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BUFN 722

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BUFN 722

ch-10

Market Risk

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- This chapter discusses the nature of market risk and appropriate measures
- Dollar exposure
- RiskMetrics
- Historic or back simulation
- Monte Carlo simulation
- Links between market risk and capital requirements

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- Market risk is the uncertainty resulting from changes in market prices . It can be measured over periods as short as one day.
- Usually measured in terms of dollar exposure amount or as a relative amount against some benchmark.

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- Important in terms of:
- Management information
- Setting limits
- Resource allocation (risk/return tradeoff)
- Performance evaluation
- Regulation

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- Generally concerned with estimated potential loss under adverse circumstances.
- Three major approaches of measurement
- JPM RiskMetrics (or variance/covariance approach)
- Historic or Back Simulation
- Monte Carlo Simulation

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- Idea is to determine the daily earnings at risk = dollar value of position × price sensitivity × potential adverse move in yield or,
DEAR = Dollar market value of position × Price volatility.

- Can be stated as (-MD) × adverse daily yield move where,
MD = D/(1+R)

Modified duration = MacAulay duration/(1+R)

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- If we assume that changes in the yield are normally distributed, we can construct confidence intervals around the projected DEAR. (Other distributions can be accommodated but normal is generally sufficient).
- Assuming normality, 90% of the time the disturbance will be within 1.65 standard deviations of the mean.

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- Suppose that we are long in 7-year zero-coupon bonds and we define “bad” yield changes such that there is only 5% chance of the yield change being exceeded in either direction. Assuming normality, 90% of the time yield changes will be within 1.65 standard deviations of the mean. If the standard deviation is 10 basis points, this corresponds to 16.5 basis points. Concern is that yields will rise. Probability of yield increases greater than 16.5 basis points is 5%.

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- Price volatility = (-MD) (Potential adverse change in yield)
= (-6.527) (0.00165) = -1.077%

DEAR = Market value of position (Price volatility)

= ($1,000,000) (.01077) = $10,770

Note if MD = -6.527, what is R?

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- To calculate the potential loss for more than one day:
Market value at risk (VAR) = DEAR × N

- Example:
For a five-day period,

VAR = $10,770 × 5 = $24,082.45

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- In the case of Foreign Exchange, DEAR is computed in the same fashion we employed for interest rate risk.
- For equities, if the portfolio is well diversified then
DEAR = dollar value of position × stock market return volatility where the market return volatility is taken as 1.65 sM.

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- Cannot simply sum up individual DEARs.
- In order to aggregate the DEARs from individual exposures we require the correlation matrix.
- Three-asset case:
DEAR portfolio = [DEARa2 + DEARb2 + DEARc2 + 2rab × DEARa × DEARb + 2rac × DEARa × DEARc + 2rbc × DEARb × DEARc]1/2

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- Advantages:
- Simplicity
- Does not require normal distribution of returns (which is a critical assumption for RiskMetrics)
- Does not need correlations or standard deviations of individual asset returns.

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- Basic idea: Revalue portfolio based on actual prices (returns) on the assets that existed yesterday, the day before, etc. (usually previous 500 days).
- Then calculate 5% worst-case (25th lowest value of 500 days) outcomes.
- Only 5% of the outcomes were lower.

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- Convert today’s FX positions into dollar equivalents at today’s FX rates.
- Measure sensitivity of each position
- Calculate its delta.

- Measure risk
- Actual percentage changes in FX rates for each of past 500 days.

- Rank days by risk from worst to best.

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- Disadvantage: 500 observations is not very many from statistical standpoint.
- Increasing number of observations by going back further in time is not desirable.
- Could weight recent observations more heavily and go further back.

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- To overcome problem of limited number of observations, synthesize additional observations.
- Perhaps 10,000 real and synthetic observations.

- Employ historic covariance matrix and random number generator to synthesize observations.
- Objective is to replicate the distribution of observed outcomes with synthetic data.

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- BIS (including Federal Reserve) approach:
- Market risk may be calculated using standard BIS model.
- Specific risk charge.
- General market risk charge.
- Offsets.

- Subject to regulatory permission, large banks may be allowed to use their internal models as the basis for determining capital requirements.

- Market risk may be calculated using standard BIS model.

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- Specific risk charge:
- Risk weights × absolute dollar values of long and short positions

- General market risk charge:
- reflect modified durations expected interest rate shocks for each maturity

- Vertical offsets:
- Adjust for basis risk

- Horizontal offsets within/between time zones

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- In calculating DEAR, adverse change in rates defined as 99th percentile (rather than 95th under RiskMetrics)
- Minimum holding period is 10 days (means that RiskMetrics’ daily DEAR multiplied by 10.
- Capital charge will be higher of:
- Previous day’s VAR (or DEAR 10)
- Average Daily VAR over previous 60 days times a multiplication factor 3.

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- The Corporate Treasurer’s Financial Risk Management Problem- Manage Risk – Not avoid it
- The Market Value of the Firm and Channels of Risk

- Accounting Measures of Foreign Exchange Exposure
- Exposure of the Balance Sheet: Translation Exposure
- Exposure of the Income Statement: Transaction Exposure
- U.S. Accounting Conventions: Reporting Accounting Gains and Losses

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- Economic Measures of Foreign Exchange Exposure
- The Regression Approach
- The Scenario Approach

- Empirical Evidence on Firm Profits, Share Prices, and Exchange Rates
- Arguments for Hedging Risks at the Corporate Level

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- Financial Strategies Toward Risk Management
- The Currency Profile and Suitable Financial Hedging Instruments

- Policy Issues - International Financial Managers
- Problems in Estimating Economic Exposure
- Picking an Appropriate Hedge Ratio
- The International Investor’s Currency Risk Management Problem
- The Value at Risk Approach

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- Policy Issues - Public Policymakers
- Disclosure of Financial Exposure
- Financial Derivatives and Corporate Hedging Policies

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- Corporate treasurers are directly responsible for managing the firm’s exposure to financial risk.
- The risks that remain are held by the investor, who can reduce these risks through a diversified portfolio of shares, or by applying some of the same hedging techniques available to the corporate treasurer.

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- Credit risk
- Risk of default or failure of borrower or counterparty; unwilling to service loan; e.g., 1998 Russia 90-day moratorium on debt pay.

- Adverse changes in market prices, rates, exchange rates

- Cash flows not sufficient to meet bank’s financial commitments

- Earnings & returns fluctuate with changes in interest rates

- Potential losses due to breakdown in information, communication, transaction processing, settlement systems, fraud, unauthorized transactions by employees

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- Screening
- Monitoring
- Long-term customer relationships
- Loan commitments
- Collateral
- Compensating balances
- Credit rationing

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The Value at Risk (VAR) Approach

- The VAR approach is a relatively new approach for measuring the exposure of financial assets.
- It can be applied to any portfolio of assets (and liabilities) whose market values are available on a periodic basis and whose price volatilities () can be estimated.
- Assuming normal price distributions, calculate the loss in value of the portfolio if an unlikely (say, 5% chance) adverse price movement occurs. The result of this calculation is the value at risk.

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- Value at Risk
- Estimates the largest expected loss to a particular investment position for a specified confidence level

- Deriving The Maximum Dollar Loss
- VAR = estimated potential loss from its trading business that could result from adverse movements in market prices.

- Common Adjustments To The Value-At-Risk Applications

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VAR is a risk measurement that estimates the largest expected loss to a particular investment position for a specified confidence level. This method became popular in the late 1990s after some mutual funds & pension funds experienced abrupt large losses. VAR is intended to warn investors about potential maximum loss that could occur. If investors are uncomfortable with the potential loss that could occur in a day or week, they can revise their investment portfolio to make it less risky.

VAR focuses on pessimistic portion of probability distribution of returns from the investment of concern. E.g., a port. mgr. Uses a 90% confidence level, which estimates the max. daily expected loss to an asset in 90% of the trading days over an upcoming period. The higher the confidence level desired, the larger the maximum expected loss that might occur for a given type of investment. E.g., one may expect that the daily loss from holding a particular asset won’t be worse than -5% when using a 90% confidence level & < -8% if a 99% confidence level.In essence the more confidence investors have that the actual loss won’t be > the expected maximum loss, the further they move into the left tail of the probability distribution.

VAR is also used to measure risk of a portfolio. Some assets have high risk when assessed individually, but low risk when part of a portfolio because the likelihood of a large loss in the port. Is influenced by the probabilities of simultaneous losses in all of the component assets for the period of concern.

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- More precisely, VaR measures the worst possible loss that a bank could expect to suffer over a given time interval, under normal market conditions, at a given confidence level. E.g., a bank might calculate that the daily VaR of its trading portfolio is $35 million at a 99% confidence interval. This means that there is only 1 chance in 100 that a loss > $35 million would occur on any given day. Note: this is NOT a maximum loss; e.g., if a bank regularly measures VaR at the 99% confidence level, the actually losses should exceeds its estimate 1% of the time, or 1 day out of 100.
- Methods of determining the maximum expected loss
- Use of historical returns
- Example: count the percentage of days an asset drops a certain level

- Use of standard deviation
- Used to derive boundaries for a specific confidence level

- Use of beta
- Used in conjunction with a forecast of a maximum market drop

- Use of historical returns

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- Deriving the maximum dollar loss
- Apply the maximum percentage loss to the value of the investment

- Common adjustments to the value-at-risk applications
- Investment horizon desired
- Length of historical period used
- Time-varying risk
- Restructuring the investment portfolio

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- Easy to understand
- BIS meeting at Basel in 1995, at which major central banks amended the 1988 accord requiring financial institutions to hold capital against their exposure to market risk; this created an incentive for banks to develop sophisticated internal risk measurement systems to calculate VaR and thus avoid more regulatory requirements. Therefore, in 1998, large banks with substantial trading businesses began using their own internal measures of market risk to adjust their capital requirements. They use a VAR model, usually with a 99 percent confidence interval
- JP Morgan made its RiskMetrics system available free from charge over the Internet; this system provided financial data & methodology to calculate a portfolio’s VaR. www.riskmetrics.com

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- Testing the validity of a bank’s VAR
- Uses backtests with actual daily trading gains or losses
- If the VAR is estimated properly, only 1 percent of the actual trading days should show results worse than the estimated VAR

- Related stress tests
- Bank identifies a possible extreme event to estimate potential losses

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- Distribution of price changes, normal or otherwise
- Extent to which today’s change in the price of an asset may be correlated to past price changes
- Extent to which the characteristics of mean U and standard deviation (volatility) are stable over time
- Relationship between 2 or more different price moves
- Data series to which these assumptions apply.
- Financial managers use historical market data on various financial asses to create their VaR model.

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- Maximum estimated losses in the market value of a given position that may be incurred before the position is neutralized or reassessed.
- VaRx = Vx x dV/dP x Dpi
Vx = market value of position x

dV/dP = sensitivity to price move per $ market value

Dpi = adverse price movement over time i; e.g, if the time horizon is one day, then VaR becomes daily earnings at risk DEAR = Vx x dV/dP x DPday

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- Prices of financial instruments follow a stable random walk; thus, price changes are normally distributed
- Price changes are serially uncorrelated; there is no correlation between change today and changes in the past
- Standard deviation (volatility) of price or rate changes is stable over time; i.e., past movements may be used to characterize future movements.
- Interrelationships between 2 different price movements follow a joint normal distribution.

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- Markets are NOT normal
- Portfolios are non-linear
- Volatility is NOT constant
- Markets move together but no one knows how

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- Technique that relies on computer modeling of different scenarios and computation of results of those scenarios on a bank’s portfolio.
- E.g., Sept 11 bombing of WTC; political assassination
- E.g., Mexican peso devalued by 30%.
- All assets in portfolio are revalued using new environment, creating a new estimate for the return on the portfolio
- Many such scenarios lead to many such exercise, so that a range of values for return on the portfolio is derived
- By specifying the probability for each scenario, mangers can then generate a distribution of portfolio returns, from which VaR can be measured
- The advantage of this method is that it allows risk managers to evaluate possible scenarios that may be completely absent from historical data.

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- Subjective- difficult to brainstorm scenarios that have never occurred
- Choice of scenarios may be affected by bank’s portfolio position, itself – where portfolio is invested
- Poor handling of correlations – stress testing examines effect of a large movement on one financial variable at a time, so it is not well suited to large, complex portfolios such as those held by international banks.
- Stress testing is supplement to VaR, not a replacement

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- Financial institutions relied mostly on four different techniques in stress testing (technique and “stress test result”)
- Simple sensitivity test
Change in portfolio value for 1 or more shocks to a single risk factor

- Scenario analysis
Change in portfolio value if scenario were to occur (historical or hypothetical)

- Maximum loss
Sum of individual trading units’ worst case scenarios

- Extreme value theory
Probability distribution of extreme losses

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- Most difficult to quantify
- “Rogue trader” losses
- Risk of computer or telephone outage disrupting operations systems in critical areas
- Best safeguard is internal control.

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- GAP = RSA – RSL
- Repricing or funding gap
- GAP: the difference between those assets whose interest rates will be repriced or changed over some future period (RSAs) and liabilities whose interest rates will be repriced or changed over some future period (RSLs

- Rate Sensitivity
- the time to reprice an asset or liability
- a measure of an FI’s exposure to interest rate changes in each maturity “bucket”
- GAP can be computed for each of an FI’s maturity buckets

- Multiply GAP times change in interest rate reveals effect on bank income
- Alternative method: Duration gap analysis examines sensitivity of market value of financial institution’s net worth to changes in interest rates; duration measures average lifetime of security’s stream of payments

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NIIi = (GAP)j ij = (RSAj - RSLj) ij

where

NIIj = change in net interest income in the ith

maturity bucket

GAPj = dollar size of the gap between the book

value of rate-sensitive assets and rate-

sensitive liabilities in maturity bucket i

ij = change in the level of interest rates

impacting assets and liabilities in the

jth maturity bucket

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Duration gap - a measure of overall interest rate

risk exposure for an FI

D = - % in market value of a security

i/(1 + i)

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Disclosure of Financial Exposure

- The possibility that individual firms may face substantial exposure to exchange rate changes, as well as the increased trading in financial derivatives in recent years, create a genuine concern among investors and regulators regarding corporate exposure to financial risks.
- Note that a firm without a financial position may still face substantial currency and interest rate risk due to its ongoing operations.

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Financial Derivatives and Corporate Hedging Policies

- The findings of various studies were consistent with the notion that firms used derivatives to lower the variability of their cash flows or earnings.
- It was also found that the likelihood of using derivatives was positively related to foreign pretax income, foreign sales, and foreign-denominated debt.

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- The market value of a firm at time t (MVt) is the summation of the firm’s cash flows (CF) over time discounted back to their present value by an appropriate discount factor (i):

- Cash flows in each currency are discounted at their own appropriate interest rate and multiplied by a spot exchange rate.

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€

- The sensitivity of the market value of the firm to a change in an exchange rate measures exchange rate exposure.
- For the $/€ exchange rate, the sensitivity measure can be expressed as:

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Direct Economic

Exposure

Home Currency

Strengthens

Home Currency

Weakens

Sales AbroadUnfavorableFavorable

Revenue worth less in home currency terms

Revenue worth more

Source AbroadFavorableUnfavorable

Inputs cheaper in home currency terms

Inputs more expensive

Profits AbroadUnfavorableFavorable

Profits worth less

Profits worth more

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Indirect Economic

Exposure

Home Currency

Strengthens

Home Currency

Weakens

Competitor thatUnfavorableFavorable

sources abroad

Competitor’s margins improve

Competitor’s margins decrease

Supplier thatFavorableUnfavorable

sources abroad

Supplier’s margins improve

Supplier’s margins decrease

Customer thatUnfavorableFavorable

sells abroad

Customer’s margins decrease

Customer’s margins improve

Customer thatFavorableUnfavorable

sources abroad

Customer’s margins improve

Customer’s margins decrease

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- Note that virtually any firm could be exposed to exchange rate risk through a financial channel.
- In the long run however,
- The firm can make changes in response to an unexpected exchange rate change.
- Other economic events that follow the exchange rate change may lessen the impact on the firm.

- Nevertheless, the short-run exposure is critical since the firm must survive the shock to get to the long run.

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- Net = exposed – exposed
exposure assets liabilities

- Accounting exposure can be subdivided into translation and transaction exposures.
- Translation exposure focuses on the book value of assets and liabilities as measured in the firm’s balance sheet.
- Transaction exposure focuses on the economic value of transactions denominated in foreign currency that are planned or forecast to occur in the next reporting period.

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- Under Statement 52 of the Financial Accounting Standards Board (FASB-52), translation gains and losses are accumulated in a translation adjustment account.
- FASB-52 focuses on a parent’s net investment in a foreign operation to measure the effect of exchange rate changes.
- Transaction gains and losses represent realized exchanges and are reported in current income.
- Under FASB-133, derivatives that do not qualify as hedges of the underlying exposures must be marked-to-market, with the resulting gains or losses included in either current or deferred income.

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- Economic exposure captures the entire range of effects on the future cash flows of the firm, including the effects of exchange rate changes on customers, suppliers, and competitors.
- MV/S reflects economic exposure. Two approaches for measuring economic exposure are the regression approach and the scenario approach.

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- The regression approach directly measures the exposure of a firm to exchange rate changes by estimating the relationship between the firm’s market value at time t (MVt)and the spot rate (St) using the equation:
MVt = a + bSt + et

- The coefficient b measures the sensitivity of the market value of the firm to the exchange rate.

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- To interpret the regression analysis, three results need to be examined:
- The magnitude of b.
- b > 0 an asset exposure in the foreign currency
- b < 0 a liability exposure
- b = 0 no exposure to the exchange rate

- The t-statistic of b.
- Statistical significance is necessary for confidence in the results.

- The R2 of the regression.
- R2 measures the percentage of variation in the market value explained by the exchange rate.

- The magnitude of b.

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- To measure the firm’s exposure to multiple exchange rates, a multiple regression can be estimated:
MVt = a + b1S$/€,t + b2S$/£,t + b3S$/¥,t + et

- If the firm has data on cash flows at the level of a subsidiary or project, the exposure of these smaller units can also be measured:
CFt = a + bSt + et

- Note that exposure tends to be lower in the long run due to PPP (which tends to hold better in the longer run) and the ability of firms to make adjustments in response to exchange rate changes.

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- Given a scenario, we can estimate the firm’s cash flows (and its market value) conditional on an exchange rate path.
- The scenario approach is well suited to a spreadsheet analysis where one is encouraged to ask a variety of “what-if” questions.

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A*

The slope measures the exposure of the firm at the initial exchange rate.

Present Value of Cash Flows

(Millions)

$39.577

O

$35.222

A

- 15%

- 10%

- 5%

5%

10%

15%

$/A$$0.5435$0.5682$0.5952$0.6250$0.6563$0.6875$0.7188

A$/$A$1.84A$1.76A$1.68A$1.60A$1.52A$1.45A$1.39

Consider the impact of a permanent 5% appreciation of the US$, holding all other factors constant.

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A*

The slope of BOB* is flatter than AOA* since the firm has less exposure now.

B*

Present Value of Cash Flows

(Millions)

$39.577

O

$35.222

B

A

- 15%

- 10%

- 5%

5%

10%

15%

$/A$$0.5435$0.5682$0.5952$0.6250$0.6563$0.6875$0.7188

A$/$A$1.84A$1.76A$1.68A$1.60A$1.52A$1.45A$1.39

Suppose the firm can pass along part of the exchange rate change

to its Australian customers.

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- During the Bretton Woods pegged-rate period, the general stock market index tended to move up (down) immediately after a devaluation (revaluation) of the local currency.
- Studies also indicated that exposure coefficients vary from firm to firm within the same industry and over time, and that exchange rate changes can have a substantial impact on the overall economy.

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- Shareholders may not favor hedging since they can select well-diversified portfolios to rid themselves of firm-specific risks.
- However, in view of transaction costs and taxes, hedging that reduces the volatility of cash flows may be favored.
- If the tax credits of a firm which has incurred losses over several successive periods cannot be carried forward to reduce future tax payments, then another firm with a less volatile pattern of earnings will enjoy greater after-tax cash flows and a higher market value.
- A firm with more volatile cash flows is also more open to the costs of financial distress.

- For the same reasons, banks and bondholders will prefer firms with less volatile cash flows (holding average cash flows equal) and reward them with greater borrowing capacities and higher credit ratings.

- An important step in the process of determining the appropriate financial hedging instruments for a firm is to analyze the nature of the firm’s currency cash flows.
- Note that a hedging strategy may offset certain risks, while leaving open or increasing other risks.

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Characteristics of

Currency Exposure

Suitable Financial

Hedging Instruments

Frequency of cash flows

Single period

Multiple periods

Single contract (futures/options)

Sets (“strips”) of contracts/swaps or present value hedge

Currency dimension

Single currency

Multiple currencies

Contracts on one currency

Contracts on an index (ECU, US$) or synthetic hedge

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Characteristics of

Currency Exposure

Suitable Financial

Hedging Instruments

Certainty about cash flows

Certain, contractual cash flows

Uncertain, estimated cash flows

Naïve hedge to match contract size of financial instrument and exposure

Option hedge or dynamic futures hedge to match probability of cash flows

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Problems in Estimating Economic Exposure

- Using market data presumes that financial markets are efficient, and that share prices respond quickly and appropriately to exchange rate changes.
- The approach is unsuitable for newly organized or reorganized firms for which there is not a large sample of consistent observations.
- For the exposure coefficient to be useful, the relationship between exchange rate changes and market value must remain stable in the future.

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Picking an Appropriate Hedge Ratio

- If the exchange rate is expected to change favorably, hedging may not be desirable.
- Complete hedging may be achieved by taking offsetting positions (-bi).
- Otherwise, an intermediate solution may be chosen, with hedge positions in between 0 and bi.
- Note that the more direct approach is to restructure the firm’s long-term financing, so as to permanently alter the firm’s financial exposure.

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The International Investor’s Currency Risk Management Problem

- A portfolio’s exposure to foreign exchange risk can be measured using the regression approach in much the same way as the treasurer measures the firm’s exposure.
- The investor can hedge foreign exchange risk using forward contracts, or retain the risk using a risk-return decision criterion.

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For information on the BIS framework, visit:

Bank for International Settlements www.bis.org

Federal Reserve www.federalreserve.gov

Citigroup www.citigroup.com

J.P.Morgan/Chase www.jpmorganchase.com

Merrill Lynch www.merrilllynch.com

RiskMetrics www.riskmetrics.com

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