Sunday, 2 February 2014

Portfolio Rebalancing – A Fine Balancing Act

I have been thinking about setting up a portfolio that needs minimal attention. In setting up the portfolio, a few questions come to mind, such as:
  • What is the allocation between stocks and bonds?
  • How frequent to rebalance?
  • What stocks and bonds (or unit trusts) to buy?

On the first question, a common rule of thumb is to allocate to bonds your age in percentage. For example, if your age is 30, you allocate 30% of your portfolio to bonds and 70% to stocks. This rule of thumb is on the basis that the younger the person is, the more risk he can take. It is a sound rule of thumb.

On the second question, it is usual to rebalance the portfolio on a yearly basis. There is an alternative way of rebalancing the portfolio which is based on the amount of volatility the portfolio has gone through. For example, if the original portfolio allocation is 30% in bonds and 70% in stocks, the portfolio would be rebalanced only when the allocation deviates from the original allocation by say, a 5% margin.

To study the most optimal margin for rebalancing, I carried out back-testing based on the Straits Times Index (STI) and the longest Singapore Government Securities (SGS) bond yields for the last 26 years since 1988. An initial capital of $10,000 is assumed invested in the portfolio comprising of 70% stocks and 30% bonds. The stock component is assumed to be invested in STI while the bond component is assumed to be invested in a 10-year SGS bond carrying 3% coupon. This bond is an artificial bond computed based on the present value of all coupons discounted at the longest SGS bond yield. All dividends and coupons are ignored for this analysis. The portfolio values for each allocation (left column) and rebalancing margin (top row) at the end of 26 years are shown below.

Highest & Lowest Portfolio Value at Different Allocations & Rebalancing Margins

For each allocation, the portfolio that delivers the highest value is highlighted in green while the portfolio that delivers the lowest value is highlighted in orange. A few trends could be seen from this analysis. The portfolio with the lowest value tends to concentrate around the 0% rebalancing margin for all allocations except at very high or very low allocations, while the portfolio with the highest value tends to be parabolic, i.e. the portfolio with the highest value increases with increasing rebalancing margin until the margin reaches 9% before decreasing again.

On hindsight, it should not be difficult to explain these trends. With a high rebalancing margin, the stocks or bonds are allowed to run longer on their momentum before rebalancing takes place. For example, assuming stocks are on the rise, the stocks are allowed to run further before they are sold. This is consistent with letting your profits run. Conversely, if stocks are declining, they are allowed to decline further before the bonds are sold and invested in the stocks, hence, investors avoid catching a falling knife along the way down.

However, at very high or very low allocations, the optimal rebalacing margin reduces to around 5%. This is because a high rebalancing margin at these allocations means that the stocks or bonds need to go through very large changes before rebalancing takes place. For example, at 90% stock / 10% bond allocation, a 9% rebalancing margin would require bonds to rise or fall by 90% before rebalancing takes place. This is practically impossible, hence, the optimal rebalancing margin reduces at very high or very low allocations.

The figure above also shows what everybody knows, which is that portfolio allocation is an important factor in determining the final portfolio value. The higher the allocation to stocks, the higher is the portfolio value. However, between portfolio allocation and rebalancing margin, which has a higher influence? Based on the above case study, on average, a 1% increase in the allocation to stocks increases the portfolio value by $232. On the other hand, a 1% increase in the rebalancing margin increases the portfolio value by $101. So, portfolio allocation plays a more important role than the rebalancing margin in determining the final portfolio value. Nevertheless, the rebalancing margin can be used together with the portfolio allocation to enhance the portfolio value.

In practical terms, it should be highlighted that a high rebalancing margin would mean rebalancing only when stocks or bonds have undergone large changes. For example, with a 70% stock / 30% bond portfolio and rebalancing at 10% margin, with the STI at around 3,100 currently, rebalancing will only occur when the portfolio reaches either 80% stock / 20% bond or 60% stock / 40% bond allocation. Assuming the bond component does not change, the STI must rise to 5,300 points (71% rise) or drop to 2,000 points (36% drop) for rebalancing to take place. At a 5% rebalancing margin, the corresponding STI values are 4,000 points and 2,500 points.

Finally, it should be noted that the above analysis is based on the historical price changes actually encountered. With a different price history, the optimal rebalancing margin might be different. Nevertheless, the theory that it is better to rebalance less frequently to let your profits run or avoid catching a falling knife is still applicable.

Wishing everybody a Happy, Healthy and Prosperous Chinese New Year!

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