Fixed Income Report.docx

Topic: Fixed Income Index

Sr. No.

Title

Page No.

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Primary and Secondary Debt market

2

2

Types of fixed income securities

2

3

Types of return

4

4

Terms related to Bond

6

5

Types of bonds

8

6

What are Credit spreads?

9

7

Term structure of interest rates

10

8

Duration

13

9

Convexity

14

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Primary and Secondary Debt Markets Primary Market The primary markets deal with the trading of newly issued securities. Entities in Primary market: 

Issuer/borrower: Governments and companies that issue securities when they want to raise money



Investors/lenders: Buyers (retail or qualified) who purchase the bonds

In the primary market, newly issued securities can be sold to public through a public offering or sold only to qualified investors through a private placement. Secondary Market The secondary market refers to the trading of previously issued bonds. The bonds issued in primary markets are then traded in the secondary market. Bond trades are cleared through a clearing system, just as equity trades are. Settlement for government bonds is either the day of trade or next business day (T+1). Corporate bonds typically settle on T+2 or T+3.

Types of Fixed Income Securities Bonds The most common type of fixed income securities are bonds. The borrower, or issuer of bond, promises to pay interest, called the coupon, on an annual or semi-annual basis until a set date. The issuer returns the principal amount, also called the face or par value, to the investor on the maturity date. Bonds may be issued at par, premium and discount depending on its coupon and YTM. Government Securities G-Sec is a tradeable instrument issued by the Central Government or the State Governments. Such securities are short term (usually called treasury bills, with original maturities of less than one year) or long term (usually called Government bonds or dated securities with original 2

maturity of one year or more). It is a way in which the government raises funds through its banker i.e. RBI. G-Secs are issued through auctions conducted by RBI. Commercial Banks, Insurance Companies, Mutual Funds, Provident Funds, etc can buy G-Sec from the auction. Treasury Bills Treasury bills (T-bills) are money market instruments, i.e., short-term debt instruments issued by the Government of India, and are issued in three tenors—91 days, 182 days, and 364 days. The T-bills are zero coupon securities and pay no interest. They are issued at a discount and are redeemed at face value on maturity. New issues of T-Bills can be purchased at auctions through a bidding process held by the government. Previously issued ones can be bought on the secondary market. Certificate of Deposit It is a negotiable money market instrument that can be issued by scheduled commercial banks and some other financial institutions (as permitted by RBI) against funds deposited by investors for a specified time period. CDs can be issued to individuals, corporations, companies (including banks), trusts, funds, associations, etc. The minimum deposit that could be accepted from a single subscriber should not be less than Rs.1 lakh, and in multiples of Rs. 1 lakh thereafter. The maturity period of CDs issued by banks should be 7 days to 1 year. Commercial Paper Commercial paper is an unsecured, short-term debt instrument issued by a corporation. Firms use commercial paper to fund working capital and as a temporary source of fund prior to issuing longer term debt. Only those companies that fulfill Net worth and Credit rating requirement prescribed by RBI are eligible to issue CPs. CPs can be issued for maturities between a minimum of 7 days and maximum of 1 year and in denominations of Rs.5 lakh or multiples thereof. Individuals, banking companies, other corporate bodies, Non-Resident Indians (NRIs) and Foreign Institutional Investors (FIIs) etc. can invest in CPs.

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Types of return 1. Holding Period Return (HPR) Holding period return is the total return received from holding an asset or portfolio of assets over a period of time, generally expressed as a percentage. It takes into account both current return (eg. Interest or coupon payment) and capital return (capital appreciation) on an investment. It is particularly useful for comparing returns between investments held for different periods of time. HPR = Coupon + (Maturity Value – Purchase Price) Purchase Price Example: A bond with a face value of Rs. 1000 is issued at Rs. 900. Coupon payable on the bond is 5%. HPR = 50+ (1000-900)/900 = 16.66% 2. Simple Annualized Returns This measure helps to annualize the return when holding period is less than a year. Therefore, it helps in comparing the returns on investments with different maturities. Here’s how to calculate it:

((1+ HPR)^(365/no. of days))-1

Example: An investment of Rs. 1000 has grown to Rs. 1250 in 210 days. The HPR in this case is 25% over 210 days. Simple Annualized return = ((1+0.25)^(365/210))-1 = 47.38%

3. CAGR The compound annual growth rate (CAGR) is the mean annual growth rate of an investment over a specified period of time longer than one year. CAGR takes into account the effect of compounding of returns. 4

This can be written as follows:

Example: You invested Rs. 1000 in a fund for 5 years. The end value of investment at the end of each year is given below Year

Value

1

750

2

1000

3

3000

4

4000

5

4500

Here, CAGR = (4500/1000)^1/5 – 1 = 35.09% 4. Time-Weighted Rate of Return It eliminates the distorting effects created by inflow and outflow of money caused by interim investments and redemptions. To compute TWRR for any period, calculate the returns for every sub-period before any contribution or withdrawal occur and then geometrically link these subperiod

returns

together

to

compute

the

return

over

the

period.

The time-weighted rate of return of an investment can be calculated using the following formula, where: 

N = Number of sub-periods



HPR = (End Value - Initial Value + Cash Flow) / (Initial Value + Cash Flow)



HPRN = Return for sub-period N

Time-Weighted Rate of Return = [(1 + HPR1) * (1 + HPR2)... * (1 + HPRN)] – 1

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Example: X invested Rs. 1000 on 1st January into a debt fund. Three months later the value of this investment rises to Rs. 1100. Thereafter he invests another Rs. 1000 in the fund. At the end of 6 months the value of investment is Rs. 2300. To calculate TWRR we need to break the calculation into 2 sub periods. Period 1 = ($1,100-$1,000)/$1,000 = 10% Period 2 = ($2,300-$2,100)/$2,100 = 9.5% TWRR = [(1+0.10)(1+0.095)]-1= 20.45%

Terms related to Bond 

Par value or Face Value Par value is the face value of a bond. Par value is important for a bond or fixed-income instrument because it determines its maturity value as well as the value of coupon payments.



Yield When investors buy bonds, they essentially lend bond issuers money. In return, bond issuers agree to pay investors interest on bonds throughout their lifetime and to repay the face value of bonds upon maturity. The money that investors earn is called yield. Investors do not have to hold bonds to maturity. Instead, they may sell them for a higher or lower price to other investors, and if an investor makes money on the sale of a bond, that is also part of its yield.



Coupon Bonds typically pay interest periodically at the pre specified rate of interest. The annual rate at which the interest is paid is known as the coupon rate. The dates on which the interest payments are made are known as the coupon due dates.



Maturity

6

The maturity of a bond is the length of time until the bond comes due and the bondholder receives the par value of the bond. 

Accrued interest This is the interest that has been earned by an investor but not become due for payment to the investor. Bond buyers pay bond sellers accrued interest whenever a bond is purchased between its interest payment dates.



Frequency The interest in bonds can be paid monthly, quarterly, half-yearly or yearly. This frequency of interest payments is specified at the time of issue of the debt instrument.



Dirty

price

The price of a bond is calculated by discounting all future cash flows. The concept of "dirty" price is relevant for bond prices in the secondary market as they are not always traded on the coupon payment date and hence the seller needs to be compensated for the number of days he/she has held the bond in between coupon payments. For example, let's consider a bond pays interest semi-annually and the payment dates are June 30 and December 31; if it gets sold on, say, March 21, then the seller would have forgone the coupon payment due on June 30. The "dirty" price of the bond includes the interest due but not paid up to March 31. 

Clean Price Clean price is the price of a coupon bond not including any accrued interest. A clean price is the discounted future cash flows, not including any interest accruing on the next coupon payment date. The clean price is calculated as Clean Price = Dirty Price - Accrued Interest 

Current Yield

It is a measure to calculate yield on bond. But it looks at just one source of return: a bond’s annual interest income. It does not consider capital gains or losses or reinvestment income. Current yield = Annual cash coupon payment/Bond Price

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Types of bonds Municipal bonds These are issued by states or cities to finance its capital expenditure. Say your city corporation wants to set up a new Metro rail network. It can issue municipal bonds to fund the project. Institutional investors as well as the public can buy these bonds. Revenues from the Metro will then be used to repay the interest and principal on these bonds. Such bonds where the cash flow from a particular project is used to repay the interest obligation are Revenue bonds. But Municipal bonds are not so popular in India. Corporate bonds These are issued by private and public corporations. Corporate bonds are characterized by higher yields because there is a higher risk of a company defaulting than a government. The upside is that they can also be the most rewarding fixed-income investments because of the risk the investor must take on. The company's credit quality is very important: the higher the quality, the

lower

the

interest

rate

the

investor

receives.

Zero coupon bonds Zero coupon bonds are issued at deep discount and does not pay any amount before maturity date. On the maturity date, investors are paid the par value. The difference between the par value and the price at which the bond is issued is the return of investors. Callable bond It gives the issuer the right to redeem all or part of a bond issue at a specific price (call price) if they choose to. A call option has value to the issuer because it gives the issuer the right to redeem the bond and issue a new one if the market yield on the bond declines. This could occur either because interest rates in general have decreased or because the credit quality on the bond has increased (default risk has decreased). Putable bond A put option gives the bondholder the right to sell the bond back to the issuing company at a prespecified price, typically at par. Bondholders are likely to exercise such an option when the fair value of the bond is less than the put price because interest rates have risen or the credit quality of the issuer has fallen. A putable bond sells at a higher price (lower yield) compared to an otherwise identical option free bond. Perpetual bonds 8

A perpetual bond is a fixed income security with no maturity date which means that these bonds are not redeemable. They pay periodic interest forever. Since investors do not get their principal back, as compensation the coupon on these bonds is higher. Most perpetual bonds have a call option embedded in it. Example, the perpetual bonds that were issued by the UK government in 1917 to finance WW1 were called back by the government in 2017. Convertible bond Convertible bonds, typically issued with maturities of 5-10 years, give bondholders the option to exchange the bond for a specific number of shares of the issuing company’s common stock. Because the conversion option is valuable to bondholders, these bonds can be issued with lower yields compared to otherwise identical straight bonds. Essentially, the owner of this bond has downside protection (compared to equity) of a bond, but at a reduced yield, and the upside opportunity of equity shares.

What are Credit spreads? A Credit spread is the yield spread. It refers to the difference in the interest rates between a corporate bond and a comparable government bond. The credit spread is a measure to compare the creditworthiness of different borrowers in the capital markets. Suppose interest rate on a fiveyear corporate bond is 6% and that on a similar five-year Government bond is 5%. This means that the interest on a corporate bond consists of risk-free rate of 5% plus a credit spread of 1%. Credit spreads narrow as the economy strengthens and investors expect firm’s credit metrics to improve. Conversely, spreads widen as economy weakens. Yield spreads are useful for analyzing factors that affect bond yields. If a bond’s yield increases but yield spread remains the same, the yield on its benchmark must have increased which suggests macro factors caused bond yields to increase in general. However, if yield spread increases, it suggests increase in bond’s yield was caused by micro factors such as credit risk or issue’s liquidity.

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Term structure of interest rates The term structure of interest rates, also called the yield curve, is a graph that plots the yields of similar-quality bonds against their maturities, from shortest to longest. The yield curve represents the changes in interest rates associated with a particular security based on length of time until maturity. It enables investors to quickly compare the yields offered on short-term, medium-term and long-term bonds. The term structure of interest rates takes five primary shapes:

1. Normal Yield Curve If short-term yields are lower than long-term yields, the curve slopes upwards and the curve is called a positive (or "normal") yield curve. This yield curve is considered "normal" because the market

usually

expects

more

compensation

for

greater

risk.

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2. Inverted Yield Curve If short-term yields are higher than long-term yields, the curve slopes downwards and the curve is called a negative (or "inverted") yield curve. Inverted yield curves present a point where shortterm

rates

are

more

favorable

than

long-term

rates.

3. Flat Yield Curve A flat term structure of interest rates exists when there is little or no variation between short and long-term rates of bonds with same credit quality. This type of yield curve is often seen during transitions

between

normal

and

inverted

curves.

4. Steep Yield curve:

A steep curve indicates that the long-term yields are rising at a faster rate than short-term yields. Steep yield curves have historically indicated the start of an expansionary economic period. Both the normal and steep curves are based on the same properties but the only difference is that a steeper curve has a larger difference between short term and long term return expectations. 11

5. Humped Yield Curve: A humped yield curve is when medium-term yields are greater than both the short-term yields and long-term yields. A humped yield curve is rare and typically indicates a slowing of economic growth. The Humped Yield Curve is quite rare and rarely occurs.

In general, when the term structure of interest rates is positive, this indicates that investors desire a higher rate of return for taking the increased risk of lending their money for a longer time period. Many economists also believe that a steep positive curve means that investors expect strong future economic growth with higher future inflation (and thus higher interest rates), and that a sharply inverted curve means that investors expect sluggish economic growth with lower future inflation (and thus lower interest rates). A flat curve generally indicates that investors are unsure about future economic growth and inflation.

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Duration Duration is used as a measure of bond’s interest rate risk or sensitivity of a bond’s price change to a change in its yield. It is calculated as the weighted average of the number of years until each of the bond’s promised cash flows is to be paid, where the weights are the present values of each cash flow as a percentage of bond’s full value. Example: Find the duration of a 6-year bond with FV= Rs. 500, yield = 8% and paying a coupon of 5% annually. Period

Cash Flows

Discount

Factor DF x Cash /flows

(DF)

(A)

(A) X Period

1

25

1/(1.1)^1 = 0.909

22.72

22.73

2

25

1/(1.1)^2 = 0.826

20.65

41.32

3

25

1/(1.1)^3 = 0.751

18.775

56.35

4

25

1/(1.1)^4 = 0.683

17.075

68.3

5

25

1/(1.1)^5 = 0.621

15.525

77.62

6

525

1/(1.1)^6 = 0.5644

296.31

1778.09 Sum = 2044.41

Duration = 2044.41/FV of bond = 2044.41/500 Duration = 4.08 years

Modified Duration Modified duration provides an approximate % change in a bond’s price for a 1% change in YTM. It is calculated as Modified duration = Duration (1+YTM) For the above example, modified duration = 4.08/(1+0.08) = 3.78 years

The price change for a given change in YTM can be calculated as: Approximate % change in bond price = -ModDur x ∆YTM

Based on ModDur of 3.78, the price of bond should fall by approximately 3.78*0.1%=0.378% in response to 0.1% change in YTM.

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Effective Duration We can effective duration directly using bond values for an increase in YTM and for a decrease in YTM of the same size. The calculation is based on a given change in YTM. Effective Duration = (V_- V+)/(2*Vo*∆YTM) V_ is price of bond if YTM is decreased by ∆YTM and V+ is price of bond if YTM is increased by ∆YTM. The formula uses average of the magnitudes of price increase and decrease, which is why numerator is divided by 2. Example: For a 3 year, 4% annual pay bond currently trading at par, calculate the effective duration based on a change in yield of 25 basis points.

Price of bond at yield of 4%+0.25%: Period

Cash Flow

Present Value

1

4%*1000 = 40

40/(1+4.25%)^1 = 38.36

2

40

40/(1+4.25%)^2 = 36.805

3

1040

40/(1+4.25%)^3 = 917.92 Sum = 993.09

Similarly, price of bond at yield of 4%-0.25% = Rs. 1006.97 Effective Duration = (1006.97-993.09)/(2*1000*0.25%) = 2.77 Approximate change in price for a 1% change in YTM is 2.77%.

Convexity Modified duration is a linear estimate of relation between a bond’s price and YTM, whereas the actual relation is convex, not linear. This means that modified duration provides good estimates of bond prices for small changes in yield, but increasingly poor estimates for larger changes in yield as the effect of curvature of price yield curve is more pronounced. Therefore, the duration based estimates of a bond’s price for a given change in YTM will be different from actual prices. The price estimates can be improved by using convexity which is a measure of curvature of price-yield relation. Convexity is increased or decreased by the same bond characteristics that affect duration. A longer maturity, lower coupon rate, or lower YTM will increase convexity. 14

Convexity = (V_+ V+ - 2Vo)/(2*Vo*∆YTM2) Example: FV = Rs. 2000, Tenure = 40 years, Coupon = 10%, Yield = 10%, %∆YTM = 1% YTM

Price of Bond (actual)

Change in price

9%

2215.15

+215.15

10%

2000

11%

1820.98

-179.02

As can be observed 1% change in YTM leads to uneven change in price. This is convexity. Convexity = [2215.15+1820.98-2*2000]/[2*2000*(0.01)2] = 90.32

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