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Yield Curve Presentation Transcript
1.Yield Curve
2.Yield to Maturity (YTM)
Current Yield
Yield to Call
Realized Compound Yield
Holding Period Return
Current Yield
Yield to Call
Realized Compound Yield
Holding Period Return
3.Yield to Maturity
The Yield to Maturity is defined as the discount rate that makes the present value of the future bond payments (coupons and par) equal to the price of the bond
Ever hear of something like that? What do we call discount rates like that?
YTM is a bond equivalent yield, or annual percentage rate (APR), which comes from applying simple interest rules (annualize by multiplying, not raising to a power)
YTM is just 2 x semi-annual YTM, not (1+ semiYTM)2 – 1
When people talk about “yield”, they’re almost always talking about yield to maturity
The Yield to Maturity is defined as the discount rate that makes the present value of the future bond payments (coupons and par) equal to the price of the bond
Ever hear of something like that? What do we call discount rates like that?
YTM is a bond equivalent yield, or annual percentage rate (APR), which comes from applying simple interest rules (annualize by multiplying, not raising to a power)
YTM is just 2 x semi-annual YTM, not (1+ semiYTM)2 – 1
When people talk about “yield”, they’re almost always talking about yield to maturity
4.Calculating YTM
5.Current Yield
6.Yield to Call
For callable bonds that look likely to be called prior to maturity, it makes more sense to calculate a yield to call than a YTM
The yield to call is just like the YTM, just replace maturity date with expected call date and replace par amount with call price
What type of bonds get called? Premium or discount bonds? Premium
For callable bonds that look likely to be called prior to maturity, it makes more sense to calculate a yield to call than a YTM
The yield to call is just like the YTM, just replace maturity date with expected call date and replace par amount with call price
What type of bonds get called? Premium or discount bonds? Premium
7.YTM and Reinvestment Risk
VERY IMPORTANT : YTM assumes that all coupon payments can be invested at the YTM
In other words, you will only earn the YTM – even if you hold the bond to maturity – if you can reinvest all the coupon payment at the YTM until maturity
How likely is that?
This is called reinvestment risk
VERY IMPORTANT : YTM assumes that all coupon payments can be invested at the YTM
In other words, you will only earn the YTM – even if you hold the bond to maturity – if you can reinvest all the coupon payment at the YTM until maturity
How likely is that?
This is called reinvestment risk
8.Reinvestment Risk in Fixed Income
Fixed Income makes periodic payments
The calculated YTM on an FI instrument assumes the holder will reinvest all coupon payments at the YTM
How realistic is that?
The risk that an investor will not be able to reinvest coupon payments at the YTM is called reinvestment risk
Fixed Income makes periodic payments
The calculated YTM on an FI instrument assumes the holder will reinvest all coupon payments at the YTM
How realistic is that?
The risk that an investor will not be able to reinvest coupon payments at the YTM is called reinvestment risk
9.Yield Spreads
Nominal Spread is the spread between a bond and equivalent term treasury bond.
Zero volatility spread is a spread over the entire treasury spot rate curve which equates the present value of cash flows from a bond to its current price
Nominal spread is a spread against a point in the treasury yield curve whereas Z spread measures a static spread over the entire curve
Nominal Spread is the spread between a bond and equivalent term treasury bond.
Zero volatility spread is a spread over the entire treasury spot rate curve which equates the present value of cash flows from a bond to its current price
Nominal spread is a spread against a point in the treasury yield curve whereas Z spread measures a static spread over the entire curve
10.Yield Spreads
Options embedded in the bond structure change the cash flow characteristics of the bond with interest rate volatilities
Zero Volatility spread does not capture change in the cash flows due to interest rate volatility
Option Adjusted Spread is the spread that shows the spread over treasury curve for arriving at market value of the price of a bond with embedded options
Options embedded in the bond structure change the cash flow characteristics of the bond with interest rate volatilities
Zero Volatility spread does not capture change in the cash flows due to interest rate volatility
Option Adjusted Spread is the spread that shows the spread over treasury curve for arriving at market value of the price of a bond with embedded options
11.Yield Spreads
Option cost
= Z Spread --Option Adjusted Spread
Option cost
= Z Spread --Option Adjusted Spread
12.A normal Yield Curve
13.An Inverted Yield Curve
14.A Flat Yield Curve
15.An Humped Yield Curve
16.Theory of Term Structure
17.Theory of Term Structure
Broadly three school of thought are there for explaining the shape of yield curve
•Pure expectation theory
•Liquidity premium theory
•Market segmentation theory
Broadly three school of thought are there for explaining the shape of yield curve
•Pure expectation theory
•Liquidity premium theory
•Market segmentation theory
18.Theory of Term Structure
Pure expectation theory
• The term structure at a given time only represents the current market expectations regarding the future short term rates
• If the future short rates are expected to be the same in every year as the present short rate, the present long term rate will equal the present short rate and the yield curve will horizontal.
• If short term rate are expected to rise then the expected short rate are greater than long term rate. The yield curve will upward sloping.
Pure expectation theory
• The term structure at a given time only represents the current market expectations regarding the future short term rates
• If the future short rates are expected to be the same in every year as the present short rate, the present long term rate will equal the present short rate and the yield curve will horizontal.
• If short term rate are expected to rise then the expected short rate are greater than long term rate. The yield curve will upward sloping.
19.Pure Expectation Theory
Conversely if the short term rates are expected to fall , the yield curve will be downward sloping.
Thus, whatever the shape of the yield curve , the pure expectation theory can explain it by assuming that short rates are expected to change in a particular direction.
This theory was stated by Hicks in 1939
Conversely if the short term rates are expected to fall , the yield curve will be downward sloping.
Thus, whatever the shape of the yield curve , the pure expectation theory can explain it by assuming that short rates are expected to change in a particular direction.
This theory was stated by Hicks in 1939
20.Criticism of Pure Expectations Theory
It assumes individuals expectation of future short rates is to be held with certainty, or individuals are not concerned with the risk that arises from uncertain expectations.
•It assumes that individuals hold expectations of what future short rates will be until year N
•It assumes that all lenders and borrowers have the same expectations.
•The model does not give any account of how expectations of future short rates are formed.
It assumes individuals expectation of future short rates is to be held with certainty, or individuals are not concerned with the risk that arises from uncertain expectations.
•It assumes that individuals hold expectations of what future short rates will be until year N
•It assumes that all lenders and borrowers have the same expectations.
•The model does not give any account of how expectations of future short rates are formed.
21.Liquidity premium theory
Forward rates are not unbiased predictors for markets expectations of interest rates
Risk premium is positively related to term to maturity
In other words, Liquidity premium hypothesis is that the markets adds premia Lt to yields for term-to-maturity t that would otherwise exist, with 0=L1<L2<L3<….<Ln implying that these liquidity premia are positive and rise with longer maturity.
Forward rates are not unbiased predictors for markets expectations of interest rates
Risk premium is positively related to term to maturity
In other words, Liquidity premium hypothesis is that the markets adds premia Lt to yields for term-to-maturity t that would otherwise exist, with 0=L1<L2<L3<….<Ln implying that these liquidity premia are positive and rise with longer maturity.
22.Market Segmentation Theory
It propounds that investors have preferred zones of the yield curve to which they usually confine them selves
Major reason for yield curve shapes is the Asset Liability Management Constraints of Investors and Lending Constraint of Lenders
The theory has been developed by Culbertson(1957,1965) and Conard(1959)
It propounds that investors have preferred zones of the yield curve to which they usually confine them selves
Major reason for yield curve shapes is the Asset Liability Management Constraints of Investors and Lending Constraint of Lenders
The theory has been developed by Culbertson(1957,1965) and Conard(1959)
23.Market Segmentation Theory
Market Segmentation Theory: Illustration
Short term preference
•Bank, Primary Dealers, etc
Medium Term Preferences
•Corporate Bond, Banks
Long term preference
•lnsurance company,Provident Fund etc
Market Segmentation Theory: Illustration
Short term preference
•Bank, Primary Dealers, etc
Medium Term Preferences
•Corporate Bond, Banks
Long term preference
•lnsurance company,Provident Fund etc
24.Market Segmentation Theory: Criticism
•A bank may make investment in long term securities, whereas insurance companies who trade in debt market segment invest in the short-term securities
•Investors may be willing to shift out of preferred maturity sector to take advantage of imbalances in different maturity sectors.
•A bank may make investment in long term securities, whereas insurance companies who trade in debt market segment invest in the short-term securities
•Investors may be willing to shift out of preferred maturity sector to take advantage of imbalances in different maturity sectors.
25.Shift in Yield Curves
The Yield Curve is representative of Yield to Maturity across various time periods
•There can be shift in the term structure of rates/ yields across maturities
•Broadly the shifts can be classified as
–Parallel: Shift in rates is equal across maturities
–Non Parallel : Shift in rates is not equal across maturities
The Yield Curve is representative of Yield to Maturity across various time periods
•There can be shift in the term structure of rates/ yields across maturities
•Broadly the shifts can be classified as
–Parallel: Shift in rates is equal across maturities
–Non Parallel : Shift in rates is not equal across maturities
26.Shift in Yield Curves
Non Parallel shifts could be
Twists:
Steepening
Flattening
Butterfly Shifts:
Positive
Negative
Non Parallel shifts could be
Twists:
Steepening
Flattening
Butterfly Shifts:
Positive
Negative
27.A Parallel Shift
28.Non Parallel Flattening
29.Non Parallel Steepening
30.Non Parallel Positive Butterfly
31.Non Parallel Negative Butterfly
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