A 6.78% yield portfolio, with a 6% default rate, and a 50% recovery rate, returns 3.78% (excluding convexity issues). It's 0.94*6.78+.06*-50, not 0.94*6.78. 

Ok, I made a pretty bad mistake calculating either 6.78% or 0% performance (assuming a recovery that equals current market price) ;D.

Nevertheless, what are the durations of the indexes? 

The Gov't index is a blend of Treasuries >5yrs, so I figure it's a similar duration to the Merrill HY Index.

as for
Hence, most of the time holding risky bonds yielded better returns than holding riskless bonds.

On average, over the entire 12 years, they were the same. I don't think it's reasonable to 't exclude the bad years because they bring the average down. 

... sorry about my unclear formulations. I did not want to emphasize the point that risky bonds are better investments. I just wanted to say that most of the time investors are rewarded for taking risk. But, as it seems in your example, this reward is not of a permanent nature which I absolutely don't understand.

I did a quick simulation on the parameters default prob (varying 30% around its mean) and recovery value (15% off by its mean) by introducing iid random variables (... and having no idea about their true distributions). After 1,000 runs I got an expected return of 3.34% with 59% of the returns within a range of 2.8% to 4.2%. Hence, the expected return should be less.

At my internship I had to play around with a few benchmarks. When stretching the duration for half a year to 4.5 years then the performance over the analysed time span (1 year) increased by 40 BP. If this is not the case here then I resign and accept your argument to be valid :D

Please note that I have a bad day doing calculations today. 

good idea to put the recovery rate assumption in the text!

This sample period included a big decline in rates, so anything that increases duration generates better returns.

In any case, HY seems a poor investment.