How does a mortgage-backed security issued by a bank allows it to borrow cheaper and make more loans? I am currently reading a book called "Austerity, the history of a dangerous idea" by Mike Blythe. I am not an economist, but I am interested to learn more. 

Blythe writes (p.24): 


  "The old 3-6-3 model presumed that the bank that issued a loan to a
  customer held the loan until it was paid off, with profits accruing
  from the interest payments it received. But what if these loan
  payments could be separated out and sold on to someone else? What if
  many such loans, mortgages for example, could be bundled together as a
  pool of mortgage payments and sold to investors as an
  income-generating contract called a mortgage-backed security? That
  way, the bank that issued the loan could borrow cheaper and make more
  loans because the risk of the loan not being paid back was no longer
  on its books, and the borrower would get better rates. It was win-win,
  as they say."


I don't understand how selling them to investors can borrow money cheaper. Is it the investors' money directly? For example, if I am a bank, can I raise private capital (i.e. from investors) with the agreement of giving them a mortgage-back security? 

Thank you for your input!
Here are two ways by which selling mortgage-backed securities (MBS) benefited banks:


The MBS is less costly (or equivalently, more valuable) in the hands of the investor than in the hands of the bank.
The investor is misinformed/misled about the MBS and overpays for it.


Analogy for #1: When you buy car/fire/health/whatever insurance, you transfer the risk to another party (the insurance company) for whom that same risk is less costly (for example because they are able to pool/diversify risk across large numbers). This is the traditional, orthodox "markets are good" view. In this view, MBS's were a good development that further and more efficiently spread out risks and benefited everyone.

Analogy for #2: You suspect you have cancer and go buy some expensive health insurance. So you transfer this toxic asset (or risk) to another party (the insurance company) who, not knowing what you know, incorrectly judges the magnitude of this risk. This is to a large extent what actually happened.

(Note though that #1 and #2 are not mutually exclusive possibilities. Some of both probably did occur and continue to occur. But unfortunately, leading to the financial crisis, more of #2 and less of #1 occurred than was ideal.)