Portfolio Management: Convex versus Concave Strategies

In the past few weeks, everyone has been talking about GSE preferred stock. The impetus for this was far better results reported by Freddie Mac last week where they reported a provision slightly over $150M, down over 90% from the previous quarter. There are various flavors of both Fannie and Freddie prefs with the more liquid instruments trading at a slight premium to others (also certain dividend language, par value, etc has its effects). Some of the smartest funds in the world are very long Freddie prefs in a very big way on a notional basis, and have been for some time. Now more and more people are picking up the idea and running with it (piling on)

A friend pointed this out to me today and its something I completely missed: Most distressed funds HAVE to have some leverage to the upside in GSE preferred because the return asymmetries are so large, if certain events play out, those not playing would be left behind in the dust in terms of returns. Let's say a distressed fund has a 3% allocation to Freddie Mac prefs and the securities are reinstated with 100% of their dividend. That fund just made ~30%+ (assuming buy FMCKJs at 2.5 for simplicity) and you are trailing them by the same amount if you are not involved.

Many people draw parallels between poker and investing. Some great investors are also great poker players. (David Einhorn being the most prominent - I still hate the way ESPN characterized Einhorn during the coverage of the Big One for One Drop tournament. I.E. he should have gotten a lot more credit). Poker is a game of odds and expected value. You calculate the odds the pot is laying you versus the chance you have the best of it using not just the cards in your hands but also the actions of players around the table in the current hand and hands played previously. I've played in the main event in a previous, post Moneymaker WSOP, and welcome any chance I get to play poker.

Investing is similar in that none of us have perfect information. We do not know the future. We do not know if an overcard will hit on the river when you have queens in the hole, blanks on the board, and two loose players sticking around for no logical reason. Instead we calculate expected values of plausible scenarios, using conservative estimates, and determine if a security's current price gives you a margin of safety. If my worst downside case is $20, with an expected value of $40, and a distressed bond is trading at $22, I think that's an investment you make all day long. Asymmetric risk / return profile with a margin of safety is the holy grail - these are the bets I make in my personal account with smaller distressed positions that have money left for shareholders under all scenarios.

Investment lore often discusses the transition Warren Buffett made from going from his time at Graham-Newman to the Warren Buffett we know today. It is often cited that the realization and input of Charlie Munger on the benefits of "high quality businesses" and their nature to generate massive internal capital for shareholders was the key difference. In effect, he replaced his cigar butt investing that are effectively concave bets with high quality business investing which are indeed convex bets.

Being long Freddie Mac prefs is a convex bet. I can make many many many times my money for the potential downside.(I know you could make the case that the curve should actually end with a flat line for par value, but I can envision scenarios things could get a little crazy). Being a distressed bond is similar. If I buy a bond at 20 cents on the dollar, my downside is 20 points, with my upside being many multiples of that. And the most famous example: Being long protection on subprime in 2006/2007 was most surely a convex bet.

Being long a bond at par is the opposite. I buy a bond at par, I risk 100 points down and maybe 20 points up (higher in the IG universe due to duration impacts) ex coupon. The reason high yield works as an asset class is that the default rate and expected recovery rate relative to coupons, yield, and spread makes for a positive expected value in certain scenarios. Vanilla merger arb investing is similar (risk a deal break for limited upside) and that's why you see some of the best option guys out there also doing the best in merger arb (options allow investors to change concave curves into convex curves via various strategies attempting to play overbids or deal breaks).

The argument can, and has been made, that convex bets are really lottery tickets. Freddie Mac prefs fit this bill. Is there a a real margin of safety in those preferreds? I'm not sure. The chance of permanent capital loss is a real number - some people think its very high and some think its very low. The expected value though is probably positive though as the positive tail is just so big. A huge recovery multiplied by a small chance moved the needle when you are buying that security at 10% of par.

Concave strategies are not all bad. It would be a fool's errand to believe every investment you make has limitless upside with minimal to no downside. In fact, a solid set of concave strategies can pay for aforementioned lottery tickets. The problem of course is that investors are overconfident and when applying probabilities to various scenarios can get themselves in trouble when return and risk profiles are inherently concave (i.e. limited upside for lots more downside). Betting on stressed issuers paying off their maturity profiles is a common example. Let's take an example:

SVU (Supervalue Inc) have 7.5% 2014 bonds that trade in the 96 context. If SVU pays off that maturity, I'll make 4 points. If they default, I'll recover 40 (Recovery locks 35/45). I risk 56 points to make 4. If you believe, SVU has less than a ~7% chance to default before the maturity, one could argue that you should make that bet. I think that's a crazy bet unless you are 100% they will not default on that obligation: You are not a calculator that can pinpoint to the decimal point if SVU will file. The jump risk makes this bet a suicide trade because there aren't a lot of scenarios where the bonds hang out in the 60s, 70s, or 80s if they default. You are hit by a train and forced to take a 60 point loss.

The flip side is different though. When buying a bond at 4 with a target price of 60, you risk 4 points to make 56 (mirror image of last example). What is different here is that more often than not the trade is not binary: Its not 0 or 60. In fact its probably a set of recoveries from 0-60 (or higher) with distinct probabilities that drive positive expected value. The downside is bracketed by zero whereas upside accelerates higher. Here's the graph:

And I think this is where money management and poker begins to diverge: A poker player's bank roll is determined by the skill of a player with volatility swings on account of bad luck. A good poker player will know how to manage his bank roll to avoid ruin. A money manager's bank roll, i.e. AUM, is not determined by the skill of the investment manager unless all their money is completely locked up. Instead, a money manager's AUM is determined by the vagaries and emotions of his or her investors, which are cued off of returns. Investors across the board always get out at the bottom and pile in at the top - a concave strategy if I've ever heard of one. Because of this, being wrong on too many concave bets where results can seriously be hampered by just a few misses can lead to investors withdrawing and you not having any chips left to play. I'd rather buy 24 different bonds at 4, than one bond at 96, especially if you've done the hard work to put yourself in the right position for real upside.