Rethinking Our Thinking about Interest Rates

CFA Institute

Rethinking Our Thinking about Interest RatesAuthor(s): Richard W. McEnallySource: Financial Analysts Journal, Vol. 41, No. 2 (Mar. - Apr., 1985), pp. 62-67Published by: CFA InstituteStable URL: http://www.jstor.org/stable/4478823 .

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by Richard W. McEnally

Rethinking our Thinking about

Interest Rates

Fixed income portfolios are suppliers of capital. As such, they gain when the price of capital-the interest rate-increases. Unfortunately, they also lose when rates increase, because the value of existing portfolio assets declines. Although attention has commonly focused on the loss in present value, rather than the gain from the reinvestment opportunity created by higher interest rates, in reality the gain will dominate the loss when the portfolio's investment horizon exceeds the portfolio's duration.

Interest rate increases thus represent favorable developments for many portfolios, includ- ing thosefor IRA accounts, pension funds and life insurance companies. To evaluate properly the condition of these portfolios, it is necessary to utilize estimates of future portfolio value that explicitly incorporate forecasts of future reinvestment rates. In given interest rate environments, however, it is still appropriate to use short-term total returns to evaluate portfolio performance.

T HE DRAMATIC FALL in interest rates during the second half of 1982 led to total returns of over 40 per cent on long-term

bond portfolios, higher returns than in any other year in the postwar period. So this must have been the best of all possible years for fixed income investors, right?

If the general euphoria of bond portfolio managers is any guide, 1982 was indeed the best of all possible years for them. But a strong case can be made for the proposition that 1982 was a dis- aster for many fixed income portfolios. The es- sence of the argument is that most portfolios have objectives that are better served by higher rates of interest than by lower rates. A lower interest rate environment, even though it may produce an increase in the value of existing portfolios, makes it much more difficult to invest new money profitably and to attain long- run return targets on existing portfolios.

Alternative Portfolio Goals and Strategies To assess the impact of interest rate changes on fixed income portfolios, it is first necessary to consider the portfolio's goals. There are at least three:

* current income, * accumulation of value, and * holding period returns. Current income is the traditional basis for in-

vesting in bonds. This goal is typified by ele- mosynary portfolios from which only coupon income may be spent, or an income beneficiary- remainderman trust where priority attaches to the income objective.

Changes in the value of income portfolios are of secondary importance. The primary concern is maintaining or raising the level of the income stream. Incremental inflows of capital into the portfolio increase income, but they increase income more when rates are rising, rather than falling. And to the extent that declining interest rates motivate issuers to call their bonds in order to take advantage of refinancing opportunities, the level of the income stream may be impaired by falling rates even in "no new money" portfolios. I (Footnotes appear at end of article.)

A second goal of fixed income portfolio man-

Richard McEnally is Meade Willis Professor of In- vestment Banking at the University of North Caro- lina at Chapel Hill.

FINANCIAL ANALYSTS JOURNAL / MARCH-APRIL 1985 O 62



agement emphasizes growth in portfolio value. Cash thrown off by such a portfolio is reinvested, and withdrawals are neutral in the sense that they are unrelated to coupon receipts or changes in value over short intervals. IRA accounts are prototypical accumulation portfolios, as are most pension funds. Life insurance company reserves also represent accumulation portfolios, even though accounting conventions may keep them from being pure examples. Be- cause of the relative importance of these portfolios, accumulation of value is probably the dominant goal of fixed income investment to- day.

When all intermediate cash flows are reinvested, the obtainable rate of return is critical to the rate of growth of value. The higher the reinvestment rate, the greater the growth. Al- though a decline in interest rates will tend to raise the value of existing portfolio assets, the reduced rate of return on reinvested funds will usually more than offset this gain in value. The adverse effects of interest rate declines are ex- acerbated if the portfolio normally experiences inflows of new money, as an IRA account or a pension fund covering a youthful work force does.

A third goal is to achieve maximum holding period returns without reference to the source of returns or the reinvestment rate. Judging by all the attention given to total returns over fairly short horizons, one would be forced to conclude that this is the dominant fixed income portfolio goal, if not the goal. But situations in which the holding period return goal makes sense for fixed income investment-as opposed to those in which it is a criterion for evaluation-are sur- prisingly difficult to identify. They would be most likely to arise within broader portfolios managed for total return, where debt securities are regarded as just another investment me- dium and there is no long-term commitment of a portion of the portfolio to such securities. Here one might well invest in bonds from time to time simply because they looked as though they would provide superior returns in the period ahead, it being understood that in subsequent periods the funds would be shifted into new areas of opportunity. Accounts managed for in- dividuals, with wide flexibility to shift among stocks, bonds and other investment media, probably typify this investment goal.

If the goal is indeed to generate maximum total returns in the period ahead, then obviously "interest rate plays" are the way to do

this, and interest rate declines are desirable whereas increases are undesirable. With this goal, 1982 was the best of all possible years for fixed income investors-provided they ceased to be fixed income investors at the end of the rally!

Interest Rate Considerations in Accumu- lating Portfolios Because of the importance of the accumulation goal in the fixed income investment scheme of things, and because the misapprehension of the benefits of interest rate changes appears to be especially pronounced in this case, accumulating portfolios deserve a closer look.

An accumulating portfolio has three charac- teristics:

(1) It is dedicated to growth of value over time. (2) It involves a continuing commitment to fixed income securities. (3) Intermediate cash flows over the investment horizon will normally be reinvested- that is, the portfolio will be managed as though there will be no withdrawals.

Formally, the investment horizon can be of any length, but the interesting problems arise when the horizon is long compared to, say, a semian- nual coupon period.

The primary objective of such a portfolio is to generate the highest growth rate of value over the investment horizon relative to the level of risk assumed. In the fixed income area, the growth rate of value is appropriately measured by the realized compound yield-the single rate of return or discount rate that equates the initial value of an investment in the portfolio with its value at the end of the investment horizon. The realized compound yield will depend on three things-the rate at which the funds are initially invested, the rate at which cash flows thrown off by the portfolio can be reinvested, and the market value of the portfolio's assets at the end of the horizon.

The initial investment rate is known at the time funds are contributed to the portfolio; both the reinvestment rates and the market value of the portfolio will be determined by the general movement of interest rates. Changing levels of interest have opposite effects on the accumulation from "interest on interest" and on the market value of the portfolio. If interest rates rise, reinvestment rates and the accumulation from interest on interest will be higher, but the value of the beginning portfolio will be reduced. And vice versa.




Intuition and market lore suggest that when the investment horizon is "short" and the term to maturity of the securities in the portfolio is "long," the portfolio will gain overall from a decline in interest rates; the increased market value will overwhelm the lost interest on interest, and the realized compound yield will exceed the initial investment rate. This is why, for example, a bond dealer will welcome a decline in interest rates and the effect it has on the overall value of the dealer's portfolio. What seems to be less well understood is that the effect is reversed when the horizon is long and the term of the securities is short. Here, a decrease in rates will hurt; losses from rolling over coupon receipts and maturing or called bonds at lower rates will more than offset price increases of securities in the portfolio. The realized compound yield will be less than the initial investment rate.

Long and Short How long is "long" and how short is "short"?

The answer is complex and depends on the time path of interest rates and the pattern of portfolio cash flows. However, valuable insights can be gained by assuming that there is a single initial contribution to the portfolio and a specific investment horizon, and that interest rates change in one fell swoop after the portfolio is established, so that the reinvestment rate is the same as the rate at which the portfolio is valued at the end of the horizon. Under these conditions:2

realized compound yield-(portfolio duration/horizon length) (initial interest rate) + (1 - portfolio duration/horizon length) (subsequent interest rate). Suppose the subsequent rate turns out to be

below the initial yield-that is, interest rates decline. Assume, for example, that the initial yield of 10 per cent declines to 8 per cent. If the investment horizon is one year and the portfolio duration is eight years, then over this year:

realized compound yield = (8/1)(10%) + (1 - 8/1)(8%) = 24%.

Alternatively, suppose the investment horizon is 40 years but the same portfolio is held. Then, over the 40 years:

realized compound yield = (8/40)(10%) = (1 - 8/40)(8%) = 8.4%. In the first situation, the portfolio gains dra-

matically from a decline in rates. In the second case, however, the portfolio suffers; its realized compound yield falls considerably short of the yield at which the funds were initially invested. Over the 40-year horizon, the initial investment

will grow to only $25.19 (= 1.084 4") for every dollar invested initially versus $45.26 (= 1.104"1) if it had been possible to earn 10 per cent over the investment horizon.3

Unfortunately, the relation between horizon length and portfolio duration in the second example is much more representative of accumulating portfolios than is the first. As long as the horizon exceeds the portfolio duration, the net outcome from a decline in interest rates is negative. When the differences are extreme, as in this example, the impact of the rate decline can be dramatic. But these are not unrealistic numbers. A portfolio duration of eight years is about as long as one can obtain on conventional coupon-paying bonds, given double-digit interest rates, but investment horizons of 40 years are not uncommon for pension funds or life insurance companies. Unless zero-coupon issues or financial futures are used to lengthen the effec- tive portfolio duration, such portfolios will surely suffer when interest rates decline, even though the associated temporary increase in market value-such as produces the 14 per cent capital gain and 24 per cent total return on this portfolio in the first year-may create the illu- sion of investment success. Unfortunately, the gain in market value dpe to lower rates is readily evident, whereas the lost interest on interest tends to go unnoticed, providing a classic example of the concept of "error visibility."4

Suppose, on the other hand, that interest rates increase to 12 per cent immediately after the portfolio is established. At the end of one year, the portfolio looks bad indeed, as it has lost 4 per cent of its value.5 But if yields remain at this level, the realized compound yield over the 40- year horizon will be 11.6 per cent, and the value of the portfolio at the end of this horizon will be $80.64 (= 1.11640) for everv dollar initially invested, versus $45.26 if rates remain un- changed.6

The latter example leads to an important point for practical, real-world management of accumulating portfolios. In retrospect, with the increase in rates it would have been better to invest the funds short until the increase in rates o,curred, then to lock in the higher rate without experiencing the first-year loss. Given that the portfolio was initially invested the way it was, the increase in rates still benefits the accumulating portfolio in the long run, even though it makes the performance numbers look bad in the short run. And this is the way it is in practice. The portfolio will always benefit if the

FINANCIAL ANALYSTS JOURNAL / MARCH-APRIL 1985 DH 64



manager can properly anticipate the pattern of interest rate evolution over time. Situations will frequently arise when, in retrospect, it would have been better had the portfolio been invested in some other way. But these past decisions are akin to sunk costs. The fact remains that the increase in rates still benefits, rather than hurts, the long-run accumulating portfolio.

Emphasizing Capital Gain or Loss If declining interest rates are actually undesirable and rising rates desirable in most fixed income portfolio investment situations, why does conventional wisdom suggest the opposite? At least three factors appear to be at work:

* the popularity of "total return" performance evaluation,

* the pervasiveness of a "dealer mentality" in the fixed income markets, and

* perverse effects of accounting conventions. Investing for total returns is the predominant

goal in the common stock area, and it is difficult to make a case for any alternative, given the uncertainty regarding future flows from common stocks. In the early '60s, single-period holding period returns became an accepted means of evaluating equity investment performance; again, it is difficult to make a case for any alternative scheme of equity portfolio performance evaluation. The problem is that the single-period total return criterion has been carried over without much thought or analysis into the fixed income area, where investment horizons typically span many periods.7

The result has been a mindset that emphasizes near-term gains or losses in portfolio value to the exclusion of all else. Fixed income portfolio managers, not being fools, understand that debt portfolios must compete with equity portfolios for pension and other savings dollars. On these grounds, a decline in interest rates is going to make bonds, as an investment vehicle, and their managers look good, whereas an increase in rates is going to have the opposite effect. Things have been reversed so that the performance evaluation criterion has become the portfolio objective. The long-run, multiperiod nature of many fixed income portfolio objectives has been lost in the process.

The short-run impact of price change on dealers in any commodity is very simple: They make profits on their inventory position when prices increase, and they sustain inventory losses when prices decline. Bond dealers are no different. In fact, the structure of their balance sheets tends

to make them even more exposed than many other types of dealers. Therefore, unless they hedge their positions in the futures markets, they are very vulnerable to interest rate rises and welcome interest rate drops. The problem is that they also talk to their customers-indeed, they are the major source of investment advice and prognostications for fixed income investors-and their attitude toward interest rate changes tends to be adopted by their customers. There is little appreciation of the fact that what is good for dealers, the shortest run of investors, may be undesirable for their customers with longer investment horizons.

Contemporary accounting practice tends to promote the view that increases in bond value are a positive outcome even when the long-run impact of the associated decline in interest rates is negative, and the converse. Consider just two examples.

The life insurance industry is allowed to carry fixed income securities at amortized cost only, provided there is no transaction that realizes a gain or loss. Many insurance company managers thus find themselves locked into bond positions because the sale of the associated securities would cause them to book a loss, even when the funds can be rolled over into assets whose future payoffs will equal or exceed those of the divested assets. At the other extreme, an insurance company must book a gain when a bond is called away for refunding at lower interest rates, even though, over the life of the original bonds, it must surely lose from having to reinvest at a lower interest rate.

Pension accounting provides another example. Portfolio assets are marked to market to evaluate the adequacy of a plan's assets to fund future benefits. In a rising interest rate environment, fixed income holdings will be written down even though the higher rates improve the ability of the existing assets to fund future benefits. Unless the actuarially assumed rate of return is raised correspondingly-and this rarely seems to happen, at least in the short run-the result is that the value of pension assets falls relative to the present value of pension liabili- ties, and the plan sponsor is pressured to increase contributions to the plan.

Fixed Income Investors as Suppliers of Capital

One of the more striking effects of the present interest-rate mindset is provided by attitudes towards the supply and demand for funds. Al-

FINANCIAL ANALYSTS JOURNAL / MARCH-APRIL 1985 E 65



most universally in business, an increased relative demand for a product is regarded favorably-and properly so, for it raises the market clearing price. Suppliers are especially gleeful if the increment of demand comes from the federal government, for it tends to be an especially large (and not always terribly price- conscious) customer. However, fixed income investors, who are simply suppliers of funds at a price given by the interest rate, seem to react in the opposite way. They appear to view an increase in the relative demand for capital as an undesirable development, even though it tends to raise interest rates. Incremental demand com- ing from Treasury financing activities is viewed especially grievously. In any other industry they'd love it! It is noteworthy that users of funds, whose interests must be antithetical to those of suppliers, are more clearsighted; they seem to understand perfectly well that higher rates hurt them while lower rates are beneficial.8

A legitimate case that interest rate increases are bad for suppliers can obviously be made on occasion by referring to "second order" considerations. If the real rate is relatively constant, for example, and the increase is due to a rise in anticipated inflation, then the capital supplier may lose in noninvestment areas because of increased inflation. Pension funds, for instance, may be pressured for increased benefits. The liability structure of specific life insurance companies, or their exposure to demand for poli- cyholders' loans, could generate offsets to the salutary effects of interest rate increases. If the fixed income investor is a taxable entity, then taxation on the inflation increment of interest rates-which is effectively a return of capital- could reduce the after-tax real rate of return. But it is not evident that such situations are common enough to account for the pervasiveness of present attitudes towards interest rate changes, which appear to center around effects on portfolio value.

Appraising Portfolios, Evaluating Managers It is well understood that performance evaluation of portfolio managers should proceed on different grounds than the appraisal of portfolios. That is why, in the equity area, a distinction is made between time-weighted returns-which ignore the pattern of flows into or out of a portfolio and concentrate on what the manager did with the resources at his disposal-and value- weighted returns-which both consider the

timing of inflows or outflows and attempt to measure the rate at which the portfolio is grow- ing.,

Similar issues arise in the fixed income area. In evaluating performance across portfolio managers, it is appropriate to compare holding period returns, as it is to compare the total returns produced by a single manager with those on some broad index or unmanaged "baseline" portfolio. Such comparisons acknowledge that the general movement of interest rates was whatever it was and concentrate on how the manager did, given the interest rate environment. The emphasis is, properly, on how well the manager anticipated interest rates, how well he positioned the portfolio with respect to yield/ price movements in different bond market sec- tors, or how effectively he traded the portfolio. As long as such comparisons are made against other portfolios, rather than some absolute standard (e.g., "Was the value of the portfolio up or down?"), they are perfectly acceptable.

The appraisal of the portfolio in terms of its investment objectives is another matter. Neither the standard nor the measurement of achieve- ment should be stated in terms of holding period returns (except for the relatively unimpor- tant class of portfolios that are indeed holding- period-return oriented). Rather, the standard should be attainment of some target rate of cash flows or satisfactory progress toward some target for the value of the portfolio at the end of the investment horizon, accompanied by acceptable levels of risk and liquidity.9

How does one evaluate the progress of an accumulating portfolio toward some horizon value? The only way this can be done in any reasonable way is by taking account of likely future reinvestment rates. For reasons that should now be evident, any method that con- centrates on realized rates of return is going to be hopelessly misleading.

One possibility is to employ an "actuarial" evaluation method that looks at the value of the portfolio at the horizon date in the future, under an assumed reinvestment rate or schedule of reinvestment rates. If this estimated terminal value is above target, then the condition of the portfolio is satisfactory; if it has risen over the preceding time period, then the performance of the portfolio has been satisfactory. What interest rates have done, or how portfolio values have changed, is immaterial.Ln

Such a procedure should incorporate realistic "best guess" forecasts of reinvestment rates, as

FINANCIAL ANALYSTS JOURNAL / MARCH-APRIL 1985 Q 66



opposed to the low-side estimates of obtainable returns commonly employed in actuarial com- putations. One obvious possibility for forecast- ing these rates is to assume that future reinvestment rates will remain equal to the existing structure of interest rates; this possibility in effect accepts the notion of a "random walk" in interest rates, according to which the best esti- mate of the future is the present. Another possibility is to use the schedule of future rates im- plicit in the term structure.E

Footnotes 1. Such portfolios can gain from increasing rates in

another, more subtle, way, provided they are tax- exempt. The yield to maturity on discounted bonds tends to be lower than on current coupon bonds because of the built-in capital gains on the discounted issue. Therefore, by swapping portfolio holdings that have gone to a discount for current coupon issues, it is frequently possible to raise portfolio income. Of course, it is always possible to raise the coupon income from such a swap even when the yields to maturity are the same, but there is no economic gain in this case.

2. This formula was originally presented by Guil- ford C. Babcock in "A Modified Measure of Du- ration," a paper presented at the Annual Meeting of the Western Finance Association in 1976. A fur- ther exposition of the formula is presented in Richard W. McEnally, "How to Neutralize Rein- vestment Rate Risk," Journal of Portfolio Manage- ment, Spring, 1980, pp. 59-63. It must be empha- sized that the formula is presented here for expositional purposes only; in actual practice, calculations tracing out the time paths of invest- ments and withdrawals would be necessary.

3. When the portfolio duration and the investment horizon are equal, the weight given the initial interest rate is unity and the subsequent interest rate drops out of the equation. Under these conditions, there is no uncertainty due to reinvestment rate variations, and the portfolio is said to be "immunized." Intuitively, what happens is that an increase (decrease) in portfolio value is just offset by the decrease (increase) in interest on interest.

4. Error visibility is a hypothesis to the effect that people will overweight errors that are obvious to their superiors and evaluators and underweight errors that are not so evident in choosing a course of action.

5. (8/1)(10 %) + (1 - 8/1)(12 %) = -4%. 6. (8/40)(10%) + (1 - 8/40)(12%) = 11.6%. 7. Total return performance evaluation has its roots

in modern asset pricing theory, especially in the paradigm of the Capital Asset Pricing Model, and

in this context-in the academic community, at least-the limitations of looking at single periods only are well known. In the academic literature in this area it is customary to acknowledge at the outset the assumption of a single-period investor, and considerable attention has been given to multiperiod models as a means of coping with the "myopic" limitations of the single-period model. Unfortunately, only the most primitive messages of modern asset pricing theory have been carried over to performance evaluation.

8. The position of the fixed income investor is a bit more complex than that of the typical supplier. It is somewhat akin to that of a supplier who has entered into a contract to provide a good or service at a fixed price over an extended period. If the value of the good or service increases, then the contract may become a burden rather than a blessing. While the bad news is that the existing contract is less valuable, the good news is that the supplier will gain as productive capacity is grad- ually diverted from satisfying the old contract to new contracts. For long-term investors, this good news regarding subsequent investment opportunities should overwhelm the bad news about present portfolio values.

9. To determine the target terminal value of accumulating portfolios, the following procedure is suggested. When the portfolio is initially set up, identify a reasonable rate of return over the horizon and compute the terminal value of the initial contribution at this rate. As additional contributions are made, engage in the same process and add the terminal value of the contribution to that of the existing portfolio.

10. An alternative, but approximately equivalent, ap- proach is to compare present market values with the target terminal value of the portfolio, ad- justed back to the present by the anticipated reinvestment rate or rates. The differences in these two values may also be looked at over time. This procedure is akin to the determination of the "trigger value" of contingent immunization. In contingent immunization, a target value for the portfolio is computed in a way similar to that out- lined in the preceding footnote. At each evaluation point, a determination is made of the value the portfolio must have in order to reach the target if it is then immunized at prevailing interest rates. This value is the trigger value. If the actual value of the portfolio drops to the trigger value, the portfolio is in fact immunized; otherwise, it is actively managed. See Martin L. Leibowitz and Alfred Weinberger, "The Uses of Contingent Im- munization," Journal of Portfolio Management, Fall, 1981, pp. 51-55, and Leibowitz and Weinberger, "Contingent Immunization-Part I: Risk Control Procedures," Financial Analysts Journal, Novem- ber/December 1982, pp. 17-31.




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Rethinking Our Thinking about Interest Rates