I am in the process of creating a program that generates status-quo variance-free portfolio (at least theoretically), and my question is pretty fundamental, which may just mean dumb. I am sorry if that is the case.

So, since most of the formulas I have seen for a "risk-free" portfolio say that you are basically replicating the return of the archetypal risk-free asset (treasury bonds, in the case of my textbook), why would we want to replicate that if they are readily available?

Again, sorry if that is a dumb question.


You are absolutely right that no one would like to replicate return of risk free assets when such instrument is easily available in the market and can be bought directly. So, why financial managers put their time and energy in creating such risk free portfolio?

  1. The application of creating risk free portfolio is mostly used in pricing derivative securities. This is done to ensure that model price does not provide arbitrage opportunities. This concept emerge from the fact that if a portfolio consists of 2 risky securities but risk of the portfolio is zero, then it must provide risk free return (irrespective of composition of portfolio). This is base on the premise that you can always buy the cheaper assets (or portfolio) and sell the overpriced portfolio (or assets).
  2. Just think of a situation when investors face restrictions on borrowing. In such scenario, zero-beta portfolio come at handy.

I think the goal of the exercise is to create some sort of risk-free portfolio with a positive return after borrowing costs. Then, theoretically, you can lever it up.

And of course, at 10x leverage, you should be pretty sure that is really is risk-free.


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