Reward is measured by average annual total returns.  The total return of an investment (fund, security or portfolio) is the sum of all dividends, interest and capital gains/losses generated during the year.

Risk can be measured in various ways.  The most popular way is to calculate the standard deviation (or mean dispersion) of an investment using historical performance data.  Other ways to calculate risk includes using high-low ranges and options implied volatility.

The efficient frontier is a modern portfolio theory concept developed by Harry Markowitz that says that there is a limit to how far we can optimize the trade-off between reward and risk, given mix of investments in our portfolios.  There are star fund managers who occasionally may exceed the boundary, but over time they are likely to revert to the mean, and fall back inside the efficient frontier.

The highest reward (average annual total return) was generated by stocks (the S&P 500), with an AATR% of 11.6% in nominal terms.

Commodities (the CRB index) has generated an AATR% of merely 1.6% - which is actual below the average annual rate of inflation in the United States (3%/yr). 

Just as stocks have generated the highest reward, they have also exhbited the highest risk.  Annualized standard deviation is about 20%.  

The lowest risk asset class is investment grade bonds (as measured by the performance of the Barclays Aggregate Bond Index).  It's annualized standard deviation is about 5%, one quarter the amount of risk of the stock market.

The highest reward-to-risk ratio asset class is investment grade bonds at 0.59  The worst reward-to-risk asset class is commodities (the CRB index) with a post-CPI Q Sharpe ratio of -0.09.

The optimal mix is impossible to attain for passive investors especially because of the fact that we can only try to maximize reward-to-risk based on historical data.  With new data always coming into the picture, by the time we allocate positions the optimal point has already changed and will continue to change on the fly.