1、Introduction
Fixed Income Securities
Fixed income securities are financial claims with promised cash flows of fixed amount paid at fixed dates. However, that does not mean that they are risk-free.
eg:
Treasury: government bonds issued by various governments, US treasuries, Japanese government bonds, German bonds.
Federal agency
Municipal securites(exempt from federal tax)
Corportate bond
Mortgage backed and asset backed bond
Market Participants
Issuers, intermediaries, investors.
Issuers
※ Governments
※ Municipalities
※ Corporate
Intermediaries
※ Primary Dealers and other dealers:
Primary dealers play a special role in the sense that they participate in the auctions of government securities. So they are the first ones to absorb the supply of government bonds. Other dealers facilitate transactions in the secondary market among investors.
※ Investment banks:
Investment banks serve multiple functions. They can act as a dealer holding an inventory of bonds. They can act as a broker making matches between buyers and sellers of fixed income securities. And they can also help corporations or municipalities issue their bonds. So they can help in the primary transactions. They can help structure bonds and place them with investors.
※ Credit Rating Agency
Credit rating agency serve to provide information about the quality of fixed income securities. They rate credit quality. They attach credit rating to different securities that indicates the relative riskiness. This information can be then used by the investors to decide on how to allocate their capital across different types of assets.
2、Yield Curve
Cash Flows of Fixed Income Securities
There are three elements, maturity, principal and coupon. Maturity refers to the time to maturity, coupon is the nominal rate of interest on a fixed-interest security and principal is the sum of money invested.
eg:
A 3-year bond with principal of $1000 and annual coupon payment of 5%.
answer:
Maturity is 3 years. You get $50 annually in Year 1,2,3 and your principal of $1000 will be returned in Year 3.
Valuation of Riskless Cash Flows
Without risk, only time value of money is relevant.
Spot interest rate
Spot interest rate is the current annualized interest rate for maturity date t:
rt is for payments only on date t; rt is different for each date t.
3、Discount Bonds vs Coupon Bonds
Discount Bond
With no coupon payment, a discount bond will give you an interest at the end of the period.
Coupon Bond
With annual coupon payment, a coupon bond gives you a principal payment at the end of the period.
4、Relative valuation of bonds
eg:
answer:
Let's denote the present value of $1 in Year 1,2,3 by P1,P2,P3
5、Yield to Maturity
YTM vs Coupon Rate
Bond price is inversely related to YTM.
If coupon<YTM, the bond sells at a discount.
If coupon=YTM, the bond sells at par.
If coupon>YTM, the bond sells at a premium.
Yield to maturities cannot be used to compare bonds to each
other. A bond with a high yield to maturitydoes not necessarily pay a higher return or represent a better deal to the investors. Again, these are simply quoting conventions. Based on the definition, yield to maturity is a somewhat complex weighted average of spot rates across maturities. It's a weighted average of interest rates.
6、Yield Curve Dynamics
Expectations Hypothesis
If you invest $1 in a 10-year discount bond, according to arbitrage pricing theory, that equals to investing $1 in a 9-year discount bond and reinvesting for 1 more years at the prevailing spot rate.
We can further find that:
Why long-term bonds may earn a positive premium?
Short-term bonds are more money-like: hold value better in the shortrun.
Nominal bonds are exposed to inflation risk – lose value wheninflation spikes.
7、Interest Rate Risk and Bond Duration
Interest Rate Risk
As interest rates change over time, bond prices also change. The value of a bond is subject to interest rate risk.
eg:
At the yield of 5%, the price of a bond is $90. At the yield of 4%, the price of a bond is $91.8.
answer:
The rate of price change is 2% while the change in the yield is 1%, we can use 2%/1% to get 2. This can be seen as the bond duration.
Bond Duration
Measure of Bond Risk= -1/B*dB/dy
Macaulay Duration
Here ONLY introduces its calculation. As we can see, the Macaulay duration for a discount bond is t, which is proportional to Modified Duration, which is t/(1+y).
eg:
answer:
Macaulay duration: D=738.28/103.5=7.13
Modified duration: MD=D/1.03=6.92
For small yield changes, pricing by MD is accurate. For large yild changes, pricing by MD is inaccurate.
Convexity
Bond convexity can be used, together with bond duration, to approximate the impact of yield curve changes on bond prices.