Rebalancing

Let’s say you have one asset that returns 20% one year and -10% the next. The average return is 5%. Does that mean you earn 5% per year? Here’s what investing 1 dollar in that asset looks like after 50 years.

Dollars at the end of 50 years is $6.85
The annual return was 4.21%

What happened? Our investment that averages 5% only returned 4.21%. We can see that if we plot an investment on same chart, you can see it laps our investment.

Dollars at end of 50 years is $11.47

We would have had $11.47 cents if we earned 5%. How come we didn’t earn that?

The answer is volatility! If you drop 10%, it takes you more than 10% to get back to even. The average return of your investment doesn’t tell you everything about future returns. For the same average return, the higher the volatility, the lower the annual return.

What happens if we can diversify our investment? Let’s say there’s another asset that has the same return profile but in opposite years? Let’s take a look at if we invest 50 cents in Investment A and 50 cents in investment B.

Dollars at the end of 50 years is $6.85
The annual return was 4.21%

First of all, that chart looks awesome. But look at the result. You would have figured that diversification would have helped us out, but it didn’t. That’s because diversification means more than splitting your money up and investing in different things. It means investing in different things, but also rebalancing when one performs better than the other. Let’s try investing 50 cents in both Investment A and B, but rebalancing to a 50/50 portfolio at the end of each year.

Dollars at end of 50 years with annual rebalancing is $11.47

When we rebalance, we get the same result as we did when we assumed the 5% average annual return! Rebalancing essentially removed volatility’s negative effect on return. Magic! Clearly this is an abstract example, so let’s see if we can see a same effect in portfolio construction.

Assume that equities will earn you the best return, but you can’t deal with huge drawdowns so you commit half of your portfolio to bonds. You have the choice of investing in government bonds, which don’t earn as much but are negatively correlated with equities, or corporate bonds which earn a bit more and have no correlation to equities. Let’s examine what these portfolio returns and risks look like. Portfolios are invested for 50 years and rebalanced annually. Here are the assumptions:

Equity expected return: 7%
Equity standard deviation: 15%

Government Bond expected return: 1%
Government Bond standard deviation: 7%

Corporate Bond expected return: 2%
Corporate Bond standard deviation: 7%

Equity / Government Bond Correlation: -0.3
Equity / Corporate Bond Correlation: 0.0
Government / Corporate Bond Correlation: 0.8

I randomly generate 50 years of multivariate returns with the assumptions above and examine how a 50/50 portfolio would perform if bonds were all government bonds and how it would perform with all corporate bonds. I examine the total return, standard deviation, and Sharpe ratio of both portfolios. I then run the simulation again 1,000 over.

Here are the results:

The average return with Govt Bonds was 4.095%
The average return with Corp Bonds was 4.103%
The average std. dev. with Govt Bonds was 7.159%
The average std. dev. with Corp Bonds was 8.164%
The average Sharpe with Govt Bonds was 0.576
The average Sharpe with Corp Bonds was 0.502

Almost no difference in returns, but risk is far lower and Sharpe’s are far higher! Take a look a the distribution plots below. You can see that the distribution of returns are pretty similar regardless of whether you use government or corporate Bonds, but risk is lower and Sharpe’s are higher for portfolios with government Bonds.

Leaving aside arguments that corporate bond yields overstate performance due to downgrades and other issues, there is a strong argument for government bonds based solely on their negative correlation with equities. This can be attributed to what is referred to as the rebalancing bonus. If you have assets that are both volatile and low/negatively correlated, your return for the portfolio is greater than the sum of the parts. Rebalancing bonus can justify holding other volatile assets with low expected returns and low correlation to equities, like Gold, Bitcoin, or Tail Risk strategies.