A leveraged recapitalisation is a company borrowing a large sum and handing it to shareholders, usually as a special dividend, occasionally as a self-tender for a large slice of the stock. What remains listed afterwards is a stub: a small equity claim sitting on top of a lot of debt, on the same operating business as before.
The arithmetic is a two-line consequence of conservation of value. Ridgeline Components has 40 million shares at $25.00, so $1,000 million of equity, plus $200 million of net debt, giving an enterprise value of $1,200 million on EBITDA of $150 million, or 8.0 times. It borrows $700 million and pays a special dividend of $17.50 a share. Net debt becomes $900 million, or 6.0 times EBITDA. If the recapitalisation creates nothing, the enterprise is still worth $1,200 million and the stub is worth 1,200 − 900 = $300 million, which is $7.50 a share, exactly the old price minus the dividend.
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What drives the value of the stub?
Two things about that stub deserve more attention than the arithmetic.
The first is leverage. The stub is 25.00% of enterprise value, so it moves 4.0 times as much as the enterprise does. A 16.67% fall in enterprise value takes the stub down 66.67%; a 33.33% fall takes it to zero. The multiplier is arithmetic rather than a figure of speech about risk, and it is the number that decides position size.
The second is that the recapitalisation is not quite value-neutral, because the new debt carries a tax shield. At a 24% tax rate, $700 million of permanent debt is worth $168 million of shield, which would lift enterprise value to $1,368 million and the stub to $11.70 a share. So the honest model is a range, $7.50 with no shield and $11.70 with a permanent one, and where the market prices the stub inside that range tells you what it believes about the durability of the leverage.
Suppose the stub trades at $6.60. It is not paying for any of the shield; it is 12.00% below the value that assumes no shield at all, and 43.59% below the full-shield value. That is the orphan discount, and it is what the event-driven investing page predicted: the shareholders who wanted a $25 industrial company do not want a $6.60 lottery ticket, the dividend gave them a reason to leave, and there is no natural buyer yet.
How big a position can a stub justify?
Now size it, and this is where the ruin constraint earns its place. Put five enterprise-value outcomes on the table at $800, $1,000, $1,200, $1,400 and $1,600 million with probabilities of 0.15, 0.20, 0.30, 0.25 and 0.10. The stub is worth $0.00, $2.50, $7.50, $12.50 and $17.50 respectively, so its expected value is $7.625000, and against a price of $6.60 the expected return is 15.53%.
A Kelly calculation on that distribution returns a full-Kelly fraction of 23.77% of capital and a half-Kelly of 11.88%. Both numbers are wrong to act on, and the reason is in the first row of the table: 15% of the time the position is worth nothing. Committing 11.88% of a portfolio to a bet with a 15% chance of total loss means a one-in-seven chance of a 12-point permanent hole, and a portfolio that runs six such positions is not diversified, it is a coin-flip machine. A ruin constraint that caps the loss from any single position at 2% of capital sizes this at 2%, which is 5.94 times smaller than half-Kelly.
Kelly maximises the growth rate of a bankroll that is played infinitely often by a player who cannot be fired. Neither condition holds. When the two rules disagree, the ruin constraint wins, and it should win by a wide margin whenever the loss case is a zero.