our weighted average discount rate on our measurement date primarily by reference to annualized rates earned on high quality fixed income investments and yield-to-maturity analysis specific to our estimated future benefit payments. We used a weighted average discount rate to value the obligations of 4.11% and 4.94% at December 31, 2012 and 2011 , respectively. Our weighted average discount rate for net periodic pension benefit cost in each of the past three years has varied from the rate selected on our measurement date, ranging from 4.95% to 5.93% between 2010 and 2012 .  

 

Expected Long-Term Rate of Return. Our expected long-term rate of return on plan assets of 9% is based primarily on plan-specific investment studies using historical market return and volatility data. Modest excess return expectations versus some public market indices are incorporated into the return projections based on the actively managed structure of the investment programs and their records of achieving such returns historically. We also expect to receive a premium for investing in less liquid private markets. We review our rate of return on plan asset assumptions annually. Our annual investment performance for one particular year does not, by itself, significantly influence our evaluation. Our actual historical annualized 20year rate of return on plan assets for our defined benefit pension plans exceeded 9% as of December 31, 2012 . The investment strategy for our defined benefit pension plan assets is to use a diversified mix of global public and private equity portfolios, public and private fixed income portfolios and private real estate and natural resource investments to earn a long-term investment return that meets or exceeds our annualized return target. Our expected long-term rate of return on assets for net periodic pension benefit cost for the year ended December 31, 2012 was 9%.  

 

Funding. Our funding obligations for qualified defined benefit plans are governed by the Employee Retirement Income Security Act. The Pension Protection Act of 2006 allows commercial airlines to elect alternative funding rules (“Alternative Funding Rules”) for defined benefit plans that are frozen. Delta elected the Alternative Funding Rules under which the unfunded liability for a frozen defined benefit plan may be amortized over a fixed 17-year period and is calculated using an 8.85% interest rate.  

 

While the Pension Protection Act makes our funding obligations for these plans more predictable, factors outside our control continue to have an impact on the funding requirements. Estimates of future funding requirements are based on various assumptions and can vary materially from actual funding requirements. Assumptions include, among other things, the actual and projected market performance of assets; statutory requirements; and demographic data for participants. For additional information, see Note 11 of the Notes to the Consolidated Financial Statements.  

 

Recent Accounting Standards  

 

Presentation of Comprehensive Income  

 

In June 2011, the FASB issued "Presentation of Comprehensive Income." The standard revises the presentation and prominence of the