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Chapter 13 BOND PORTFOLIO MANAGEMENT The Passive and Active Stances

Chapter 13 BOND PORTFOLIO MANAGEMENT The Passive and Active Stances. OUTLINE Interest Rate Sensitivity Duration Convexity Passive Strategies Immunisation : A Hybrid Strategy Active Strategies Interest Rate Swaps. PASSIVE VERSUS ACTIVE STRATEGY

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Chapter 13 BOND PORTFOLIO MANAGEMENT The Passive and Active Stances

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  1. Chapter 13 BOND PORTFOLIO MANAGEMENT The Passive and Active Stances

  2. OUTLINE • Interest Rate Sensitivity • Duration • Convexity • Passive Strategies • Immunisation : A Hybrid Strategy • Active Strategies • Interest Rate Swaps

  3. PASSIVE VERSUS ACTIVE STRATEGY • A PASSIVE STRATEGY SEEKS TO MAINTAIN AN • APPROPRIATE BALANCE BETWEEN RISK AND • RETURN. • AN ACTIVE STRATEGY STRIVES TO ACHIEVE • RETURNS THAT ARE MORE THAN • COMMENSURATE WITH THE RISK EXPOSURE

  4. INTEREST RATE SENSITIVITY 1. THERE IS AN INVERSE RELATIONSHIP BETWEEN BOND PRICES AND YIELDS. 2. AN INCREASE IN YIELD CAUSES A PROPORTIONATELY SMALLER PRICE CHANGE THAN A DECREASE IN YIELD OF THE SAME MAGNITUDE. 3. PRICES OF LONG-TERM BONDS ARE MORE SENSITIVE TO INTEREST RATE CHANGES THAN PRICES OF SHORT-TERM BONDS. 4. AS MATURITY INCREASES, INTEREST RATE RISK INCREASES BUT AT A DECREASING RATE. 5. PRICES OF LOW-COUPON BONDS ARE MORE SENSITIVE TO INTEREST RATE CHANGES THAN PRICES OF HIGH-COUPON BONDS. 6. BOND PRICES ARE MORE SENSITIVE TO YIELD CHANGES WHEN THE BOND IS INITIALLY SELLING AT A LOWER YIELD.

  5. RELATIONSHIP BETWEEN CHANGE IN YIELD TO MATURITY AND CHANGE IN BOND PRICE

  6. DURATION - 1 DURATION IS A MEASURE OF THE AVERAGE LIFE OF A DEBT INSTRUMENT. IT IS DEFINED AS THE WEIGHTED AVERAGE TIME TO FULL RECOVERY OF PRINCIPAL AND INTEREST PAYMENTS.USING ANNUAL COMPOUNDING WE CAN DEFINE DURATION (D) AS:n Ct x t t=1 (1+r)tD =n Ct t=1 (1+r)tt = TIME PERIOD IN WHICH THE COUPON / PRINCIPAL PAYMENT OCCURSCt = INTEREST & / OR PRINCIPAL … tr = MARKET YIELD ON THE BOND

  7. DURATION - 2 TO ILLUSTRATE HOW DURATION IS CALCULATED CONSIDER BOND A. BOND AFACE VALUE RS 100COUPON (INTEREST RATE) 15 PERCNET PAYABLE ANNUALLYYEARS TO MATURITY 6REDEMPTION VALUE RS 100CURRENT MARKET PRICE RS 89.50YIELD TO MATURITY 18 PERCENT CALCULATION OF DURATION

  8. DURATION AND VOLATILITY – 1 D* = D/(1+y) D* = modified duration D = duration y = the bond’s yield to maturity P/P  – D*y Percentage price  Modified Change in yield change duration in decimal form Example D* = 3.608 y = 0.2 percent P/P  – 3.608 x 0.2 = – 0.722 percent — X

  9. PROPERTIES OF DURATION –1 1. THE DURATION OF A ZERO COUPON BOND IS THE SAME AS ITS MATURITY. 2. FOR A GIVEN MATURITY, A BOND’S DURATION IS HIGHER WHEN ITS COUPON RATE IS LOWER. 3. FOR A GIVEN COUPON RATE, A BOND’S DURATION GENERALLY INCREASES WITH MATURITY. 4. OTHER THINGS BEING EQUAL, THE DURATION OF A COUPON BOND VARIES INVERSELY WITH ITS YIELD TO MATURITY. 5. THE DURATION OF A LEVEL PERPETUITY IS: (1 + YIELD) / YIELD

  10. PROPERTIES OF DURATION 6. THE DURATION OF A LEVEL ANNUITY APPROXIMATELY IS: 1 + YIELD NUMBER OF PAYMENTS - YIELD (1 + YIELD) NUMBER OF PAYMENTS -1FOR EXAMPLE, A 15 YEAR ANNUAL ANNUITY WITH A YIELD OF 10 PERCENT WILL HAVE A DURATION OF: 1.10 15 = = 6.28 YEARS 0.10 1.1015 - 1 7. THE DURATION OF A COUPON BOND APPROXIMATELY IS: 1 + y (1 + y) + T (c - y) -yc [(1 + y)T - 1] + y WHERE y IS THE BOND’S YIELD PER PAYMENT PERIOD, T IS THE NUMBER OF PAYMENT PERIODS, AND c IS THE COUPON RATE PER PAYMENT PERIOD.

  11. DURATION OF A COUPON BOND 1 + y (1 + y) + T (c - y) -yc [(1 + y)T- 1] + y C : COUPON RATE PER PAYMENT PERIODT : NUMBER OF PAYMENT PERIODSy : BOND’S YIELD PER PAYMENT PERIOD 14% COUPON BOND, 8 YRS MATURITY, PAYING COUPONS SEMI-ANNUALLY YTM = 8 PERCENT PER HALF-YEAR PERIOD 1.08 (1.08) + 16(.07 - .08) - .08 .07 [)1.08)16 - 1) + .08 = 9.817 HALF-YEARS = 4.909 YRS NOTE : MAINTAIN CONSISTENCY .. TIME UNITS OF PAY’T PERIOD & INT. RATE

  12. CONVEXITY • IF THE DURATION RULE WERE AN EXACT RULE, THE PERCENTAGE CHANGE IN PRICE WOULD BE LINEARLY RELATED TO THE CHANGE IN YIELD. YET WE KNOW FROM THE BOND-PRICING RELATIONSHIPS DISCUSSED EARLIER THAT THE ACTUAL RELATIONSHIP IS CURVILINEAR. • THE DURATION RULE PROVIDES AN APPROXIMATION WHICH IS FAIRLY CLOSE, FOR SMALL CHANGES IN YIELD. HOWEVER, AS THE YIELD CHANGE BECOMES LARGER, THE APPROXIMATION BECOMES POORER.

  13. CONVEXITY 20-YEAR MATURITY, 9 PERCENT COUPON BOND, SELLING AT AN INITIAL MATURITY OF 9 PERCENT. MODIFIED DURATION IS 9.95 YEARS. THE FOLLOWING EXHIBIT SHOWS THE STRAIGHT LINE PLOT OF -D*y = - 9.95 x y AS WELL AS THE CURVED LINE REFLECTING THE ACTUAL RELATIONSHIP BETWEEN YIELD CHANGE AND PRICE CHANGE

  14. CONVEXITY • THE TRUE PRICE-YIELD RELATIONSHIP IS CONVEX, MEANING THAT IT OPENS UPWARD. • CLEARLY, CONVEXITY IS A DESIRABLE FEATURE IN BONDS. PRICES OF BONDS WITH GREATER CONVEXITY (CURVATURE) INCREASE MORE WHEN YIELDS FALL AND DECLINE LESS WHEN YIELDS RISE. • SINCE CONVEXITY IS A DESIRABLE FEATURE, IT DOES NOT COME FREE. INVESTORS HAVE TO PAY FOR IT IN SOME WAY OR THE OTHER.

  15. PASSIVE STRATEGIES TWO COMMONLY FOLLOWED STRATEGIES BY PASSIVE BOND INVESTORS ARE: BUY AND HOLD STRATEGY AND INDEXING STRATEGY. A BUY AND HOLD STRATEGY SELECTS A BOND PORTFOLIO AND STAYS WITH IT AN INDEXING STRATEGY CALLS FOR BUILDING A PORTFOLIO THAT MIRRORS A WELL-KNOWN BOND INDEX

  16. DURATION AND IMMUNISATION - 1 CAPITAL VALUE INTEREST RATE RETURN ON RE- INVESTMENT OF INTEREST CAPITAL VALUE INTEREST RATE RETURN ON RE- INVESTMENT OF INTEREST FOR IMMUNISATION SET DURATION EQUAL TO INVESTMENT HORIZON

  17. DURATION AND IMMUNISATION - 2 • MAY BE DEFINED . . PROCESS … FIXED INCOME PORTFOLIO IS CREATED HAVING . . AN ASSURED RETURN FOR A SPECIFIED TIME HORIZON IRRESPECTIVE OF INTEREST RATE CHANGE. MORE CONCISELY, THE FOLLOWING ARE IMPORTANT CHARACTERISTICS • SPECIFIC TIME HORIZON • ASSURED RATE OF RETURN • INSULATION FROM THE EFFECTS OF POTENTIAL ADVERSE INTEREST RATE CHANGE ON PORTFOLIO VALUE • CAPITAL CHANGES • BALANCE • INVESTMENT RETURN

  18. ILLUSTRATION AN INVESTOR WHO HAS A FOUR-YEAR INVESTMENT HORIZON WANTS TO INVEST RS.1,000 SO THAT HIS INITIAL INVESTMENT ALONG WITH REINVESTMENT OF INTEREST GROWS TO RS.1607.5. THIS MEANS THAT THE INVESTOR WANTS HIS INVESTMENT TO EARN A COMPOUND RETURN OF 12.6 PERCENT [1,000 (1.126)4 = 1,607.5 THE INVESTOR IS EVALUATING TWO BONDS, A & B Bond A Bond B Par value Rs.1,000 Rs.1,000 Market price Rs.1,000 Rs.1,000 Coupon rate 12.6% 12.6% Yield to maturity 12.6% 12.6% Maturity period 4 years 5 years Duration Less than 4 years 4 years Rating A A EXHIBIT 13.4 SHOWS WHAT HAPPENS WHEN THE INVESTOR BUYS BOND A AND BOND B UNDER DIFFERENT ASSUMPTIONS ABOUT MARKET YIELD

  19. TERMINAL VALUE WITH BONDS A AND B contd

  20. TERMINAL VALUE WITH BONDS A AND B

  21. CASH FLOW MATCHING CASH FLOW MATCHING INVOLVES BUYING A ZERO COUPON BOND THAT PROMISES A PAYMENT THAT EXACTLY MATCHES THE PROJECTED CASH REQUIREMENT. IT AUTOMATICALLY IMMUNISES A PORTFOLIO FROM INTEREST RATE RISK BECAUSE THE CASH FLOW FROM THE BOND OFFSETS THE FUTURE OBLIGATION. A DEDICATION STRATEGY INVOLVES MATCHING CASH FLOWS ON A MULTIPERIOD BASES.

  22. ACTIVE STRATEGIES • HENRY KAUFMAN, A RENOWNED BOND EXPERT, • ARGUES THAT “BONDS ARE BOUGHT FOR • THEIR PRICE APPRECIATION POTENTIAL AND • NOT FOR INCOME PROTECTION” • MANY BOND INVESTORS SUBSCRIBE TO THIS • VIEW AND PURSUE ACTIVE STRATEGIES. THEY • SEEK TO PROFIT BY: • FORECASTING INTEREST RATE CHANGES • AND/OR • EXPLOITING RELATIVE MISPRICINGS • AMONG BONDS.

  23. INTEREST RATAE FORECASTING - 1 IRF1  MODELS BASED UPON FORECASTING EXPECTED INFLATION EXPECTED INFL’N .. KEY DETERMINANT SOLID EVIDENCE .. LINK+S  RELATIVELY SIMPLE APPROACH-S  MAY NOT HELP IN SHORT TERM FORECASTING EXPECTED INFL’N .. NOT EASY .. PREDICT  MODELS THAT FORECAST INTEREST RATES BASED UPON PAST INTEREST RATE CHANGES THESE MODELS EMPHASIZE THE TIME SERIES BEHAVIOR OF INTEREST RATES & USE DISTRIBUTED LAGS OF PAST INTEREST RATES IN PREDICTING FUTURE INT. RATES + SIMPLE .. INFOR’N AVAILABLES- SHIFTS .. FUNDAMENTAL FACTORS … BREAK IN TRENDS

  24. INTEREST RATE FORECASTING - 2 MODELS THAT ASSUME THAT INTEREST RATES MOVE IN A NORMAL RANGE (WHICH IS KNOWN) MEAN REVERSION+ IF THE NORMAL RANGE .. KNOWN … SIMPLE TO BUILD … ONLY SPEED ADJUSTT FACTOR - THE NORMAL RANGE .. MAY SHIFT OVER TIME IF FUNDAMENTAL VARIABLES (LIKE INTEREST RATE SHIFT)  COMPREHENSIVE MULTI - SECTOR MODELS OF THE ECONOMY THAT ATTEMPT TO PREDICT INTEREST RATES MODEL ALL FLOWS .. ECONOMY S & D OF FUNDS IMBALANCE INT. RATE CHANGES+ COMPREHENSIVE … FUNDAMENTALS - NUMEROUS INPUTS .. ERRORS IN THESE INPUTS … ERRORS IN INTEREST RATE FORECASTS

  25. INTEREST RATE FORECASTING - 3 PERFORMANCE OF INTEREST RATE FORECASTING MODELS GENERALLY, IRFMs HAVE NOT PERFORMED WELL IN FORECASTING SHORT - TERM MOVEMENTS. THEY PERFORM BETTER IN EXPLAINING WHY INTEREST RATES HAVE MOVED & IN PREDICTING LONG - TERM MOVEMENTS IN INTEREST RATES.

  26. HORIZON ANALYSIS HORIZON ANALYSIS IS A METHOD OF FORECASTING THE TOTAL RETURN ON A BOND OVER A GIVEN HOLDING PERIOD. IT INVOLVES THE FOLLOWING STEPS.

  27. EXPLOITING RELATIVE MISPRICINGS AMONG BONDS • SUBSTITUTION SAWP • PURE YIELD PICKUP SWAP • INTERMARKET SPREAD SWAP • TAX SWAP

  28. INTEREST RATE SWAPS • AN INTEREST RATE SWAP (IRS) IS A TRANSACTION INVOLVING AN EXCHANGE OF ONE STREAM OF INTEREST OBLIGATIONS FOR ANOTHER. • KEY FEATURES • NET INTEREST DIFFERENTIAL IS PAID OR • RECEIVED • NO EXCHANGE OF PRINCIPAL REPAYMENT • OBLIGATIONS • STRUCTURED AS A SEPARATE TRANSACTION • OFF BALANCE SHEET TRANSACTION

  29. INTEREST RATE SWAP

  30. SUMMING UP • Interest rate risk is measured by the percentage change in the • value of a bond in response to a given interest rate change. • The duration of a bond is the weighted average maturity of • its cash flow stream, where the weights are proportional to • the present value of cash flows. • The proportional change in the price of a bond in response to • the change in its yield is as follows: • P/P  D* y • The two commonly followed passive strategies for bond • portfolio management are: buy and hold strategy and • indexing strategy.

  31. If the duration of a bond equals the investment horizon, the • investor is immunised against interest rate risk. • Those who follow an active approach to bond portfolio • management seek to profit by (a) forecasting interest rate • changes and /or (b) exploiting relative mispricings among • bonds. • A wide range of models are used for interest rate forecasting. • Horizon analysis is a method of forecasting the total return • on a bond over a given holding period. • An interest rate swap is a transaction involving an exchange • of one stream of interest obligations for another.

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