Re-estimating an NHL team's Picasso value
Sports franchises are different from "regular" businesses in one important way -- they're a lot more fun. If you own a team, you get any profit it makes, but you get lots of perks in addition to that. You get to be on TV a lot. You get the best seat in the house. You get to hire and fire staff. You get quoted in the paper any time you want. You get to be a hero in your local community. And so on.
Because of this, you'd expect team owners to be willing to pay more for a team than its future earnings are worth; they want the "consumption value" in addition to the investment value. You can call this the "Picasso effect," because owning an expensive sports team is a bit like owning an expensive painting; you do it partly for the pride of ownership.
In the previous post, I tried to estimate the Picasso value this way: I ran a regression to predict team market value from team earnings (both values as estimated by Forbes). The equation came out
Market Value = 4 * annual earnings + $200 million
From that, I suggested that Picasso value was $200 million: that is, since the $200MM term didn't have anything to do with the success of the business, it must be the value that owners are willing to pay just to own the team.
But, following a post by Dackle over at "The Book" blog, I realized that isn't quite right.
The problem is that team value -- at least that portion that has to do with earnings -- is based on *future* prospects. And future prospects don't correlate 100% with current prospects. In effect, some of today's earnings is random noise -- the economy might be good in that particular city, or a promotion works well, or the team is just having a good year.
The more random noise, the higher the Picasso estimate. For instance, suppose that profits were completely random, and had nothing to do with any particular attribute of the team. Then, all teams would be valued equally, and the equation would be
Market Value = 0 * annual earnings + $220 million
And it would look like the entire value was Picasso, when, in reality, it could be that the value is driven entirely by earnings.
So to do the calculation right, you have to remove the noise from the earnings.
To try to figure out how to do that, I started by running a regression on Forbes 2008 earnings vs. 2007 earnings. If earnings were completely random, the correlation coefficient would be zero. Of course, it wasn't zero; the Leafs were profitable not because they were lucky that year, but because there are millions of loyal idiots like me who worship the team even though it continues to suck. The correlation coefficient was actually a very high .93. I'll put that in courier font:
One-year earnings correlation coefficient = .93
An r of .93 doesn't suggest a lot of noise, so it won't change things much. But maybe the .93 is still too high. Remember, the economic value of the team is the present value of *all* future earnings, not just next year. And earnings might change more in future years. For instance, between one year and the next, team performance is usually similar. Good teams stay good teams, and poor teams stay poor teams. Maybe that all evens out after, say, five years.
If we take .93 to the fifth power, in effect "compounding" the regression to the mean, we get about .70. This seems reasonably generous to me; a correlation of .7 is an r-squared of .5, which implies that the "fixed" component of a team's earnings has the same variance as the "variable" component.
That means that to get a team's "true" earnings from its 2008 earnings, we regress the number 30% towards the mean. To take one example: the Rangers had earnings of $30.7MM in 2008. The mean is $4.7MM. Regressing $30.7MM thirty percent towards $4.7MM gives $22.9 MM. So we assume that the expected value of the Rangers' "real" earnings was $22.9MM, and the remaining $7.8MM was due to random factors specific to that season.
If we do that for all 30 teams, and rerun the analysis using our regressed estimates of earnings, we now get
Market Value = 5.6 * annual earnings + $193 million
Not much different ... but better, I think. I'm more comfortable with a higher earnings multiple (5.6, in this case, rather than 4.0), since, for publicly traded securities, ratios (I think) tend to range between 7 and 11.
So this reduces our estimate of "Picasso value" from $200 million to $193 million. Not much. And it's easy to see why not much: according to the Forbes data, the money-losing teams are worth an average of about $160 million. If you believe these teams will continue to lose money, then, obviously, the Picasso value must be at least $160MM, since they're worth zero as a going concern.
I believe some of the $193 million is Picasso value, and some of it is hopes that the team will eventually be profitable: either by moving it to a city where it can make money, or by making more money in other ways (like a better TV deal).
Anyway, getting back to the Zimbalist/Balsillie question of how much more a team is worth in Hamilton ... if we run the revised numbers, we get an even bigger difference -- which makes sense, since the more profits matter, the more a team is worth in a money-making city as compared to a money-losing city.
The regressed estimate for Phoenix earnings is a loss of $5.4MM. For Hamilton, we continue to use Balsillie's own estimate of $11MM (we don't regress that since it's an estimate and not an actual observation).
That means, by this method,
$163MM market value for Phoenix
$255MM market value for Hamilton
Still, about the same as in the previous analysis. The benefit to the move is around $90MM, and three-quarters of the value of the Hamilton franchise is Picasso value.
(Thanks again to Dackle for the comment that led to this post.)