A recent article in The Wall Street Journal discusses how wealth managers are increasingly investing their clients’ money in mutual funds that use hedge-fund strategies. The idea behind these “alternative” investments is a low correlation of their returns to those of the general market, which is supposed to protect portfolios during market downturns. Unfortunately, the price paid for this is a sub-par performance of such investments in normal market conditions.

Let’s take a look at correlations of some of the funds mentioned in the article. Correlation coefficients can be reverse-engineered from data provided by Morningstar:

Fund |
Ticker |
Beta |
Fund StDev |
Market StDev |
Correlation |

Natixis ASG Global Alternatives |
GAFYX |
0.43 |
8.30 |
14.02 |
0.73 |

TFS Market Neutral |
TFSMX |
0.33 |
6.32 |
14.02 |
0.73 |

Highbridge Statistical Market Neutral |
HSKSX |
0.11 |
3.45 |
14.02 |
0.45 |

The above figures are based on the most recent three-year period. As can be seen, correlations of these funds to the market are quite high.

For further reference, here are average correlations of three types of “traditional” alternative assets, i.e. REITs, commodities, and hedge funds, with stocks and Treasury notes, as calculated by Leuthold Group:

In the last four years, these correlations were much higher than their long-term historical averages.

Even institutional investors keep pursuing alternatives in the name of diversification. However, true diversification of a portfolio requires not only low correlations but also high returns of assets being added. While it may still turn out that alternative investments provide some degree of portfolio protection during the next market downturn, this assumption is becoming questionable.

A recent article in the Wealth Management Report of The Wall Street Journal provides recommendations from industry experts on what portion of the portfolio an individual investor should invest in foreign securities. The expert opinions focus on equity, rather than bond or currency, allocation in the portfolio. Although the sample of just seven experts is small, statistics show that opinions do not vary a lot:

Statistic |
Value |

Mean |
27.5% |

Median |
30.0% |

Standard Deviation |
6.9% |

So, is a foreign equity allocation in the high 20s percent points appropriate? It depends on whether this brings the benefit of high and uncorrelated returns to the rest of the portfolio. In his bestselling book, David Swensen recommends the following asset allocation as the starting point for individual customization:

Asset Class |
Policy Target |

Domestic Equity |
30% |

Foreign Developed Equity |
15% |

Emerging Market Equity |
5% |

Real Estate |
20% |

U.S. Treasury Bonds |
15% |

U.S. Treasury Inflation-Protected Securities |
15% |

This implies an explicit foreign equity exposure of 20% of the total portfolio and about 28.6% of its equity portion (20% in a portfolio with 70% of “assets that promise equity-like returns”). Swensen also discusses currency exposure that stems from foreign investments:

“Fortunately, finance theorists conclude that some measure of foreign exchange exposure adds to portfolio diversification. Unless foreign currency positions constitute more than roughly one-quarter of portfolio assets, currency exposure serves to reduce the overall portfolio risk. Beyond a quarter of portfolio assets, the currency exposure constitutes a source of unwanted risk.”

Unfortunately, the diversification provided by foreign equities tends to fail when it is needed most. Since the most recent financial crisis, correlations between foreign and domestic equity returns shot up. Vanguard reports that from October 2007 through February 2009, that correlation was 0.93 for developed international markets and about 0.83 for emerging markets.

At the same time, even a domestic equity portfolio has an implicit exposure to foreign markets. That is because about 46% of revenue of companies in the S&P 500® index has been historically obtained abroad. In sum, an explicit allocation of close to 30% of the equity portfolio to foreign securities, which on average experts recommended, may be on the high side.

A recent article from Morningstar states that

“Correlation is bound between negative 1.0 and 1.0. A correlation of 1.0 indicates perfect positive correlation, meaning that as one investment rises (falls), the other rises (falls) **at the same rate**.”

And, in email correspondence with Alpholio™, a prominent blogger for one of the well-known financial publications (who shall remain anonymous) stated that

“If you’re then going to hang your hat on the distinction between equity and high-yield bonds, I’d point you to the correlation of JNK and HYG to the stock market – about 85% with the financial sector the last three years. Your bond-equity distinction here just doesn’t hold.”

Well, these statements create a good opportunity to explain what correlation really means. First, the correlation in question is a Pearson correlation coefficient between two time series of periodic returns within an analysis interval. In most of practical calculations, the return period is chosen to be one month (daily or weekly returns are considered too “noisy”) and the analysis interval to be three years. In addition, either linear or logarithmic returns are used (the latter to account for continuous compounding).

Second, a high correlation does not imply causation. The fact that two entities are strongly correlated does not imply that one makes the other happen.

Third, and most importantly in the context of this discussion, a high correlation does not imply identity. The fact that two entities are generally moving in the same direction in each period does not mean that they are identical. That is because the magnitude of each respective move can be very different.

To illustrate this, let’s take a look at correlations and returns of the following indexes and securities in the most recent three-year and five-year intervals:

It turns out that the differences between linear and logarithmic return correlations are very small in this case (0.001). The following table shows the latter ones:

Interval |
S&P 500 |
SPY |
SSO |

3 Years |
1.000 |
0.998 |
0.998 |

5 Years |
1.000 |
0.998 |
0.996 |

In both analysis intervals, correlations of both SPY and SOO to the S&P 500® were virtually equal to one (correlation of the S&P 500® with itself equals one by definition).

The following table shows correlations between HYG and VFH:

Interval |
VFH |
HYG |

3 Years |
1.000 |
0.769 |

5 Years |
1.000 |
0.669 |

In neither analysis interval was the correlation close to 0.85 mentioned above.

Now, let’s look at cumulative returns. In the simplest approach, price returns can be used:

Interval |
S&P 500® |
SPY |
SSO |
VFH |
HYG |

3 Years |
59.9% |
60.1% |
151.6% |
45.1% |
10.7% |

5 Years |
28.8% |
29.1% |
31.5% |
7.7% |
0.0% |

The SPY did a pretty good job tracking its underlying S&P 500® index — its price returns were actually slightly higher than those of the index in both analysis intervals.

However, to make things equal (with the exception of the index), total returns, which factor in the reinvestment of respective dividends, should be used. The following table shows the results:

Interval |
S&P 500® |
SPY |
SSO |
VFH |
HYG |

3 Years |
N/A |
69.6% |
155.1% |
52.8% |
35.9% |

5 Years |
N/A |
43.1% |
36.3% |
19.0% |
50.0% |

The above data clearly demonstrate that even when correlations are close to one, as is the case with SPY and SSO to the S&P 500, returns of securities can be very different. Moreover, there the returns of HYG and VFH were quite different in both intervals. Hence, high correlations do not imply that “investments rise and fall at the same rate” or that they are “indistinguishable.”