HDMI transfers digital audio, while your stereo RCA audio inputs require analog audio. A simple cable will not do it.
There are many HDMI splitters which allow you to separate the digital audio from the HDMI output, which you can then plug in to any device that can convert digital audio to analog audio. These can be found as S/PDIF to RCA converters as well as more professional DAC boxes.
However, this is probably going to be costly, and a mess with the wires. If at all possible, I would suggest either buying a new stereo which takes in digital audio directly (or even HDMI), or buying a USB connected sound card with good quality sound output.