As I was analyzing Alliance Bernstein (NYSE:AB) it struck me how the stock is, in part, a call option on the stock market. Of course it's not a pure arbitrage, but the comparison is enlightening.
For this comparison to be true you need to believe the following:
- 1) AB's cost base is fixed. 4 x Q3 operating cost is roughly $2.2B in annual costs. These costs are mainly employees and real estate, hence mostly do not vary with revenue.
- 2) AB's revenue derives primarily from a cut of assets under management (43bps on average from their Q3 numbers), which in turn depend on the level of the markets. As of December 2011 AB reported $132B in equity assets and $279B in other assets (mainly fixed income). I'm assuming here that the fees on fixed income and equity products are equivalent, which is again, a simplifying assumption.
- 3) Other revenues (beyond equity management fees) are largely fixed. This one stretches credibility a little as clearly bond market fees vary with the level of bond prices, but given that bonds are less volatile than equities we'll make that simplifying assumption.
- 4) I'm making a simplifying assumption by using the S&P 500 as a proxy for the markets in which AB operates, however, a significant portion of their equity funds are oversees, and of course could over or underperform the S&P 500 over time.
So, on the above assumptions, we have a fixed cost base and revenue that varies with the market. Assuming a 30% corporate tax rate and a constant valuation of 15x earnings, you get the following picture in terms of how the AB share price would theoretically varies with the S&P 500.
This graph may look familiar to anyone who's charted option payoffs, it suggests that AB trades like an S&P 500 call option, and, more specifically an S&P call option with a strike price of around 1050 expiring in Dec 2014. Ideally I'd want longer duration than 2014 but that's the best I could find. That particular option is currently trading at $347.
Given the payout structure (i.e that AB's share price increases at a slower rate than the payout of an option with the same strike price), a single AB share is roughly 0.07 of an S&P 500 1050 Dec 2014 call option and would therefore be worth $347*0.07=$24.
AB's current price is just over $16. This analysis requires some pretty heroic assumptions that you could drive a bus through, so I wouldn't put an arbitrage trade on any time soon, but it is possible that if you have a long-term bullish view on the markets, buying investment management firms with significant equity under management, might be an interesting way to achieve similar exposure perhaps at lower cost.
Please note I have not discussed the fundamentals of AB's business in terms of management, fund performance etc. I am aiming to give an assessment on the fundamental drivers of the business more than deep qualitative analysis of the company in this article.
Disclosure: I am long AB.