Yield Pickup Swaps and Realized Losses
The Pure Yield Pickup Swap
Probably a majority of institutional bond swaps are done purely for the purpose of achieving an immediate gain in return, either in terms of current coupon income or in terms of yield-to-maturity or both. These swaps can be made and often are made without reference to substitutions or to yield spreads, interest rate trends, or overvaluation or undervaluation of the issues involved. For example, suppose the investor swaps from the 30-year 4's at 67.18 to yield 6.50% into the 30-year 7's at 100 to yield 7.00%, just as in the earlier example, but this time for the sole purpose of picking up the additional 105 basis points in current income or the 50 basis points in yield-to-maturity. He is not motivated by a judgment that the intermarket spread will shrink or that yields will rise or fall. He has no explicit concept of a workout period—he intends (at least at this point) to hold the 7's to maturity. As far as this investor is concerned, he is making a "portfolio improvement" leading only to improved yield in a long-term high-grade investment vehicle. Hence, the name we have assigned.
It is not uncommon that this is the only type of swap that pension fund managers are allowed to consider. Even then, the portfolio manager's freedom to evaluate and carry out these swaps is frequently constrained by rigid, sometimes arbitrary rules, occasionally inconsistent formulae, and often unnecessary inhibitions against realizing losses (see below).
The evaluation of the benefits of such a seemingly simple swap is not as simple as it looks and in practice it is sometimes computed fallaciously. Obviously the increase in the current yield from 5.95% to 7% vastly overstates the benefit from the swap because it ignores the guaranteed 48.8% appreciation of the 4's when they are paid off at maturity. But even the 50 basis points Yield Book increase in yield, which takes full account of the prospective appreciation of the 4's, is an overstatement of the basis point benefits of the swap. We shall see below that the true guaranteed gain from the swap (if the 7's are held to maturity and are not called) will not be 50 basis points but may range between 20 basis points per year (if the reinvestment rate is 6%) to 29 basis points per year (if the reinvestment rate is 8%). These gains, however, are very worthwhile.
This narrowing of the yield gain from that suggested by "yield-to-maturity" occurs over an extended holding period because the same reinvestment rate will prevail for reinvesting the coupons of both the H-bond and the P-bond, and this reinvestment rate naturally benefits the bond with the lower starting yield relative to the bond with the higher starting yield. Thus, it pulls the total returns together. The relative benefit of the reinvestment rate to the lower yielding of two issues will be greater at low future reinvestment rates and less at high future rates.
A proper evaluation of a swap of this sort, which is based on holding the P-bond to maturity, must take account of three factors for both issues (see Table 39): 1) the coupon income; 2) the interest-on-interest (which varies with the assumed common reinvestment rate); and 3) the amortization to par. A fourth factor, which is so dominant in many other sorts of swaps, namely, interim market price changes, may here be ignored. A simple addition of the above three money flows, divided by the dollars invested, will give a total return in dollars which, with the aid of Compound Interest Tables, will give the total realized compound yield as a percent of each dollar invested.
In Table 39, this switch from 4's to 7's is evaluated in this way. It
Sell: Buy:
TABLE 39
Evaluating a Pure Yield Pickup Swap
H-bond 30-Year 4's 0 67.182 to Yield 6.50% $671.82 par of P-bond 30-Year 7's 9 100 to Yield 7.00%
Coupon Income Over 30 Years Interest-on-Interest at 7% Amortization Total Return $ Realized Compound Yield
Coupon Income Over 30 Years Interest-on-Interest 6 7% Amortization Total Return $ Realized Co.'npound Yield
Gain in Basis Points at 7% Reinvestment Rate
Rain 0 6'1 Reinvestment Rate Gain 0 8£ Reinvestment Rate
- 1,200.00 2,730.34 328.18 $4,258.52 6.76%
- 1,410.82 3,210.02 0
- 4,620.84 7.00%
- 362.32
24 Basis Points Per Annum
20 Basis Points Per Annum 29 Basis Points Per Annum will be seen that although the principal invested in both issues is only $671.82 per bond (the price of the H-bond) the switch over a period of thirty years results in a gain of $210.82 per bond in coupon income, a much more important gain of $479.68 per bond in interest-on-interest (at a common assumed reinvestment rate of 7%) and a loss of the $328.18 per bond in capital gain to maturity which the H-bond will enjoy while the P-bond will not. These three factors add up to a net gain from the switch of a large $362.32 per bond which amounts to 54% of the investment. This is a net gain of 24 basis points per year, i.e., total return rises from 6.76% for the 4's to 7% for the 7's.
The true yield of the 4's rises above the Yield Book yield of 6.50% to a fully compounded yield of 6.76% because the assumed reinvestment rate of 7% is above the 4's implicit reinvestment rate of 6.50%. For the 7's, the 7% assumed reinvestment rate is identical to their yield-to-maturity and hence full compounding does not change this rate.
Alternatively, as the table shows, at a 6% future reinvestment rate the advantage of the switch shrinks to 20 basis points per year or $244.63, while at an 8% reinvestment rate the advantage of the switch rises to 29 basis point per year or $508.49. It seems evident that efforts to evaluate such switches without reference to an assumed reinvestment rate are apt to be misleading.
The table shows that if we ignore interim price changes and the possibility that the 7's will be called this is a valuable swap at any reasonable reinvestment rate. It will be worth something between $244.63 and $508.49 per bond depending on the reinvestment rate. Even if the 7's are called in a 6% market, the switch will be worth at least $75.24 per bond to maturity.
Why then do such riskless spreads exist in the market and indeed are often exceeded (doubled!)? Why do not holders of lower yielding issues who are relatively indifferent to interim price movements generally switch for yield pick ups even of 10 basis points or 20 basis points, which are common and often are safe from call risk and from unfavorable relative market fluctuations?
Realized Losses from Swaps
The answer unfortunately often lies in generally accepted accounting practices which make an artificial distinction between realized profits or losses and book profits or losses and between coupon income and amortized capital gains or losses. The result is that many funds with large book losses are frozen and are thus prevented from realizing large risk-free gains in both principal and interest. It can be estimated that many tax-free funds could be earning at least 1% more than they are, and from the same type of investments, if they were free to make even obvious risk-free swaps.
Any well-considered "yield pickup swap" pays a net gain to the swapper regardless of the cost of the H-bond. The profit from the swap is the same whether the H-bond is sold at a profit or at a loss. The net gains from the swap detailed in Table 39 are over and above recovery of the whole book loss incurred in selling the H-bond, whatever that might be. In this case the gains are after subtracting the $328.18 per bond loss if these H-bonds were purchased at 100. This book loss is equivalent to the amortization gain which the holder of the H-bond will automatically receive and the seller lose—regardless of his cost.
Nevertheless, on the books of this swapper, if conventionally kept, this swap would show a loss of $328.18 per bond in the year of the swap and an offsetting income gain of only $7.03 per bond that year. Some accountants would even charge this realized loss to the fund's income account for the year of the swap and this could lead to an increase in required contribution in spite of the fact that the fund's cash flow and ability to pay benefits has increased as a result of the swap. Indeed if through some market aberration the P-bond were identical with the H-bond, but priced 5 points lower (an immediate clear gain of $50 per bond or 7.4%) the books would show a loss which might well force the portfolio manager to decline what is in effect a free and valuable accession of assets. Funds which value at market are often free to ignore costs and, therefore, to make profitable portfolio improvements. However, many funds carry their bonds at amortized cost and as a result are inhibited from making portfolio improvements if they involve realizing large losses.*
One unsound accounting practice leads to others. For example, it has become fashionable to evaluate bond swaps by computing the number of years which will be required for the additional cash flow from the P-bond to recoup the book loss from the swap.
Even if we are forced by convention to accept this artificial and unsound "time test" for evaluating swaps, we should consider the wide differences in the methods by which the loss-recovery period is computed. Since interest-on-interest is a large component of total
*Note that the authors of this book are, or have been, bond dealers and hence have a vested interest in encouraging bond market activity.
return, it should be considered in comparing the cash flows of the P-bond with the cash flow of the H-bond. Often, however, it is overlooked.
Returning to our original example of the 30-year 4's at 6.50% into the 30-year 7's at par, let us see how this recovery time may be computed. For every H-bond sold at 67.182, the dollar amount of $671.82 is used to purchase the 7's at 100. The annual coupon payment from this .67182 fraction of a 7% P-bond is just .67182 of $70 or $47.03. Subtracting the H-bond annual coupon of $40, we obtain a net annual coupon gain of $7.03 per H-bond sold.
This cash flow can be reinvested and compounded at some interest rate. Depending on the assumed average reinvestment rate, the dollars accrued from the added cash flow, including the interest-on-interest, grow from year to year as shown in Table 40. When the extra dollars accumulated reach the point of equalling the book loss, then it is argued the book loss will have been recouped and the time to that point will define the recovery time. After the recovery time, the additional cash flow is considered to be all profit.
As Table 40 demonstrates, the recovery time is critically dependent on the unknown reinvestment rate. At a 6% rate, the recovery time for this swap is twenty-three years. At an 8.00% rate, it drops to twenty years. These are long and discouraging time spans for a transaction which in fact is immediately profitable, and they seem to illustrate the unsoundness of this guide.
One common error is to compute the recovery time by simply dividing the book loss by the annual coupon gain. This ignores the all-important compounding of "interest-on-interest." In this example, this method would lead to $328.18 + ($7.03 per year) = 46.68 years, a dismally excessive time by any standard, indeed exceeding the 30-year life of both bonds. This is equivalent to taking the first year's gain of $7.03 as representative of all future gains when in fact due to compounding it will always be the smallest gain of any future year. From Table 40, one sees that this method also corresponds to an implied 0% reinvestment rate.
Many "pure yield swaps" are more complex than the above example, involving P-bond amortization and differing maturities.
TABLE 40
Timing of Additional Cash Flow from a Pure Yield Pickup Swap_
Sell: 30-Year 4's @ 67.182 to Yield 6.50« Buy: 30-Year 7's 6 100 to Yield 7« Additional Cash Flow at Various Reinvestment Rates
TABLE 40
Timing of Additional Cash Flow from a Pure Yield Pickup Swap_
Sell: 30-Year 4's @ 67.182 to Yield 6.50« Buy: 30-Year 7's 6 100 to Yield 7« Additional Cash Flow at Various Reinvestment Rates
|
Elapsed Years |
0« |
6.00« |
6.50« |
7.00« |
7.50« |
8.00« |
|
1.0 |
$ 3.51 7.03 |
$ 3.51 : 7.13 |
> 3.51 7.14 |
$ 3.51 7.15 |
$ 3.51 7.16 |
$ 3.51 7.17 |
|
20.0 |
140.55 |
264.92 |
280.45 |
297.08 _ |
314.85 |
1 333.881 |
|
20.5 |
144.06 |
276.39 |
293.08 |
310.99 [ |
330.17 1 |
350.73 |
|
21.0 21.5 |
147.58 151.09 |
288.19 300.35 |
306.12 319.58 |
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