Universidade Nova de Lisboa Faculdade de Economia FIXED INCOME I. Bond portfolio management II. 1 Paulo Leiria/11

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1 Universidade Nova de Lisboa Faculdade de Economia FIXED INCOME I Bond portfolio management II 1

2 Outline: Matched funding strategies - Pure cash-matched dedicated portfolio - Dedicated cash-matched with reinvestment Portfolio immunization - Horizon date immunization - Cash flow matching (micro hedge) - Net worth immunization (macro hedge) 2 FIXED INCOME I

3 Matched funding strategies Matched-funding techniques incorporates passive buyand-hold strategy and active management strategies The manager tries to match specific liability obligations due at specific times to a portfolio of bonds in a way that minimizes the portfolio's exposure to interest rate risk These techniques typically require constant monitoring and many transactions to achieve the intended goal 3 FIXED INCOME I

4 Matched funding strategies Pure cash-matched dedicated portfolio The most conservative method. Construct a bond portfolio with a stream of payments to exactly match specific liability schedule Requires estimating future obligations and then choosing zero-coupon bonds that have maturity dates exactly when funds are needed 4 FIXED INCOME I

5 Matched funding strategies Pure cash-matched dedicated portfolio This is an entirely passive portfolio strategy that requires no reinvestment (zero coupon bonds pay no cash coupon payment and matures the day you need the funds Technically it is difficult to determine exactly WHEN your cash flow payouts will be due, so it is best to apply a somewhat less conservative approach 5 FIXED INCOME I

6 Matched funding strategies Dedicated cash-matched portfolio with reinvestment Assumes that cash flows don't always come when needed (may come earlier) and will be reinvested Therefore, will require smaller sums of initial funds to meet future goals. 6 FIXED INCOME I

7 Portfolio immunization Immunization strategies: - Horizon date immunization - Cash flow matching (micro hedge) - Net worth immunization (macro hedge) 7 FIXED INCOME I

8 Portfolio immunization - horizon date immunization Classical immunization: a process by which a bond portfolio is created to have an assured return for a specific time horizon irrespective of interest rate changes This process try to guarantee that the assets value is sufficient to cover a specified liability (bullet) in a target date 8 FIXED INCOME I

9 Portfolio immunization - horizon date immunization In this respect, we should structure the portfolio that balances the change in the value of the portfolio at the end of the investment horizon with the return from the reinvestment of portfolio cash flows The loss or gain in reinvestment income = loss or gain in portfolio value If this is the case, we will show the assets (bonds) duration should be equal to the maturity of the liability 9 FIXED INCOME I

10 Portfolio immunization - horizon date immunization Lets see this result with an example The value of a bond will depend on the evolution of interest rates until the maturity date If a portfolio of assets (bonds) and liabilities has the same payoff no matter the yield curve, we say this portfolio is immunized (against interest rate changes) 10 FIXED INCOME I

11 Portfolio immunization - horizon date immunization Suppose a firm has a liability (bullet) of L to be paid in time N Its present value is: PV 0 1 L y N being y the appropriate discount rate 11 FIXED INCOME I

12 Portfolio immunization - horizon date immunization Suppose this liability is hedged by a bond, with price P B equal to the present value of the liability (L) C P N t B t (1 y) 1 t PB PV0 Suppose the interest rate now moves from y to y+y 12 FIXED INCOME I

13 Portfolio immunization - horizon date immunization PV 0 P B ΔPV ΔP 0 B PV PV P P B B 0 0 Δy Δy 13 FIXED INCOME I dpv dy dp dy B 0 -N 1 y y y t C 1 L N 1 N t t 1 N 1 y

14 Portfolio immunization - horizon date immunization If these two equations are equal, a change in interest rates will not change the portfolio value PV 0 -N L N t C y P t N t N B y 1 1 y 1 y 1 1 Remember that: P B PV 0 L (1 y) N 14 FIXED INCOME I

15 Portfolio immunization - horizon date immunization Simplifying, we get: 1 N t 1 B P t Ct (1 y) t N Which means that for the portfolio to be immunized, the duration of assets (bonds) have to be equal to the duration (maturity) of liabilities 15 FIXED INCOME I

16 Portfolio immunization - horizon date immunization Market yield will fluctuate over the investment horizon Duration of the portfolio will change as the market yield changes, also, duration will change simply because of the passage of time A portfolio can be immunized if it is rebalanced periodically so that its duration is readjusted to the duration of the liability 16 FIXED INCOME I

17 Portfolio immunization - horizon date immunization How often to rebalance? Frequent rebalancing increases transaction costs, thus reducing the likelihood of achieving target returns Infrequent rebalancing will result in the portfolio s duration wandering from the target duration, thus reducing the likelihood of achieving target returns Manager must deal with the trade-off and find a happy medium 17 FIXED INCOME I

18 Portfolio immunization - cash flow matching More often than having a single liability payable at a horizon date, investment funds have to pay a number of liabilities a no single horizon corresponds to the schedule of liabilities Just having the portfolio duration match the liabilities duration is not sufficient for immunizing multiple liabilities In this case, we can employ a cash flow matching strategy 18 FIXED INCOME I

19 Portfolio immunization - cash flow matching A bond is selected with a maturity that matches the last liability The amount invested in this bond is such that the principal plus final coupon payment is equal to the last liability The remaining elements of the liability stream are then reduced by the coupon payments of this bond 19 FIXED INCOME I

20 Portfolio immunization - cash flow matching Another bond is chosen for the next to last liability and this sequence is continued until all liabilities have been matched by payments on securities selected for the portfolio 20 FIXED INCOME I

21 Portfolio immunization - cash flow matching Cash flow matching automatically immunizes the portfolio from interest rate movement because the cash flow from the bond and the obligation exactly offset each other Cash flow matching on a multi-period basis is referred to as a dedication strategy In this case, the manager selects either zero-coupon or coupon bonds that provide total cash flows in each period that match a series of obligations 21 FIXED INCOME I

22 Portfolio immunization - cash flow matching The advantage of dedication is that it is a once-and-forall approach to eliminating interest rate risk Once the cash flows are matched, there is no need for rebalancing Cash flow matching is not more widely pursued probably because of the constraints that it imposes on bond selection 22 FIXED INCOME I

23 Portfolio immunization - net worth immunization Bank liabilities very short-term in nature, e.g., deposits Bank assets are of longer duration, e.g. corporate loans, mortgages In periods when interest rates increase unexpectedly, banks can suffer serious decreases in net worth - their assets fall in value by more than their liabilities 23 FIXED INCOME I

24 Portfolio immunization - net worth immunization Techniques called gap management were developed to limit the gap between asset and liability durations, e.g. the introduction of bank certificates of deposit with fixed terms to maturity serves to lengthen the duration of bank liabilities 24 FIXED INCOME I

25 Portfolio immunization - net worth immunization There are basically 4 steps in the process of duration gap (DGAP) analysis: Interest rate forecast Estimative of the market value of assets, liabilities, and market value of equity (MVE) Estimative of assets and liabilities duration (including off-balance sheet instruments) DGAP Estimative of MVE changes in different interest rate scenarios 25 FIXED INCOME I

26 Portfolio immunization - net worth immunization To immunize the MVE, the bank should set DGAP equal to zero: DGAP = D A ud L in which: D A = average duration of assets D L = average duration of liabilities u = L / A 26 FIXED INCOME I

27 Portfolio immunization - net worth immunization ΔMVE = ΔA - ΔL with: ΔA = - D A [Δy / (1 + y)] A ΔL = - D L [Δy / (1 + y)] L MVE D A y 1 y A D y A D L D A (1 y 1 y L 27 FIXED INCOME I L L y)

28 Portfolio immunization - net worth immunization Considering that: DGAP = D A ud L And replacing in previous expression, we get: MVE A D A LD y A DGAP (1 y) L y (1 y) 28 FIXED INCOME I