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The Only Right Way to See Things Is in the Whole

In recent posts on GNMAs, high-yield bonds and the Vanguard total bond market fund, we saw that it's not sufficient to consider an asset's risk and return in isolation, or in comparison only to similar investments. The right way to think about investments is how their addition impacts the risk and return of the overall portfolio.

The following example, created by my Buckingham Asset Management colleague Vladimir Masek, shows how even an investment that loses money persistently can add value to a portfolio. It also demonstrates why rebalancing is an integral part of the strategy of diversification of risk. (In a sense, that's a trivial observation because without rebalancing, each investment will do what it does, and at the end of the investment horizon you just have two undiversified portfolios that have been put together.)

Consider two investments with the same distribution of returns:

  • Half the years, they each return +60 percent
  • Half the years, they each return -40 percent
If you invest $100 in each, you expect to have lost about 4 percent for every two years of the horizon (1.6 * 0.6 = 0.96, or 4 percent loss) over the long term. If you never rebalance, both investments will be worth less than $100 at the end of the horizon -- at least in expectation. Why would you ever invest in such an asset? To answer that question, we need more information.

At this point, you don't even care what the correlation is between the two assets because you're considering the assets in isolation. However, you need to know the correlation if you rebalance.

Now consider the following case of a portfolio with an allocation of 50 percent to each asset, rebalanced annually. In the most extreme case (with the assets having a correlation of -1), you don't know beforehand which asset will go up 60 percent and which will lose 40 percent in any given year. However, you don't care. You always rebalance back to 50/50 each year. So, what's the result of combining these two money-losing assets in a portfolio that's rebalanced annually? If you rebalance, your total $200 investment is now earning exactly 10 percent every year. It's like a Treasury bill investment with a very high interest rate.

Of course, this is an extreme example. However, it demonstrates the importance of considering how the addition of an asset impacts the overall portfolio. It also demonstrates that assets with negative correlation can have low expected returns and high volatility and still add value to a portfolio.

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