Are bond funds more risky than the bonds they hold? That is, might a fund incur avoidable losses when interest rates rise because of the way it is constituted? If so, should fixed income investors reduce their risk by holding bonds directly? According to one argument, the answer to these questions is yes. If interest rates rise, investors with direct holdings have capital protection because they can retain depreciated bonds in their portfolios until they mature at which time they will get back the par value. However, bonds which belong to a fund may be traded away, locking in a capital loss. Indeed, a manager will have no choice but to sell a depreciated bond that no longer satisfies the terms of the fund's prospectus, for instance because its maturity falls below some threshold. Thus, many people, including investment professionals such as Suze Orman, believe that investors concerned about capital preservation are better off holding bonds directly (see, for examples, Orman, Investopedia, bonds.about, Kiplinger, Forbes).

However, this logic is fundamentally flawed. If interest rates rise, bond holders will indeed suffer a capital loss. But after that it makes no difference whether they decide to hold the same bonds or trade them for new ones. The original bonds will eventually recoup their capital loss but pay a lower coupon, while new bonds will realize the capital loss and have a lower par value, but pay a higher coupon. The lower par value and higher coupon just offset each other and the dollar values of discounted cash flows (DCFs) and total returns will be the same whatever investors decide to do.

In other words, the option to time sales of specific bonds in the portfolio offers no protection from interest rate risk. The confusion arises because investors planning to hold their depreciated bonds to maturity should (but don't) mark-to-market. If they did, they would easily see that their decision affects nothing but the breakdown of total return into income and capital gains.

If interest rates continue to trend higher, the choice between holding bonds and trading them may indeed be consequential because the timing of the cash flows differs between bonds trading at- and below-par. The cash flow of a bond trading below par - the case of a depreciated bond held to maturity - occurs somewhat later because coupons are smaller and the eventual redemption is bigger compared to a bond trading at par. As a result, a change in interest rates will have a bigger impact on its DCF. However, in most cases the difference will be small. Moreover, contrary to the argument above, it is the original bond, now trading below par, that is at a disadvantage. A rise in interest rates will reduce both its current market value and total return by a larger amount. In other words, investors retaining their original bonds face *more* interest rate risk rather than less.

## An example

To illustrate, consider the example in Table 1. Suppose the interest rate is 3% and you own a $1,000 bond with a 5 year maturity, as shown in row 1. The right hand panel of the table shows the cash flows in years 1-5, consisting of a coupon payment of $30 in years 1-4, and a final coupon of $30 plus the return of the principal in year 5. Row 2 of the table shows the net present value (NPV) of the cash flows discounted at 3% and sums these up in the column headed "Market value." At a 3% discount rate, the DCF sums up to the par value of $1,000. Instead of discounting forward, the column headed "Total return" calculates the cumulative return on the investment at the end of year 5, assuming the coupons are reinvested at the going interest rate. For the 3% bond trading at par in row 2, the final cash payout is $1,159.3.

Table 1 - Rising interest rates and bond returns

Now suppose the interest rate rises to 4%. Row 3 discounts the cash flows in row 1 at 4%, and sums these up for a market value of $955.5. You are unambiguously worse off, because your bond has incurred a capital loss of $44.5, or 4.5%. However, if you hold on to maturity, you'll continue to receive the $30 coupons annually and the capital loss will be reversed as the bond returns its par value of $1,000 at the end of year 5. In fact, reinvesting the coupons at the higher rate of 4% will make you slightly better off than before, with a total return of $1,162.5 compared to $1,159.3.

An alternative would be to sell the bond, now worth $955.5, and buy a new issue such as the one shown in row 4, with a coupon of $40 per $1,000 each year and a final redemption of $1,040 in year 5. This bond trades at par, so you can only afford a face value of $955.5, which will generate annual coupon payments of $38.1 and be redeemed for $955.5 at maturity. Though in this case you never recover your capital loss, the higher dividends just make up for that, so that the market value and total return in rows 3 and 5 are the same. So are the values at any intermediate time. For instance, reinvesting the year 1 and 2 coupons at 4% and then selling either bond at its end-year 2 market price (the DCF of years 3-5) would leave you with $1,033.5 in either case. (Note: the example assumes the yield curve is flat, otherwise values may diverge, though not by much except in extreme cases.)

To summarize: *you are completely indifferent between continuing to hold the same bond to maturity or trading it in for a new one*. And since it is precisely such details of the portfolio that you relinquish to a fund manager, there is neither more nor less interest rate risk in holding your investments through a fund. (You may not trust the fund manager to make wise decisions, but that's a different issue.)

## What if interest rates keep rising?

Comparing the DCFs in rows 3 and 5 of Table 1 shows that the one in row 3 is shifted back in time. That is, the earlier payments are smaller and the final one is bigger. For instance, the final payment is $846.6 in row 3, compared to $816.7 in row 5. Technically, the bond in row 3 has a longer duration. This means that any subsequent change in rates will have a bigger impact on its price and return, because cash flows are discounted over a longer period. Table 2 calculates the impact of a further rise in rates from 4% to 5% on the alternative holdings in Table 1. Row 1 copies row 3 from Table 1, and row 2 shows that the market price with a 5% interest rate drops from $955.5 to $913.4. Row 3 copies row 5 from Table 1, and row 4 shows that with a 5% interest rate the price drops by slightly less to $914.1. As with market value, the total return is also higher for the 4% coupon bond - $1,166.7 v. $1,165.8. For a small change in interest rates, the difference between rows 2 and 4 in Table 2 will be negligible. Nevertheless, the example shows that in a "bond bear market" of continually rising rates, there is no advantage to holding on to a depreciated bond until maturity. If anything, the advantage goes the other way

Table 2 - The impact of rising rates on bonds trading below and at par *(click to enlarge)*

## Conclusion

An investor may prefer individual bonds to a bond fund because of management fees or tax considerations, or because fixed coupons will make cash flows more predictable. But preserving capital by retaining control over the timing of purchases and sales should not be a factor in the decision as this is of little or no value. Indeed, other things equal, holding below par bonds to maturity in a secular bond bear market exposes investors to greater interest rate risk. The error of believing otherwise stems from failing to mark-to-market and recognize capital losses when they occur.

Comments()