Tuesday, August 3, 2010

Cheap Stock or Delusional Investors? Neither...Or Both?

A recent Bloomberg story about Och-Ziff Capital Management raises an endless array of interesting questions.  The headline says "Och-Ziff Hedge Fund's 23% Return Lures Big Investors Even as Shares Falter."  How can that be?

A hedge fund partnership investor (HFP) puts her capital at risk by investing in a hedge fund with the expectation that the hedge fund manager will earn attractive returns on that capital.  Alternatively, a hedge fund equity investor (HFE) puts capital at risk by investing in the management company that earns attractive returns by collecting performance fees on managed capital.

Wait!  Those are exactly the same!  What's going on?  How is it possible, as Bloomberg notes, for the fund to do well and the management company to perform poorly?  Let's look more precisely.

When HFP invests, she buys at book value the assets held by the hedge fund manager (HFM).  When she redeems, she sells at book value over the period held held the investment.  She earns profits linear to HFM's actual skill at earning returns.

Next, lets really simplify HFE's actions.  When HFE invests, assume he buys at market value a fraction of HFM's share of expected future gains on assets managed on behalf of HFP.  When HFE sells, he sells at market value those same expected future gains, minus any distributions he received during the holding period.  (This is no different than any other equity investment.)

At least three differences drive the wedge between the value to HFP and the value to HFE. 

First, HFE holds a payoff that is convex to perceived skill of HFM.  HFE owns a fraction of performance fees generated by HFM using HFP's assets.  Performance fees behave like call options: a claim on the upside and no (direct financial) responsibility for the downside.  That translates into a convex payoff, (or "operating leverage" as stock analysts like to say.)

Second, HFE's expected value depends on current and future assets.  Mutual fund results show assets flow non-linearly  in performance, (for those not familiar, in the academic fashion, this is a gratuitous plug for my own dissertation.)  I'll assume the same thing holds for hedge funds.  A convex relationship between performance today and asset flows tomorrow means option value exists in HFE.

Lastly, and most importantly, public equity markets provide a means to discount the future.  Thus, as too many investors forget, all stock prices have embedded the rate at which the market discounts future risky earnings.  That's what Price-to-Book and Price-to-Earnings ratios reflect: shorthand for discounting future earnings.  These ratios carry very high correlations across sectors (whether asset managers or widget makers) because they reflect our collective view of risk.

So, to summarize, HFE and HFP values differ because HFE will always have a convex payoff relative to HFP, and HFE reflects equity risk premia.  (I may go into more detail on these points.  Not only might HFP have convex risks, it often has concave risks, or short volatility, which I've discussed before.  In addition, to the degree HFP holds long equity market risk, it too has embedded equity risk premia.)

So, how can Bloomberg's observation be correct?  Easily: inflated risks perceived in the equity market may be steeply discounting future earnings...but then again, CNBC can tell you that all day long!

For the advanced reader: What's wrong with the thinking of the big pension plan that indexes their equity portfolio, yet hires OZM for their "alternative investment" allocation? Hint: They index their equities because idiosyncratic risk isn't compensated.

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