By Raphaël Mennicken, Investment Director @ InvestEngine

#### What is rebalancing?

Rebalancing is the process of bringing a portfolio back in line with the original target allocation for the different market investments held. It matters, because a portfolio’s investment allocation determines its risk level and markets (domestic shares, international shares, government bonds, corporate bonds, commodities) fluctuate all the time. These fluctuations are of course part and parcel of investing.

Back in 1952, Nobel Prize winner Harry Markowitz defined the *risk *of a portfolio as its *volatility* (the variations of the portfolio’s return around the expected value). Markowitz showed how to calculate portfolio volatility (risk) from the volatility of the assets in the portfolio and their correlations. A change in allocation will result in a change in the portfolio’s expected risk, and this is something we want to avoid. We cannot eliminate risk, but we want to keep it in check. The easiest way to do it is to make sure we stick to our original target allocation.

#### Why rebalance and what’s involved?

Rebalancing is done by periodically calculating the current allocation in your portfolio and deciding which securities to buy, and which securities to sell (if any), to ensure the portfolio’s actual allocation matches the original target allocation, and therefore the expected risk level.

In practice, that means adding up the value of all of your holdings, calculating the percentage represented by each asset, comparing this to the target allocation, calculating which quantity of each asset needs to be bought and sold, and instructing or executing the trades.

Although the maths involved in these calculations is not complicated, this rebalancing needs to be performed frequently (ideally daily) and, of course, every time that cash is added to the portfolio. As this can be quite time consuming, the systems at InvestEngine perform these checks every day and then make the appropriate trades to rebalance the portfolio, at no additional cost to you.

Keeping portfolio risk on track is therefore a key benefit of rebalancing. Another benefit is that it evens out returns** **in the short run and enhances them in long run.

We will illustrate this by looking at the impact of rebalancing on various portfolios. First we’ll use a simple example and then go on to examine what would have happened during a very volatile 12 months period (the year following the bankruptcy of Lehman Brothers). Finally we’ll look at the benefits of rebalancing over a much longer period.

#### A tale of two portfolios

Let’s take the example of a simple portfolio composed of 60% Equities and 40% Bonds. With this portfolio comes a certain level of risk, which we want to maintain at all times because we have established that this portfolio best suits our risk profile.

Let’s assume for simplicity that the stocks components of the portfolio is represented by an ETF tracking the FTSE 100 and the bonds component by an ETF tracking Gilts (debt issued by the UK Government.

We will look at two versions of this portfolio: Portfolio A and Portfolio B, each with an initial investment of £20,000. Like an InvestEngine portfolio, Portfolio B will be periodically rebalanced. Portfolio A will not.

We assume that we rebalance the allocations when they fall outside a range of +/- 2% around the target, as illustrated below.

When we initially invest the portfolios, they both look identical.

Let’s now assume a small rally in the equity market, where equity prices increase by 10%, and bond prices decline by 1%. Both portfolios rise to a value of £21,120, which is obviously a positive outcome.

However, the portfolios moved away from their target allocation, as can be seen in the table below. The percentage of equities is higher than the top of the range we set. As equities are typically significantly riskier than bonds, both portfolios’ expected risk levels are now too high.

To resolve this for Portfolio B, we need to sell equities and buy bonds. We calculate the excess equity allocation and determine that we need to sell 4.8 shares at £110 ((62.5% – 60%)*£21,120/£120). With the proceeds we buy £6.67 bonds at £79.20 per share.

After these trades, Portfolio B is back in line with the target allocation. We leave Portfolio A unchanged.

What happens through a market cycle?

In the table and chart below, we show a series of market moves and their impact of the Equity allocation of Portfolio A over time. Portfolio B is rebalanced as needed, so its allocation stays on track.

Portfolio A’s variations from the target allocation may seem minor when we look at the chart – however they have an impact on the portfolio value over time:

When equity markets are rising, it looks like a good idea to let the allocation of Portfolio A drift towards a higher percentage of equities. After 3 consecutive 10% increases in equities without rebalancing, Portfolio A’s value increases above that of Portfolio B.

For someone with perfect foresight and an infinite appetite for risk, this would seem like a good strategy. For everyone else, adverse market moves will quickly ensure that the rebalanced portfolio (Portfolio B) outperforms the non-rebalanced portfolio.

This can be seen in the table below. After the three consecutives 10% increases in equity prices, the return of Portfolio B is 0.9% lower than the return on Portfolio A. However, a single 10% decrease (a ‘correction’ in financial jargon), instantly results in Portfolio B’s return becoming 0.3% higher than that of Portfolio A. To put this into context, a 10% correction can occur in a matter of a few days.

The table below assumes the correction extends to a full blown ‘bear market’ (a decline of equity prices greater than 20%) followed by a recovery.

At the end of this ‘cycle’, the return on Portfolio B is now 1% higher than the return on Portfolio A. Furthermore, Portfolio A is still overexposed to Equity risk (65.3% vs a target allocation of 60%), which makes it even more sensitive to the next downturn in equities.

We can conclude that rebalancing is a portfolio management technique that has clear benefits because markets are volatile. In the short term, rebalancing evens out returns (shallower peaks and troughs). In the long run, a non-rebalanced portfolio is likely to become too exposed to risky assets (equities in our example) and at some point and will therefore experience levels of volatility that could result in underperformance compared to a portfolio that is rebalanced systematically.

Note that the magnitude of the moves in equity prices we used in the analysis above are very realistic – such a “cycle” can actually occur in the space of 12 to 18 months.

So, what happens if we look at real price movements that have occurred in the past?

#### Rebalancing after Lehman

If we look at the 12 months period that followed the demise of Lehman Brothers (September 2008 to September 2009), we observe a very high volatility in the UK equity markets (38.2%, more than double the long-term historical average).

We’ll use the same portfolios as above (£20,000, 60/40 allocation with a 2% tolerance, where only Portfolio B gets rebalanced). Based on our previous analysis we would expect that Portfolio B would have been rebalanced quite often, and that the benefits of rebalancing would be easy to see.

To verify this, we will check daily whether the portfolios are in line with the target allocation, and trade accordingly.

To verify this, we will check daily whether the portfolios are in line with the target allocation, and trade accordingly.

From the chart above, it is indeed easy to see that a high level of volatility has the effect on performance we already witnessed in our simple example.

High volatility results in non-rebalanced portfolios underperforming, quite visibly in this case.

Over this very volatile 12 months period, our rebalancing methodology would have resulted in 16 rebalances, and an extra performance after 12 months for Portfolio B of £413, or 2.06%.

We chose this particular period to illustrate our point because of the magnitude of the price movements. This doesn’t however mean that rebalancing only works in very volatile markets. Rebalancing also works well in the long run, where periods of low volatility alternate with periods of high volatility.

#### The long term view

If we perform the same analysis on Portfolio A (not rebalanced) and Portfolio B (rebalanced) over a longer period (Aug 2003 to date), we see that Portfolio B outperformed Portfolio A again (see chart below).

If we perform the same analysis on Portfolio A (not rebalanced) and Portfolio B (rebalanced) over a longer period (Aug 2003 to date), we see that Portfolio B outperformed Portfolio A again (see chart below).

This period firstly saw the recovery from the Tech crash, and then the increased volatility that preceded the 2008 market crash. This was followed by a strong recovery which is still ongoing.

If we delve into basic statistics for the two portfolios over the entire period, we see that:

- Portfolio B is worth £2,446 more than Portfolio A. Both started with an initial investment of £20,000
- This outperformance translates to an excess return of 0.4% per year
- Portfolio B experienced lower risk than Portfolio A, with an annualised volatility 0.4% lower
- At the end of the period, Portfolio A is significantly different from its target allocation. It is riskier, as it contains 67.8% equity, instead of 60%. This means that it will continue to be too risky and will also underperform Portfolio B in the long run.

Conclusion

Rebalancing is a portfolio management technique that allows you to

- Keep your portfolio allocation on target
- Keep risk in check
- Smooth returns in the short term
- Improve risk and return in the long term

And the good news is that InvestEngine does all the hard rebalancing work for you, so you don’t have to!

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