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# P2.T7.510. Balance sheet leverage (Malz)

#### Nicole Seaman

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Learning outcome: Explain the impact on a firm’s leverage and its balance sheet of the following transactions: purchasing long equity positions on margin, entering into short sales, and trading in derivatives.

Questions:

510.1. On opening day, Lever Brothers Multistrategy Master Fund LP has the following economic balance sheet: $100 in Cash,$20 in Debt, and Equity of $80. This corresponds to an initial placement of$80 in Equity by the fund's owners plus a loan of $20 by a commercial bank. Assume Lever Brothers finances a long position in$100 worth of an equity at the Reg T margin requirement of 50%. It invests $50 of its own funds and borrows$50 from the broker. Immediately following the trade, its margin account has $50 in equity and a$50 loan from the broker (The broker retains custody of the stock as collateral for the loan). If firm leverage is defined, per Malz, as Assets/Equity, then what is the change in the firm's economic balance sheet?

a. From 1.000 to 1.500
b. From 1.250 to 1.875
c. From 1.250 to 1.500
d. From 1.500 to 1.500

510.2. On opening day, Lever Brothers Multistrategy Master Fund LP has the following economic balance sheet: $100 in Cash,$20 in Debt, and Equity of $80. Assume Lever Brothers creates a short position in a stock, borrowing$100 of the security and selling it. It has thus created a liability equal to the value of the borrowed stock, and an asset, equal in value, consisting of the cash proceeds from the short sale. The cash cannot be used to fund other investments, as it is collateral; the broker uses it to ensure that the short stock can be repurchased and returned to the stock lender. It remains in a segregated short account, offset by the value of the borrowed stock. The stock might rise in price, in which case the $100 of proceeds would not suffice to cover its return to the borrower. Lever Brothers must therefore in addition put up margin of$50. After the trade, what is the leverage in the firm's economic balance sheet?

a. 1.25
b. 1.50
c. 1.75
d. 2.50

510.3. On opening day, Lever Brothers Fund LP has a simple economic balance sheet: $100 in Cash, and Equity of$100. This corresponds to an initial placement of $100 in equity by investors, and no debt. Suppose Lever Brothers now adds three derivatives positions: • A one month currency forward, in which Lever Brothers is short$150 against the euro
• An at-the-money (currently 50-delta) three month long call option on S&P 500 equity index futures, with an underlying index value of $100 • Short protection on Ford Motor Co. via a five year credit default swap, with a notional amount of$200
Assume that the nonoption positions are initiated at market-adjusted prices and spreads, and therefore have zero NPV. Also assume that the counterparty is the same for all the positions, namely the prime broker or broker-dealer with which they are executed. If the initial margin on this derivatives portfolio (i.e., all three derivative positions) is \$50, what is the leverage of the firm's balance sheet after the trades?

a. 2.5
b. 3.5
c. 4.0
d. 5.0