Is there an average rate of return when investing in blue chip stocks or market indexes versus ETFs like PowerShares?

Thanks for your question! It's kind of hard to answer your question, for two reasons.

1) It depends what time period you look at. You can look up or calculate an average return for US equities (stocks) going back almost a century.

2) It depends what market segment you look at. All US stocks? All US large companies?

Additionally, in your question, you say "blue chip stocks or market indexes versus ETFs like PowerShares?" These are not necessarily different things. A market index could be all blue chip stocks--that is what the Dow Jones Industrial Average (Dow 30) is.  Many ETFs (PowerShares and others) are all blue chip stocks; and many are market indices.

The following website shows historical return information for the S&P 500 and other investment benchmarks : https://pages.stern.nyu.edu/~adamodar/New_Home_Page/datafile/histretSP.html.

Bear in mind that that there is no way to invest directly in an index, even an index fund will have some small cost associated with it.

Please let me know if I can further assist.

Regards,

Chris

The financial industry loves to trot out the long-term historical average annual return of around 10% (give or take) in US stocks. 
But while that may be roughly accurate for a 30-year period, the reality is that yearly stock returns swing wildly above and below the mean. For example, one year they might be +15%, the next year +2%, and the year after -24%. It'd be rare that you actually have a year where the return lands on the long-term annual average.
Caution: beware of expecting to earn the annual average when you're starting from a high watermark of overpriced assets...like today. Due to global monetary policy on steroids, most assets (stocks, bonds, real estate, so on) are currently overpriced vs. a more normal, sustainable economic environment. My own view is that we're likely to see subpar returns over the next 7 to 10 years or so.

The stock market since 1871 has returned 2.25 percent over inflation plus dividends that average 4.4 percent per year or 6.65 percent plus inflation.  If you add up 2.25 percent growth, 4.4 percent dividend, and the average inflation rate 2.2 percent over that period you'll get 8.85 percent.  That's what you can expect over a very long period, but the market has gone for long periods, like 1885 to 1950, and currently from 1999 to now, without any gain over inflation.  Today, inflation is low 0.2 percent and since P/E ratio, 24 vs 15,  are high, dividends are low, closer to 2.2 percent now.  So you can probably expect a long-term gain of closer to four percent  (2.25 gain + 2.2 dividend) plus inflation - if the historical patterns hold.  But, already noted the market is volitile and there may be much larger short-term gains and loses.  https://www.multpl.com/inflation-adjusted-s-p-500

Chris has given you good information. Now I'm going to add a variable. Using the Standard & Poors 500 Average for discussion, you can buy Exchange Traded Funds (ETF's) that replicate this average. Guggenheim has such an ETF, symbol RSP. The State Street Spider symbol SPY is also an S&P 500 ETF.

Several years ago, you could have bought both ETF's and held them until now. If you bought 100 shares of each on the same day, your RSP holding would be worth more than your SPY. They own the same 500 stocks. How could that be? The answer lies in the fact that RSP is equally weighted. Theoretically, you own one share of 500 individual securities in your ETF. SPY is capitalization weighted. Apple Computer before its recent sell of made up 14% of the S&P's total value so your SPY share is 14% Apple. For the last several years, equal weighted index ETF's have outperformed cap weighted ETF's by a fair margin. And I call the S&P 500 "blue chip", so while indexes are indexes, not all indexes are created equal. Your challenge as an investor is to know the difference or fiind and work with someone who knows the difference and iinvests client funds accordingly.

As for the average return portion of your question, the answer is "it depends". It depends on which index you choose and over what time you want to compare or quote returns.