Will Bonds Deliver Crisis Alpha in the Next Crisis?

Bonds are often viewed as being great diversifiers due to the perception that they perform well during tough times for stocks.

Historically this has been a true statement. But will it continue?

Our answer: unclear.

Most investors use correlation to measure the diversification benefit an investment might provide an existing portfolio.  However, this article uses a slightly different approach to measuring diversification – Crisis Alpha.  Crisis Alpha, as defined by Dr. Kathryn Kaminsky in her articles (and fantastic book Managed Futures the Search for Crisis Alpha), is the excess return of an asset (the asset’s return less the return of cash) given that the US stock market is in “crisis,” meaning it has declined by more than 5% in a month.

Crisis alpha in simple terms: How much does an investment return above cash when US stocks had an especially bad month?

For example, in August 2015 the S&P 500 declined 6.03% (it was quite a bad month).  In the same month, the Ibbotson Associates US Government Long-Term TR index returned 0.12% while cash returned 0%.  This means that the Crisis Alpha for the Ibbotson Associates Government Long-Term TR index is 0.12% (0.12% – 0% = 0.12%) for the month of August 2015.

Alternative Crisis Alpha Measurements

As astute readers, you might be asking yourself the following questions:

• Why use excess returns instead of the total return of the asset?
  • We use the excess return because it is important to isolate the return of cash (historically it’s always been more than 0%) from the return of the asset in excess of cash.  We do this because the return of cash is a common component of all investment assets (and has historically always been positive), we remove it to attempt to isolate the extra return (risk premium) that each investment provides.


• Why not use correlation to measure the diversification benefit?
  • We use crisis alpha because correlation is constantly changing and evolving over time.  In addition, most people don’t want diversification in up markets (they want the whole portfolio to be up together) but do want diversification in down markets (since this will provide some downside protection).  Crisis Alpha helps isolate people’s diversification preferences by only looking at how different asset classes have performed in down markets.


• Why are you defining Crisis Alpha as the excess return of an asset class when stocks were down more than 5% in a month?
  • There are different ways you can define Crisis Alpha (drawdown of stocks of more than X%, months where VIX increases more than X%, etc.).  We choose this method as it provides a large number of measurement periods across history.

Core results

We use data from Ibbotson Associates for this analysis.  Specifically, we use Ibbotson Associates US Large Cap Stocks TR for stock returns, Ibbotson Associates 30 Day T-bill TR for the return of cash and Ibbotson Associates US Government Long-Term TR for the return of bonds.  Unless otherwise specified, all monthly returns are arithmetic and all returns are excess returns (total return for the month less the return of cash for the month “ER”). The data period is from 1/1926 to 4/2016.

Here is a visual depiction that makes the result clear:

What we see when we look at investment returns through the lens of Crisis Alpha is that stock returns are considered “normal” (stocks have a return greater than -5%) in about 90% of months.  However, in about 10% of months, stocks lose more than 5%.

In the months where stocks have a return greater than -5%, they have an arithmetic average return of 2.05% and in months where stocks lose more than 5% they have an arithmetic average return of -9.02% (this makes sense as they have to have at least a -5% return to make it into this category).

We also see that, historically, cash has averaged a total return of about 0.28% in “normal” months and 0.24% in Crisis Alpha months.  The attribute of having a positive return in Crisis Alpha months provides fantastic diversification to a stock portfolio.

Moving on to bonds, we see that historically bonds have provided a 0.21% excess return over time and have had a positive excess return in 56% of all months.  In “normal” months bonds have provided a 0.22% excess return and had a positive excess return 56% of the time.  In Crisis Alpha months, bonds provided a 0.12% excess return and had a positive excess return 56% of the time.

When we view bonds through the lens of Crisis Alpha, a couple of characteristics emerge:

• Bonds do provide some diversification benefits – they provide positive excess return in Crisis Alpha months
• However, the diversification benefit of bonds may be smaller than people realize – bonds have produced a positive excess return only 56% of the time in Crisis Alpha months (no more frequent than in “normal” times) and they have only provided an excess return of 0.12% in Crisis Alpha months (compared with 0.22% for “normal” months).
• Surprisingly, bond excess returns decrease during Crisis Alpha months! Even though bond excess return don’t go negative, they have followed the same return pattern of stocks (stocks are just far more dramatic) where their returns are greater in “normal” times than they are during Crisis Alpha months.

We can study the return characteristics of bonds even more closely by decomposing bond returns into two different pieces 1) income return and 2) price return and analyze how the components behave during “normal” months and Crisis Alpha months.

We use the Ibbotson Associates Long-Term US Government Bond Capital Appreciation TR index for the price return component and we derive the income return component as the difference between the US Long-Term US Government Bond TR index and the Ibbotson Associates Long-Term US Government Bond Capital Appreciation TR index (i.e., total return – price return = income return).  We then subtract the return of cash from the income return series to make it an excess return.

And here is the visual:

There are some interesting observations to make when analyzing the components of bond returns:

• Historically, the majority of bond’s excess returns have come from the income component of returns not price changes.
• Historically, the income return component has delivered positive excess return in almost 90% of the months, including Crisis Alpha months.
• Historically, bond price changes have actually been negative (on average) during Crisis Alpha months! Given that bond price changes have been positive about 52% of Crisis Alpha months, the negative average return is due to some less frequent large losses during Crisis Alpha months.

What might these results imply for an investor today?

Bonds do diversify a stock portfolio – they have historically provided a positive excess return during Crisis Alpha months. This means that an investor looking to diversify stock risk in their portfolio should own some bonds.

Although bonds diversify a stock portfolio, they have not been a fantastic diversifier.  Historically, bonds have returned only 0.12% per month above cash during Crisis Alpha months, which isn’t that large of a return!  In addition, bond excess returns during Crisis Alpha months have been positive only 55% of the time. This means that they don’t consistently provide positive returns during times when diversification is most needed.

Historically, bond performance during Crisis Alpha months has been dominated by the income return component. The income return component delivers more than 100% of the Crisis Alpha month performance and the income return component is positive almost 90% of the time.
Historically (and surprisingly), the price return component of bond returns is negative during Crisis Alpha months!

Today, we have lower yields and the duration of bond indices is much longer than average. These changes may impact how bonds perform during Crisis Alpha months in the future which will affect the diversification benefit of bonds:

• Because bond yields are lower than historical average this decreases the income return we can expect from bonds. Given that the income portion of returns has historically comprised more than 100% of the return of bonds during Crisis Alpha months, this means that bond performance during Crisis Alpha months going forward is likely to be more muted.
• Bond index durations are longer than they have been historically. This means that the price component of bond returns will likely be a larger component of returns going forward.

Having price changes compose a larger portion of bond returns going forward isn’t good for a couple of reasons:

• Bond price performance isn’t likely to be very large (historically it is only 33% of bond total performance).
• Bond price performance during Crisis Alpha months has actually been negative historically!
• Bond price performance during Crisis Alpha months has only been positive about 52% of the time.

This analysis shows that bonds have provided some diversification benefit (positive performance during Crisis Alpha months) historically but that going forward, we may want to lower our expectations of bond performance during Crisis Alpha months.  It might be time to start looking for other investments or investment strategies to generate positive excess return during Crisis Alpha months.