P2.T5. Market Risk Measurement & Management. Hull, Options, Futures, and Other Derivatives, 9th Edition.

Transcription

1 P2.T5. Market Risk Measurement & Management Hull, Options, Futures, and Other Derivatives, 9th Edition. Bionic Turtle FRM Study Notes By David Harper, CFA FRM CIPM

2 Hull, Chapter 9: OIS Discounting, Credit Issues, and Funding Costs EXPLAIN THE MAIN CONSIDERATIONS IN CHOOSING A RISK-FREE RATE FOR DERIVATIVES VALUATION DESCRIBE THE OIS RATE AND THE LIBOR-OIS SPREAD, AND EXPLAIN THEIR USES

3 Hull, Chapter 9: OIS Discounting, Credit Issues, and Funding Costs Explain the main considerations in choosing a risk-free rate for derivatives valuation. Describe the OIS rate and the LIBOR-OIS spread, and explain their uses. Explain why the OIS rate is a good proxy for the risk-free rate. Describe how to construct the OIS zero curve and determine forward LIBOR rates. Explain the main considerations in choosing a risk-free rate for derivatives valuation. The valuation of almost any derivative requires risk-free discounting: the standard procedure involves setting up a risk-free portfolio and arguing that in a no-arbitrage world it should earn the risk-free rate. For example, swaps are portfolios of FRAs or forward contracts and their valuations rely on risk-free discounting. In the United States, the rates on Treasury bills, Treasury notes, and Treasury bonds are natural candidates for risk-free rates. These instruments are issued by the US government and denominated in US dollars. Most believe it is unlikely that the US government will ever default on the instruments as it always has the opportunity of increasing the money supply in order to repay lenders. Similar arguments can be made for instruments issued by other governments in their own currencies. However, derivatives market participants tend not use treasury rates as risk-free rates because treasury rates are considered to be artificially low. Some of the reasons for this are given in Hull s Business Snapshot 9.1 (see below). Business Snapshot 9.1 What Is the Risk-Free Rate? Derivatives dealers argue that the interest rates implied by Treasury bills and Treasury bonds are artificially low because: 1. Treasury bills and Treasury bonds must be purchased by financial institutions to fulfill a variety of regulatory requirements. This increases demand for these Treasury instruments driving the price up and the yield down. 2. The amount of capital a bank is required to hold to support an investment in Treasury bills and bonds is substantially smaller than the capital required to support a similar investment in other instruments with very low risk. 3. In the United States, Treasury instruments are given a favorable tax treatment compared with most other fixed-income investments because they are not taxed at the state level. Traditionally derivatives dealers have assumed that LIBOR rates are risk-free. But LIBOR rates are not totally risk-free. Following the credit crisis that started in 2007, many dealers switched to using overnight indexed swap (OIS) rates as risk-free rates, at least for collateralized transactions. 3

4 Pre-2008, market participants used LIBOR rates and LIBOR-for-fixed swap rates as risk-free rates. LIBOR is the short-term (1 year or less) rate of interest at which creditworthy banks can borrow from other banks. Prior to the credit crisis that started in 2007, LIBOR was viewed as virtually risk-free. The chance of a bank defaulting on a loan lasting 1 year or less, when the bank is rated AA at the time the loan is granted, was thought to be very small. During the credit crisis, LIBOR rates soared because banks were hesitant to lend to each other. The TED spread, which is the excess of 3-month Eurodollar deposit rate over the 3- month US Treasury bill rate, is less than 50 basis points in normal market conditions. Between October 2007 and May 2009, it was rarely lower than 100 basis points and peaked at over 450 basis points in October Banks did not regard loans to other banks as close to risk-free during this period. Following the credit crisis, most banks changed their risk-free discount rates For collateralized transactions, banks changed from LIBOR to overnight indexed swap (OIS) rates. Collateralized derivatives are funded by the collateral, and OIS rates provide an estimate of the funding cost for these transactions. The OIS rate is a rate swapped for the geometric average of the overnight federal funds rate. It is not perfectly risk-free because a default on an overnight loan or the swap is always possible. However, it is much closer to risk-free than LIBOR. For non-collateralized transactions banks continue to use LIBOR, or an even higher discount rate. This reflects a belief that the discount rate used by a bank for a derivative should represent its average funding costs, not a true risk-free rate. The average funding costs for a non-collateralized derivative is considered to be at least as high as LIBOR. Describe the OIS rate and the LIBOR-OIS spread, and explain their uses. An overnight indexed swap (OIS) is a swap where a fixed rate for a period is exchanged for the geometric average of the overnight rates during the period. If, during a certain period, a bank borrows funds at the overnight rate (rolling the interest and principal forward each day), the interest rate it pays for the period is the geometric average of the overnight interest rates. If the bank lends money at the overnight interest rate every day (rolling the interest and principal forward each day), the interest it earns for the period is also the geometric average of the overnight interest rates. An OIS allows overnight borrowing or lending for a period to be swapped for borrowing or lending at a fixed rate for the period. The fixed rate in an OIS is referred to as the OIS rate. If the geometric average of daily rates for the period proves to be less than the fixed rate, there is a payment from the fixed-rate payer to the floating-rate payer at the end of the period; otherwise, there is a payment from the floating-rate payer to the fixed-rate payer at the end of the period. Example 9.1 Suppose that in a US 3-month OIS the notional principal is $100 million and the fixed rate (i.e., the OIS rate) is 3% per annum. If the geometric average of overnight effective federal funds rates during the 3 months proves to be 2.8% per annum, the fixed-rate payer has to pay 0.25 x ( ) x $100,000,000 or $50,000 to the floating-rate payer. (This calculation does not take account of the impact of day count conventions.) 4

5 Overnight indexed swaps tend to have relatively short lives (often 3 months or less). However, transactions that last as long as 5 to 10 years are becoming more common. An OIS lasting longer than 1 year is divided into 3-month subperiods. At the end of each subperiod the geometric average of the overnight rates during the subperiod is exchanged for the OIS rate. The swap rate in a plain vanilla LIBOR-for-fixed swap is a continually refreshed LIBOR rate (i.e., the rate that can be earned on a series of short-term loans to AArated financial institutions). Similarly, the OIS rate is a continually refreshed overnight rate (i.e., it is the rate that can be earned by a financial institution from a series of overnight loans to other financial institutions). Suppose that Bank A engages in the following transactions: 1. Borrow $100 million in the overnight market for 3 months, rolling the interest and principal on the loan forward each night. 2. Lend the $100 million for 3 months at LIBOR to another bank, Bank B. 3. Use an OIS to exchange the overnight borrowings for borrowings at the 3-month OIS rate. This will lead to Bank A receiving the 3-month LIBOR rate and paying the 3-month overnight indexed swap rate. We might expect the 3-month overnight indexed swap rate to equal the 3-month LIBOR rate, but it is generally lower. This is because Bank A requires some compensation for the risk it is taking that Bank B will default on the 3-month LIBOR loan. The overnight lenders to Bank A bear less risk than Bank A does when it lends to Bank B for 3 months because they have the option of ceasing to lend to Bank A if Bank A s credit quality declines. The excess of the 3-month LIBOR rate over the 3-month overnight indexed swap rate is known as the 3-month LIBOR-OIS spread. It is used as a measure of stress in financial markets. Its values between 2002 and 2013 are shown in Figure 9.1. In normal market conditions, it is about 10 basis points. However, it rose sharply during the credit crisis because banks became less willing to lend to each other for 3-month periods. In October 2008, the spread spiked to an all-time high of 364 basis points. A year later it had returned to more normal levels. It has since increased in response to stresses and uncertainties in financial markets. For example, it rose to about 50 basis points at the end of December 2011 as a result of concerns about the economies of European countries such as Greece. 5