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The adjusted hit rate is a trade hit rate calculated on all inquiries, with the exception of observations, where any of the following applies:
A trade hit rate calculated on all inquiries excluding those that elicit less than two responses.
A trade hit rate on outright inquiries, excluding those that have ended with less than two quotes or no quotes at or better than the Tradeweb composite (during US trading hours).
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Used to measure the highness or lowness of the price relative to previous trades. Bollinger Bands consist of:
Typical values for N and K are 20 and 2, respectively. The simple moving average is of the trailing type, not the centered type; in the trailing type, the average is plotted at the time-coordinate of the n-th price, not at the median time-coordinate of the set of N prices.
Difference between net repo, or break-even repo, and the actual repo rate. If this spread is positive, the bond is said to be earning positive carry. That is, the revenues from the bond exceed the financing cost. If the spread is negative, meaning that the net repo rate is less than the actual repo rate, the bond is said to be earning negative carry. The cost of financing the position in the repo markets is greater than what the bond is yielding.
In a positive yield curve environment, where yields of longer-term maturities are greater than shorter ones, holding longer-term notes and bonds and financing them overnight generates positive carry. If the yield curve is inverted, where short-term yields are higher than long-term yields, then financing bonds overnight will generate negative carry.
Cash flow analysis calculates the effective return of a bond and incorporates all cash flows of the bond from purchase to maturity. When purchased, the cash outflow of the bond includes price plus accrued interest. At maturity, the cash inflows comprise:
First day on which the security begins accruing interest.
Note: If the security has been re-issued or re-opened, the Dated Date still applies to the original security.
The duration, or Macaulay’s Duration, named after its originator, is the present value of a security’s cash flows weighted by time. This is a popular risk measurement for market participants.
The formula for calculating duration for a series of cash flows is as follows:
Duration = (1 x CF1/(1 + Y) + 2 x CF2/(1 + Y)**2 + ... ...+ n x Cfn/(1 + Y)**n)/P
where: CF1, CF2, ..., Cfn are cash flows 1 through n Y is the yield of the security n is the number of cash flows P is the price of the security including accrued interest
Duration calculates the average time of all cash flows received for the security quoted in years. That is, all the payments distributed over time are equivalent to one large payment at duration.
The following diagram depicts the cash flow of a typical bond. At settlement, the buyer must pay price plus accrued interest to purchase the bond. If the security is held to maturity, the bondholder will receive regular coupon payments up to and including maturity. At maturity, the bondholder will receive the full face value of the bond.
Price + Accrued Interest Principal + Coupon n ↓ Coupon 1 Coupon 2 ↓ ↓ ↑ ↑ ↓ |-------------------------------Maturity-------------------------------|
The series of cash flows for the bond is equivalent to one cash flow at duration, as depicted in the following diagram.
Price + Accrued Interest Cash flow ↓ ↑ ↓ ↑ |---------------- Duration -------------| |---------------------------- Maturity -------------------------|
Mapping all the cash flows into one period makes it easy to evaluate the interest rate risk of various securities.
The following example illustrates the duration of a bond. Consider again the U.S. Treasury bond, 7.625 of 2/15/2025. It was offered at 100-25 for settlement on 2/27/95. The duration is 12.198 years.
Though the bond matures about 30 years from the settlement date, its duration is only about 12 years. In theory, this bond behaves as one cash flow that is only 12 years out.
Basic discounted cash flow analysis explains this phenomenon. Coupons closer to the settlement date are worth considerably more than cash flows near maturity. Even the principal amount of 100% when discounted from 30 years at a yield of 7.558% is worth only 10.8% of face value. The duration calculation weighs the earlier cash flows more heavily than the later cash flows due to the time value of money. This explains why even a 30-year bond has an effective duration of 12 years.
Market participants frequently use the concept of duration to immunized portfolios. Since many institutional investors have liabilities that must be met on schedule with the proceeds of a bond portfolio, immunization attempts to ensure that regardless of what happens to interest rate levels between the present and the due date of one’s liabilities, enough cash will be available to meet them.
Duration allows investment managers to construct a portfolio that immunizes a fixed-income portfolio against liability streams. Bond immunization, using duration as a tool, is a financial technique employed to protect a series of future cash flow requirements funded by a fixed-income portfolio from interest rate changes.
For example, a fund manager may have a liability at a known future date for which he wants to have sufficient funds. He wants to buy a bond today to cover this future liability without having to worry about inevitable changes in interest rates. That is, he wants to make immune his future liability from interest rates. By buying a bond with a duration equal to his investment horizon, the future liability will be covered mostly by the bond for a range of interest rate environments.
To understand how duration works, one must first understand market risk and reinvestment risk.
Market RiskMarket risk, also called price risk, measures the price sensitivity of a bond with respect to changes in interest rates. When interest rates rise, the price of the bond falls; when interest rates fall, the price of the bond rises. The change in price due to a change in interest rate levels is called market risk. Market risk has an immediate impact on the price of the bond when interest rates change.
A bondholder receives periodic coupon payments from his investments. These coupon payments can be reinvested to earn additional income. Assuming the bondholder keeps the bond until he sells it at his investment horizon, he would receive the following cash flows: (1) the price plus accrued interest from the buyer of the bond at the horizon date, (2) all the coupon payments he received since he purchased the bond, and (3) the interest on interest he received from reinvesting his coupon payments.
The first cash flow component is market risk. Interest rate changes directly affect the price of the bond. The second cash flow component, the coupon payments, is fixed. That is why bonds are called fixed-income securities. The coupon payment is known; and therefore, its cash flow is not affected by changes in interest rates. The last cash flow component, interest on interest, is reinvestment risk. It is affected by changes in interest rates.
When interest rates rise, the reinvestment income is higher. When interest rates fall, the reinvestment income is lower. Therefore, when general levels of interest rates change, they affect both market risk, the price of the bond, and reinvestment risk, the future income derived from reinvesting coupon payments. Reinvestment risk affects investments in the long term.
The interesting thing about market risk and reinvestment risk is that they tend to offset each other. When interest rates rise, bond prices fall but reinvestment income increases. When interest rates fall, bond prices rise but reinvestment income falls.
From the previous section we know that market risk and reinvestment risk tend to offset each other when interest rate levels change. If the investment horizon is equal to the duration of the bond, the market risk is equal to the reinvestment risk.
This is the special property of duration. With an investment horizon equal to the duration, the return on the investment to the horizon date will remain relatively constant for various interest rate scenarios. The change in the price of the bond is offset by the change in the reinvestment income. Therefore, the total return to the horizon date is the same. Duration is a powerful tool for an investment manager to buy a bond to protect a future liability with a fair degree of immunization from interest rate movements.
Value Date Duration Maturity | Increasing | Increasing | | <-- Market Risk | Reinvestment Risk --> | ---------------------------------------------------------------
Market risk is greatest if the investment horizon is close to the current valuation date. If you are planning to sell the bond tomorrow, you are not concerned about reinvestment income; however, you are concerned if rates rise considerably between today and tomorrow as your bond will tank (drop rapidly in price). Traders that are in and out of the markets for short periods of time are much more concerned about market risk.
Reinvestment risk is greatest if the investment horizon is at maturity. The compounding effect of reinvested coupons is very significant. If the bond is being held to maturity, there is no market risk. The bond at maturity will return a 100% face value. If interest rates rise or fall, the bond will still return face value at maturity - no more, no less.
At an investment horizon equal to duration, the market risk is equal to the reinvestment risk. They cancel each other out. By using duration, portfolios can be structured to fully defend a future series of cash flows, which is called bond immunization.
Rebalancing a Portfolio
Investment managers must periodically reevaluate the duration of their portfolios for several reasons. First, as time passes, a bond’s duration decreases. Secondly, duration is also affected by large price changes. Thus, even though a dedicated bond portfolio may have immunized cash flow liabilities, the investment manager must reevaluate it regularly. Changes in assumptions or liability streams will also affect the portfolio. Adjustments may be necessary to actively manage the portfolio. That is, the portfolio must be rebalanced to match the investment objectives.
The duration of a zero-coupon bond is equal to its maturity. Since duration is a weighted average time to a bond’s cash flow, the weighted average time to one cash flow at maturity, which is the cash flow of a zero-coupon bond, is exactly equal to its maturity. In fact, for any security that has one payment at maturity, such as many money market instruments, the duration is equal to the maturity.
Given a regular coupon-paying bond and a zero-coupon bond of the same maturity, the zero-coupon bond will have a higher duration and therefore a higher interest rate risk.
Duration is frequently used as a measure of interest rate risk. Generally, the higher the duration of a security, the more sensitive it is to interest rate changes. By calculating the duration for various securities, market participants can compare on a relative basis their interest rate sensitivity.
Duration is a better risk measurement than maturity. A longer maturity does not necessarily imply higher interest rate risk. Maturity does not take into account the coupon effect to interest rate risk of the bond. Bonds with lower coupons have higher interest rate risk since most of the cash flows are received later, whereas bonds with higher coupons have lower duration and therefore lower interest rate risk. Given two bonds with identical maturities, the duration of a lower coupon bond will be higher than a bond with a higher coupon.
For most bonds, the first coupon is the same as any other coupon. However, if the dated date is different than the normal anniversary dates of coupon payments, the first coupon may be different than the regular coupons. This is called an odd-first coupon. If the coupon is greater than the normal coupon, it is referred to as a long-first coupon. If the coupon is less than the normal coupon, it is referred to as a short-first coupon.
If an issuer decided not to pay the extra day of accrued interest and opted instead to have the dated date be the same as the issue date, the first coupon would be a short-first coupon. It would have one day less interest than a normal coupon. All subsequent coupons would be regular coupon payments.
A trend following indicator designed to identify trend changes. It's generally not recommended for use in ranging market conditions. Three types of trading signals are generated:
The signal line crossing is the usual trading rule. This is to buy when the MACD crosses up through the signal line, or sell when it crosses down through the signal line. These crossings may occur too frequently, and other tests may have to be applied.
The histogram shows when a crossing occurs. When the MACD line crosses through zero on the histogram it is said that the MACD line has crossed the signal line. The histogram can also help visualizing when the two lines are coming together. Both may still be rising, but coming together, so a falling histogram suggests a crossover may be approaching.
A crossing of the MACD line up through zero is interpreted as bullish, or down through zero as bearish. These crossings are of course simply the original EMA(12) line crossing up or down through the slower EMA(26) line. Positive divergence between MACD and price arises when price makes a new sell-off low, but the MACD doesn't make a new low (i.e. it remains above where it fell to on that previous price low). This is interpreted as bullish, suggesting the downtrend may be nearly over. Negative divergence is the same thing when rising (i.e. price makes a new rally high, but MACD doesn't rise as high as before), this is interpreted as bearish.
Pool of securities backed by assets, like mortgages, and securitized by an agency, which passes through the principal and interest payments to the pool owners, pro rata, keeping a portion of the interest. In essence, a homeowner's payment is passed from the lending bank to investors through a GSE like Fannie Mae or Freddie Mac.
Note: The pass-through rate is lower than the interest rates on the loans due to the GSE and servicing institutions' fees.
Similar to a Consumer Price Index (CPI), RPI is used to adjust inflation-indexed securities. Measuring changes in goods and services used by UK households, it samples retail consumption.
Note: Since 2003, the UK government has tended to set inflationary targets on CPI rather than RPI. Unlike CPI, RPI includes mortgage interest payments and housing depreciation.