Welcome to Banking Quest

Session Coverage

• Bond Pricing
• Yield Calculation
• Tools for Market Risk Management
• Duration measure 
• Modified Duration
• Immunization 
• Convexity

INVESTMENT PORTFOLIO OF A BANK

 SLR Portfolio: 

• Government Securities (Gsecs)
• State Development Loans (SDLs)
• Treasury Bills, CMB
• Any other securities as directed by the RBI 

Non-SLR Portfolio:

• Commercial Papers
• Certificate of Deposit
• Equity / Preference Shares
• Units of Mutual Funds
• Bonds and Debentures
• Subsidiaries & Joint Ventures etc
  

Characteristic Features of a Bond

• Debt instrument which provides a fixed income in the form of periodical coupon payments irrespective of any change in the interest rate in the system/market.
• A bond is a stream of cash flows in the form of periodic coupons and the fact value at maturity (redemption).
• Price of a bond will always change with the change in market interest rate 

 Face Value

• Also known as the par value and stated on the face of the bond. It represents the amount borrowed by the firm, which it promises to repay after a specified period. Bonds are generally issued at par or the face value.

 Coupon Rate 

• A bond carries a specific rate of interest, which is also called the coupon rate. It’s actually a rate of interest liability attached to a security. In the good old days there used to be interest coupons attached or issued for interest payment and hence the word coupon. 

Maturity

• A bond is issued for a specified period. Maturity date or maturity date relate the end date on which the bond is to be repaid.

 Redemption Value

• Unlike shares, all bonds are repayable and the amount which the bondholder gets on maturity is the redemption amount which generally is the face value.

 Market Value

• This is applicable where the bonds are listed and traded on a stock exchange. The price at which such bonds are traded is the market price or value. Listing offers the bondholder an option to get money earlier but from the market and it has no impact on redemption date.

 Day count conventions

• It is a method of calculating interest earned or accrued on a bond. On Govt Sec (30/360), 
• On T Bills, Corp Bonds , CP, CD (Actuals/365) 

 Market Risks in a Bond Portfolio

 A Bond portfolio faces Market risk due to a change in the market interest rate scenario resulting  in variations in its net interest earnings or in its value.

 i) Re-pricing or Gap Risk 

• The existence of different maturity profiles of a bank’s assets and liabilities result in interest rate maturity gaps, which exposes a bank to interest rate risk. 
• Example: an asset maturing in two years at a fixed rate of interest has been funded by a liability maturing in six months

 (ii) Basis Risk : Though the maturity profiles of the assets and the liabilities of a bank are matched, the bank could still carry interest rate risk . 

• Reason of Basis Risk::  It may happen due to the Risk of the bank's assets and liabilities being priced on different bases. 

 Example: While both the assets and the liabilities could be priced for 1 year floating rates(i.e the asset pegged to  364 day T-Bill cutoff, while the liabilities could be pegged to 91 day T-Bill or 1 year CD rate.

When it will happen: 

• In a rising interest rate scenario asset interest rate may rise in different magnitude than the interest rate on corresponding liability, thus creating variation in net interest income (NII). 

 (iii) Embedded Option 

(A)No maturity Gaps/ mismatch

(B) Asset and/or the liability products carry Put/Call options in the product

(C) Reason for this Risk: 

                    (i)  If there is a Reputation Risk of the Financial Institution 

                    (ii) If there is Rating downgrade of the Financial Institution 

(iii) Systemic Risk causing premature withdrawals. 

(D) Impact : NII may be adversely affected

(E)Examples: 

(a) A depositor exercising the option of closing a deposit account when interest rates in the market are high and the bank would need to incur higher costs to replace the deposit. 

(b) Similarly, a client would repay his loan to the bank at a time when the rates in the market are lower than the ones contracted, leaving the bank to deploy funds at a lower rate.

 (iv) Net Interest Position (NIP)

• The bank’s NIM (net interest income divided by average earning assets) can vary  even if there is 
• NO maturity Mismatch/gaps 
• No Embedded Options is exercised

(1) REASON: variation in the bank’s net interest position. 

(2) Scenario: When     RSA > RSL   turns into  RSL > RSA

                 When Positive  NIP  turns into  Adverse NIP 

(3) +ve NIP : When Interest earning assets >interest bearing liabilities.

• • • • • Assumption:: Assets are funded out of shareholders’ funds and interest cost on deposits is quite low. 
        • A positive NIP adds to the bank’s net interest margin (NIM). 
        • NIM could come under pressure when its NIP position alters or falls. 

 (v) Yield Curve  Risk : 

• Re-pricing mismatches can also expose a bank to changes in the slope and shape of the yield curve. 
• Yield curve risk arises when unanticipated shifts of the yield curve have adverse effects on a bank’s income or underlying economic value. 
• Example :  the underlying economic value of a long position in 10-year government bonds hedged by a short position in 5-year government notes could decline sharply if the yield curve steepens, even if the position is hedged against parallel movements in the yield curve. 

 Parallel Yield Curve:

Rates across the maturity spectrum change by a constant amount and the slope of the  yield Curve  remains consistent.

 NON- Parallel Yield Curve:

The slope of the yield curve becomes flatter (the spread between short and long term yields narrows) or steeper (the spread between short and long term yields widens)

 BOND VALUATION and BOND DYNAMICS

Bond is a contractual obligation that pays:

1. 1. Fixed coupon at fixed intervals and
   2. Par value or principal amount at maturity

Price of a bond is therefore:

i. Present value of the future stream of cash flows

ii. Discounted by a rate that people place on their time value of money i.e. market interest rate

iii. Ideally, at the time of issue, coupon rate = market interest rate

 Bond Characteristics

 Example of a typical GOI bond

• Par Value of Rs. 100
• Coupon rate of 8% payable semiannually
• Maturity period of 12 years

Explanation::

• The holder of the bond gets Rs 100 at the end of 12 years
• An annual interest of 8%  (4% semi annually) on the face value 
• At every six months

Bond Price Formula::

• If “P” is the Bond Price, 
• ‘r’ is the current or expected interest rate , 
• “C” is periodical coupon amount and 
• “M” is the redemption amount on maturity then the bond price can be expressed as - 

Bond Price Calculations::

Example 1

• What is the price of a 12 year bond of Rs 1000 par value with an annual coupon of 8% with an expected return of 10%?
• 1. Coupon = Rs 80/- p.a.
• 2. Face Value = 1000/-
• 3. Market Yield = 10% or 10/100
• 4. Maturity = 12 years
• Price =???

Bond Price with Semi Annual Coupon Payment

• Price of Semiannual coupon paying bonds
• Annual coupon rate will be divided by two i.e.(C/2)
• number of periods will be twice the no. of years i.e. (2n)
• discount rate will be half of annual discount rate i.e.(r/2)

Bond Price calculation

• Eight year bond (FV Rs 1000/-) with 12% coupon paid semiannually. What is the price of the bond if required yield is 14% per annum
• Solution:: C=Rs 60 ;    M = Rs 1000;      r = 7%  ;    n= 16;    P=???

acealYIELD OF A BOND

• Nominal yield/Coupon rate: Stated interest rate of the bond which is paid semi-annually. Thus, a bond with a Rs 100 par value that pays 6% coupon will make 2 semi-annual payments of Rs 3 each.
• Current yield: Coupon/Current market price. Hence, if a bond trades at discount, Current yield will be higher than coupon. And if it trades at a premium, Current yield will be lower than coupon.
• Yield to Maturity (YTM): Rate of discount at which all the future cash flows of the bond are discounted to arrive at a present value (PV) which is equal to the market price of the bond. 

Current Yield

• It measures the return that a bond gives without taking into account the capital gain or loss on redemption. (If the security is bought for less than its redemption value, there is a capital gain and vice versa). 

ILLUSTRATION::

(1) Face Value= Rs 100 ;  coupon = 8% p.a.

Market Price= Rs. 105 (including accrued interest), 

The current yield = 8 *100/105= 7.62% p.a.

 (2)if the purchase price of the bond is Rs 95 (face Value =Rs 100; 

The current yield =8*100/95 = 8.42%

Yield to Maturity (YTM) OR  (IRR)
YTM::Interest rate which equates the future coupon and principal redemption  cash flows from the bond with its current market price. 

• Solving for  “r” in the formula (formula assumes 180 days coupon intervals and 360 days in a year):
• c/ (1 + r)^1 + c/(1 + r)^2 + ...... c/ (1 + r)^n + M /(1 + r)^n = Price(P) 
• Where :
• c = annual coupon payment
• n = number of years to maturity
• B = par value
• P = purchase price
• r= YTM/ Market Rate/ IRR
• Value of r can be calculated by trial & error method or through excel formula

Calculating Yield

Computation of yield requires trial and error procedure

Example: Bond with par value of Rs 1000 carrying a coupon of 9%  p.a. currently selling at Rs. 800. Maturity 8 years, What is the YTM?

• 1. Face Value =Rs 1000/-
• 2. Coupon =RS 90/- p.a.
• 3. Maturity =8 years
• 4. Price = 800/-
• What is the r(yield)?       Let us place the values in the formula

Calculating Yield when Price is given

3. Calculating for  r = 13%

 Note:: Price at (Higher Rate)14% is Rs 768.1 and at (Lower rate)13% Rs 808 

•  Apparently the value of “r” lies between (Higher rate)14% and (Lower Rate)13%
• Now the yield rate is proportionately decided as below: 
• (Higher rate)14% and (Lower Rate)13% respectively ; 
• Higher pv = Rs808  ; Lower pv 768.10 ; 
• mv = Rs800 ; 
• Lower rate +(Diff. between the two rates)*   (diff. betw. higher  pv and the  mv) 

                                                                                                        (diff betw. higher pv  and the lower pv)

 BOND    PORTFOLIO    STRATEGIES

 Immunization  Strategy   (Duration Approach)

 WHAT IS DURATION??

• Duration is the weighted-average measure of a bond’s life, where the various time periods in which the bond generates cash flows are weighted according to the relative size of the present value of those cash flows. 
• Duration is the measure of average time for receipt of the cash flows from a bond in present value terms.
• This is also the point in time in the life of the bond when the capital gain/loss is exactly countervailed by their reinvestment loss/gain. 
• Duration of coupon Bond is always less than the residual maturity.
• Duration of a Zero coupon bond is equal to the residual maturity of the bond.

Understanding Duration Approach

• If a bond is sold exactly at the point of its Duration the investor will not suffer any loss in return and his realized yield will be the same as the Expected Yield at the time of purchase of bond. 
• In other words, investment is immunized from loss if bank takes care to ensure that the investment horizon matches with the duration of his portfolio
• If the investment horizon is two years, the duration of the portfolio should be two years and as such, the nominal maturity will be higher. 

 Approach to Immunization

• Immunization has to be a continuous process, as duration changes with the change in yields as also the remaining period to maturity. 

 Let us see a Hypothetical Situation::

(1)  If the initial investment horizon is three years, the initial duration of the portfolio should be three years. 

(2) After say 6 months, investment horizon will be  2 and half years, 

(3)  but the duration of the portfolio would be different from two and half years on account of changes in the market yields and the nominal residual maturities of the bonds in the portfolio reducing by six months.

(4) The portfolio will now have to be rebalanced by buying/selling appropriate bonds such that the duration is brought to two and half years

 Limitations of Immunization Technique

• Continual rebalancing of the portfolio would entail considerable transaction cost.
• When the market is illiquid, it may not be possible to bring about the desired changes in the portfolio.

 ASSUMPTIONS INVOLVED IN DURATION:: 

• The coupon cash flows before maturity are reinvested at the IRR (YTM). 
• However, The actual (post-facto) IRR will invariably be different as the coupon reinvestment rates will not be the same as the YTM calculated today.

DURATION - An important concept for managing investment portfolio

• In all aspects of  bond valuation the underlying assumption is that the periodic interest ( Coupon)  is reinvested at the prevailing  market rate at the time of purchase .

Concept of Bond Dynamics::

• The duration of a bond is the concept arising from the fact that when the interest rate in the market increases, the market price of the bond comes down but the holder of the bond gains on the reinvestment of his periodic interest receipts and vice versa. 

How to Calculate Duration?

 Suppose the annual coupon is 8% on a G-Sec.  The face value of the  6 yr bond is 

Rs.1000 and the current YTM is 8%.

Solution:: Par Value= Rs1000 ; C= Rs 80 ; t = 6 yrs  ; y = 8%   ; D = ????

 time Ct   Pt (weights) Pt X t

1 80   74.07   74.07

2 80   68.59   137.18

3 80   63.51   190.53

4 80   58.80   235.20

5 80   54.45   272.25

6 1080 680.58         4083.48

1000.00         4992.71

 Quantitative properties of duration

• Duration of bonds with 5% yield as a function of maturity and coupon rate.

 PROPERTIES OF DURATION::

• Duration measures the interest rate sensitivity of a bond.
• The duration of a bond portfolio is the weighted average of the durations of individual bonds in the portfolio. 
• However, this will not accurately measure the interest rate change impact on the portfolio, unless the yield curve shift is entirely parallel.
• Duration is the spot measure of interest rate sensitivity. It keeps changing with YTM and time. 
• The dealer should keep on buying and selling securities such that the specified duration is maintained at the policy level at all time.
• Depending on their risk appetite , the banks’ board to decide a level within which they desire to maintain the portfolio duration
• Duration is a point of time within the maturity period and hence is always less than the maturity term of the bond. 
•  Price volatility  (Duration) of a long term bond is greater than that of a short term bond.
• The duration of a Zero Coupon bond is equal to its residual maturity. 
• Duration and YTM are inversely related;  Larger the coupon rate, smaller the duration of a bond.
• Low coupon bonds are more volatile and price sensitive to changes in market rates than high coupon bonds. 
• An increase in the frequency of coupon payments decreases the duration, while a decrease in  frequency of coupons increases it. 
• Duration of a bond declines as the bond approaches maturity.

 BOND DYNAMICS

• Value of a bond will change if there is a change in interest rate for a similar type of instrument. 
• If the interest rate goes up, the value of the bond will fall and vice versa.
• If the interest rate goes up then periodical coupons can be reinvested at higher market rates (since interest rates have gone up).
• If the interest rates move upward, the base purchase price of the bond will be lowered, which will attract more buyers in expectation of capital gains.
• More demand for the bond tends to appreciate the price of the  bond which leads to lowering of YTM of the bond.(Bond prices are inversely related to YTM or Interest rates)
• Investors will gain on pricing of  the bond but lose on reinvestment of the future coupons at higher interest rates.

Such equilibrating adjustment in bond is the crux of bond dynamics.

 Modified Duration - Concept, Uses & Calculation Method

• Modified duration measures the price sensitivity of a bond when there is a change in the yield to maturity. 
• If interest rates increase 1%, the present value of cash flows decreases about MD%.
• If duration for assets and liabilities is equal, the surplus will not be subjected to interest rate risk from the liabilities (or their supporting assets). 
• More specifically, the percentage change in price is equal to the modified duration times the change in interest rate. 
• Numerically, the Change in Price/Price = Duration/(1 + Yield) × Change in yields or 
• Percentage change in price = Modified duration × change in rates, where modified duration is given as Duration/(1 + yield).

 MODIFIED DURATION OF A BOND

• This is obtained by dividing the Duration of a bond by (1+y) where y is the YTM of the bond, expressed as a fraction.
• Thus, Modified Duration = Duration/ (1+y)

Example::

• In our earlier example the duration of the bond =4.993 and the yield rate =8%
• Modified duration = 4.993/1.08=4.6231%
•  It means with every shift in the market yield @100 bps the price of the bond will change by (+/-)4.6231%
• However, this concept is useful only in case of smaller yield changes (say upto 1%). 
• In case of higher changes in yields we have to depend on the convexity of the Bond