LPI benefits: A free alpha dessert on top of the risk management main?

Delta hedging is an options trading strategy that aims to reduce, or ‘hedge’, the directional risk associated with price movements in the underlying asset. In this instance, a rebalancing delta hedge may do more than manage inflation risk and may either generate or destroy alpha in some circumstances.

Depending on the cap and floor and the extent to which inflation is range-bound, rebalancing could potentially end up selling when expected inflation is high (‘expensive’) and buying when expected inflation is low (‘cheap’) and therefore generate positive alpha.

To understand this requires a back-test. A challenge, however, is what to measure alpha relative to. We need something that is not itself rebalancing, given we are trying to show the impact of rebalancing. We also want something that on average has the same inflation exposure as the rebalanced strategy, to exclude the impact of the average level of inflation simply being higher or lower than expected over the period.

Accordingly, for rolling three-year periods, we compare two strategies:

• The first strategy rebalances on a frequent basis in line with the ‘dynamic’ deltas^
• The second strategy is static but has perfect foresight of what the average inflation exposure of the first strategy will be for the next three years

The alpha of the strategy for a given three-year period is calculated as the excess return of the second strategy over the first strategy.

Alpha opportunities?

In the below we’ve done a calculation for a liability that receives yearly LPI (0, 5) increases – that is increases in line with the retail price index (RPI) each year but with a floor of 0% and a cap of 5%, with the pension payment falling due in 2047. The green line in the chart below plots the (annualised) alpha (calculated as above). We’ve also plotted a blue line, which represents the volatility* of inflation expectations over the same three-year periods.

Our first observation is that generally alpha is positive. Our second observation is that there is a strong correlation between the alpha generated and the volatility of inflation expectations – the more volatile inflation expectations are, the more alpha is generated.

If inflation expectations are range-bound, say between 2% and 4%, this makes perfect sense. In that case LPI rebalancing does involve buying low and selling high, explaining the positive alpha. The reason can be seen from the below chart of how the delta of the strategy varies with the level of inflation.

Does this mean delta hedging with regular rebalancing offers a free alpha dessert on top of the risk management main? Not so fast…

Hold on to your hat

What if inflation expectations wander outside this ‘normal’ range? It is common in history to see ‘anchoring’ of inflation expectations at the longer end of the market curve, which is founded upon the explicit objective of the Bank of England to stabilise prices.

But such anchoring is much weaker at the shorter end of the curve, especially recently. Inflation expectations have exceeded that central bank target range by a very wide margin: the current one-year RPI inflation expectation is around 10% whereas the equivalent Bank of England inflation target range in RPI terms is around 2% to 4%.

When such anchoring of inflation expectation breaks down, beating the performance of our ‘second strategy’ becomes far more difficult.

To illustrate, below is a similar back-tested three-year rolling return difference chart, for a bullet LPI (0, 5) cashflow maturing in 2027 (so about 10 years away). The green line still represents annualised alpha once more, and the purple line is the inflation expectation at the end of the corresponding three-year period. To illustrate the inverse relationship, the scale of the purple line is upside down.

As you can see high expected inflation levels tend to lead to negative alpha because the rebalancing strategy has sold exposure to inflation but then inflation has continued to go up.

Take a direct view?

The ‘main course’ of delta hedging is the risk management, not ‘accidental’ alpha generation for dessert. If trustees or managers wish to take a view on how expensive or cheap inflation is, it may potentially be better to do that with an explicit view and an outright position that is sized appropriately relative to other active views.

^based on a market-consistent LPI valuation approach where LPI volatility surface based on LGIM source of market data and the SABR methodology

*annualised one-week change