sapm - bonds
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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
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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?
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CouponCoupon Value Market Price
100 at par 100
100 above par 110
100 below par 90
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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?
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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?
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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) ?
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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
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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
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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
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RISKSYSTEMATIC RISK
Risk that affects the entire marketTypes:
Market risk ( e.g.: Greek crisis, China crisis)Interest rate riskPurchasing power risk ( Inflation)
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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
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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
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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
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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
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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
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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
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