A popular strategy among many investors is that of ‘phasing’ in or out of risky growth strategies. Phasing in is often justified by the idea of pound cost averaging.^{1} Phasing out, on the other hand, often corresponds to the de-risking glidepaths many investors follow as they get closer to withdrawing their money.

De-risking can be driven by a combination of factors. One important factor in DC accumulation (i.e. pre-retirement) is that from a ‘total’ asset perspective we should include the value of a member’s future contributions, sometimes called human capital. If their human capital is fairly bond-like, then as it reduces over time it can justify de-risking of financial capital to compensate.

Another important driver is psychological: de-risking can help manage member expectations and increasing loss aversion. This can mean that even from a *total* asset perspective, investors may choose to reduce growth exposure over time.

### Level with me

Phasing in or out of *total* capital is often at odds with what financial theory tells us, and generally leads to a loss in investment efficiency. That may well be okay because psychological aspects matter too – but it’s interesting to explore how big that loss in efficiency is, to understand the trade-off.

Under sensible assumptions, the most risk-efficient approach is actually to hold a level^{2} percentage of total capital in growth. Other than delving into the theory, there are a few intuitive ways to understand this perhaps surprising result:

- The end value of the portfolio is simply the initial value compounded up with subsequent returns. The first year’s return is equally impactful to the ultimate outcome as the last year’s. As such there is no reason to take less risk in the last year than in the first, or indeed any year.
- Phasing introduces sequence risk: with a level glidepath the order of returns doesn’t matter, but with a non-level glidepath outcomes are more sensitive to returns when there is a higher percentage in growth.
- Phasing concentrates exposure on how markets do in a particular period, rather than spreading exposure out over time as evenly as possible. A level glidepath is the antithesis of market timing.

### Unlucky number 13

So how much does phasing in or out of total capital cost you? The answer to that is quite easy to remember: de-risking completely out of risky assets in a straight line (or phasing into risky assets in a straight line) dents glidepath efficiency by unlucky number 13. That is, about 13% of risk efficiency, as measured by the Sharpe ratio, is lost.^{3} This doesn’t depend on the time horizon involved or the risk premium assumed for growth assets.

As a simple example, the charts and table below compare linearly phasing out of growth assets into risk-free assets over a 10-year period, compared with holding 50% in growth throughout. The growth assets earn 4% per annum over risk-free with 10% volatility.

The Sharpe ratio of the de-risking strategy is reduced from 0.40 to 0.40 x (1 – 13%) = 0.35.

If you are phasing between two different growth assets that are different but correlated, this rule-of-thumb no longer applies and the dent would be smaller. But any psychological benefits of phasing would also be lower.

### De-risking drivers

There can be solid ‘rational’ reasons for phasing not captured by this analysis. For example:

- As I mentioned above, in DC accumulation, consideration of human capital can justify a degree of de-risking.
- In DC decumulation you may want the longevity hedging benefits from annuities as you get older, but be unable to maintain growth exposure due to leverage constraints.
- For DB schemes, the inability to buy-out instantaneously should the scheme reach full funding can be a good reason to de-risk as funding levels improve (more on this here).
- If you are a big investor (say a very large pension fund) it may be good to phase in or out of some markets gradually, to avoid pushing prices against you.

However, in some cases investors should recognise phasing is psychologically driven and that it comes with an associated price tag: 13% of the Sharpe ratio.

*The supposed benefit of pound cost averaging is that you buy more units when assets are ‘cheap’ and fewer when they are ‘expensive’. But such concepts make no sense if markets are efficient. Tim Harford, among others,**has argued against**pound cost averaging.**The classic paper to cite here is Paul Samuelson's ‘The long-term case for equities and how it can be oversold’ (1994).**Let me know if you would like the mathematical proof! The actual number is 1 – sqrt(3)/2.*