Let's look at the combination of 50% Large Company Stocks and 50% Intermediate-Term Government Bonds for the years 1928 through 2013 with yearly rebalancing and using the yearly returns data in the 2014 Ibbotson Stocks, Bonds, Bills and Inflation Classic Yearbook.

It turns out that from 1928 through 2013, Large Company Stocks and Intermediate-Term Government Bonds moved in opposite directions in only 51 of the 86 years, or 59% of the time. If there were no correlation between the directions of movement between these asset classes

**we had a large sample size (and 86 years is**

*and***a large sample size) then we would expect that number to be close to 50%. It's unclear whether this deviation from 50% is caused by the alleged correlation or statistical variation due to a small sample size.**

*not*Let's calculate the Compound Annual Return (CAR) and risk expressed as Standard Deviation (STDEV) of the 50/50 mix.

Let's then randomized the sequence of the years of the bond data to undo the alleged correlation of stocks and bonds having the tendency to move in opposite directions for any given year and recalculate CAR and STDEV. When this randomization process is repeated, the resulting CAR and STDEV vary a bit from one try to the next, so let's run this process several times and look at the lowest and highest values of CAR and STDEV and "averaged" the CAR and STDEV by calculating the geometric means.

**The results:**

When using 50 sets of randomized data, both the CAR and STDEV of the original, non-randomized combination were right smack in the middle of the sets of results of those 50 randomized sets and were extremely close to the geometric means of the CAR and STDEV of the randomized set. Here are the numbers:

CAR of original set and geometric mean of CAR of random set: 8.09% and 8.08%.

Minimum and maximum CAR of random set: 8.00% and 8.20%.

STDEV of original set and geometric mean of STDEV of random set: 10.44% and 10.48%.

Minimum and maximum STDEV of random set: 9.32% and 11.33%.

**Conclusions:**

1. Both CAR and STDEV of the original set are extremely close to the geometric mean of the randomized set (with deltas of 0.01% and 0.04% respectively) and almost dead center of the CAR and STDEV populations of the randomized set

2. While it is true that the original set had an ever-so-slightly better return of 0.01% and an ever-so-slightly better STDEV of 0.04%, it's open to debate whether those minute deltas are caused by an alleged correlation between stocks and bonds in the sense that they move in opposite directions, or pure statistical variation.

3. The claim that stocks and bonds move in opposite directions and noticeably improve results is false.

**Note:**I repeated the calculations for 50/50 combinations of Large Company Stocks & Long-Term Government Bonds, Large Company Stocks & Long-Term Corporate Bonds, and Small Value Stocks & Intermediate Term Government Bonds and the results were very similar.

Your comments are very welcome.