Define interest rate risk and discuss tools to manage that risk.
Define and compute duration of a single asset and of a portfolio.
Use duration to measure the change in value attributable to a change in yields.
Explain the use of equity duration to manage interest rate risk.
Describe the use of swaps in managing interest rate risk; explain how the use of swaps separates the risk of interest changes from the risk of changes in the firm’s credit quality.
Insurance is the most common method firms use to reduce risk.
Property Insurance
A type of insurance companies purchase to compensate them for losses to their assets due to fire, storm damage, vandalism, earthquakes, and other natural and environmental risks
A type of insurance that covers the costs that result if some aspect of a business causes harm to a third party or someone else’s property
Business Interruption Insurance
A type of insurance that protects a firm against the loss of earnings if the business is interrupted due to fire, accident, or some other insured peril
When the NPV from selling insurance is zero because the price of insurance equals the present value of the expected payment
14.
Insurance Pricing in a Perfect Market (cont'd)
If r L is the appropriate cost of capital given the risk of the loss, the actuarially fair premium is calculated as follows:
Actuarially Fair Insurance Premium
r L depends on the risk being insured.
15.
Insurance Pricing in a Perfect Market (cont'd)
Consider again the oil refinery. The risk of fire is specific to this firm and, therefore, diversifiable.
By pooling together the risks from many policies, insurance companies can create very-low-risk portfolios whose annual claims are relatively predictable. In other words, the risk of fire has a beta of zero, so it will not command a risk premium. In this case, r L equals the risk-free interest rate.
16.
Insurance Pricing in a Perfect Market (cont'd)
Not all insurable risks have a beta of zero.
Some risks, such as hurricanes and earthquakes may be difficult to diversify completely.
For risks that cannot be fully diversified, the cost of capital r L will include a risk premium.
17.
Insurance Pricing in a Perfect Market (cont'd)
By its very nature, insurance for non-diversifiable hazards is generally a negative beta asset (it pays off in bad times).
Thus, the risk-adjusted rate r L for losses is less than the risk-free rate r f , leading to a higher insurance premium in the actuarially fair insurance premium equation.
While firms that purchase insurance earn a return r L < r f on their investment, because of the negative beta of the insurance payoff, it is still a zero-NPV transaction.
As the owner of a concession booth in a major airport, you decide to purchase insurance that will pay $2 million in the event the airport terminal is destroyed by terrorists. Suppose the likelihood of such a loss is 0.05%, the risk-free interest rate is 3%, and the expected return of the market is 8%. If the risk has a beta of zero, what is the actuarially fair insurance premium? What is the premium if the beta of terrorism insurance is −3?
The expected loss is 0.05% × $2 million = $1,000. If the risk has a beta of zero, we compute the insurance premium using the risk-free interest rate: ($1,000)/1.03 = $970.87. If the beta of the risk is not zero, we can use the CAPM to estimate the appropriate cost of capital.
Given a beta for the loss, β L , of −3, and an expected market return, r mkt , of 8%:
r L = r f + β L (r mkt − r f ) = 3% − 3 (8% − 3%) = −12%
In this case, the actuarially fair premium is ($1,000)/(1 − 0.12) = $1,136.36. Although this premium exceeds the expected loss, it is a fair price given the negative beta of the risk.
What is the NPV of purchasing insurance for an airline that would experience $25 million in financial distress costs and $15 million in issuance costs in the event of a loss if it were uninsured?
The total benefit of the insurance to the railroad is $100 million plus an additional $40 million in distress and issuance costs that it can avoid if it has insurance.
When a firm is subject to graduated income tax rates, insurance can produce a tax savings if the firm is in a higher tax bracket when it pays the premium than the tax bracket it is in when it receives the insurance payment in the event of a loss.
Because insurance reduces the risk of financial distress, it can relax the tradeoff between leverage & financial distress costs and allow the firm to increase its use of debt financing.
By eliminating the volatility that results from perils outside management’s control, insurance turns the firm’s earnings and share price into informative indicators of management’s performance.
Insurance companies specialize in assessing risk and will often be better informed about the extent of certain risks faced by the firm than the firm’s own managers.
For insurance to be attractive, the benefit to the firm must exceed the additional premium charged by the insurer.
Insurance is most likely to be attractive to firms that are currently financially healthy, do not need external capital, and are paying high current tax rates.
They will benefit most from insuring risks that can lead to cash shortfalls or financial distress, and that insurers can accurately assess and monitor to prevent moral hazard.
Refers to the merger of a firm and its supplier or a firm and its customer.
Because an increase in the price of the commodity raises the firm’s costs and the supplier’s revenues, these firms can offset their risks by merging.
Vertical integration can add value if combining the firms results in important synergies.
Vertical integration is not a perfect hedge.
46.
Hedging with Vertical Integration and Storage (cont'd)
Long-term storage of inventory is another strategy for offsetting commodity price risk.
For example, an airline concerned about rising fuel costs could purchase a large quantity of fuel today and store the fuel until it is needed. By doing so, the firm locks in its cost for fuel at today’s price plus storage costs.
However, storage costs may be too high for this strategy to be attractive.
47.
Hedging with Vertical Integration and Storage (cont'd)
Long-term storage of inventory also requires a substantial cash outlay upfront.
If the firm does not have the required cash, it would need to raise external capital and would suffer issuance and adverse selection costs.
Maintaining large amounts of inventory would dramatically increase working capital requirements for the firm.
In early 2000, when oil prices were close to $20 per barrel, the CFO developed a hedging strategy to protect the airline from a surge in oil prices. By the time oil prices soared above $30 per barrel later that year Southwest had signed contracts guaranteeing a price for its fuel equivalent to $23 per barrel.
However, had oil prices fallen below $23 per barrel in the fall of 2000, Southwest’s hedging policy would have obligated it to pay $23 per barrel for its oil.
Southwest accomplished it’s objective by locking in its cost of oil at $23 per barrel, regardless of what the price of oil did on the open market.
Long-term supply contracts cannot be entered into anonymously; the buyer and seller know each other’s identity.
This lack of anonymity may have strategic disadvantages.
The market value of the contract at any point in time may not be easy to determine, making it difficult to track gains and losses, and it may be difficult or even impossible to cancel the contract if necessary.
The buyer’s cumulative loss is the sum of these daily amounts and always equals the difference between the original contract price of $81 per barrel and the current contract price.
If the price of oil is ultimately $59 per barrel, the buyer will have lost $22 per barrel in her margin account.
Thus her total cost is $59 + $22 = $81 per barrel, the price for oil she originally committed to.
Through this daily marking to market, buyers and sellers pay for any losses as they occur, rather than waiting until the final delivery date. In this way, the firm avoids the risk of default.
66.
Table 30.1 Example of Marking to Market and Daily Settlement for the July 2012 Light, Sweet Crude Oil Futures Contract ($/bbl)
The potential benefits of hedging commodity price risk include reduced financial distress and issuance costs, tax savings, increased debt capacity, and improved managerial incentives and risk assessment.
Fluctuating exchanges rates cause a problem known as the importer–exporter dilemma.
Consider a U.S. firm that imports parts from Italy.
If the supplier sets the price of its parts in euros, then the U.S. firm faces the risk that the dollar may fall, making euros, and therefore the parts, more expensive.
If the supplier sets its prices in dollars, then the supplier faces the risk that the dollar may fall and it will receive fewer euros for the parts it sells to the U.S. firm.
71.
Figure 30.3 Dollars per Euro ($/ € ), 1999-2009
By entering into a currency forward contract, a firm can lock in an exchange rate in advance and reduce or eliminate its exposure to fluctuations in a currency’s value.
84.
Cash-and-Carry and the Pricing of Currency Forwards (cont'd)
An investor can convert euros to dollars today at the spot exchange rate, S $/ € .
By borrowing or lending at the dollar interest rate r $ , an investor can exchange dollars today for dollars in one year.
An investor can convert euros today for euros in one year at the euro interest rate r € .
85.
Cash-and-Carry and the Pricing of Currency Forwards (cont'd)
The cash-and-carry strategy consists of the following simultaneous trades
Borrow euros today using a one-year loan with the interest rate r €
Exchange the euros for dollars today at the spot exchange rate S $/ €
Invest the dollars today for one year at the interest rate r $
86.
Cash-and-Carry and the Pricing of Currency Forwards (cont'd)
In one year’s time, an investor will owe euros and receive dollars. That is, they have converted euros in one year to dollars in one year, just as with the forward contract.
Because the forward contract and the cash-and-carry strategy accomplish the same conversion, by the Law of One Price they must do so at the same rate.
87.
Cash-and-Carry and the Pricing of Currency Forwards (cont'd)
Combining the rates used in the cash-and-carry strategy leads to the following no-arbitrage formula for the forward exchange rate:
Covered Interest Parity
88.
Cash-and-Carry and the Pricing of Currency Forwards (cont'd)
Letting T equal the number of years, the no-arbitrage forward rate for an exchange that will occur T years in the future is
89.
Cash-and-Carry and the Pricing of Currency Forwards (cont'd)
Covered Interest Parity Equation
States that the difference between the forward and spot exchange rates is related to the interest rate differential between the currencies
Currency options are another method to manage exchange rate risk.
Assume that in December 2005, the one-year forward exchange rate was $1.20 per euro. A firm that will need euros in one year can buy a call option on the euro, giving it the right to buy euros at a maximum price.
If the spot exchange rate is less than the $1.20 per euro strike price of the option, then the firm will not exercise the option and will convert dollars to euros at the spot exchange rate.
If the spot exchange rate is more than $1.20 per euro, the firm will exercise the option and convert dollars to euros at the rate of $1.20 per euro. Adding in the initial cost of the option gives the total dollar cost per euro paid by the firm.
If the current spot exchange rate is S dollars per euro and the dollar and euro interest rates are r $ and r € , respectively, then the price of a European call option on the euro that expires in T years with a strike price of K dollars per euro is:
Where C t is the cash flow on date t , PV(C t ) is its present value (evaluated at the bond’s yield), and P= Σ t PV(C t ) is the total present value of the cash flows
Therefore, the duration weights each maturity t by the percentage contribution of its cash flow to the total present value, PV(C t ) ∕ P .
Duration and Interest Rate Sensitivity: If r, the APR used to discount a stream of cash flows, increases to r + , where is a small change, then the present value of the cash flows changes by approximately :
Where k is the number of compounding periods per year of the APR
These institutions hold short-term deposits (checking and savings accounts, certificates of deposit, etc.). They also make long-term loans (car loans, home mortgages, etc.).
Most S&Ls face a problem because the duration of the loans they make is generally longer than the duration of their deposits.
Therefore, if interest rates rise by 1%, the value of Acorn’s equity will fall by about 40%.
This decline in the value of equity will occur as a result of the value of Acorn’s assets decreasing by approximately $16 million, while the value of its liabilities decrease by only $9.9 million. Acorn’s market value of equity therefore declines by $6.1 million or 40.67%.
5.33% × $300 million = $16 million
3.47% × $285 million = $9.9 million
($16 million – $9.9million) ∕ $15 million = 40.67%
To fully protect its equity from an overall increase or decrease in the level of interest rates, Acorn needs an equity duration of zero.
A portfolio with a zero duration is called a duration-neutral portfolio or an immunized portfolio , which means that for small interest rate fluctuations, the value of equity should remain unchanged.
Adjusting a portfolio to make its duration zero is referred to as immunizing the portfolio.
Acorn would like to reduce the duration of its equity from 40.7 to 0.
Because the duration of the mortgages will change from 8 to 0 if the S&L sells the mortgages for cash, Acorn must sell $76.3 million worth of mortgages.
A duration-neutral portfolio is only protected against parallel shifts in the yield curve.
If short-term interest rates were to rise while long-term rates remained stable, then short-term securities would fall in value relative to long-term securities, despite their shorter duration.
In a standard interest rate swap, one party agrees to pay coupons based on a fixed interest rate in exchange for receiving coupons based on the prevailing market interest rate during each coupon period.
An interest rate that adjusts to current market conditions is called a floating rate . Thus the parties exchange a fixed-rate coupon for a floating-rate coupon, which explains why this swap is also called a “fixed-for-floating interest rate swap.”
Consider a five-year, $100 million interest rate swap with a 7.8% fixed rate. Standard swaps have semiannual coupons, so that the fixed coupon amounts would be $3.9 million every six months.
The following slide shows the cash flows of the swap under a hypothetical scenario for LIBOR rates over the life of the swap.
For example, at the first coupon date in six months, the fixed coupon is $3.9 million and the floating-rate coupon is $3.4 million (½ × 6.8% × $10 million = $3.4 million), for a net payment of $0.5 million from the fixed- to the floating-rate payer.
139.
Table 30.6 Cash Flows ($ millions) for a $100 million Fixed-for-Floating Interest Rate Swap
Each payment of the swap is equal to the difference between the fixed- and floating rate coupons.
Because the $100 million swap amount is used only to calculate the coupons but is never actually paid, it is referred to as the notional principal of the swap.
The fixed rate of the swap contract is set based on current market conditions so that the swap is a fair deal (i.e., has an NPV of zero) for both sides.
It needs to borrow $10 million to fund this expansion. Currently, the six-month LIBOR is 4% and the ten-year interest rate for AA-rated firms is 6%. Given ACC’s low current credit rating, the bank will charge the firm a spread of 1% above these rates.
ACC’s managers are considering whether they should borrow on a short-term basis and then refinance the loan every six months or whether they should borrow using a long-term, ten-year loan.
To eliminate the risk of an increase in r t in the future, ACC can enter into a ten-year interest rate swap in which it agrees to pay a fixed rate of 6% per year in exchange for receiving the floating rate.
A swap contract will alter the duration of a portfolio according to the difference in the duration of the corresponding long-term and short-term bonds.
Swaps are a convenient way to alter the duration of a portfolio without buying or selling assets.
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