The following is an excerpt from Dr. Thomas Holland's Crowned With Glory, ©2000, used with permission.
Hebrews 10:23 - "profession of our faith"
"Let us hold fast the profession of our faith without wavering; (for he is faithful that promised;)"
The common word for faith is the Greek word pistis. However, the word used here is elpidos, usually translated as hope. This does not mean the translation of elpidos as faith is a mistranslation. In fact, the King James translators stated that they were not bound by strict word counts, and that sometimes the context demands that the same Greek word be translated differently.
The English words faith and hope carry the idea of trust, assurance that what has been told will occur. The word hope means confidence, faith, reliance, trust, belief, and assurance. There is within Scripture a clear connection between faith and hope. "Faith is the substance of things hoped for" (Hebrews 11:1). The Scriptures state, "By whom also we have access by faith into this grace wherein we stand, and rejoice in hope of the glory of God." (Romans 5:2). And in reference to Abraham, the word of God says, "Who against hope believed in hope, that he might become the father of many nations, according to that which was spoken, So shall thy seed be. And being not weak in faith, he considered not his own body now dead, when he was about an hundred years old, neither yet the deadness of Sara's womb." (Romans 4:18-19). We are saved by hope (Romans 8:24) and yet we are saved by grace through faith (Ephesians 2:8). We are told to place our faith and hope in God (1 Peter 1:21).
The context of Hebrews ten informs us that we are to have full assurance of faith (verse twenty-two) and the One we are trusting is "faithful" (verse twenty-three). The context of the Greek word elpis in this verse can be expressed by the English words faith, hope, or trust. Dr. Gerhard Kittle notes the comparison of faith and hope when defining the Greek word elpis (hope). He even notes that in the Greek Septuagint (LXX) there is an "interrelating" of the two Greek words for faith and hope. 
Faith, trust, and hope are used interchangeably. A related word to elpis (hope) is elpizo. It is translated as hope in places such as Luke 6:34 and Romans 8:25. However, it is mostly translated as trust in places such as Matthew 12:21 and Romans 15:24. A related word to pistis (faith) is pistio. It is translated as believe in places such as Matthew 8:13 and John 3:16. However, it is also translated as trust in 1 Timothy 1:11 (as is another form of it in 1 Thessalonians 2:4 which is translated as trust). The context of Hebrews ten and eleven permits this type of trust be translated as faith instead of its normal translation hope.
 Kittle, Vol. II, 531.