Chapter 10 & 11 - Analysis of Debt Securities Flashcards
What are the only 2 variables required to calculate the value of a strip bond?
The price (when calculating yield) or yield (when calculating price), days to maturity. The FV is always 100.
What type of return is the yield to maturity of a bond? Why is this only sometimes can accurate return?
Internal rate of return. Given that it’s the PV of a series of cash flows, it’s only a true return if the bond is held to maturity and all cash flows are received and reinvested at a rate equal to the YTM.
How do you calculate the yield of callable and putable bonds?
Must not only calculate the YTM, but the yield to call or yield to put. If there are multiple potential dates, you would normally calculate the yield to each date. The lowest yield (yield to worst) is taken as the assumed yield.
What is the yield to worst?
For callable or putable bonds, it’s the lowest yield to call or yield to put. This is the value that is used as the assumed yield of the bond.
Which function on the financial calculator do you use to calculate a bond’s yield?
IRR
How do you calculate the yield of a bond portfolio?
The yield is NOT the weighted average of the yields of the individual bonds in the portfolio. Instead, it is the “cash flow yield” which is the IRR of all expected cash flows.
What happens if a bond is purchased between coupon payment dates?
The buyer must compensate the seller for interest accrued since the last coupon payment date that has not yet been paid (accrued interest).
What are the 4 different “day count methods” for calculating accrued interest and which applies for which type of bond?
- Actual/365 - Government of Canada & Prov Bonds
- Actual/Actual - US Treasury, Cdn Corp
- Actual/360 - Eurobonds
- 30/60 - US agency, US municipal, US corp
What is the actual/365 day count method and what does it apply to?
Govt of Canada + Prov bonds.
Accrued interest = coupon rate x DSLC (days since last coupon) / 365
What is the actual/actual day count method and what does it apply to?
Cdn corp bonds and US treasury notes.
Accrued interest = (coupon rate / 2) x days since last coupon / DCP (# of days since last coupon to the next)
Example: 73 days since last coupon, 183 days total between last coupon + next coupon
How does the actual/360 day count method work and what bonds does it apply to?
Applies to eurobonds. The year is assumed to have 360 days.
Does the 30/360 day count method work and what bonds does it apply to?
A year is assumed to be 360 days and each month is 30 days. When calculating the number of days accrued, no month can count for more than 30 days. Applies to US agency bonds, US municipal bonds, and US corp bonds.
Are money market yields calculated in the same way as strip coupon yields?
No. T-bills, bankers’ acceptance and commercial paper in Canada is quoted as the “bond equivalent yield” (BEY).
BEY = (100 - price) / price x 365/n
where n = # of days to maturity
In US, the “bank discount rate” BDR method is used.
BDR = (100 - price) / 100 x 360/n
How does calculating the price of a money market security differ if it’s Canadian or US?
For Canadian, you use the BEY. US is the BDR. For Canadian, the calculation is 100 / [1 + (BEY x n/365)]
For US, it’s 100 - (100 x BDR x n/360)
BEY and BDR are the quoted yields.
What is the term structure of interest rates?
The relationship between interest rates and time to maturity, represented by a yield curve.
What are the 3 terms that describe the yield curve?
Normal
Flat
Inverted
What are the 3 TYPES of shifts that can occur in the yield curve?
- Parallel shifts up and down
- Twists (flattening or steepening)
- Humps (positive or negative)
When do parallel shifts in the yield curve occur?
When yields at all maturities move up or down by nearly the same amount.
When do twists in the yield curve occur?
Twists cause the curve to steepen or flatten. They occur when either yields at one end of the curve move up or down by more than yields at the other end, or yields at the other end move in the opposite direction.
When do humps in the yield curve occur?
These occur when the yield at a certain maturity moves up or down independently, or in greater amounts, than yields at all other maturities. These can be positive humps or negative humps.
Which type of shift in the yield curve is rare?
Humps. Most shifts are parallel or twists.
What tends to happen to a normal yield curve when it shifts upward?
It also becomes flatter as short-term yields rise more quickly than longer-term yields.
What are the Government of Canada’s 7 benchmark securities?
3-month T-Bill
6-month T-Bill
1-Year T-Bill
2,5,10,30 year bonds
What happens to old benchmark bonds when new benchmark securities are issued by the Government of Canada?
Old benchmark bonds are said to be “off-the-run” bonds while new ones eventually become the “on-the-run” issue for that benchmark maturity.
How does the growth phase of the economic cycle impact interest rates?
Demand for goods and services increases, resulting in increased demand for credit. This pushes interest rates higher as the supply of credit cannot meet the increase in demand.
How does the boom phase of the economic cycle impact interest rates?
Rising pace of growth leads to increased employment. Labour becomes scarce, so wages rise. Demand for input materials also rises. Rising prices, combined with continued demand for credit, push interest rates higher.
How does the contraction phase of the economic cycle impact interest rates?
Too much inventory is combined with high costs and tight credit conditions. This results in reduced profitability and therefore reduced incentive to invest and expand further. Production slows and the economy slows. Reduced demand for credit pushes interest rates lower.
How does the trough phase of the economic cycle impact interest rates?
Demand is low, profits decline further, unemployment rises , and the need for investment is reduced. Inflation declines and the demand for credit remains low, resulting in further declines in interest rates.
Why do debt market participants watch GDP?
GDP growth rates are barometers of the economic cycle. Growth in GDP is the key measure of an economy’s increase in output over time. These numbers can give an idea as to where Canada is at in the economic cycle.
What is the trade balance and why is it an important factor to watch for debt market participants?
The difference between exports and imports. It can be interpreted in many ways. For example, a trade deficit (more imports than exports) has a negative effect on GDP due to the need to draw in capital to finance foreign liabilities, it also signals strong consumer demand.
What are the 3 primary measures of inflation in Canada?
- Consumer Price Index
- In the US, Producer Price Index (prices for a broad range of goods and commodities). In Canada, Industrial Product Price Index and Raw Materials Price Index would be comparable.
- GDP price deflator covers all goods and services purchased/produced in an economy.
What is the Index of Leading Economic Indicators?
Composite index that consists of an average of economic variables, attempts to anticipate future economic activity. However, most components are released first, so it’s a lagging indicator to the leading indicators.
What are the 2 primary tools the BoC uses to implement monetary policy?
Interest rate policy
Open market operations
How does the BoC’s official interest rate work?
It is enforced indirectly since the central bank is a lender of last resort. To ensure trading in the overnight market stays within a certain range, the BoC’s target for the overnight rate is at the centre of an operating band that is 50 basis points wide.
What are open market operations?
The purchase or sale of T-bills and government bonds.
What is quantitative easing?
Released by the Fed in response to the global financial crisis. The concept is to increase the reserves in the commercial banking system, which will minimize liquidity problems in the short-term. In a QE transaction, the Fed purchases collateral (such as US treasury bonds) from commercial banks and credits their respective Fed reserve accounts. This results in greater liquidity, with a mid-term impact of increasing lending activities and spurring economic growth.
What is Modern Monetary Theory?
Reemerged in 2016 as a viable concept. According to MMT, a country should not worry about running a fiscal deficit in pursuit of a domestic economy with full employment and little spare capacity. Each country has a unique monopoly on printing its own currency, making it impossible to default on sovereign debt outstanding.
What are the 2 important conditions associated with modern monetary theory?
- A country must not depend on debt financing denominated in foreign currencies.
- Once full employment is reached and all capacity has been used up, any additional money printing/govt spending can increase the risk of creating an inflationary environment. Inflation can be eliminated by raising taxes.
How does modern monetary theory posit that a domestic economy run at full employment?
Governments will typically used federally funded, locally administered job programs to provide employment opportunities to the unemployed. These programs will be more in use during times of contraction/trough.
What is the risk of modern monetary theory with foreign currency denominated debt?
Increasing the amount of domestic currency (printing money) can potentially devalue that currency relative to the foreign currency, making it more costly to service.
Which government bonds trade similarly to Canadian bonds?
US treasuries, as well as Australian/New Zealand government bonds given economic and political similarities in the eyes of international investors.
How do equity markets influence debt markets?
Strong equity markets draw investment funds away from debt markets, while soft equity markets create interest in debt markets through a ‘flight to quality’. Growth in equity markets can have a negative effect on debt markets because of the prospect of rising interest rates.
How do commodity markets influence debt markets?
Strong commodity markets generally have a negative influence on bond markets. Rising commodity prices reflect strong growth, which directly indicates rising prices. Inflation negatively affects bond markets. As well, a rise in the price of “investment” commodities may reduce the relative attractiveness of debt securities.
What is spread?
The difference between the yields on 2 debt securities, expressed in basis points.
Why are spreads so important in the Canadian bond market?
The market moves according to flows in benchmark govt issues, as every trade in a bond almost always triggers a comparable trade in a govt bond. By selling bonds to clients, traders (often) leave themselves in short positions. They will purchase comparable govt securities to hedge their position.
What are the primary risks investors incur with non-Government of Canada bonds?
Credit risk, option risk, liquidity risk.
What is credit spread?
The portion of a bond’s spread attributable to the difference in credit risk.
Why do provincial government bonds with a AAA rating still have a credit spread?
This reflects the Government of Canada’s larger tax base and its ability to print money.
What happens to a bond’s spread if it contains options?
If the option benefits the issuer, the spread will be greater. The spread will be lower if it benefits the investor.
What are the 3 primary types of embedded bond options? Which option benefits who?
- Calls - benefit the issuer
- Puts - benefit the investor
- Conversions - benefit the investor
Why does a lower level of liquidity translate into greater risk for bond investors?
Wider bid/ask spread. This means that the bond must be bought/sold at a value further from its true value (mid point of the bid/ask).
What are the 2 basic theories behind the behaviour of spreads?
- Quality spread theory
- Interest rate volatility theory
What is the quality spread theory?
It attempts to explain the behaviour of credit spreads and is based on the view that the economic cycle affects credit spreads.
This means that investors are more comfortable shifting funds to riskier assets during an economic recovery. As more money moves to lower-credit bonds, the price relative to Govt of Canada bonds increases, and spreads tighten. Conversely, there is a flight to quality that occurs during an economic downturn, causing spreads to widen.
What is interest rate volatility theory?
Used to explain the behaviour of the portion of a bond’s spread that is due to embedded options. This theory poses that during times of high interest rate volatility, yield spreads on callable bonds widen and spreads on putable bonds narrow. As volatility subsides, the opposite is true. Higher volatility therefore increases the value of both call and put options, while lower volatility decreases their value.
Call options become more valuable to the ISSUER during times of high volatility as they own the option, so the price of the bond falls. This falling bond price results in a greater yield, which translates into a wider yield spread.
Conversely, when volatility subsides, callable bond prices rise and spreads are compressed.
Putable and redeemable bonds react in the opposite way since the investor owns the option, not the issuer. The bond’s value rises when volatility increases as the put option’s value increases. This causes yields to shrink relative to Govt of Canada bonds.
What happens to putable bonds during periods of interest rate volatility?
The investor owns the option. Higher volatility results in the value of the put option increasing. This raises the value of the bond. Yield spreads shrink relative to Government of Canada bonds.
What happens to callable bonds during periods of interest rate volatility?
The issuer owns the call option and the options becomes more valuable to the issuer during times of high volatility. Therefore, the price of callable bonds falls and the yield spread between callable bonds and Govt of Canada bonds widen.
How does a change in yield affect bonds with the same coupon rate and yield?
Greater change in the price of longer-term bonds than shorter-term bonds.
How does a change in yield affect bonds with the same term to maturity and yield?
Greater change in price of bonds with lower coupon rates than those with larger coupon rates.
What are the two primary features that determine the volatility of a given bond?
Coupon rate and term to maturity.
How can one compare the volatility of bonds with different coupon rates AND maturities?
DURATION
What is the Macaulay Duration?
The weighted average term to maturity of the PV of the bond’s cash flows, including all coupon payments and the principal repayment. The PV of each coupon is determined using the bond’s yield to maturity. The weight given to each is equal to the PV of the payment divided by the price of the bond.
What happens if you calculate the Macaulay duration of a zero-coupon bond/strip coupon?
The Macaulay duration is the same as the bond’s term to maturity, regardless if using annual or semi-annual yield.
What is the main purpose of the Macaulay duration?
Used to calculate modified duration, which is a more useful measure of a bond’s price volatility.
How do you calculate modified duration?
Macaulay duration / (1 + (yield/# of annual coupon payments)
Example: 7.99 / (1 + (0.05/2)) = 7.80 modified duration
What is modified duration used to determine?
The approximate percentage change of a bond’s price given a certain change in its yield.
How do you calculate the approximate percentage change of a bond’s price given a certain change in its yield?
= - modified duration x the change in yield (decimal) x 100
Example:
= -7.80 x (-0.005) x 100 = 3.90%
Bond’s price would increase by approximately 3.90%.
What factors lead to the greatest increases/decreases in a bond’s modified duration?
Longer term to maturity increases, lower coupon rates increases, lower yield increases.
How do you calculate the modified duration of a bond portfolio?
First, calculate the weight of each bond based on the total market value. If a bond is trading at $85 and you own $50,000 face value of it, then 85/100 = 0.85 * 50,000 = 42,500.
Then, for each bond, it’s the modified duration of the bond x (the bond’s market value / total portfolio market value)
Add these values together to get the total portfolio modified duration.
How do you calculate the approximate dollar change (dollar duration) of the price of a bond/bond portfolio?
= - modified duration x percent change in yield x market value of bond/bond portfolio
Example:
-7.80 x (0.005) x 50,000 = -1950, expect a decline of $1,950.
What two assumptions must hold true for duration to work as an approximate measure of bond volatility?
- Changes in YTM are small
- Yield curve shifts in a parallel manner
Does modified duration overstate or understate changes in price when yields fall/rise?
Understates the change in price when yields fall, overstates the change in price when yields rise.
Why does modified duration either understate or overstate changes in the price of bonds when yields change?
Convexity. There is an asymmetry in percentage changes in price and modified duration is unable to capture the asymmetry, which is directly related to the convex nature of the price-yield relationship.
Essentially, modified duration is a straight line on a price/yield chart, while the actual bond price is a curved (convex) line.
Modified duration is fairly accurate at predicting smaller price changes, but far more inaccurate for large price changes due to this convexity.
What tool can be used to adjust the duration calculation for the convexity of the price-yield curve?
The bond’s convexity
What is the bond’s convexity calculation and how is it used alongside modified duration?
Apprx % change in price due to convexity = convexity / 2 (change in yield)^2 x 100
Plug the bond’s convexity into the calculation and it will produce a percentage change. Add this to the approximate percentage price change calculated using duration to find the total percentage change in a bond’s price.
How does convexity differ for debt securities with embedded options vs option-free bonds?
For option-free bonds, the change in value resulting from the convexity term is always positive. Debt securities with embedded options can occasionally have negative convexity, meaning the duration overstates the price of a debt security for a given change in yield.
When will the price volatility characteristics of a callable bond be similar those of an equivalent option-free bond? What about those of a putable bond?
At high yield levels, since there is little change of the bond being called.
For a putable bond, it’s low yield levels where there is little chance an investor will redeem the bond and it will behave in the same manner as an option-free bond.
Why do diversification requirements depend on credit quality?
It takes fewer issues to diversify a portfolio of high-quality issues than it does to diversify a lower-quality portfolio.
What are the 4 primary active strategies for debt securities?
- Interest rate strategies
- Yield curve strategies
- Intermarket spread strategies
- Intramarket spread strategies
How do interest rate strategies work for active debt security management?
Active investors attempt to exploit differences between their own interest rate forecasts and the forecast embedded in market interest rates. They do this by adjusting the duration of their portfolios.
If these investors expect rates to fall, they will often increase duration (and vice versa).
What is the active interest rate strategy of “riding the yield curve”?
Riding the yield curve is a trading strategy that involves buying a long-term bond and selling it before it matures so as to profit from the declining yield that occurs over the life of a bond. Investors hope to achieve capital gains by employing this strategy.
As a trading strategy, riding the yield curve works best in a stable interest rate environment where interest rates are not increasing. Additionally, the strategy only produces excess gains when longer-term interest rates are higher than shorter-term rates.
How do yield curve strategies work for active debt security management?
Designing a bond portfolio as either a bullet portfolio or barbell portfolio, which will result in different degrees of convexity (even though the portfolios may have roughly equal duration). Each type of portfolio will perform better depending on the shape of the yield curve.
What is a bullet portfolio and what is a barbell portfolio?
A bullet portfolio contains bonds with roughly equal durations. A barbell portfolio combines bonds with short durations with bonds with long durations.
Generally, barbell portfolios will have the greatest convexity.
The barbell portfolio will generally outperform when the yield curve flattens while the bullet portfolio will generally outperform when the yield curve steepens. If there is a parallel shift in the yield curve, the barbell portfolio outperforms if the shift is great. For small parallel shifts, the barbell’s greater convexity is not enough to offset the bullet’s yield advantage, and the bullet outperforms.
How do intermarket spread strategies work?
Attempt to capitalize on the difference and expected changes in yield spreads between different sectors of the bond market. They attempt to anticipate changes in the direction of credit spreads and modify their exposure to each sector of the market based on this anticipation. Considering that credit spreads tend to widen during economic downturn and narrow during periods of growth.
What are intramarket spread strategies?
These are also known as “substitution swaps”, which involves swapping bonds that are largely similar. This can involve swapping bonds from different similar corporations, or swapping securities of the same issuer (such as favoring senior secured debentures to subordinated debentures or vice versa).
What are the two passive strategies for debt securities?
- Indexation
- Laddering
What are the two common sampling procedures used to replicate an indexed portfolio?
- Stratified sampling or cell approach
- Optimization approach
How does the stratified sampling or cell approach work for indexed bond portfolios?
Takes a market index and divides it into parts (cells) that represent a cross-section of different portfolio characteristics, such as duration, coupon, maturity, sector, credit rating and call features. Each cell can then be divided into subsections.
The goal is then to choose securities that best represent the characteristics of an entire cell.
What is the optimization approach to indexing?
This approach builds on the stratified sampling approach by using mathematical programming to optimize the portfolio based on return objectives and constraints.
Why is tracking error lower for government bond indexes?
The corporate sector has lower liquidity, lack of transparency, larger bid/offer spreads. This results in greater tracking error and more problems for investors.
How does the laddering bond strategy work?
Involves building a portfolio of debt securities with staggered maturities so portions of the portfolio mature at regular intervals. As securities mature, they are reinvested at the long-term end of the ladder. Over time, the portfolio comes to include only debt instruments that were originally purchased with the longest allowable maturity date.
What are the 3 different types of dedicated bond investment strategies?
- Cash-flow matching
- Immunization
- Contingent immunization
Who typically uses immunization and contingent immunization strategies to bond portfolio construction?
Institutional investors
How does cash-flow matching work as a dedicated bond strategy?
This is often used when an investor needs funds at a certain date typically by purchasing zero-coupon bonds with a maturity equal to the value needed at the date.
What is the “Dollar Bloc”?
Consists of the US, Canada, Australia and New Zealand. Canada tends to be similar to the US, and the US is the largest bond market in the world. Australia and New Zealand have similar economies.
Therefore, these markets all often trade in close relation to one another.
What is the Eurozone trading bloc?
Consists of the member states of the EU that adopted the euro as a currency. All new debt issues are denominated in euros and they share the same central bank. Therefore, they trade in close relation to one another.
What is the periphery Europe trading bloc?
Nations that make up the balance of Western Europe. Their trading is separate from the larger Eurozone bloc given the size of the markets and their independent economic situation.
Why is the Japanese bond market in its own trading bloc?
It is the second-largest bond market in the world. The market is dominated by domestic banking and internal political issues, and trades somewhat separately from other major bond markets.
What is the greatest risk when investing in emerging market government bonds?
Though they generally do not default, they do restructure.
