The Volatility of Yields
Heretofore we have used and compared two ways of measuring the volatility of yields: 1) by percentage change (+3373%); and 2) by basis point change (+100 basis points). We have found that the valuation of a pure coupon stream exactly follows percentage changes in yield and that the valuation of a pure lump sum payment loosely follows basis point changes in yield (see Table 15). Which standard of yield volatility is true to real life?
Common sense says that yields fluctuate according to percentages of starting yields; that is to say, a yield change from 6% to 8% (or vice versa) is as likely in a high yield market as a yield change from
3% to 4% (or vice versa) is in a low yield market, or that a yield change by 100 basis points between 8% and 9% is less significant and more common in a high yield market than is a change by 100 basis points from 3% to 4% in a low yield market. As we are attempting to estimate price volatility as yields change, it is an essential first step to determine whether percentage yield changes or basis point yield changes should provide our standards of volatility.
Common sense is right. Table 17 shows that in the postwar years in periods of high yields there were usually greater basis points ranges of yield fluctuations. High or low percentage yield fluctuations merely reflected dynamic periods and stable periods. Indeed, the percentage average annual range in the disastrous years of 1966-70 when the total range was 4.87-9.35% was exactly the same as in the also dynamic years 1956-60 when the range of yields was 3.15-5.15%. The percentage fluctuations certainly did not fall as yields rose, which they must have done if basis points were the right standard of fluctuation.
TABLE 17
Yield Fluctuations, New Aa Utility Bonds
Range of Average Annual Yield Average Annual
Yields Range 1n Basis Points Range in it
1966-70 4.87 to 9.35 129 19
Therefore, from this point on in our analysis we will assume that in real life percentage yield changes are a sound standard for measuring yield and price volatility. It is against this standard that we tabulated the volatility increases that occur as coupons decline and the volatility increases that occur as yields rise.
In summary, we have seen that volatility of a pure coupon stream is always proportionate to a percentage yield change, but the volatility of the lump sum payment at maturity is not only greater than for the coupon stream but increases rapidly as yields rise.
Therefore, high coupon bonds are less volatile than are lower coupon bonds with the same maturity, and, furthermore, the volatility of all bonds with a reasonable maturity rises rapidly as yields rise, so that, for example, a 10% yield increase around the 8% yield level creates a much larger price fluctuation than a 10% yield increase around the 4% yield level. The volatility of any conventional high-grade bond thus results from the interactions of three factors: maturity, coupon and the starting level of yields. The first two are matters of choice to the portfolio manager. The third is beyond his control, but he can take it into account in planning his portfolio.
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