# LO 54.6: Explain the impact on a firms leverage and its balance sheet of the

LO 54.6: Explain the impact on a firms leverage and its balance sheet of the following transactions: purchasing long equity positions on margin, entering into short sales, and trading in derivatives.
Purchasing stock on margin or issuing bonds are examples of using leverage explicitly to increase returns. However, there are other transactions that have implicit leverage. It is important to understand the embedded leverage in short positions and derivatives, such as options and swaps. By constructing economic balance sheets for investors and/or firms, it is possible to measure the implicit leverage of these transactions.
Margin Loans and Leverage
First, consider margin loans. The stock purchased with the margin loan is collateral for the loan. The haircut (h) is the borrowers equity and 1 h is loaned against the market value of the collateral. The leverage is calculated as 1 / h. The Federal Reserve requires that an investor put up a minimum of 50% equity (i.e., h = 50%) in a stock purchase using borrowed funds.
First, assume that a firm has \$100 cash invested by the owners (i.e., no borrowed funds). The balance sheet in this case is:
Assets
Cash Total assets
\$100 \$100
Liabilities and Equity Debt \$0 \$100 Equity \$100
TL and OE
If the firm uses the cash to purchase stock, the balance sheet is:
Assets
Stock Total assets
\$100 \$100
Liabilities and Equity Debt \$0 \$100 Equitv \$100
TL and OE
Thus, the leverage ratio is equal to 1 (i.e., \$100 / \$100 or 1.0 / 1.0).
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Topic 54 Cross Reference to GARP Assigned Reading – Malz, Chapter 12
Next, assume that the firm uses 50% borrowed funds and invests 50% (i.e., h = 50%) equity to buy shares of stock. Immediately following the trade, the margin account balance sheet has 50% equity and a \$50 margin loan from the broker. That is:
Assets
Stock Total assets
\$100 \$100
Liabilities and Equity \$50 \$50 \$100
Equity
Margin loan
TL and OE
The full economic balance sheet as a result of the borrowed funds (remember, owners put in \$100 of equity initially so the firm now has \$100 of stock and \$50 of cash) is:
Assets
Cash Stock Total assets
\$50 \$100 \$150
Margin loan
Liabilities and Equity \$50 \$100 \$150 Equity Equity TL and OE
Thus, the leverage ratio has increased to 1.5 (i.e., \$150 / \$100 or 1 / 0.667). Note that the broker retains custody of the stock to use as collateral for the loan.
Short Positions and Leverage
In a short trade, the investor borrows the shares of stock and sells them. The transaction lengthens the balance sheet because the cash generated from the short sale along with the value of the borrowed securities appear on the balance sheet.
Assume the firm borrows \$100 of stock and sells it short. The firm has an asset equal to the proceeds from selling the stock and a liability equal to the value of the borrowed shares. However, the firm cannot use the cash for other investments as it is collateral. It ensures that the stock can be repurchased and returned to the lender. It is in a segregated short account. In the event that the stock price increases rather than decreases, the firm must also put \$50 in a margin account.
Immediately following the trade, the margin account and short account has \$50 equity and a \$50 margin loan from the broker.
Assets
\$150 due from broker: Margin Short sale proceeds Total assets
Liabilities and Equity
\$50 \$100 \$150
Borrowed stock
\$100
Equity
TL and OE
\$150
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Topic 54 Cross Reference to GARP Assigned Reading – Malz, Chapter 12
The firms full economic balance sheet given the short sale is:
Assets
Cash Due from broker Total assets
\$50 \$150 \$200
Borrowed stock
Liabilities and Equity \$100 \$100 \$200
Equitv
TL and OE
Thus, the leverage ratio has increased to 2.0 (i.e., \$200 / \$100 or 1 / 0.50). The leverage is higher in this case than in the previous margin example because the full value of the stock is borrowed in a short transaction. Leverage is inherent in the short position but is a choice in the long position. The firm only borrows 50% of the balance of the stock in the long position.
If the short position plays a hedging role in the portfolio, the position will reduce market risk. This means that leverage will overstate the overall risk because it ignores the potential risk reducing benefits of the short positions. As such, a distinction must be made between gross and net leverage. Gross leverage is the value of all the assets, including cash generated by short sales, divided by capital. Net leverage is the ratio of the difference between the long and short positions divided by capital.
Derivatives and Leverage
Derivatives allow an investor to gain exposure to an asset or risk factor without actually buying or selling the asset. Derivatives also allow investors to increase leverage. Although derivatives are generally off-balance sheet, they should be included on the economic balance sheet as they affect an investors returns. Derivatives are synthetic long and short positions. To estimate the economic balance sheet, find the cash-equivalent market value for each type of derivative. Derivatives include: Futures, forward contracts, and swap contracts. These contracts are linear and
symmetric to the underlying asset price. The amount of the underlying instrument represented by the derivative is set at the initiation of the contract so values can be represented on the economic balance sheet by the market value of the underlying asset. These contracts have zero net present values (NPVs) at initiation.
Option contracts. These contracts have a non-linear relationship to the underlying
asset price. The amount of the underlying represented by the option changes over time. The value can be fixed at any single point in time by the option delta. Thus, on the economic balance sheet, the cash equivalent market values can be represented by the delta equivalents rather than the market values of the underlying assets. These contracts do not have zero NPVs at initiation because the value is decomposed into an intrinsic value (which may be zero) and a time value (which is likely not zero).
In this next example, the counterparty is assumed to be the prime broker or broker-dealer executing the positions. This means that margin will be assessed by a single broker on a portfolio basis.
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Topic 54 Cross Reference to GARP Assigned Reading – Malz, Chapter 12
First, assume the firm enters a 1-month currency forward contract and is short \$100 against the euro and the 1-month forward exchange rate is \$1.25 per euro. The balance sheet is:
Assets
Liabilities and Equity
\$100 equivalent of 80 bank deposit
Broker loan
\$100
Now, assume the firm buys a 3-month at-the-money call option on a stock index with an underlying index value of \$100. The calls delta is currently 50%. The transaction is equivalent to using a \$50 broker loan to buy \$50 of the stock index. That is:
Assets
\$50 long index position
\$50
Liabilities and Equity Broker loan
\$50
Next, assume the firm enters a short equity position via a total return swap (TRS). The firm pays the total return on \$100 of ABC stock and the cost of borrowing the ABC stock (i.e., the short rebate). This is equivalent to taking a short position in ABC. Assuming the market price of ABC is \$100, we have:
Assets
\$100 due from broker (proceeds from short sale)
Liabilities and Equity
\$100
Borrowed ABC stock
\$ 100
Finally, assume the firm adds short protection on company XYZ via a 5-year credit default swap (CDS) with a notional value of \$100. This position is equivalent to a long position in a par-value 5-year floating rate note (FRN) financed with a term loan.
The firms combined economic balance sheet that includes all of the derivatives positions is:
Assets
Cash Due from broker
\$50 margin \$ 100 short sale proceeds
Equivalent of 80 bank deposit Long equity index XYZ FRN Total assets
\$50 \$150
\$100 \$50 \$100 \$450
Liabilities and Equity
Short-term broker loan
\$150
Term loan Borrowed ABC stock
Equitv TL and OE
\$100 \$100
\$100 \$450
The firm has increased its leverage to 3.5 in its long positions. The long positions combined with the short position (the ABC TRS) means the firm has gained economic exposure to securities valued at \$450 using \$50 of cash.
Notice that computing leverage is complex when derivatives are used. Also, correctly interpreting leverage is important since risk may be mitigated if short positions are used to hedge. For example, currency and interest rate risks can be hedged accurately. However, the positions are of the same magnitude as the underlying assets. If the positions are carried on the economic balance sheet, leverage will be overstated and other material risks in the portfolio may be ignored.
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