio).

I think a very simple example is edifying. Imagine you face a binary set of possible outcomes on an investment. There is a 2/3 chance you double your money (+100%) and a 1/3 chance you lose it all (-100%). And assume this investment is uncorrelated to anything else on Earth. Two things seem very obvious:

• The multi-period compound return on this investment viewed alone is clearly going to hit -100% soon and viewed alone stay there. Thus, putting your whole portfolio in this wouldn’t be such a swift idea.
• Anyone should put part of their portfolio in this investment. It’s a very positive expected return and -100% on a small part of an overall portfolio is eminently survivable. When you lose (or win) you just reload and do it again.

Now let’s try a more complicated example by making up some numbers I think are pretty reasonable (I assume cash is 5% with E[excess] below being the expected return of each asset over cash):

With the correlation of stocks and bonds being 0.30, 26 and the correlation of alts with both stocks and bonds being 0.00. Long-term compound returns, what you indeed care about on the whole portfolio, in this continuous framework are the expected return of the portfolio minus ½ the portfolio’s variance. 27 This second term is a mathematical version of the intuitive “volatility drag” discussed earlier with basic examples like +50% followed by -50% being -25%.

Now we’re going to solve for the optimal portfolio, defined here as the highest expected compound return with a maximum allowable volatility of 10% and not allowing any leverage (so portfolio weights must add to less than or equal to 100%). Let’s first ignore the alts and just optimize over stocks and bonds. Over just stocks and bonds this would be the optimal portfolio and these would be its characteristics: 28

Stocks/bonds/alts = 58/42/0

E[compound] = 8.9%

Total vol = 10%

Now let’s do the same allowing the 10% vol alts into the mix:

Stocks/bonds/alts = 62/0/38

E[compound] = 9.3%

Total vol = 10%

Not surprisingly the optimization gets better when you allow an additional asset (40 bps per annum better 29 ). Maybe a bit surprising is the alts almost exactly replaced the bonds, which aren’t desired now. With these assumptions alts are essentially just a better version of bonds. They have the same Sharpe ratio as bonds but at zero correlation to the very volatile equity portion. And, because you can’t lever (total weights must be less than or equal to 100%) there’s no room for bonds anymore.

Now imagine the same set-up but the alts are run at 25% vol. That means they now have an expected excess return of 7.5%. 25% vol is pretty scary on its own! So, what would the optimization want now?

Stocks/bonds/alts = 48/28/24

E[compound] = 9.8%

Total vol = 10%

Well, of course it wants a nice slug of the alts (though a bit less than half as much as when the alts were at 10% vol – the optimization is controlling the alts volatility by the amount it invests). You now make 90 bps a year more than not having any access to the alts, and 50 bps more a year than when the alts were only available at 10% vol. Perhaps most interesting though is the bond allocation is resurrected. What’s going on? Well, bonds with these assumptions are a pretty good investment, just not as good as alts (same Sharpe but more correlation to equities makes them worse). When the alts aren’t very volatile you need to allocate a lot of dollars to them, and that boxes out the bonds. But when the alts are more volatile you don’t want or need as many, and there’s room again in the portfolio for bonds, which still have low correlation to equities and none to alts, raising the compound return and Sharpe of the full portfolio.

Now one more. Let’s relax the no leverage constraint (here I am using the 25% vol alts but it doesn’t really matter, as when you can lever or de-lever, the asset-level vols don’t matter since you can create any vol you want). Results:

Stocks/bonds/alts = 43/52/22

E[compound] = 9.8%

Invested at = 118% (i.e., now levered at 1.18x)

Total vol = 10%

Yeah, I know, the same compound return as the prior case. In actuality it’s 8 bps a year more, but I’m rounding in both cases. But that’s the point. It’s only such a little gain, as when you have the 25 vol alts you are not very constrained at all by the “no leverage” rule. In fact, if the vol of the alts were another slug higher than 25, the no-leverage and leverage-allowed cases would be precisely the same (as you don’t need any leverage when the assets are sufficiently volatile on their own).

Another way to see this is to do the same optimization but with the 10% volatility alts (still allowing leverage):

Stocks/bonds/alts = 42/53/56

E[compound] = 9.8%

Invested at = 151% (i.e., now levered at 1.51x)

Total vol = 10%

Same exact result but you need more leverage. The optimizer is simply putting 2.5x more (10 vs. 25 vol) into the alts (2.5 x 22% = 55% — again some rounding is going on, I promise with more decimals places it would all be exact).

Allowing leverage is equivalent to choosing whatever vol you want on everything.

What Is Going On?What is going on is simply capital efficiency. A low-vol alternative that could be run at much higher vol may still be additive to a portfolio in this sedate form, but it is not as capital efficient as it could be. And, if (if!) you can live with the swings in the line items, you really want to be capital efficient.

Also note the extreme importance of rebalancing. In my initial example of the binary 2/3 chance of +100% and 1/3 chance of -100%, what I called “reloading” was just rebalancing (the amount to reload will vary slightly by the performance of the rest of the portfolio). Similarly, in the other examples, particularly when the alts are higher vol, it’s vital to rebalance the portfolio in both directions.

That’s it. High-vol uncorrelated assets are capital efficient and must be rebalanced within a diversified portfolio with great discipline to make it all work. If so, and if they are good to begin with, and if you can stick with it, I think they can really help and help more so than low-vol versions (which also help!). 30

The Robert Vesco Scenario 31

Now I’m going to a place no marketing department wants me to visit. What if the alternative “blows up”? That is, goes down -100%. Well, then it’s likely better you did it at higher vol with fewer dollars. If Mr. Vesco embezzles your money, having given him half at double the targeted vol was actually a much better idea! 32 Similarly, -100% may be limited to -100% only because of the limited liability nature of most such investments. In that case you again really wanted to have put half in at double the vol. Imagine the true return at the double vol was a -150% crash (i.e., the alternative manager lost more than all the money). If you put 10% in, you lost 10% in your portfolio (your asset “only” fell -100% because of limited liability). But if you put 20% in at half the vol, the line item was -75% (half of the -150%) and you lost 15% of your portfolio. These are (I hope!) very extreme, very rare events. But it’s kind of fun that in these true disaster scenarios the “less money at higher vol” strategy is actually safer. 33 , 34

Conclusion

Alternatives should be offered in palatable vol for those who need that. They are still useful particularly if the investor can shift somewhat from less- to more high-risk, high-return assets elsewhere (like bonds to equity as we saw a bit of in the exercise above, when adding low-vol alternatives replaced the bond allocation and led to a slightly larger equity allocation). But they are generally more effective in higher-vol versions (the fees should be proportional to be fair). The latter is mostly (not entirely) missing from the market today and should take on a bigger role.

Of course, the hurdle is big. The biggest problem with these investments is sticking with them, and I am advocating making it harder! Essentially, whatever the opposite of volatility laundering is, I am advocating for it. “Lean in to volatility” is the motto of this piece.

I truly get the line-item risk having lived it. A 25% vol investment having a -2 standard deviation year is ugly to explain, especially if it’s not been explained well up front! I get this risk to investors, that they’ll bail at the exact wrong time, and I get the analogous business risk to managers of high-vol products. Some, many, maybe most, won’t be able to do it and thus shouldn’t. But as is usual when doing the right thing is hard, the expected improvement if you can is real and can move the dial in a way that easy things can never seem to achieve. In particular, if such a program is chosen consciously (e.g., everyone knows they are giving 1/3 the money at triple the vol and discussed what that will occasionally look like up front), I hope it would make the inevitable occasional bad times easier to explain/tolerate and to follow your rebalancing plan with discipline. It turns out not offering investors the low-vol option, as we did in 1998, isn’t a good plan. But my hope is by offering both it makes the choice and tradeoffs clearer and the path thus easier to stick to.

Some difficulties are just too difficult. Not everyone has to do this. But in general, we shouldn’t default to “I guess we just don’t have the <whatever> to do what is right.” Rather we should look at these things as challenges to overcome that, if we can do them, lead to a better ex ante portfolio. I mean, in a real sense that’s our collective job! That the right path can be difficult is why everyone cannot produce a better portfolio, but it is also why those who can overcome these difficulties can outdistance those who cannot.