FinancialMarkets –BONDS

Viswajyothi School ofManagement Studies

NJ Jaissy

Objective ( Module 2)Learn of investment alternative – Bonds

Bond ValuationYTC / YTM/ Bond DurationBond Returns & PricingBond Rating, Bond Management strategies

Understand Risk : Risk – Return AnalysisSystematic & Unsystematic Risk

References: SAPM texts byPunithavathy PandianPrassana Chandra NJ Jaissy

BONDSFixed instrument – with defined ‘coupon’payments at specified intervals. (Quarterly, semi annually, annuallySold at ‘par’ value: face value of thebond is redeemed at maturityAlso have discount bonds sold below‘par’ value and redeemed at par valueat the maturity dateMarket price maybe different from par

NJ Jaissy

Bond RisksInterest rate risk: relationship betweencoupon rate and interest rate risk. Ifinterest rate goes up, price of the bonddeclines & vice versaDefault risk; role of rating agenciesMarketability riskCallability risk; the ‘call option’

NJ Jaissy

Time Value of Money1 Rs now is more valuable than 1 Rs in thefuture..Investors part with money now hoping forhigher returns in future

PV = ( 1+R) after one time periodPV = ( 1 +R)^t after ‘t’ time periods whereR is the rate of interest per period ‘t’

NJ Jaissy

Present ValueFV = PV (1+R)

Hence PV = FV / ( 1+R) after one period

PV = FV / ( 1+FV)^t after ‘t’ periods where Ris the interest rate per period

NJ Jaissy

Bond ReturnReturn = Coupon payment + Price Gain / Loss

Beginning price

a)Price in Jan = 900Price in Dec = 1000Coupon payment received = 100

b) a)Price in Jan = 900Price in Dec = 1000Coupon payment received = 100

NJ Jaissy

Interest rates & Bond pricesAssume Bond A is issued at par ( Rs 100) and with a10% coupon rate for 3 years

Two scenarios of interest rates:If interest rates go down to say 7%, your bondbecomes more valuable to investors and they startbuying it more – pushing up the bond priceIf interest rates go up to 12%, your bond loses valuefor investors and they sell it – pushing down bondprices

Hence bond prices are inversely related to interestrates

NJ Jaissy

Yield to maturityYTM is the discount rate at which the

present value of all future gains = currentmarket price of the bond

Assumes no default of any paymentsInvestor holds bond till maturityCoupon payments reinvested at the sameinterest rates as the yield to maturity ofbondYTM = coupon1/(1+y) + coupon2(1+y)^2 +(coupon n + face value) /(1+y)^n

NJ Jaissy

Current Yield

Current yield = Annual coupon paymentMarket Price

If a bond of Rs 100 par value has a couponrate of 10% and is trading at Rs 80, what isthe annual coupon payment and what isthe current yield?

NJ Jaissy

CouponCoupon Value Market Price

100 at par 100

100 above par 110

100 below par 90

NJ Jaissy

YTM: ExampleA Rs 100 par value bond bearing acoupon rate of 11% matures after 5 years.The expected yield to maturity is 15%. Thepresent market price is Rs 82. Can theinvestor buy it?

NJ Jaissy

YTM Exam questionNovex debentures have three yearsremaining to maturity. A 15 per centcoupon is paid annually on Rs 100parvalue. What is the promised YTM if thedebentures are selling at Rs 88?

NJ Jaissy

Bond TheoremsBond Pricing : Depends on

coupon rate,maturity period &yield to maturity or the required rate ofreturn

Basis this – Bond theorems have beendeveloped

NJ Jaissy

Bond Theorem - 11. As Bond market price increases, yield decreases

and vice versa:

Assume Bond A is issued at par ( Rs 100) and with a10% coupon rate for 3 years

Two scenarios of interest rates:If interest rates go down to say 7%, your bondbecomes more valuable to investors and they startbuying it more – pushing up the bond priceIf interest rates go up to 12%, your bond loses valuefor investors and they sell it – pushing down bondprices

Hence bond prices are inversely related to interestrates

NJ Jaissy

Bond Theorem - 2If the YTM or yield stays the same – the discount orpremium depends on the maturity periodHigher term to maturity means a higher discountor premiumShort term to maturity means lower discount

Bond 1 Bond 2Par value = 1000 Par value = 1000Coupon rate = 10% Coupon rate = 10%YTM 15% YTM 15%

Maturity period = 5 yrs Maturity = 4 yrsIf Price = 900 Price =(< 900 or >900) ?

NJ Jaissy

Bond Theorem - 3For a given Yield, the bond reaches its ‘face value’or par value as the bond approaches maturity ORFor a given yield, the discount or premium amountwill decease at an increasing rate as the life getsshorter

Maturity dateYears

Price Premium

Discount

NJ Jaissy

Bond Theorem 4An increase in the bond price for a fall in

the bonds’ yield is greater than the fall inthe bonds price for a raise in the yield

Yield to maturity

Price Concept of Convexity

NJ Jaissy

Bond Theorem 5If the coupon rate is higher, then thechange in bond price for a % change inyield is lower ie Price – Bond yieldsensitivity is lower the higher the couponrate

NJ Jaissy

RISKSYSTEMATIC RISK

Risk that affects the entire marketTypes:

Market risk ( e.g.: Greek crisis, China crisis)Interest rate riskPurchasing power risk ( Inflation)

NJ Jaissy

RISKUNSYSTEMATIC RISK

Risk that affects a particular company orindustryTypes:

Business RiskInternal ( Factors affecting the business – sales,people costs, products etc)External ( Regulations, Social / Environmental norms,political, business cycle)

Financial Risk ( if the company is highly leveraged,net profits available for shareholders decreases)

Investor needs to take steps to protect himselffrom these risks. ( How?)

NJ Jaissy

RISKS associated with BondsSystematic Risk:

Purchasing Power RiskAnnual % change in price or the change in thecost of living ( Inflation can ‘reduce’ the effectivevalue of bond returns

Interest Rate RiskRising Interest rates can drive down Bond Pricesreducing the effective bond returns to theinvestor. This can be further broken down into:

Price RiskReinvestment Risk

NJ Jaissy

Volatility: Changes in BondPrice ( Price Risk)

With same % change in yield, Volatility ofthe price of Bond increases :

a) As the maturity lengthens ( highermaturity, higher price volatility)

b) As the coupon rate declines ( lowercoupon rate, higher the price volatility)

c) As the yields increase ( higher the yieldlevel at which a fluctuation starts, highervolatility)

BONDS - SYSTEMATIC RISK

NJ Jaissy

Interest Rate Risk:As interest rates fall, Coupon paymentscannot be reinvested at the proposedyield to maturity

If interest rates fall, the coupon paymentswill be reinvested at a lower rate therebydecreasing the effective ‘yield tomaturity’.

BONDS - SYSTEMATIC RISK

NJ Jaissy

BOND: UNSYSTEMATIC RISKBUSINESS & FINANCIAL RISK

Default Risk : This is addressed by assessing the creditworthiness of the bonds – via CREDIT RATING ( S&P (Standard & Poor), Moodys etc.)

Factors in the Bond Rating process:a) Assess the ‘covenants’ / indentures in place to

protect the bond investorb) Assess the company & industry ( Using financial

ratios & Porters Competitive framework (industry)c) Assess the collateral available ( usually done

with weaker companies)

BONDS - UNSYSTEMATIC RISK

NJ Jaissy

Covenants / IndenturesThese are clauses states the rights andobligations between the lender & theborrower. Examples:

A clause might be a limitation on thecreation of additional debtRestriction on sale & lease of assets

Factors in Bond Rating

NJ Jaissy

Assessing Earnings powerEarnings power to be assessed:

Assess the industry ( Use Porter’s competitiveframework) Entry barriers – threat of newentrants, Is there a Monopoly of either asupplier & customer, substitution riskAssess using ratios:

Free Cash flow ratios ( Free cash flow: Interest)Leverage ratios ( Debt :Capital)Earnings cover ratios ( EBDIT / Interest)

Assess the management of the company &their strategy

Factors in Bond Rating

NJ Jaissy

Other factors affecting Yield:Marketability ( or liquidity of the Bond)

The call featureThe issuer sometimes puts in a ‘call’ featuregiving the issuer the right to redeem the bondbefore maturity

Tax factors : In India, infrastructure bondshave tax benefits making them moreattractive

NJ Jaissy

Duration of a BondDuration is a measure of the ‘weightedaverage life of the bond – factoring in thesize and time of each cash flow.Weight assigned to each time period is thepresent value of the cash flow paid at thattime as a proportion of the price of thebondWhen calculating PV, YTM is taken as thediscount rate

NJ Jaissy

Duration of a bondDuration = (PVC1*1 + PVC2 *2 +..PVCn*n)/V0

Where PVC1 =PV of the cash flow receivable atthe end of Yr 1V0 = Current value of the bond

Duration of a bond = length of time that elapsesbefore receiving the average Rupee of Presentvalue from the bond

NJ Jaissy

Duration: Bond AFace Value = Rs 100Coupon ( interest rate) = 15% p.aYears to maturity = 6Redemption value = Rs 100Current market price = 89.5Yield to Maturity = 18%

Compute the duration of the bond:

NJ Jaissy

Modified DurationDuration can be used to measure sensitivity with respectto interest rate changesModified Duration D* = Duration / (1+y)

(Note: What is the modified Duration in previous example?)

For small changes in yield, the price change isproportional to modified duration:

Delta P/ P = - D*x Delta YWhere Delta P/P = price change %Delta Y = yield change

(Note: In previous example – what is the price change for a0.2% change ( 20 basis points) in Yield?) NJ Jaissy

Bond Management Strategies:Passive Strategy : Buy and hold

Ie: Spend time to evaluate & choose good qualitybonds and then stay with the portfolio; do not keepchanging bonds to improve returns or reduce risk.Indexing strategy: Buy bonds that mirror a Bond indexActive Strategy: Buy & sell bonds factoring in bondprice movements:

If interest rate is expected to fall, Bonds are bought forthe long term ( factoring in price appreciation)If interest rate is expected to rise, bonds are avoided

Hybrid strategy: Immunization – balancing outdecline in price with increase in reinvestment rate

NJ Jaissy

Active Strategy:Forecasting Interest rate movements

Various models have been developed; somelink interest rate to inflation rate ( one of the keymovers of interest rate).These models maybe simple but not helpful inshort term as inflation rates not easy to predictSome models use past interest rate movementsto predict future movementsOther models factor in various sectors in theeconomy – looking at demands & sources offunds in the economy from all sources

NJ Jaissy

Bond ImmunizationWhen Yield Bond Price

And when Yield Bond Price

If the decrease in yield can be set off by theincrease in Bond price – then there is no ‘loss’ ofBond returns during the investment period. Thisprocess is called “Immunization”

This is accomplished if the investment period =Duration

NJ Jaissy

Problem Set-11. A Rs 100 par value bond bearing a

coupon rate of 12 % will mature after 5years. What is the value of the bond ifthe discount rate is 15%

Rs 89.92

NJ Jaissy

Problem Set-12. The market value of Rs 1000 par value

bond, carrying a coupon rate of 14%and maturing after 5 years is Rs 1050.What is the yield to maturity on thisbond?

12.6%

NJ Jaissy

Problem set -13. A Rs 100 par value bond bears a coupon

rate of 14% and matures after 5 years.Interest is payable semi-annually.Compute the value of the bond if therequired rate of return is 16%.

Rs 93.27

NJ Jaissy