A System for BankPortfolio Planning14Commercial banks and, to a lesser degree, other financial institutions have substantial holdings of varioustypes of federal, state, and local government bonds. At the beginning of 1974, approximately twenty-fivepercent of the assets of commercial banks were held in these types of securities. Banks hold bonds for avariety of reasons. Basically, bonds provide banks with a liquidity buffer against fluctuations in demandfor funds in the rest of the bank, generate needed taxable income, satisfy certain legal requirements tied tospecific types of deposits, and make up a substantial part of the bank’s investments that are low-risk in theeyes of the bank examiners.In this chapter, we present a stochastic programming model to aid the investment-portfolio managerin his planning. The model does not focus on the day-to-day operational decisions of bond trading butrather on the strategic and tactical questions underlying a successful management policy over time. In thehierarchical framework presented in Chapter 5, the model is generally used for tactical planning, with certainof its constraints specified outside the model by general bank policy; the output of the model then providesguidelines for the operational aspects of daily bond trading.The model presented here is a large-scale linear program under uncertainty. The solution procedureemploys the decomposition approach presented in Chapter 12, while the solution of the resulting subproblemscan be carried out by dynamicprogramming, as developed in Chapter 11. The presentation does not requireknowledge of stochastic programming in general but illustrates one particular aspect of this discipline, thatof ‘‘scenario planning.’’ The model is tested by managing a hypothetical portfolio of municipal bonds withinthe environment of historical interest rates.14.1 OVERVIEW OF PORTFOLIO PLANNINGThe bond-portfolio management problem can be viewed as a multiperiod decision problem under uncertainty,in which portfolio decisions are periodically reviewed and revised. At each decision point, the portfoliomanager has an inventory of securities and funds on hand. Based on present credit-market conditions and hisassessment of future interest-rate movements and demand for funds, the manager must decide which bondsto hold in the portfolio over the next time period, which bonds to sell, and which bonds to purchase from themarketplace. These decisions are made subject to constraints on total portfolio size, exposure to risk in thesense of realized and unrealized capital losses,∗and other policy limitations on the makeup of the portfolio.At the next decision point, the portfolio manager faces a new set of interest rates and bond prices, and possiblynew levels for the constraints, and he must then make another set of portfolio decisions that take the newinformation into account.∗Realized capital losses refer to actual losses incurred on bonds sold, while unrealized capital losses refer to losses thatwould be incurred if bonds currently held had to be sold.465466 A System for BankPortfolio Planning 14.1Figure 14.1 (Typical yield curve for good-grade municipal bonds.Before describing the details of the portfolio-planning problem, it is useful to point out some of theproperties of bonds. A bond is a security with a known fixed life, called its maturity, and known fixedpayment schedule, usually a semiannual coupon rate plus cash value at maturity. Bonds are bought and soldin the market-place, sometimes above their face value, or par value, and sometimes below this value. If wethink of a bond as having a current price, coupon schedule, and cash value at maturity, there is an internalrate of return that makes the price equal to the present value of the subsequent cash flows, including both theinterest income from the coupon schedule and the cash value at maturity. This rate of return is known as the‘‘yield to maturity’’ of a bond.Given the attributes of a bond, knowing the price of a bond is equivalent to knowing the yield to maturityof that bond. Since the payment schedule is fixed when the bond is first issued, as bond prices rise the yieldto maturity falls, and as bond prices fall the yield to maturity rises. Bond prices are a function of generalmarket conditions and thus rise and fall with the tightening and easing of credit. Usually the fluctuations inbond prices are described in terms of yields to maturity, since these can be thought of as interest rates in theeconomy. Hence, bond prices are often presented in the form of yield curves. Figure 14.1 gives a typicalyield curve for ‘‘good-grade’’ municipal bonds. Usually the yield curve for a particular class of securitiesrises with increasing maturity, reflecting higher perceived market risk associated with the longer maturities.One final point concerns the transaction costs associated with bond trading. Bonds are purchased at the‘‘asked’’ price and, if held to maturity, have no transaction cost. However, if bonds are sold before theirmaturity, they are sold at the ‘‘bid’’ price, which is lower than the ‘‘asked’’ price. The spread between theseprices can be thought of as the transaction cost paid at the time the securities are sold.At the heart of the portfolio-planning problem is the question of what distribution of maturities to holdduring the next period and over the planning horizon in general. The difficulty of managing an invest-ment portfolio stems not only from the uncertainty in future interest-rate movements but from the con-flicting uses made of the portfolio. On the one hand, the portfolio is used to generate income, whichargues for investing in the highest-yielding securities. On the other hand, the portfolio acts as a liquid-ity buffer, providing or absorbing funds for the rest of the bank, depending upon other demand for funds.Since this demand on the portfolio is often high when interest rates are high, a conflict occurs, since this isexactly when bond prices are low and the selling of securities could produce capital losses that a bank isunwilling to take. Since potential capital losses on longer maturities are generally higher than on shortermaturities, this argues for investing in relatively shorter maturities.Evenwithoutusingtheportfolioasaliquiditybuffer, thereisaconflictoverwhatdistribution of maturitiesto hold. When interest rates are low, the bank often has a need for additional income from the