Arbitrage - I got the answer but could I prove with math from dat?

The question is below. I get the answer given the concept of arbitrage, but how would I prove this out mathematically from the data easily?

An analyst determines that a portfolio with a 35% weight in Investment P and a 65% weight in Investment Q will have a standard deviation of returns equal to zero.

  • Investment P has an expected return of 8%.
  • Investment Q has a standard deviation of returns of 7.1% and a covariance with the market of 0.0029.
  • The risk-free rate is 5% and the market risk premium is 7%.

If no arbitrage opportunities are available, the expected rate of return on the combined portfolio is closest to: ANSWER: 5%

By definition, no arbitrage opportunities means that a risk-free portfolio earns the risk-free rate.

There is no mathematical proof; it’s simply the definition of arbitrage.

OK thank you, I will put the pen and paper down.

Sounds like a plan.

You’re quite welcome.

Hey, can you please show your workings? Thanks!

There are no workings. That’s the point.