Do you rebalance?

Many advocate keeping a portfolio of bonds and stocks, and rebalancing them regularly. While reading the Four Pillars of Investing, I discovered a very good example of diversification and rebalancing. I will replicate it here.

Playing the long game (Chapter 14)

In order to understand rebalancing, let’s consider a model consisting of two risky assets; call them A and B. In a given year, each asset is capable of having only two returns: a gain of 30% or a loss of 10%, each with a probability of 50%. You can simulate the return for each simply by flipping a coin. Half the time you’ll get a return of  30%, and half the time you’ll get 10%.

The expected return of this “investment” is 8.17% per year. That’s because, on average, you’ll get one year of  30% for every year of  10%: 0.9 x 1.3 = 1.17, or a two-year return of 17%. If you annualise this out, you get 8.17% per year. (In other words, a return of 30% the first year and 10% the second is the same as a return of 8.17% in both.) Of course, you only get this 8.17% “expected return” if you flip the coin millions of times, so that the heads/tails ratio comes out very close to 50/50.

Now, imagine that you construct a portfolio of 50% A and 50% B. You thus have four possible situations:

One-quarter of the time, we flip two heads resulting in a  30% return. One-quarter of the time, we flip two tails, and the portfolio returns  10%. And one-half the time, we get one of each, and the return is the average of  30% and  10%, or  10%. The expected four-year return is thus 1.3 x 1.1 x 1.1 x 0.9 = 1.4157. This annualises out to a return of 9.08%. (That is, had we gotten a return of 9.08% all four years, our final wealth would be the same 1.4157 we got from the above 30%/10%/10%/-10% sequence.)

The key point is this: we got almost 1% more return (9.08%, versus 8.17%) simply by keeping our portfolio composition at 50/50. Take a look at Year 2. If we started out that year with equal amounts of asset A and asset B, by the end, we would have had much more of A because of its higher return. In order to get back to 50/50, we sold some of asset A and with the proceeds bought some asset B. The next year, asset B did better than asset A, so we turned a profit with this maneuver. Had we not rebalanced, we simply would have gotten the 8.17% return of each asset.

But that’s not all. Notice that instead of getting a return of  10% half of the time, as with a single asset, we now only get it one quarter of the time. We have reduced risk by diversifying.

How regular is regular?

William Bernstein also lets us in on how often to rebalance. Many people say bi-annually or annually, but "two to five years" is good enough. These are his exact words from the book.

The question of how often to rebalance is one of the thorniest in investing. When you try to answer this question using historical data, the answer you get is “rebalance about every two to five years,” depending on what assets and what time period you look at. But you have to be very careful in interpreting this data, because the optimal rebalancing interval is exquisitely sensitive to what assets you use and what years you study.

Personally, I think that about once every few years is the right answer for one good reason. If the markets were truly efficient, then you shouldn’t be able to make any money rebalancing. After all, rebalancing is a bet that some assets (the worst performing ones) will have higher returns than others (the best performing ones). Research has shown that this tendency for the prior best-performers to do worse in the future and vice versa (which we saw in Chapter 7 in our survey of five-year regional stock performance) seems to be strongest over about two to three years. In fact, over periods of one year or less, the reverse seems to be true—the best performers tend to persist, as do the worst.

Thus, you should not rebalance too often. The most extreme example of the advantage of waiting comes when you consider the behaviour of the U.S. and Japanese markets in the 1990s. During this period, the U.S. market did almost nothing but go up, whereas the Japanese did almost nothing but go down. The longer you waited before selling U.S. stocks and buying Japanese ones, the better.

My own thoughts

Similar to William Bernstein, I would think 2 years would be a good time lag for rebalancing. However, since I do dollar cost averaging, I guess the rebalancing should be rather minor.

On a side note, I personally feel that the book is very insightful, and highly recommend a read.
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