Pricing 50-year bonds

Telecom Italia’s trailblazing 50-year issue has left investors pondering how to price such a security. Ben Bennett gives his views on assessing the risk and fair-value spread

We have calculated the fair-value spread to swaps of 50-year credit by calculating the extra risk that investors take on by moving from 30-year to 50-year credit. We have broken down this extra risk into two parts: duration/convexity risk and default risk.

Duration/convexity risk

By moving from 30-year to 50-year credit, investors are holding a more volatile instrument, but not that much more volatile. When switching from 30-year to 50-year bonds, the time to maturity increases by two-thirds. But the duration – the number of years required to recover the true cost of a bond, considering the present value of all coupon and principal payments received in the future – increases by little over a quarter. On this note, it is also interesting to consider the future cashflow of a 50-year bond.

Assuming a 5% coupon and a par bond, the present value of the last payment of 105 is worth just over 9% out of the current par value of the bond. This is less than the present value of the first two coupons! Anxiety regarding 50-year credit purely because of the possibility that the bond will not repay the final notional value is a little misplaced.

Nonetheless, it is certainly true that by holding a 50-year bond, an investor is more exposed to credit duration. However, the increase in duration is only part of the equation. An investor also has to consider the impact of convexity, the rate at which duration changes as yield changes.

As a fixed-coupon bondholder, positive convexity works in your favour. As yields increase, you lose money (proportional to duration), but the bond’s duration decreases (proportional to convexity). In other words, convexity means you are losing money at a decreasing rate. The opposite is true when yields decrease: bondholders make money at an increasing rate. This is clearly beneficial for bondholders.

The key point regarding convexity is that the longer the maturity of the bond, the larger the convexity. So while a 50-year bond is more risky than a 30-year bond on a duration perspective, it is a more attractive asset due to its higher convexity. In order to price this payoff, it is necessary to run a number of scenarios based on historical volatility. The results of such modelling mean that for government debt, fair value for 50-year debt is 3.5–5bp wider than 30-year paper. As it happens, the new 50-year OAT was priced in this range, 4bp back of the 30-year yield.

Credit as an asset class is more volatile than government debt. As volatility increases, the convexity component becomes more and more important. Whilst it is difficult to calculate the precise fair value for moving from 30-year to 50-year credit paper, it is certainly less than the fair-value pick-up for the recent OAT. For the purposes of our calculation, we have used a very conservative estimate of 4bp, the spread that the recent 50-year OAT priced over and above the existing 30-year OAT.

Default risk

For the default calculation, it is first necessary to calculate the ratings distribution in 30 years’ time of a credit bond. In other words, what is the chance that the bond will have defaulted, or that it will be now rated triple-A, or rated double-A etc.? This distribution can be achieved by three applications of Moody’s 10-year transition probability matrices. Now that we have these ratings distributions, all that we need to work out is the premium required by bondholders for holding the bond for the final 20 years of the bond’s life, depending on the bond’s rating after 30 years. For this, we again used Moody’s data, this time for default rates over a 20-year period (assuming a 30% recovery rate). We ‘present-valued’ the spreads required for each rating category and multiplied these spreads by the 30-year ratings distributions to come up with a default premium required for 50-year credit over and above 30-year credit. For triple-B rated credit, this spread to swaps premium is 5.9bp and 6.0bp for single-A rated credit.

Adding this default risk premium to the duration/convexity risk premium, we calculate that the spread to swaps of both single-A and triple-B rated 50-year credit should trade 10bp wider than the spread to swaps of equivalent 30-year credit. This is a relatively conservative estimate and even at this premium 50-year credit is still a good investment given the potential upside offered by convexity.

Ben Bennett is a credit strategist at BNP Paribas