28Case Studies I

On 23 September 1998 fourteen banks and securities firms agreed to recapitalise a hedge fund, Long-Term Capital Management, and five days later they put in about $3.6 billion, 90% of what the fund was then worth. The fund had begun the year with $4.67 billion of capital and a balance sheet 28 times as large; by the end of August it had lost almost half, and by the recapitalisation almost all. Every number in that paragraph was the result of decisions the firm took long before: how much leverage to run, on what funding terms, in which trades, and alongside whom. This chapter and the next read three such failures from the public record, and rerun each with one decision changed.

28.1 How to read a failure

A failure seen from outside is a story, and stories favour villains and bad luck. Seen from inside a firm, it is a sequence of decisions, each of which looked reasonable with the information of its time: a limit set, a funding term accepted, a position allowed to grow, a choice to sell or hold. The useful reading keeps to what the public record establishes, reconstructs the numbers from it, and asks which decision, changed, would have changed the outcome by how much. It does not re-litigate what regulators and courts found, and it does not attribute motives the record does not state.

Two kinds of liquidity run through all three cases, and Book 1’s liquidity spiral is the mechanism that joins them.

A firm with ample funding can wait for a market to recover; a firm whose positions can be sold at once needs little funding patience. The failures that end firms combine the two: losses trigger margin calls, the calls force sales, the sales move prices, and the new prices trigger more calls (Figure 28.1).

Days to liquidate is the bridge between a position’s size and a risk model’s horizon. A one-day value at risk (Book 6) assumes the position can be exited within the day at prices near the model’s; a position of twenty days to liquidate carries twenty days of price risk, and its own sales move the price on each of them.

28.2 1998: leverage and the terms of funding

The public record here is the report of the General Accounting Office (now the Government Accountability Office) of October 1999. At the end of 1997 the fund returned about $2.7 billion of capital to its investors, leaving net assets of $4.67 billion; its balance-sheet leverage, 17 to 1 at the end of 1994, stood at 28 to 1. On 31 August 1998 it also held derivatives of about $1.4 trillion notional off its balance sheet. From January to September 1998 it lost almost 90% of its capital: 44% in August alone, after the Russian debt moratorium of mid-August sent investors towards quality and liquidity, and most of what remained in September.

A balance sheet 28 times capital means that a fall of $1/28=3.6\%$ in the value of the assets, net of hedges, wipes out the capital. The fund’s positions were mostly spread trades, long one bond or swap and short a close relative, whose net value moves far less than either leg; the leverage was sized to that small net risk. What the ratio measures is how little room the funding leaves when the spreads move together and far.

The GAO report states why the Federal Reserve facilitated a private recapitalisation: it judged that a rapid liquidation of the fund’s positions, and of related positions held by other market participants, might pose a significant threat to markets that were already unsettled. The creditors held the same trades, or were the counterparties to them; a forced sale by the fund would have marked their books too.

28.3 Tutorial: three reconstructions

def ltcm_returns():
    """Returns on capital by period, derived from the GAO figures: January to July (from the year-end NAV to the
    end-July NAV implied by August's 44% loss), August, and September to the recapitalisation (the fund's own equity
    implied by the $3.6 billion being 90% of NAV on 28 September)."""
    nav_jul = LTCM["nav_aug_1998"] / (1 - LTCM["august_loss_share"])
    nav_before = LTCM["recap"] / LTCM["recap_share_of_nav"] - LTCM["recap"]
    return {"jan_jul": nav_jul / LTCM["nav_1997"] - 1, "aug": -LTCM["august_loss_share"],
            "sep": nav_before / LTCM["nav_aug_1998"] - 1}


def capital_path(returns, start, scale=1.0):
    """Capital after each period when every period's return on capital is multiplied by `scale`."""
    out, c = [start], start
    for r in returns:
        c *= 1 + scale * r
        out.append(c)
    return out


def days_to_liquidate(position, adv, share=0.2):
    """Days to sell a position trading `share` of the average daily volume."""
    return position / (share * adv)

The reconstruction leaves the investors with $0.40 billion of their $4.67 billion, a loss of 91.4%, before the recapitalisation; the net asset value of $3.81 billion reported for 30 September includes the new money. At half the leverage the same asset returns would have left $2.01 billion, 43% of the capital, and no need for rescue. That counterfactual is generous in one way and harsh in another. It assumes the assets would have fallen as far, when part of September’s fall was the market trading against a fund known to be in distress, which a smaller fund would not have been; and it gives the smaller fund no credit for fewer counterparties calling margin at once. It also takes nothing from the returns of the years before, which half the leverage would have halved.

28.4 2006: a natural-gas fund’s concentration

The Senate subcommittee’s record describes a hedge fund, Amaranth Advisors, that built very large positions in natural gas contracts: at times 100 000 contracts in a single month, and, at times in the summer of 2006, about 40% of all the outstanding NYMEX contracts for the winter of 2006–2007 and 75% of those for November 2006. From the end of August to mid-September the natural gas positions lost more than $2 billion, and the fund liquidated its entire natural gas portfolio; Senator Coleman’s opening statement contrasted it with 1998: the Federal Reserve did not have to intervene.

A position that is 75% of the open interest in a contract has no market to sell into but the other 25%: the fund is the market. Days to liquidate makes the point in the units a risk committee uses. With an illustrative average daily volume of 25 000 contracts in the month’s contract, 100 000 contracts take 20 days at 20% participation and 40 days at 10%; a one-day risk measure of such a position describes a risk the firm could not have exited in a day. Chapter 7’s concentration limits exist for this: a limit on a position’s share of open interest and on its days to liquidate binds before a limit on its dollar risk does, because it measures what the position would cost to leave.

28.5 August 2007: the crowded exit

In the week of 6 August 2007 a number of quantitative long-short equity hedge funds had unprecedented losses, followed by a significant rebound. On 13 August Goldman Sachs filed a statement that quantitative strategies were under pressure from an increase in overlapping trades, a surge in volatility and an increase in correlations, that its response had been to reduce risk and leverage, and that it and other investors were putting $3 billion of equity into one of its funds, Global Equity Opportunities, whose net asset value was about $3.6 billion. Khandani and Lo’s study of the week, which Book 7 and Book 8 discuss, hypothesised that the losses were initiated by the rapid unwind of one or more sizable quantitative equity market-neutral portfolios, and that those losses then put pressure on a broader set of equity portfolios.

The model is Book 7’s, and the numbers are synthetic: the point is the shape. The seller’s own trades move the prices of the stocks it holds, and the holder, whose book overlaps it, marks the same moves. Through the selling days the holder loses slightly more, since it still holds its whole book while the seller’s shrinks. When the selling stops, the temporary part of the impact decays and prices partly return: the holder recovers most of it, while the seller has sold at the bottom of its own move and recovers only on the half it kept. At day 20 the seller is down 9.7% and the holder 7.9%.

What the seller’s choice buys is protection against the scenario in which it cannot hold: a lender that calls, a risk limit that forces the cut, an investor who redeems. A fund with funding that lasts through the episode, and limits set in advance for it, can choose; one without is the seller whether it chooses or not. The overlap is what turns one firm’s decision into everyone’s loss: at an overlap of 0.52 the holder loses 4.3% by day 20, and with an unrelated book nothing, while the seller’s own loss hardly changes.

28.6 What the three share

The three cases share a structure. Each firm held positions whose risk looked small in normal markets: spreads between close relatives, calendar spreads in one commodity, a hedged equity book. Each held them at a size, and with a leverage, that made its exit a market event. And each depended on others’ behaviour: lenders who could raise margins, a market with no one else on the other side, funds with the same trades. The firm-level decision that recurs is not the trade but the pairing of size, leverage and funding term with the market’s capacity to absorb the exit.

28.7 Build: the casebook, part 1

28.8 Exercises

28.9 Problem: Three Firms, Three Decisions

28.10 Interview questions