Portfolio Beta related question

[ActionDavidK]

I’m having trouble understanding how margin affects the risk of a security.
In A Random Walk Down Wall Street, Malkiel says to get a higher average long run rate of return you should increase the beta of your portfolio. A few of his examples confused me.

“An investor can get a portfolio with a beta larger than 1 by buying high beta stocks or by purchasing a portfolio with average volatility on margin. One proposed by a West Coast bank would have allowed an investor to buy the S&P average on margin, thus increasing both his risk and potential reward.”

What I find confusing

From what I understand, margin is buying a security with money borrowed from a broker.

When Malkiel writes “purchasing a portfolio with average volatility on margin,” I interpret it to meaning purchasing a portfolio with beta equal to 1 with money that you borrowed.

I interpret “One proposed by a West Coast bank would have allowed an investor to buy the S&P average on margin, thus increasing both his risk and potential reward,” to mean an investor would buy the S&P average with money borrowed from a broker and somehow it increases his risk and reward.

How do these examples make sense?