Wednesday, June 28, 2006

Asset allocation: how much is enough/too much?

Successfully outperforming the index requires identifying sufficient favorable trends to give you a distinct advantage, and then pressing that advantage to the maximum within a reasonable context of overall portfolio safety.

Said another way, for consistent outperformance, it's not good enough just to identify favorable investment opportunities, but you must also identify how much of your assets to allocate to the take full advantage of the opportunity. In other words, how much to weight your portfolio with that particular holding.

Generally, amateur investors like myself who hold focused portfolios, have some instinctual understanding that positions must be overweighted to outperform the index. We may reference general comments and schools of thought, like knowing that superinvestor Warren Buffett once held over 50% of his net worth in a single stock (GEICO), and also once invested more than 25% of his public stock holdings in American Express to help us with our portfolio weightings.

But the question remains of how much, scientifically, to allocate to a particularly favorable opportunity in our own portfolios. The Kelly Criterion (link also provides an example of how to use it, based on your own historical trading success and patterns) provides one such answer. I'm going to borrow a different and simpler example (using the Kelly Criterion) to illustrate the point.

Suppose, on a coin toss, you were to receive $2 for every time the coin turned up heads, but had to pay $1 for every time it turned up tails. How much should you allocate to maximize winnings, while ensuring that a few coin tosses don't send you to ruin? The Kelly Criterion says you can effectively maximize winnings by using this formula:
  • Edge/Odds = Allocation percentage (the answer we're seeking)
The edge is calculated by comparing how much of an advantage, over an infinite period of time, this particular coin toss strategy has. It's calculated by comparing the odds of winning, against the odds of losing. In this case, you can expect that 50% of the time, you'll win $2. This is part [a]: (50% x $2 = $1). However, in 50% of cases, you'll lose $1. This is part [b]: (50% x $1 = $0.50). You now subtract [b] from [a] to determine your edge, thusly: $1.00 - $0.50 = $0.50. This is your edge ($0.50), the top part of the equation.

The odds are calculated by knowing how often this the event will turn out favorably. Since we know the coin has only two sides, and one sides value is double the other, then we know that the odds are 2:1 (ie. $2/$1). So the odds figure is $2.

We then divide one figure (edge, $0.50), by the other (odds, $2), to arrive at the suggested allocation for the portfolio, or "the bet". In this instance, $0.50/$2.00 = 25%. This suggests we should allocate 25% of our portfolio in each particular round, to this particular "bet" (assuming all odds and edge factors remain the same).

This system has several noteworthy features:
  1. It's theoretically impossible to go bankrupt, given that money is theoretically infinitely divisible (down to the 1 cent level anyway);
  2. The system produces the maximum return in the shortest period of time, on average;
  3. The returns are very noticeable and lumpy - for example, if your first three coin tosses were negative, and you started with a $10 bankroll, you'd be down to $4.22.
If you want to use this system, I suggest you study the materials in both links I've provided until you have a good understanding of the benefits and drawbacks of it.

Hat tip to Abnormal Returns for sending us out there ...


The Confused Capitalist


Anonymous said...

Thank you Jay for the analysis of amounts of allocation. I can't recall anyone explaining that concept before. That may be a result of my newness to bloging and reluctance to expose my ideas to the light of day(other peoples ideas). Anyway , I appreciate it. Tom in Indy

Jay Walker said...

No problem. It's something I've just come across as well. I'll definitely be applying it, at least as a rough allocation screen, in the future.

As Abnormal Returns said recently, all good investors continue to learn and, in this, the internet makes it so much easier than ever.

Thanks for dropping by ...