# LO 54.8: Calculate the expected transactions cost and the spread risk factor for

LO 54.8: Calculate the expected transactions cost and the spread risk factor for a transaction, and calculate the liquidity adjustment to VaR for a position to be liquidated over a number of trading days.
Assuming that daily changes in the bid-ask spread are normally distributed, the 99% confidence interval on the transactions cost in dollars is:
+/- P x i/2(s + 2.33a )
where: P = an estimate of the next day asset midprice, usually set to P, the most recent price
observation
s = expected or typical bid-ask spread calculated as: (ask price bid price) / midprice a s = sample standard deviation of the spread
This confidence interval estimates the expected transactions costs in dollar terms. The V^(s + 2.33as) component is referred to as the 99% spread risk factor.
Example: Computing transactions cost
Brieton, Inc., recently traded at an ask price of \$100 and a bid price of \$99. The sample standard deviation of the spread is 0.0002. Calculate the expected transactions cost and the 99% spread risk factor for a transaction.
midprice = (100 + 99) / 2 = 99.50
s = (100-99)/ 99.5 = 0.01005
transactions cost = 99.50 x 1/2[0.01005 + 2.33(0.0002)] = \$0,523
spread risk factor = V4[0.01005 + 2.33(0.0002)] = 0.005258
Note that in this example, we use the current midprice as the estimate for the next day asset midprice.
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Topic 54 Cross Reference to GARP Assigned Reading – Malz, Chapter 12
A d j u s t
i n g Va R f o r P o s i t
i o n L i q u i d i t y
Liquidity-adj usted value at risk (LVaR) is a tool used to measure the risk of adverse price impact. The trader will often liquidate the position over a period of days in order to ensure an orderly liquidation of the position.
P rofessors N ote: The a ctu a l calcu lation o f liq u id ity-a d ju sted VaR (u sin g con stan t a n d exogenous spread approaches) was show n in Topic 52. H ere w e discuss h ow VaR m ay he oversta ted w hen a d ju stin g f o r d ifferen t tim e horizons (via th e square root o f tim e rule) sin ce this a d ju stm en t does n ot a cco u n t f o r th e liq u idation o f p osition s over th e tim e p er io d o f analysis.
Adjusting VaR for liquidity requires an estimate of the number of days it will take to liquidate a position. The number of trading days is typically denoted T. Assuming the position can be divided into equal parts across the number of trading days and liquidated at the end of each trading day, a trader would face a 1-day holding period on the entire position, a 2-day holding period on a fraction (T 1) / T of the position, a 3-day holding period on a fraction (T 2) / T of the position, and so on. The 1-day position VaR adjusted by the square root of time is estimated for a given position as:
VaRt x J T
However, this formula overstates VaR for positions that are liquidated over time because it assumes that the whole position is held for T days. To adjust for the fact that the position could be liquidated over a period of days, the following formula can be used:
VaRt x
(1 + T)(1 + 2T)
6T
For example, if the position can be liquidated in four trading days (T = 4), the adjustment to the overnight VaR of the position is 1.3693, which means we should increase VaR by 37%. This is greater than the initial 1-day VaR, but less than the 1-day VaR adjusted by the square root of T.
M e a s u r i n g M a r k e t L i q u i d i t y
Factors such as tightness, depth, and resiliency are characteristics used to measure market liquidity. Tightness (or width) refers to the cost of a round-trip transaction, measured by the
bid-ask spread and brokers commissions. The narrower the spread, the tighter it is. The tighter it is, the greater the liquidity.
Depth describes how large an order must be to move the price adversely. In other words,
can the market absorb the sale? The market can likely absorb a sale by an individual investor without an adverse price impact. However, if a large institution sells, it will likely adversely impact the price.
Resiliency refers to the length of time it takes lumpy orders to move the market away from the equilibrium price. In other words, what is the ability of the market to bounce back from temporary incorrect prices?
Both depth and resiliency affect how quickly a market participant can execute a transaction.
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F u n d i n g L i q u i d i t y R i s k M a n a g e m e n t
Topic 54 Cross Reference to GARP Assigned Reading – Malz, Chapter 12
Redemption requests, especially in times of market stress, may require hedge fund managers to unwind positions rapidly, exposing the fund to transactions liquidity risk. If this happens to many funds at once, fire sales may result. Hedge funds manage liquidity via: Cash. Cash can be held in money market accounts or Treasury bills and unencumbered liquidity. Cash is not wholly without risk, however, because money market funds may suspend redemptions in times of stress or crisis, and broker balances are at risk if the broker fails.
Unpledged assets. Unpledged assets, also called assets in the box, are assets not currently
being used as collateral. They are often held with a broker. Price volatility of the assets affects their liquidity. Only Treasury securities, and more specifically Treasury bills, may be used as collateral during a financial crisis. Even government agency securities were not sufficient collateral during the 20072009 financial crisis. Unpledged assets can be sold, rather than pledged, to generate liquidity. However, in times of market stress, asset prices are often significantly depressed.
Unused borrowing capacity. This is not an unfettered source of liquidity as unused
borrowing capacity can be revoked by counterparties by raising haircuts or declining to accept pledged assets as collateral when it is time to rollover the loan. These loans are typically very short term and credit can, as it did during the 2007-2009 financial crisis, disappear quickly.
During the crisis, a systemic risk event, hedge funds that had not experienced large losses still faced a liquidity crisis as investors, seeking liquidity themselves, issued redemption requests.
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Topic 54 Cross Reference to GARP Assigned Reading – Malz, Chapter 12
K e y C o n c e p t s
LO 54.1 Liquidity has two essential properties, which relate to two essential forms of risk. Transactions liquidity deals with financial assets and financial markets and is related to the ability to sell an asset quickly, cheaply, and without moving the price too much. Funding liquidity is related to individuals or firms creditworthiness.
LO 54.2 Banks only expect a fraction of deposits and other liabilities to be redeemed at any point in time. As a result, they do not hold all deposits in liquid assets, but make loans with deposits instead. This is known as a fractional-reserve bank and the process of using deposits to finance loans is known as asset-liability management (ALM).
LO 54.3 Systematic funding risks were apparent in many market sectors during the subprime mortgage crisis. Liquidity issues arose during the recent financial crisis for a variety of investment strategies.
Money market mutual funds (MMMFs) have net assets (NAVs) equal to \$1.00. However, credit write-downs can result in net asset values falling below \$1.00. This is known as breaking the buck. Liquidity risk can also cause NAVs to fall below \$1.00.
LO 54.4 Collateral markets enhance the ability of firms to borrow money. They also make it possible to establish short positions in securities. Cash and securities may be borrowed in the market for collateral.
Firms with excess cash are more willing to lend at a low rate of interest if the loan is secured by collateral. The full value of the securities is not lent. The difference is called a haircut.
Collateralized loans are used to finance securities or other assets or trades. The securities pledged to one firm are often loaned or pledged again, hence the collateral circulates. This process is known as rehypothecation or repledging.
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Topic 54 Cross Reference to GARP Assigned Reading – Malz, Chapter 12
LO 54.5 A firms leverage ratio is equal to its assets divided by equity. That is:
A _ ( E + D) E E
D E
Return on equity (ROE) is higher as leverage increases, as long as the firms return on assets (ROA) exceeds the cost of borrowing funds. This is called the leverage effect. The leverage effect can be expressed as:
rE = LrA – ( L –
1 )rD
LO 54.6 There is embedded leverage in short positions and derivatives such as options and swaps. Economic balance sheets can be constructed to help investors and/or firms measure the implicit leverage of these transactions.
LO 54.7 Transactions liquidity implies that an asset can be bought or sold without moving its price. Transactions liquidity risk is fundamentally related to the costs of searching for a counterparty, the institutions required to assist in that search, and the costs of inducing a counterparty to hold a position.
To understand transactions liquidity risk, one must understand market microstructure fundamentals. Trade processing costs, inventory management, adverse selection (i.e., dealing with informed versus uninformed traders), and differences of opinions regarding asset prices affect transactions liquidity.
Factors such as tightness, depth, and resiliency are characteristics used to measure market liquidity. Tightness (or width) refers to the cost of a round-trip transaction, measured by the bid-ask spread and brokers commissions. Depth describes how large an order must be to move the price adversely. Resiliency refers to the length of time it takes lumpy orders to move the market away from the equilibrium price.
Hedge funds manage liquidity via cash, unpledged assets, and unused borrowing capacity. In times of market stress, redemption requests may require hedge fund managers to unwind positions rapidly, exposing the fund to transactions liquidity risk. If this happens to many funds at once, fire sales may result.
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Topic 54 Cross Reference to GARP Assigned Reading – Malz, Chapter 12
LO 54.8 Assuming that daily changes in the bid-ask spread are normally distributed, the 99% confidence interval on the transactions cost in dollars is:
+/- P x i/2(s + 2.33cr)u
The spread risk factor is equal to V^(s + 2.33crs).
Liquidity-adj usted VaR is a tool used to measure the risk of adverse price impact. Traders will often liquidate positions over a period of days in order to ensure an orderly liquidation of the position.
LO 54.9 Risks associated with liquidity are interrelated and can exacerbate problems. For example, an increase in funding liquidity risk can lead to an increase in transactions liquidity risk. Also, severe stress to the financial system from a liquidity risk event would impact market participants simultaneously, suggesting that the illiquidity or insolvency of one counterparty may impact other market participants.
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C o n c e p t C h e c k e r s
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5.
Jackson Grimes, a trader for Glenn Funds, works on the repurchase agreement (repo) desk at his firm. Markets have been highly volatile but Glenn Funds has a large capital base and is sound. Grimes reports to the CEO that in the last month, the firm Glenn Funds borrows from has been consistently increasing collateral requirements to roll over repos. From the perspective of Glenn Funds, this represents: A. systematic risk. B. C. balance sheet risk. D. maturity transformation risk.
transactions liquidity risk.
Chris Clayton, an analyst for a private equity fund, noticed that merger arbitrage strategies at several hedge funds experienced large losses in late 2007 to early 2008. These losses were likely due to: A. abandoned merger plans due to a lack of available financing. B. C. acquirers filing for bankruptcy as the subprime mortgage crisis unfolded. D. idiosyncratic risks surrounding the merger arbitrage strategy.
target prices falling precipitously due to stock market corrections.
With respect to the valuation of money market mutual fund (MMMF) assets, funds: A. are not required to mark-to-market the underlying assets daily. B. must reflect changes in the values of underlying assets that are the result of changes in credit risks but may ignore value changes that are the result of changes in interest rates.
C. will set the notional values of each of the underlying assets equal to \$1.00. D. are not allowed to invest in any asset with a rating below AAA because asset
values must not fluctuate outside of a 10% range around the historical value in order to keep the notional value equal to \$1.00.
Charleston Funds intends to use leverage to increase the returns on a convertible arbitrage strategy. The return on assets (ROA) of the strategy is 8%. The fund has \$1,000 invested in the strategy and will finance the investment with 75% borrowed funds. The cost of borrowing is 4%. The return on equity (ROE) is closest to: A. 4%. B. 32%. C. 20%. D. 12%.
Brett Doninger recently placed an order to sell a stock when the market price was \$42.12. The market was volatile and, by the time Doninger s broker sold the stock, the price had fallen to \$41.88. In the market, this phenomenon is known as: A. adverse selection. B. C. slippage. D. the spread risk factor.
transactional imbalance.
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C o n c e p t C h e c k e r A n s w e r s
1. C Funding liquidity risk or balance sheet risk results when a borrowers credit position is either deteriorating or is perceived by market participants to be deteriorating. It also occurs when the market as a whole deteriorates. Under these conditions, creditors may withdraw credit or change the terms of credit. In this case, the lender is increasing the haircut and is thus changing the terms of credit. Glenn Funds creditworthiness does not actually have to decline for a lender to withdraw credit or change the terms of credit.
2. A
Systematic funding risks were apparent in many market sectors during the subprime mortgage crisis. Hedge funds engaged in merger arbitrage experienced losses in the early stages of the subprime mortgage crisis. After a merger is announced, the targets stock price typically increases and the acquirers price sometimes declines due to increased debt. The merger arbitrage strategy exploits the difference between the current and announced acquisition prices. Hedge funds experienced large losses as mergers were abandoned when financing dried up.
3. A MMMFs use a form of accounting called the amortized cost method, under the Securities
and Exchange Commissions (SEC) Rule 2a – 7. This means that MMMF assets do not have to be marked-to-market each day, as required for other types of mutual funds. However, the values of the underlying assets in the fund, despite their relative safety, are subject to change. As such, redemptions may be limited if asset values fall.
4. C debt = \$1,000 x 0.75 = \$750
leverage ratio = total assets / equity leverage ratio = \$1,000 / \$250 = 4
rE = LrA- ( L – 1)rD
where: rA = return on assets r = return on equity rD = cost of debt L = leverage ratio
return on equity = 4(8%) – [(4 – 1)(4%)] = 32% – 12% = 20%